Class 12

In this article, we will share MP Board Class 12th Hindi Solutions पद्य Chapter 3 प्रेम और सौन्दर्य Pdf, These solutions are solved subject experts from the latest edition books.

MP Board Class 12th Hindi Swati Solutions पद्य Chapter 3 प्रेम और सौन्दर्य

प्रेम और सौन्दर्य अभ्यास

प्रेम और सौन्दर्य अति लघु उत्तरीय प्रश्न

प्रश्न 1.
चातक को घातक क्यों कहा गया है? (2015)
उत्तर:
चातक अपनी बोली के द्वारा विरही हृदय को चोट (दुःख) पहुँचा रहा है इसलिए कवि ने उसे घातक कहकर सम्बोधित किया है।

प्रश्न 2.
विश्वास में विष घोलने का काम किसने किया है?
उत्तर:
विश्वास में विष घोलने का काम ‘सुजान’ ने किया है। पहले तो उसने दर्शन देने की आशा दिलाकर विश्वास दिया फिर मना करके उस विश्वास को तोड़ दिया।

प्रश्न 3.
मथुरा से योग सिखाने कौन गये थे?
उत्तर:
मथुरा से गोपियों को योग सिखाने श्रीकृष्ण के मित्र उद्धवजी ब्रज क्षेत्र में गये थे।

प्रश्न 4.
नंद के आँगन में गोपियाँ क्यों एकत्र हुईं? (2014)
उत्तर:
गोपियों ने यह सुना कि मथुरा से कोई कृष्ण का संदेश लेकर आया है, तो प्रेम में मदमाती सभी गोपियाँ यह जानने के लिए नन्द के आँगन में एकत्रित हुईं कि उनके लिए क्या लिखा है।

प्रश्न 5.
कुटीर कौन-सी नदी के किनारे बनाने की बात कही गई है?
उत्तर:
कृष्ण के सखा उद्धव अपना कुटीर यमुना नदी के किनारे बनाने की बात कहते हैं।

प्रेम और सौन्दर्य लघु उत्तरीय प्रश्न

प्रश्न 1.
‘तिरछे करि नैननि नेह के चाव मैं’ का आशय स्पष्ट कीजिए।
उत्तर:
इस पंक्ति के माध्यम से कवि घनानन्द अपनी प्रेयसी सुजान की उदासीनता व निष्ठुरता की अभिव्यक्ति करते हुए कहते हैं कि कवि प्रेम के बदले प्रेम की कामना करता है किन्तु प्रेयसी अपनी आँखें फेरकर उसके प्रेम के प्रति अस्वीकृति प्रकट करती है। प्रेयसी का यह निष्ठुर वहार कवि के हृदय को गहरा आघात पहुँचाता है और वह वेदना से भर जाता है।

प्रश्न 2.
घनानन्द सुजान को क्या उलाहना देते हैं? (2016)
उत्तर:
घनानन्द अपनी प्रियतमा ‘सुजान’ को यह उलाहना देते हैं कि पहले तो मुझे तुमने प्रेम से अपनाया फिर स्नेह को तोड़कर मुझे मँझधार में बिना आधार के क्यों छोड़ दिया? चातक की आन से कुछ सीख कर मुझे बेसहारा मत छोड़िए। प्रेम का रस पिलाने की आशा बँधा कर विश्वास में विष मत दीजिये।

प्रश्न 3.
रत्नाकर की गोपियों के मन में कौन बसा है? उनके विचार स्पष्ट कीजिए। (2017)
उत्तर:
रत्नाकर की गोपियों के मन में श्रीकृष्ण बसे हैं। वह उनके मन में इस तरह बस गये हैं कि अब निकालने से भी नहीं निकलते। उनका सन्देश आने की खबर सुन कर सभी दौड़-दौड़ कर नन्द के घर आने लगीं। उन्होंने उद्धव से कहा कि हमारे मन रूपी शीशे में कृष्ण बसे हुए हैं। तुम अपने कठोर वचन रूपी पत्थर चलाकर हमारे मनरूपी शीशे को तोड़कर अनेक मोहन (कृष्ण) हमारे हृदय में मत बसाओ। अनेक मोहन हमारे हृदय में बस कर अधिक दुःख देंगे।

प्रश्न 4.
रत्नाकर के अनुसार गोपी-ग्वालवालों की मनोदशा को समझाइए।
उत्तर:
ब्रज में गोपी-ग्वाल सभी कृष्ण के वियोग में कृशगात हो गये हैं। कृष्ण का संदेश जानने के लिए अत्यन्त व्याकुल रहते हैं। जैसे ही गोपियों ने कृष्ण का सन्देश आने की बात सुनी तो वे दौड़-दौड़ कर नन्द के घर में इकट्ठी हो गईं। प्रेमातुर गोपियाँ कमल जैसे कोमल पैरों के पंजों पर खड़ी होकर उचक-उचक कर पत्र को देखने लगीं। लेकिन जब उन्होंने उद्धव द्वारा अकथनीय बातें सनीं तो गस्से में बडबडाने लगीं.कोई पसीने से तर हो गई.कोई मच्छित होकर गिर पड़ी। उनकी व्यथा का वर्णन बड़ा कठिन है। उन्होंने उद्धव के वचनों की कठोर पाहन (पत्थर) की उपमा दी जो उनके मन-मुकुर को तोड़कर अनेक मनमोहन बसा देंगे। जब एक कृष्ण के जाने से इतना कष्ट हो रहा है तो अनेक मनमोहन हमारा सर्वनाश कर देंगे। स्वयं उद्धव ने कृष्ण से कहा है कि गोपी-ग्वालों के आँसुओं से ब्रज में बाढ़-सी आ गई है। वे सभी कृष्ण के वियोग में परम दुःखी हैं।

प्रश्न 5.
उद्धव के ब्रज आगमन की गोपियों पर क्या प्रतिक्रिया हुई?
अथवा
उद्धव के ब्रज आगमन पर गोपियों की आतुरता का वर्णन कीजिए। (2010)
उत्तर:
कृष्ण के सखा उद्धव के ब्रज में आगमन की खबर सब जगह फैल गई। जैसे ही गोपियों ने श्रीकृष्ण के सखा उद्धव के आने का समाचार सुना गोपियों के झुण्ड के झुण्ड नन्द के द्वार पर इकट्ठे होने लगे। अपने कमल से कोमल पैरों के पंजों से उचक-उचक कर पत्री को देखने लगीं। कोई तो उस पत्री को अपने हृदय से स्पर्श कराने लगी। सभी एक-दूसरे से पूछने लगी कि हमारे लिए श्रीकृष्ण ने क्या लिखा है। श्रीकृष्ण के विरह में व्यथित सभी गोपियों की हालत ऐसी है जैसे वे दुःख की पराकाष्ठा पर पहुँच गई हों। संदेश की खबर ने जितना सुख उनको दिया उससे कहीं अधिक दुःख संदेश के ज्ञान ने दिया।

प्रेम और सौन्दर्य दीर्घ उत्तरीय प्रश्न

प्रश्न 1.
संकलित कविता के आधार पर “प्रेम और सौन्दर्य” पर घनानन्द के विचार लिखिए।
उत्तर:
घनानन्द का विरह वर्णन सूरदास के भ्रमरगीत के समकक्ष है। घनानन्द की कविताओं में ‘सुजान’ का उनकी प्रेयसी होना ही अधिक समीचीन है। सुजान को श्रृंगार पक्ष के नायक और भक्ति पक्ष में कृष्ण मान लेना ही उचित दिखाई देता है। उनके प्रेम का संयोग सुजान नामक वेश्या से प्रारम्भ हुआ है जो अल्पकाल में ही वियोग में परिणत हो गया। उनकी कविता प्रिय सुजान की कठोरता के कारण प्रेमी हृदय की मार्मिकता से उमड़े आँसुओं का सागर है। वे सच्चे,सरल तथा साहित्यिक प्रेम के समर्थक हैं-
“अति सूधौ सनेह को मारग है, जहँ नेकू सयानप बाँक नहीं।
तहँ साँचे चलें तजि आपनपो, झिझकैं कपटी जो निसाँक नहीं।”

घनानन्द के संयोग का चित्रण अति अल्प है। इससे स्पष्ट होता है कि उन्हें सुजान के सामीप्य से उनकी सुन्दरता का आभास रहा है। संयोग के सुख का उल्लास देखिए जिसमें उनका हृदय आनन्द से सिक्त है। देखिए-
“डगमगी डगनि धरनि छवि ही के भार,
ढरनि छबीले उर आछी वनमाल की।”

पहले अपनाने के बाद छोड़ देना घनानन्द को अच्छा नहीं लगा-
“पहिले अपनाय सुजान सनेह सौं,
क्यों फिर नेह कै तोरियो जू।”

प्रिय के अपने पास न होने से विरह का दुःख उमड़ पड़ता है। सुख के प्रतीक भी उस विरह-जन्य कवि को दुःख ही दे रहे हैं।

प्रश्न 2.
निम्नलिखित अंशों की सप्रसंग व्याख्या कीजिए-
(अ) पहिले अपनाय सुजान सनेह सौं.
क्यों फिर नेह के तोरियै जू।
निरधार अधार है धार मॅझार,
दई, गहि बाँह न बोरियै जू।।

(आ) आए हो सिखावन कौं जोग मथुरा तैं तोपै
ऊधो ये बियोग के बचन बतरावौ ना।
कहें ‘रत्नाकर’ दया करि दरस दीन्यौ
दुःख दरिबै कौं, तोपै अधिक बढ़ावौ ना।
उत्तर:
(अ) सन्दर्भ :
पूर्ववत्।

प्रसंग :
यहाँ कवि अपनी प्रेयसी सुजान से प्रेम को न तोड़ने के लिए प्रार्थना कर रहा है।

व्याख्या :
कविवर घनानन्द कहते हैं कि हे सुजान ! पहले तो तुमने मुझे प्रेमवश अपना लिया अर्थात् मुझसे प्रेम किया परन्तु अब क्यों उस प्रेम को तोड़ दिया? मैं इस प्रेम की मँझधार में बिना किसी आधार के हूँ। ऐसी स्थिति में मेरी बाँह पकड़कर उसे छोड़ो नहीं। अर्थात् इस प्रेम मार्ग में तुम्हारे अतिरिक्त कोई और नहीं है इसलिए मेरा हाथ पकड़कर बीच राह में मेरा साथ मत छोड़ो। चातक के आनन्द धन अपने चातक के गुणों को ग्रहण करके अर्थात् उसकी टेक का ध्यान करके मेरे साथ प्रेम करना छोड़ो मत। जिस प्रकार चातक अपने प्रिय घन (बादल) को देखकर हर्षित हो जाता है। उसकी टेक है कि वह स्वाति नक्षत्र की वर्षा का जल ही पीता है। गगन में घुमड़ते घन उसको आनन्द देते हैं। इसी प्रकार कवि का चातक रूपी मन सुजान रूपी घन की ओर ही टकटकी लगाए है। मुझे प्रेम रस पिलाकर और मेरी आशा को बढ़ाकर मेरे प्रेम-रस में विष (धोखा) घोलकर न पिलाओ अर्थात् मेरे विश्वास में विश्वासघात मत करो।

(आ) सन्दर्भ :
पूर्ववत्।

प्रसंग :
यहाँ पर गोपियाँ उद्धव के कथन ‘योग’ का श्लेष अर्थ करते हुए अनेक उलाहने उद्धव को देती हैं।

व्याख्या :
गोपियाँ कहती हैं कि हे उद्धव ! जब आप मथुरा से योग (मिलन) का उपदेश देने के लिए यहाँ पधारे हो तो हमसे वियोग की कठोर बातें क्यों करते हो? कविवर रत्नाकर कहते हैं कि गोपियों ने पुनः उद्धव से प्रार्थना की कि हे उद्धव ! हमारे कष्ट को दूर करने के लिए यहाँ आकर हमें दर्शन देकर आपने बड़ी कृपा की,तो फिर ये वियोग (बिछड़ने) की बातें सुनाकर हमारे दुःख को और मत बढ़ाओ। आपसे विनम्र निवेदन है कि आप अपने ज्ञानोपदेश के कठोर वचन रूपी पत्थर भूलकर भी मत चलाना, अन्यथा हमारा मन रूपी दर्पण चूर-चूर हो जायेगा। हमारा कोमल हृदय रूपी दर्पण इतने बड़े प्रहार को सहन नहीं कर पायेगा। एक मनमोहन ने तो हमारे मन में निवास करके हमें नष्ट कर दिया है। हमें उनके विरह का दुःख भोगने के लिए छोड़ दिया है। यदि तुमने हमारे मन रूपी दर्पण को तोड़ दिया तो इस दर्पण के अनेक टुकड़ों में हमें अनेक कृष्ण दिखाई देंगे। ऐसी स्थिति में हमारी क्या दशा होगी यह अकथनीय है। इसलिए तुम हमारे मन को तोड़कर उसमें अनेक मनमोहन मत बसाओ।

प्रश्न 3.
घनानन्द को ‘प्रेम की पीर’ कहना कहाँ तक उचित है?
उत्तर:
घनानन्द प्रेम की पीर के अमर गायक हैं। उनके प्रेम का प्रारम्भ ‘सुजान’ नामक वेश्या से हुआ, लेकिन उनका प्रेम अल्पकाल में ही वियोग में परिणत हो गया। उनकी कविता प्रिय सुजान कठोरता के कारण प्रेमी हृदय की मार्मिक व्यथा से उमड़े आँसुओं का सागर है। घनानन्द की कविता में प्रिय की निष्ठुरता,प्रेमी की सहनशीलता तथा प्रकृति का विरहोद्दीपक रूप का बड़ा ही सुन्दर वर्णन हुआ है। घनानन्द तो सच्चे सरल प्रेम के समर्थक थे, लेकिन उनकी प्रियतमा के मन में सयानापन और टेढ़ापन था, जो उनके प्यार को रास नहीं आया। देखिए-
“अति सूधौ सनेह को मारग है, जहँ नेकु सयानप बाँक नहीं।
तहँ साँचे चलें तजि आपनपो, झिझक कपटी जो निसाँक नहीं।”

घनानन्द के काव्य में संयोग पक्ष का चित्रण अति अल्प है। इससे ज्ञात होता है कि सुजान का सामीप्य चाहे कम प्राप्त हुआ हो, पर रहा अवश्य है। संयोग सुख का उल्लास देखिए-
“डगमगी डगनि धरनि छवि ही के भार,
ढरनि छबीले उर आछी वन माल की।”

घनानन्द के संयोग में भी वियोग निहित है। उन्हें संयोग में भी वियोग की शंका दुःख देती है।
“यह कैसी संयोग न जानि परै जु वियोग न क्यों हूँ विछोहत है।”

घनानन्द के प्रेम में कृत्रिमता जरा भी नहीं है। अपनी प्रेयसी ‘सुजान’ विरह से जागृत हृदय की उद्दाम आकांक्षा का प्राधान्य है। डॉ. कृष्णचन्द्र वर्मा के शब्दों में “घनानन्द का सारा काव्य सुजान की बेवफाई का शिकार होने और बलि चढ़ जाने की कहानी है जो आँसुओं में लिखी गयी है और भावों की भाषा में गायी गयी है।”

प्रश्न 4.
‘उद्धव शतक’ के आधार पर सिद्ध कीजिये कि रत्नाकर को मार्मिक स्थलों की भली-भाँति पहचान है।
उत्तर:
जगन्नाथ दास ‘रत्नाकर’ ने ब्रजभाषा में उत्कृष्ट काव्य का सृजन किया है। भाव की मार्मिकता तथा कला की अभिव्यंजना में इनका काव्य अनुपम है। ब्रजभाषा के भावुक एवं रसिक कवि ‘रत्नाकर’ के काव्य में श्रृंगार रस की प्रधानता मिलती है। उद्धव शतक का मूल रस श्रृंगार रस है। श्रीकृष्ण की एकनिष्ठ प्रेमिका गोपियों पर उद्धव का ज्ञानोपदेश मार्मिक प्रहार करता है-
“टूक-टूक है है मन-मुकुर हमारौ हाय,
चूकि हूँ कठोर-बैन-पाहन चलावौ ना॥
एक मनमोहन तो बसिकै उजारयौ मोहि,
हिय में अनेक मनमोहन बसावौ ना।”

कृष्ण के सन्देश आने का समाचार गोपियों के तप्त हृदय को सान्त्वना प्रदान करता है, लेकिन संदेश का ज्ञान उन्हें पुनः वियोग के सागर में डुबो देता है। उद्धव की अकथनीय कहानी सुनकर गोपियों की हालत दयनीय हो गई। कोई तो काँपने लगी,कोई बेहोश हो गई और किसी को पसीना आ गया। गोपियों के उत्तर ने उद्धव को निरुत्तर कर दिया।-
“आये हौ सिखावन कौं जोग मथुरा तैं तोपै,
ऊधौ ये बियोग के बचन बतरावौ ना।”

रत्नाकर के काव्य में रत्नाकर की भाषा का उत्कर्ष रूप देखा जा सकता है। इनके काव्य में ब्रजभाषा के अर्थगाम्भीर्य, पद-विन्यास, वाक्य चातुर्य, चमत्कार सौष्ठव आदि वैशिष्ट्य विद्यमान हैं। उदाहरण देखिए-
“छावते कटीर कहँ रम्य जमुना के तीर,
गौन रौन-रेती सों कदापि करते नहीं।
कहैं रत्नाकर बिहाइ प्रेम गाथा गूढ़
स्रोंन रसना में रस और भरते नहीं।”

प्रेम और सौन्दर्य काव्य सौन्दर्य

प्रश्न 1.
निम्नलिखित शब्दों के पर्यायवाची शब्द लिखिए
नेत्र,मार्ग,आनन्द, दया, कठोर।
उत्तर:
नेत्र – दृग, लोचन, नयन।
मार्ग – पथ,मग,राह।
आनन्द – आमोद,प्रमोद, उल्लास।
दया – कृपा, करुणा,रहम।
कठोर – कराल,निष्ठुर, कठिन।

प्रश्न 2.
घनानन्द के संकलित छंदों में कौन-सा रस है?
उत्तर:
घनानन्द के संकलित छंदों में शृंगार रस है।

प्रश्न 3.
रत्नाकर की भाषा के सम्बन्ध में अपने विचार लिखिए।
उत्तर:
रत्नाकर’ की कविता भक्तिकालीन भावधारा एवं रीतिकालीन कला का पुट मिलने पर जीवन्त हो गई है। रचना कौशल के साथ चित्रोपमता भी अनोखी है। अनुभावों का मर्मस्पर्शी अंकन है। भाषा शुद्ध एवं कोमल है। वह दुरूह नहीं है। इनकी भाषा ब्रज है जिसमें मधुरता, सरलता, भाव सबलता,मार्मिकता एवं कोमलता है। इनकी भाषा स्वाभाविक, गहन तथा मर्मस्पर्शी है। इनकी भाषा में पद माधुर्य, भाव अभिव्यक्ति की समर्थता और भाषा की उत्कृष्टता देखी जा सकती है। इनके काव्य में ब्रजभाषा के अर्थगाम्भीर्य, पद-विन्यास, वाक्-चातुर्य, चमत्कार सौष्ठव, समाहार शक्ति आदि वैशिष्ट्य विद्यमान हैं।
उदाहरण देखिए-
“छावते कुटीर कहूँ रम्य जमुना के तीर,
गौन रौन-रेती सों कदापि करते नहीं।
कह रत्नाकर बिहाइ प्रेम गाथा गूढ़
स्त्रोंन रसना में रस और भरते नहीं।”

प्रश्न 4.
निम्नलिखित काव्य पंक्तियों में अलंकार पहचान कर लिखिए
(अ) निरधार अधार है धार मँझार।
(आ) हिय में अनेक मनमोहन बसावौ ना।
(इ) टूक-टूक है है मन-मुकुर हमारौ हाय।
(ई) एक मनमोहन तौ बसिकै उजार्यो मोहिं।
(उ) उझकि-उझकि पद कंजनि के पंजनि पै।
उत्तर:
(अ) विरोधाभास।
(आ) श्लेष।
(इ) टूक-टूक = पुनरुक्तिप्रकाश, मन-मुकुर = रूपक।
(ई) विरोधाभास।
(उ) पुनरुक्तिप्रकाश, रूपक।

प्रश्न 5.
छप्पय किन मात्रिक छंदों के योग से बनता है? उदाहरण सहित स्पष्ट कीजिये।
उत्तर:
छप्पय इस विषम मात्रिक छंद में छह चरण होते हैं। इसके प्रथम चार चरण रोला और दो चरण उल्लाला के होते हैं। रोला के प्रत्येक चरण में 11-13 की यति पर 24 मात्राएँ और उल्लाला के हर चरण में 15-13 की यति पर 28 मात्राएँ होती हैं।
उदाहरण-
जहाँ स्वतन्त्र विचार न बदलें मन में मुख में,
जहाँ न बाधक बनें सबल निबलों के सुख में।
सबको जहाँ समान निजोन्नति का अवसर हो।
शान्तिदायिनी निशा, हर्ष सूचक वासर हो।
सब भाँति सुशासित हों जहाँ, समता के सुखकर नियम।
बस उसी स्वशासित देश में जागे हे जगदीश हम॥
(रोला + उल्लाला = छप्पय)

घनानंद के पद भाव सारांश

‘घनानन्द के पद’ नामक कविता के रचयिता रीतिमुक्त कवि ‘घनानन्द’ हैं। उन्होंने अपनी प्रियतमा ‘सुजान’ के वियोग में इन पदों को लिखा है। इनमें कवि के प्रेम की परिशुद्ध भावना के दर्शन होते हैं।

घनानन्द का प्रेम अनुभूतिपरक है। वे वियोग श्रृंगार के कवि हैं। प्रिय की स्मृतियों का भावना-ग्राही रूप उनके काव्य का प्राण है। प्रस्तुत पदों में वे प्रेम के स्वरूप की चर्चा करते हैं। वे कहते हैं कि ‘अति सूधो सनेह को मारग है’। सच्चा प्रेम हृदय से किया जाता है। वे बार-बार उसके रूप को, चेष्टाओं को और उसके स्वभाव को याद करते हैं ! प्रिय द्वारा किये गये उपेक्षा-भाव की चर्चा करते हुए वे प्राकृतिक उपादानों के रूप में कोयल, वर्षा और बादलों को विरह के उद्दीपकों की तरह चित्रित करते हैं, जैसे-कारी करि कोकिल! कहाँ को बैर काढ़ति री, कृकि कूकि अबहीं करेजो किन कोरि लै। घनानन्द की उपमाएँ एकदम नवीन हैं।

घनानंद के पद संदर्भ-प्रसंग सहित व्याख्या

(1) आपुहि तो मन हेरि हँसे
तिरछे करि नैननि नेह के चाव मैं।
हाय दई ! सुविसारि दई सुधि,
कैसी करें, सौ कहौ कित जावँ मैं।।
मीत सुजान, अनीति कहा यह,
ऐसी न चाहिए प्रीति के भाव मैं।
मोहन मूरति देखिबे को,
तरसावत हौ बसि एक ही गाँव मैं॥

शब्दार्थ :
हेरि = चुराना; तिरछे = टेढ़े नेह = प्रेम; चाव = शौक; दई = भगवान, देना; सुधि = याद; करें = कहना; कित = कहाँ; अनीति = अन्याय; बसि = निवास करना।

सन्दर्भ :
प्रस्तुत सवैया रीतिकालीन कवि घनानन्द द्वारा रचित ‘घनानन्द के पद’ नामक काव्य से लिया गया है।

प्रसंग :
इस सवैया में रीतिकालीन मुक्तक काव्यधारा के श्रेष्ठ कवि घनानन्द ने अपनी प्रेयसी सुजान को उलाहना देते हुए उसे निष्ठुर कहा है।

व्याख्या :
कवि घनानन्द अपनी प्रेयसी सुजान के रूखेपन से व्याकुल हो उसे उलाहना देते हुए कहते हैं कि पहले तो तुमने मेरे मन (हृदय) को ले लिया (चुरा लिया) और अब हँसकर मेरा और मेरे प्रेम का मजाक बनाती हो। तुम अपने नेत्रों को टेढ़ा करके तथा प्रेम का प्रतिदान न करके उसे अस्वीकार करती हो। निराश कवि भगवान से कहता है कि उसकी प्रेयसी ने उसकी स्मृति को बिसरा दिया है। वह सुजान से भी पूछता है कि वह अपना प्रेम कैसे व्यक्त करे और सुजान को छोड़कर कहाँ जाये। कवि अपनी प्रेमिका को मोहन शब्द से सम्बोधित करके अपने प्रेम की व्यापकता का परिचय देता है। वह कहते हैं कि मित्र सुजान ! तुम मेरे साथ ऐसा अन्यायपूर्ण व्यवहार क्यों करती हो, जबकि प्रेम में ऐसा नहीं होता है। कवि प्रेयसी की सूरत देखने को अत्यन्त आकुल है तथा उससे मिलने की इच्छा उसके मन में और बलवती हो उठती है। कवि कहता है कि उसकी प्रेयसी एक ही गाँव, अर्थात् मुहम्मदशाह रंगीले के दरबार में नर्तकी के रूप में उपस्थित होते हुए भी, जहाँ कवि स्वयं एक दरबारी कवि है, उससे बहुत दूरी बनाये रहती है। प्रेयसी सुजान की यही निष्ठुरता कवि के लिए असहनीय है।

काव्य सौन्दर्य :

1. ब्रजभाषा का सुन्दर उपयोग हुआ है।
2. सवैया छन्द, मुक्त शैली, वियोग शृंगार रस, अनुप्रास व यमक अलंकार दृष्टव्य हैं।
3. कवि की विरह भावना व सुजान की निष्ठुरता का सजीव चित्रण है।
4. यहाँ मोहन शब्द भगवान कृष्ण व सुजान, दोनों के लिए उपयोग किया गया है।

(2) पहिले अपनाय सुजान सनेह सौं,
क्यों फिरि नेह के तोरियै जू।
निरधार अधार है धार मँझार,
दई, गहि बाँह न बोरियै ज॥
घन आनन्द अपने चातक कौं,
गुन बाँधि लै मोह न छोरियै जू।
रस प्याय कै ज्याय बढ़ाय कै आस,
बिसास में यौं विष घोरियै जू॥

शब्दार्थ :
अपनाय = अपनाकर; नेह = प्रेम; धार मँझार = धारा के मध्य में; गहि = पकड़कर; बोरियै = डुबाना; मोह = प्रेम; बिसास = विश्वास। विष = जहर।

सन्दर्भ :
पूर्ववत्।

प्रसंग :
यहाँ कवि अपनी प्रेयसी सुजान से प्रेम को न तोड़ने के लिए प्रार्थना कर रहा है।

व्याख्या :
कविवर घनानन्द कहते हैं कि हे सुजान ! पहले तो तुमने मुझे प्रेमवश अपना लिया अर्थात् मुझसे प्रेम किया परन्तु अब क्यों उस प्रेम को तोड़ दिया? मैं इस प्रेम की मँझधार में बिना किसी आधार के हूँ। ऐसी स्थिति में मेरी बाँह पकड़कर उसे छोड़ो नहीं। अर्थात् इस प्रेम मार्ग में तुम्हारे अतिरिक्त कोई और नहीं है इसलिए मेरा हाथ पकड़कर बीच राह में मेरा साथ मत छोड़ो। चातक के आनन्द धन अपने चातक के गुणों को ग्रहण करके अर्थात् उसकी टेक का ध्यान करके मेरे साथ प्रेम करना छोड़ो मत। जिस प्रकार चातक अपने प्रिय घन (बादल) को देखकर हर्षित हो जाता है। उसकी टेक है कि वह स्वाति नक्षत्र की वर्षा का जल ही पीता है। गगन में घुमड़ते घन उसको आनन्द देते हैं। इसी प्रकार कवि का चातक रूपी मन सुजान रूपी घन की ओर ही टकटकी लगाए है। मुझे प्रेम रस पिलाकर और मेरी आशा को बढ़ाकर मेरे प्रेम-रस में विष (धोखा) घोलकर न पिलाओ अर्थात् मेरे विश्वास में विश्वासघात मत करो।

काव्य सौन्दर्य :

1. ब्रज भाषा का सुन्दर प्रयोग हुआ है।
2. देशज शब्दों का प्रयोग बड़ा सटीक लगता है।
3. ‘चातक की टेक’ जैसी उक्ति का सुन्दर प्रयोग हुआ।
4. श्लेष और अनुप्रास अलंकार की छटा प्रशंसनीय है।

(3) कारी कूरि कोकिल ! कहाँ को बैर काढ़ति री,
कूकि कूकि अबहीं करेजो किन कोरि लै।
पैड़े परे पापी ये कलापी निसि-द्यौस ज्यों ही,
चातक ! रे घातक है तू हू कान फोरि लै।
आनन्द के घन प्रानजीवन सुजान बिना,
जानि कै अकेली सब घेरो दल जोरि लै।
जोलौं करें आवन विनोद बरसावन वे,
तो लौं रे डरारे बजमारे घन ! घोरि लै॥

शब्दार्थ :
कूर = कठोर; कोकिल = कोयल; बैर = दुश्मनी; काढ़ति री = निकालती है; कूकि-कूकि = कूज-कूज कर; किन कोरि लै = खरोंच कर निकाल क्यों नहीं लेती; पैड़े परे = पीछे परे हैं; कलापी = मोर; निसि-द्यौस = रात-दिन; घातक = भयानक,घात करने वाला; डरारे = डरा लें; बजमारे = वज्राहत,बहुत दुष्ट; घोरि = गर्जना।

सन्दर्भ :
पूर्ववत्।

प्रसंग :
प्रकृति के मनभावन प्रतीक भी विरह में दग्ध कवि को प्रियतम सुजान के वियोग में कष्ट दे रहे हैं।

व्याख्या :
विरह जन्य पीड़ा से पीड़ित घनानन्द कवि आनन्द की प्रतीक कोयल से कहते हैं कि हे कोयल ! तेरी मधुर आवाज भी मुझे कष्ट दे रही है। हे कोयल ! तू कौन-सा बैर मुझसे निकाल रही है। कूक-कूक कर मेरे कलेजे को ही क्यों न निकाल ले? ये पापी मोर मेरे पीछे पडे हैं जो कि रात-दिन केउ,केउ कर मेरे कष्ट को और भी बढ़ा रहे हैं। चातक जो कभी प्रिय लगता था आज वह अपनी आवाज से मेरे कान फोड़े दे रहा है। आनन्द के धन प्रानजीवन सुजान के बिना मुझे अकेली जान कर सभी ने दल बना लिए हैं और मुझे घेर कर दुःख दे रहे हैं। जब तक मेरे विनोद के देने वाले सुजान (दूसरे भक्ति के अर्थ में श्रीकृष्ण) नहीं आते, तभी तक हे दुष्ट घन (बादल) सब मिलकर गर्जना कर मुझे डरा लो यहाँ बताया गया है कि संयोग श्रृंगार में जो प्रकृति के प्रतीक सुखदायी होते हैं वे ही प्रतीक वियोग शृंगार में दुःखदायी प्रतीत होते हैं।

काव्य सौन्दर्य :

1. प्रकृति के प्रतीकों का वैचित्र्य दिखाया गया है।
2. ब्रजभाषा का प्रभावशाली वर्णन हुआ है।
3. देशज शब्दों का प्रयोग रोचक लगता है।
4. अनुप्रास, पुनरुक्तिप्रकाश और श्लेष अलंकार हैं।

उद्धव प्रसंग भाव सारांश

‘उद्धव प्रसंग’नामक कविता के रचयिता ‘जगन्नाथ दास रत्नाकर’ हैं। कृष्ण और गोपियों के प्रेम का भावनामय वर्णन उनकी संकलित कविता में है। उद्धव प्रसंग प्रेम से भरा हुआ भावुक प्रसंग है।

रीतिकाल और आधुनिक काल की देहरी पर स्थित कवि जगन्नाथ दास ‘रत्नाकर’ ने वियोग श्रृंगार को अपने काव्य का आधार बनाया है। कृष्ण और गोपियों के प्रेम का भावनामय चित्रण यहाँ पर हुआ है। गोपियों में कृष्ण द्वारा भेजे गये पत्र को पढ़ने की आतुरता, उनकी विरहजन्य दशा,उनका कृष्ण के प्रति अतिशय समर्पण का अति सुन्दर वर्णन है। रत्नाकर के पदों में शब्दालंकार के साथ रूपक और प्रतीकों का प्रयोग हुआ है। योग सिखाने आये उद्धव की दशा गोपियों के तर्क के सामने मूक हो जाती है। अन्त में उद्धव को मानना पड़ता है कि सच्चा प्रेम तो गोपियों में ही देखने को मिलता है। कृष्ण के पास जाकर उद्धव कहते हैं कि यदि आपको देखने का चाव मन में न होता तो में इधर न आकर यमुना के किनारे झोपड़ी बनाकर रहता।

उद्धव प्रसंग संदर्भ-प्रसंग सहित व्याख्या

(1) भेजे मनभावन के उद्धव के आवन की,
सुधि ब्रज-गाँवनि में पावन जब लगी।
कहैं ‘रतनाकर’ गुवालिनी की झौरि-झौरि,
दौरि-दौरि नंद-पौरि आवन तबै लगीं।
उझकि-उझकि पद कंजनि के पंजनि पै,
पेखि-पेखि पाती छाती छोहनि छबै लगीं।
हमकौं लिख्यौ है कहा, हमकौं लिख्यौ है कहा,
हमकौं लिख्यौ है कहा कहन सबै लगीं।

शब्दार्थ :
झौरि-झौरि = झुंड के झुंड। दौरि-दौरि = दौड़-दौड़ कर। नंद पौरि = नन्द के आँगन। उझकि-उझकि = उझक-उझक कर, ऐड़ी उठा-उठा कर देखना पखि-पेखि = देख-देखकर। छाती छोहनि छबै लगी = हृदय से स्पर्श करने लगीं।

सन्दर्भ :
प्रस्तुत पद्यांश कवि जगन्नाथदास रत्नाकर द्वारा रचित ‘उद्धव प्रसंग’ से अवतरित है।

प्रसंग :
प्रस्तुत पंक्तियों में कवि ने उद्धव के ब्रज आगमन की बात सुनकर कृष्ण के संदेश को सुनने के लिए आ रही गोपियों की आतुरता का अनुपम वर्णन किया है।

व्याख्या :
जब ब्रज के गाँव में श्रीकृष्ण के मित्र उद्धव के आगमन का समाचार मिला तो गोपियों के समूह दौड़-दौड़ कर नन्द के द्वार पर एकत्रित होने लगे। गोपियों में कृष्ण के सन्देश को जानने की आतुरता तो देखते ही बनती है। कविवर रत्नाकर कहते हैं कि नन्द के वर पहुँची प्रेमातुर गोपियाँ अपने कमल जैसे कोमल पैरों के पंजों के बल खड़ी होकर उचक-उचक कर श्रीकृष्ण द्वारा भेजे गये पत्र को देखने लगीं। उनका हृदय सन्देश जानने की उत्कंठा से भर गया। बार-बार पत्र को देखकर हृदय से स्पर्श कराने लगीं। सभी गोपियाँ उद्धव से बार-बार यही पूछ रही हैं कि श्रीकृष्ण ने हमारे लिए क्या लिखा है, हमारे लिए क्या लिखा है, हमारे लिए क्या लिखा है?

काव्य सौन्दर्य :

1. गोपियों की आतुरता का सजीव चित्रण किया गया है।
2. अनुभावों और संचारी भावों की सुन्दर योजना है।
3. सरल, सुबोध ब्रजभाषा का प्रयोग।
4. श्रृंगार रस का अनूठा वर्णन।
5. रूपक (पद कंजनि पै), पुनरुक्ति (दौरि-दौरि) अलंकारों का प्रयोग।

(2) सुनि सुनि ऊधव की अकह कहानी कान,
कोऊ थहरानी कोऊ थानहिं थिरानी हैं।
कहैं ‘रत्नाकर’ रिसानी, बररानी कोऊ
कोऊ बिलखानी, विकलानी, विधकानी हैं।
कोऊ सेद-सानी, कोऊ भरि दृग पानी रही,
कोऊ घूमि-घूमि परी भूमि मुरझानी हैं।
कोऊ स्याम-स्याम कह बहकि बिललानी कोऊ
कोमल करेजो थामि सहमि सुखानी हैं।

शब्दार्थ :
अकह = जो कही न जाय; थहरानी = काँप गईं; थानहिं = स्थान पर; थिरानी = स्थिर रह गईं; रिसाई = क्रोधित हुई; बररानी = गुस्से में बड़बड़ाने लगी; बिथकानी = थकी-थकी सी हो गई; सेदसानी = पसीने में भीग गई; मुरझानी = बेहोश हो गईं; बिललानी = छटपटाने लगीं; सहमि सुखानी = सहम कर मानो सूख गई हो।

सन्दर्भ :
पूर्ववत्।

प्रसंग :
उद्धव ने ब्रज में गोपियों को कृष्ण के प्रति प्रेम त्यागकर योग साधना द्वारा ब्रह्म प्राप्ति का उपदेश दिया जिसे सुनते ही विरह संतप्त गोपियाँ व्याकुल हो गईं। प्रस्तुत पद्यांश में गोपियों की इसी विकलता का सजीव वर्णन हुआ है।

व्याख्या :
उद्धव की उस ब्रह्म की अकथनीय कहानी को सुन-सुन कर गोपियाँ बेहाल हो गईं। कोई गोपी तो काँप गई और कोई अपने ही स्थान पर जड़वत् स्थिर रह गई। किसी किसी को उद्धव पर क्रोध आने लगा और कोई गुस्से में बड़बड़ाने लगी। कोई बिलख उठी, कोई व्याकुल हो उठी और कोई शिथिल होकर शरीर से थकी-थकी सी-दिखाई देने लगी। उस असह्य व्यथा के कारण किसी-किसी का शरीर तो पसीने से तर हो गया, किसी के नेत्र आँसुओं के जल से छलछला उठे। कोई-कोई चक्कर खाकर जमीन पर गिर पड़ी और मूर्च्छित हो गई। कोई बावली सी ‘स्याम-स्याम’ की रट लगाने लगी और बहक कर बड़बड़ाने लगी। कोई सहम कर सूखी हुई सी अपना कोमल हृदय थाम कर रह गई।

काव्य सौन्दर्य :

1. उद्धव के आगमन पर ‘योग’ की बातें सुनकर गोपियों के हृदय का मार्मिक चित्रण हुआ है।
2. रत्नाकर अनुभवों का वर्णन करने में सिद्धहस्त हैं।
3. अनुप्रास, पुनरुक्ति, विरोधाभास (अकह कहानी) लोकोक्ति (करेजौ थामि) अलंकारों की छटा दृष्टव्य है।

3. आए हौ सिखावन कौं जोग मथुरा तैं तोपै,
ऊधौ ये बियोग के बचन बतरावौ ना।
कहैं. रत्नाकर’ दया करि दरस दीन्यौ,
दुःख दरिबै कौं, तोपै अधिक बढ़ावौ ना।।
टूक-टूक है है मन-मुकुर हमारी हाय,
चकि हँ कठोर-बैन-पाहन चलावौ ना।
एक मनमोहन तौ बसिकै उजार्यो मोहिं
हिय में अनेक मनमोहन बसावौ ना॥ (2009)

शब्दार्थ :
जोग = योग शास्त्र; दरस = दर्शन; टूक-टूक = टुकड़े-टुकड़े मन-मुकुर = मन रूपी दर्पण; बैन-पाहन = वचनों के पत्थर; मनमोहन = श्रीकृष्ण।

सन्दर्भ :
पूर्ववत्।

प्रसंग :
यहाँ पर गोपियाँ उद्धव के कथन ‘योग’ का श्लेष अर्थ करते हुए अनेक उलाहने उद्धव को देती हैं।

व्याख्या :
गोपियाँ कहती हैं कि हे उद्धव ! जब आप मथुरा से योग (मिलन) का उपदेश देने के लिए यहाँ पधारे हो तो हमसे वियोग की कठोर बातें क्यों करते हो? कविवर रत्नाकर कहते हैं कि गोपियों ने पुनः उद्धव से प्रार्थना की कि हे उद्धव ! हमारे कष्ट को दूर करने के लिए यहाँ आकर हमें दर्शन देकर आपने बड़ी कृपा की,तो फिर ये वियोग (बिछड़ने) की बातें सुनाकर हमारे दुःख को और मत बढ़ाओ। आपसे विनम्र निवेदन है कि आप अपने ज्ञानोपदेश के कठोर वचन रूपी पत्थर भूलकर भी मत चलाना, अन्यथा हमारा मन रूपी दर्पण चूर-चूर हो जायेगा। हमारा कोमल हृदय रूपी दर्पण इतने बड़े प्रहार को सहन नहीं कर पायेगा। एक मनमोहन ने तो हमारे मन में निवास करके हमें नष्ट कर दिया है। हमें उनके विरह का दुःख भोगने के लिए छोड़ दिया है। यदि तुमने हमारे मन रूपी दर्पण को तोड़ दिया तो इस दर्पण के अनेक टुकड़ों में हमें अनेक कृष्ण दिखाई देंगे। ऐसी स्थिति में हमारी क्या दशा होगी यह अकथनीय है। इसलिए तुम हमारे मन को तोड़कर उसमें अनेक मनमोहन मत बसाओ।

काव्य सौन्दर्य :

1. इस कविता में मानव,मनोविज्ञान का सुन्दर चित्रण हुआ है। गोपियों ने ‘योग’ का अर्थ मिलन लिया जो उनकी बुद्धि में सहज समा गया।
2. मुहावरों का सुन्दर व सार्थक प्रयोग।
3. व्याकरण सम्मत ब्रजभाषा एवं व्यंग्यात्मक शैली का प्रयोग।
4. वियोग श्रृंगार का वर्णन। श्लेष (जोग) पुनरुक्तिप्रकाश (टूक-टूक) और रूपक अलंकारों का प्रयोग।

(4) छावते कुटीर कहूँ रम्य जमुना कै तीर,
गौन रौन-रेती सों कदापि करते नहीं।
कहैं ‘रतनाकर’ बिहाइ प्रेम गाथा गूढ
स्त्रोंन रसना में रस और भरते नहीं।
गोपी ग्वाल बालनि के उमड़त आँसू देखि
लेखि प्रलयागम हैं नैंक डरते नहीं।
होतो चित चाब जौ न रावरे चितावन को,
तजि ब्रज-गाँव इतै पाँव धरते नहीं।

शब्दार्थ :
छावते कुटीर = कुटिया बना लेते; रम्य = सुन्दर; रौनरेती = रमणरेती; गौन = गमन; बिहाइ = छोड़कर; गूढ़ = गम्भीर; स्रोन = कान; रसना = जीभ; लखि = देखकर; प्रलयागम = प्रलय का आना; चितावन = देखने की लालसा।

सन्दर्भ :
पूर्ववत्।

प्रसंग :
प्रस्तुत पंक्तियों में उद्धव की ब्रज के प्रति अनुराग की सुन्दर व्यंजना हुई है। उद्धव श्रीकृष्ण को सम्बोधित करते हुए कहते हैं।

व्याख्या :
उद्धव कहते हैं कि हे श्रीकृष्ण ! यदि मेरे मन में गोपियों की दशा बताने का उत्साह न होता तो हम ब्रज छोड़कर इधर की तरफ पैर भी नहीं रखते। चाहे हमें किसी भी परिस्थिति का सामना करना पड़ता, हम ब्रज में रमणीय यमुना के किनारे किसी स्थान पर कुटी बनाकर रहते और रमणरेती से इधर की ओर गमन नहीं करते। रत्नाकर कवि कहते हैं उद्धव ने कृष्ण को समझाया कि हम अपने कानों से प्रेम की गम्भीर गाथा सुनते और अपनी रसना से उसी प्रेम-रस का गुणगान करते। हम तो श्रीकृष्ण-प्रेम की कथा ही सुनते और उसे ही गाते। गोपी-ग्वालाओं के उमड़ते हुए आंसुओं को देखकर प्रलय आने की सम्मावना से भी नहीं डरते। यदि आपको देखने की लालसा न होती तो हम ब्रज छोड़कर इधर पैर भी नहीं रखते।

काव्य सौन्दर्य :

1. उद्धव का ब्रज के प्रति अनुराग का सच्चा स्वरूप व्यक्त हुआ है।
2. व्याकरणसम्मत मुहावरेदार ब्रजभाषा का प्रयोग हुआ है।
3. पदमैत्री एवं अनुप्रास अलंकार।

MP Board Class 12th Maths Important Questions Chapter 5B Differentiation

Differentiation Important Questions

Differentiation Short Answer Type Questions

Question 1.
Differentiate the function sin(cos x²) with respect to x? (NCERT)
Solution:
Let y = sin (cosx²)
\(\frac { dy }{ dx } \) = \(\frac { d }{ dx } \) sin (cos x²)
= \(\frac { d }{ dx } \) sin t, [Putting cos x² = t]
= \(\frac { d }{ dt } \) sin t \(\frac { dt }{ dx } \)
= cos t \(\frac { d }{ dx } \) cos x²
= cos (cos x²) \(\frac { d }{ dx } \) cos u, [Putting x² = u]
= cos (cos x²) \(\frac { d }{ du } \) cos u \(\frac { du }{ dx } \)
= – cos (cos x²) sin u \(\frac { d }{ dx } \) x²
= – 2x cos (cos x²). sin x².

Question 2.
Differentiate the function y = sec [tan \(\sqrt { x } \) ] with respect to x? (NCERT)
Solution:
Given:
y = sec [tan \(\sqrt { x } \) ]
\(\frac { dy }{ dx } \) = \(\frac { d }{ dx } \) sec [tan \(\sqrt { x } \) ]
= \(\frac { d }{ dx } \) sec t, [Putting tan \(\sqrt { x } \) = t]
= \(\frac { d }{ dt } \) sec t \(\frac { dt}{ dx } \)
= sec t tan t \(\frac { d }{ dx } \) tan \(\sqrt { x } \)
= sec (tan \(\sqrt { x } \)) tan (tan \(\sqrt { x } \)) \(\frac { d }{ dx } \) tan u, [Putting \(\sqrt { x } \) = u]
= sec (tan \(\sqrt { x } \)) tan (tan \(\sqrt { x } \)) sec² u \(\frac { d }{ dx } \) \(\sqrt { x } \)
= sec (tan \(\sqrt { x } \)) tan (tan \(\sqrt { x } \)) sec²\(\sqrt { x } \) × \(\frac { 1 }{ 2\sqrt { x } } \)

Question 3.
Differentiate the function y = log [cos e^x] with respect to x? (NCERT)
Solution:
Given:
y = log [cos e^x]
\(\frac { dy }{ dx } \) = \(\frac { d }{ dx } \) [log (cos e^x)]
\(\frac { dy }{ dx } \) = \(\frac { d }{ dx } \) log t, [Putting cos e^x = t]
= \(\frac { d }{ dt } \) log t \(\frac { dt }{ dx } \)
= \(\frac { 1 }{ t } \). \(\frac { d }{ dx } \) cos e^x
= \(\frac { 1 }{ cose^{ x } } \) × \(\frac { d }{ dx } \) cos u, [Putting e^x = u]
= \(\frac { 1 }{ cose^{ x } } \). \(\frac { d }{ du } \) cos u \(\frac { du }{ dx } \)
= \(\frac { -sinu }{ cose^{ x } } \). \(\frac { d }{ dx } \) e^x
= \(\frac { -(sine^{ x })e^{ x } }{ cose^{ x } } \)
= – e^x tan e^x

Question 4.
Differentiate the function y = cos [log x + e^x] with respect to x? (NCERT)
Given:
y = cos [log x + e^x]
\(\frac { dy }{ dx } \) = \(\frac { d }{ dx } \) cos (log x + e^x)
\(\frac { dy }{ dx } \) = \(\frac { d }{ dx } \) cos t, [Putting log x + e^x = t]
= \(\frac { d }{ dt } \) cos t \(\frac { dt }{ dx } \)
= – sin t \(\frac { d }{ dx } \) (log x + e^x)
= – sin (log x + e^x) (\(\frac{1}{x}\) + e^x)
= – \(\frac { (xe^{ x }+1)sin(logx+e^{ x }) }{ x } \)

Question 5.
Differentiate the function y = cos^-1(e^x) with respect to x? (NCERT)
Solution:
Given:
y = cos^-1 (e^x)
∴\(\frac { dy }{ dx } \) = \(\frac { d }{ dx } \) cos^-1 (e^x)
Putting e^x = t,
= \(\frac { d }{ dx } \) cos^-1 t = \(\frac { d }{ dt } \) cos^-1 t \(\frac { dt }{ dx } \)
= \(\frac { 1 }{ \sqrt { 1-t^{ 2 } } } \) \(\frac { d }{ dx } \) e^x
= – \(\frac { e^{ x } }{ \sqrt { 1-e^{ 2x } } } \)

Question 6.
If y + sin y = cos x then find the value of \(\frac { dy }{ dx } \)? (NCERT)
Solution:
Given:
y + sin y = cos x
Differentiating both sides with respect to x,
\(\frac { d }{ dx } \) (y + siny) = \(\frac { d }{ dx } \) cos x
⇒ \(\frac { dy }{ dx } \) + cos y \(\frac { dy }{ dx } \) = – sin x
⇒ \(\frac { dy }{ dx } \) (1 + cos y) = -sin x
⇒ \(\frac { dy }{ dx } \) = \(\frac { -sinx }{ 1+cosy } \)

Question 7.
If 2x + 3y = sin x then find the value of \(\frac { dy }{ dx } \)? (NCERT)
Solution:
Given:
2x + 3y = sin x
Differentiating both sides with respect to x,
\(\frac { d }{ dx } \) (2x + 3y) = \(\frac { d }{ dx } \) sin x
2 \(\frac { d }{ dx } \) x + 3 \(\frac { dy }{ dx } \) = cos x
⇒ 2 + 3 \(\frac { dy }{ dx } \) = cos x – 2
∴ \(\frac { dy }{ dx } \) = \(\frac{cos x – 2}{3}\)

Question 8.
If x = a cos θ, y = a sin θ then find the value of \(\frac { dy }{ dx } \)? (NCERT)
Solution:
Given:
x = a cos θ
y = a sin θ
Differentiating eqn. (1) with respect to θ.
We get, \(\frac { dx }{ d\theta } \) = – a sin θ
Again, \(\frac { dy }{ dx } \) = \(\frac { \frac { dy }{ d\theta } }{ \frac { dx }{ d\theta } } \)
⇒ \(\frac { dy }{ dx } \) = – \(\frac { acos\theta }{ asin\theta } \)
⇒ \(\frac { dy }{ dx } \) = – cot θ.

Question 9.
If x = at² and y = 2at then find the value of \(\frac { dy }{ dx } \)? (NCERT)
Solution:
Given:
x = at²
\(\frac { dx }{ dt } \) = 2at
y = 2at
\(\frac { dy }{ dt } \) = 2a
Again, \(\frac { dy }{ dx } \) = \(\frac { \frac { dy }{ dt } }{ \frac { dx }{ dt } } \) = \(\frac{2a}{2at}\)
⇒ \(\frac { dy }{ dx } \) = \(\frac { 1 }{ t} \).

Question 10.
If y = x² + 3x + 2 then find the value of \(\frac { d^{ 2 }y }{ dx^{ 2 } } \)? (NCERT)
Solution:
Given:
y = x² + 3x + 2
∴ \(\frac { dy }{ dx } \) = 2x + 3.1 + 0
\(\frac { dy }{ dx } \) = 2x + 3
Again differentiating with respect to x,
We get, \(\frac { d }{ dx } \) ( \(\frac { dy }{ dx } \) ) = 2.1 + 0
⇒ \(\frac { d^{ 2 }y }{ dx^{ 2 } } \) = 2.

Question 11.
If y = x³ + tan x then find the value of \(\frac { d^{ 2 }y }{ dx^{ 2 } } \)? (NCERT)
Solution:
Given:
y = x³ + tan x
\(\frac { dy }{ dx } \) = \(\frac { d }{ dx } \) [x³ + tan x]
= \(\frac { d }{ dx } \) x³ + \(\frac { d }{ dx } \) tan x
⇒ \(\frac { dy }{ dx } \) = 3x² + sec² x
Again, differentiating with respect to x,
⇒ \(\frac { d }{ dx } \) ( \(\frac { dy }{ dx } \) ) = \(\frac { d }{ dx } \) [3x² + sec²x]
\(\frac { d^{ 2 }y }{ dx^{ 2 } } \) = 3 \(\frac{d}{dx}\) x² + \(\frac{d}{dx}\) sec² x
⇒ \(\frac { d^{ 2 }y }{ dx^{ 2 } } \) = 6x + \(\frac{d}{dx}\) t², [Putting sec x = t]
= 6x + \(\frac { d }{ dt } \) t² \(\frac { dt }{ dx } \)
= 6x + 2t \(\frac { d }{ dx } \) sec x
= 6x + 2 sec x.secx tanx
⇒ \(\frac { d^{ 2 }y }{ dx^{ 2 } } \) = 6x + 2 sec²x tan x.

Differentiation Long Answer Type Questions – I

Question 1.
If y = tan^-1 \(\frac { x }{ \sqrt { 1+x^{ 2 } } } \) then find the value of \(\frac { dy }{ dx } \)?
Solution:
Given:
y = tan^-1 \(\frac { x }{ \sqrt { 1+x^{ 2 } } } \)
Now putting \(\frac { x }{ \sqrt { 1+x^{ 2 } } } \) = t
\(\frac { dy }{ dx } \) = \(\frac { d }{ dt } \) tan^-1t. \(\frac { dt }{ dx } \)
= \(\frac { 1 }{ 1+t^{ 2 } } \). \(\frac { d }{ dx } \) \(\frac { x }{ \sqrt { 1+x^{ 2 } } } \)

Again Putting 1 + x² = u,

Question 2.
If x = a (t + sin t) and y = a(1 – cost) then find the value of \(\frac { dy }{ dx } \)?
Solution:
Given:
x = a (t + sin t)
∴\(\frac { dx }{ dt } \) = a(1 + cos t)
Again y = a (1 – cos t)
∴\(\frac { dy }{ dt } \) = a (0 + sint) = a sin t
Hence \(\frac { dy }{ dx } \) = \(\frac { \frac { dy }{ dt } }{ \frac { dx }{ dt } } \) = \(\frac { asint }{ a(1+cost) } \)
= \(\frac { sint }{ a(1+cost) } \) = \(\frac { 2sint/2cost/2 }{ 2cos^{ 2 }t/2 } \)
⇒ \(\frac { dy }{ dx } \) = tan \(\frac{t}{2}\).

Question 3.
If x = a(2θ – sin 2θ) and y = a(1 – cos 2θ) then find the value of \(\frac { dy }{ dx } \) where θ = \(\frac { \pi }{ 3 } \)? (CBSE 2018)
Solution:
Given:
x = a (2θ – sin 2θ) ………………… (1)
y = a (1 – cos 2θ) ………………………. (2)
Differentiating eqn. (1) with respect to θ, we get
\(\frac { dx }{ d\theta } \) = a(2.1 – cos 2θ.2)
= 2a (1 – cos 2θ)
= 2a.2 sin²θ
= 4a sin²θ
Differentiating eqn. (2) with respect to θ, ………………… (3)
\(\frac { dy }{ d\theta } \) = a (0 + sin 2θ.2)
= 2a sin 2θ
= 2a.2 sin θ cos θ ……………………….. (4)
= 4a sin θ cos θ
Divinding eqn.(4) by eqn.(3),
\(\frac { dy }{ d\theta } \) + \(\frac { dx }{ d\theta } \) = \(\frac { 4asin\theta cos\theta }{ 4asin^{ 2 }\theta } \)
⇒ \(\frac { dy }{ dx } \) = cot θ
When θ = \(\frac { \pi }{ 3 } \), then
\(\frac { dy }{ dx } \) = cot \(\frac { \pi }{ 3 } \) = \(\frac { 1 }{ \sqrt { 3 } } \).

Question 4.
If y = a sin mx + b cos mx then prove that:
\(\frac { d^{ 2 }y }{ dx^{ 2 } } \) + m²y = 0?
Solution:
Given:
y = a sin mx + b cos mx ……………………. (1)
Differentiating eqn. (2) with respect to x,
\(\frac { dy }{ dx } \) = am cos mx – bm sin mx
Differentiating eqn. (2) with respect to x,
\(\frac { d^{ 2 }y }{ dx^{ 2 } } \) = – am² sin mx – bm² cos mx
⇒ \(\frac { d^{ 2 }y }{ dx^{ 2 } } \) = – m² y
∴ \(\frac { d^{ 2 }y }{ dx^{ 2 } } \) + m² y = 0. Proved.

Question 5.
(A) If y = e^msin-1x then prove that (1 – x²) y₂ – xy₁ – m²y = 0?
Solution:
Given:
y = e^msin-1x
\(\frac { dy }{ dx } \) = y₁ = e^msin-1x. \(\frac { d }{ dx } \) (msin^-1x)
⇒ y₁ = y.m. \(\frac { 1 }{ \sqrt { 1-x^{ 2 } } } \)
⇒ \(\sqrt { 1-x^{ 2 } } \) y₁ = my …………………………. (1)
Again, differentiating with respect to x,
\(\sqrt { 1-x^{ 2 } } \). y₂ + y₁. \(\frac{1}{2}\) (1 – x²)^1/2 (- 2x) = my₁
⇒ \(\sqrt { 1-x^{ 2 } } \). y₂ – \(\frac { x }{ \sqrt { 1-x^{ 2 } } } \) y₁ = m\(\frac { my }{ \sqrt { 1-x^{ 2 } } } \). [from eqn.(1)]
⇒ (1 – x²) y₂ – xy₁ = m²y
⇒ (1 – x²) y₂ – xy₁ – m²y = 0. Proved.

Question 5.
(B) If y = e^mtan-1x then prove that (1 + x²) y₂ + (2x – m) y₁ = 0?
Solution:
Solve like Q.5 (A)

Question 5.
(C) If y = e^mcos-1x then prove that (1 – x²) y₂ – xy₁ – m² y = 0?
Solution:
Solve like Q.5 (A)

Question 6.
Differentiate sin^-1 \(\frac { 2x }{ 1+x^{ 2 } } \) with respect to x?
Solution:
Let y = sin^-1 ( \(\frac { 2x }{ 1+x^{ 2 } } \) )
Again let x = tan θ ⇒ θ = tan^-1 x
y = sin^-1 ( \(\frac { 2tan\theta }{ 1+tan^{ 2 }\theta } \) )
= sin^-1 (sin 2θ) = 2θ = 2 tan^-1 x
∴\(\frac { dy }{ dx } \) = 2 \(\frac { d }{ dx } \) (tan^-1 x) = \(\frac { 2 }{ 1+x^{ 2 } } \)

Question 7.
If y = cot^-1 \(\sqrt { \frac { 1+x }{ 1-x } } \) then find \(\frac { dy }{ dx } \)?
Solution:
Given:
y = cot^-1 \(\sqrt { \frac { 1+x }{ 1-x } } \)
Let x = cos θ

Putting in eqn.(1), we get
y = cot^-1 (cot \(\frac{θ}{2}\))
⇒ y = \(\frac{θ}{2}\) = \(\frac{1}{2}\) cos^-1 x, [∵x = cos θ ⇒ ∴θ = cos^-1 x]
Differentiating both sides w.r.t. x,
\(\frac { dy }{ dx } \) = – \(\frac { 1 }{ 2\sqrt { 1-x^{ 2 } } } \)

Question 8.
If y = tan^-1 \(\sqrt { \frac { 1+x }{ 1-x } } \) then find \(\frac { dy }{ dx } \)?
Solution:
Solve like Q.No.7
Answer:
\(\frac { dy }{ dx } \) = \(\frac { 1 }{ 2\sqrt { 1-x^{ 2 } } } \)

Question 9.
If y = cot^-1 ( \(\frac { cosx+sinx }{ cosx-sinx } \) ) then find the value of \(\frac { dy }{ dx } \)?
Solution:
Given:
y = cot^-1 ( \(\frac { cosx+sinx }{ cosx-sinx } \) )

⇒ \(\frac { dy }{ dx } \) = \(\frac { d }{ dx } \) ( \(\frac { \pi }{ 4 } \) – x) = -1.

Question 10.
y = tan^-1 \(\frac { \sqrt { 1+x^{ 2 }-1\quad } }{ x } \) Differentiate with respect to x?
Solution:
Given:
y = tan^-1\(\frac { \sqrt { 1+x^{ 2 }-1\quad } }{ x } \) ……………….. (1)
Put x = tan θ in eqn. (1)
∴ θ = tan^-1 x

⇒ y = \(\frac { \theta }{ 2 } \) = \(\frac{1}{2}\) tan^-1 x
∴\(\frac { dy }{ dx } \) = \(\frac{1}{2}\) tan^-1 x
∴\(\frac { dy }{ dx } \) = \(\frac{1}{2}\) \(\frac { d }{ dx } \) (tan^-1 x ) = \(\frac{1}{2}\) \(\frac { 1 }{ (1+x^{ 2 }) } \)

Question 11.
If y = cot^-1 \(\left[\frac{\sqrt{1+x^{2}}+1}{x}\right]\) then find the value of \(\frac { dy }{ dx } \)?
Solution:
y = cot^-1 \(\left[\frac{\sqrt{1+x^{2}}+1}{x}\right]\)
Put x = tan θ,

⇒ y = \(\frac{1}{2}\) tan^-1x
⇒ \(\frac { dy }{ dx } \) = \(\frac{1}{2}\). \(\frac { 1 }{ 1+x^{ 2 } } \).

Question 12.
If y = x^sinx then find the value of \(\frac { dy }{ dx } \)?
Solution:
Given:
y = x^sinx
Taking log on both sides with respect to x.
\(\frac { 1 }{ y } \) \(\frac { dy }{ dx } \) = sin x × \(\frac{1}{x}\) + logx cos x
∴\(\frac { dy }{ dx } \) = y.[ \(\frac{sinx}{x}\) + log x.cos x]

Question 13.
If y = \(\sqrt { \frac { 1-x }{ 1+x } } \) then prove that \(\frac { dy }{ dx } \) = \(\frac { y }{ x^{ 2 }-1 } \)?
Solution:
Given:
y = \(\sqrt { \frac { 1-x }{ 1+x } } \)^1/2
By taking log , log y = log \(\sqrt { \frac { 1-x }{ 1+x } } \)^1/2
⇒ log y = \(\frac{1}{2}\) [log (1 – x) – log (1 + x)]
Differentiating both sides with respect to x,

Question 14.
If y = (sin x)sinxsinx ………. ∞ then find the value of \(\frac { dy }{ dx } \)?
Solution:
Given:
y = (sin x)sinxsinx ………. ∞
⇒ y = (sin x)^y
⇒ log y = y log sin x
Differentiating both sides with respect to x,
\(\frac{1}{y}\) \(\frac{dy}{dx}\) = y \(\frac{d}{dx}\) (log sin x) + log sin x \(\frac{dy}{dx}\)

Question 15.
(A) If y = \(\sin x+\sqrt{\sin x+\sqrt{\sin x+\ldots+\infty}}\) then prove that:
\(\frac{dy}{dx}\) = \(\frac{cos x}{2y – 1}\)
Solution:

Differentiating both sides with respect to x,
2y \(\frac{dy}{dx}\) = cos x + \(\frac{dy}{dx}\)
⇒ 2y \(\frac{dy}{dx}\) – \(\frac{dy}{dx}\) = cos x
⇒ (2y – 1) \(\frac{dy}{dx}\) = cos x
∴\(\frac{dy}{dx}\) = \(\frac{cos x}{2y – 1}\).

(B) If y = \(\cot x+\sqrt{\cot x+\sqrt{\cot x+\ldots+\infty}}\) then prove that:
\(\frac{dy}{dx}\) = \(\frac { cosec^{ 2 }x }{ 1-2y } \)
Solution:
Solve like Q.No. 15 (A).

(C) If y = \(\begin{aligned}
&x+\sqrt{\tan x+\sqrt{\tan x+\ldots \infty}}\\
\end{aligned}\) then find the value of \(\frac{dy}{dx}\)?
Solution:
Solve like Q.No 15 (A)

Question 16.
If y = e\($x+e^{x+e^{x+e}}-$\) then prove that:
\(\frac{dy}{dx}\) = \(\frac{y}{1-y}\)?
Solution:
Given: y = e\(x+e^{x+e^{x+e}}-x\)
⇒ y = e^x+y
Taking log on both sides,
log y = log e^x+y
log y = x + y
Differentiating both sides with respect to x,
\(\frac{1}{y}\) \(\frac{dy}{dx}\) = 1 + \(\frac{dy}{dx}\)
⇒ \(\frac{dy}{dx}\) ( \(\frac{1}{y}\) – 1) = 1
⇒ \(\frac{dy}{dx}\) ( \(\frac{1-y}{y}\) ) = 1
⇒ \(\frac{dy}{dx}\) = \(\frac{y}{1-y}\) Proved.

Question 17.
Differentiate \(\frac { 1 }{ (x+a)(x+b)(x+c) } \) with respect to x?
Solution:
Let y = \(\frac { 1 }{ (x+a)(x+b)(x+c) } \)
Applying log on both sides,
log y = log 1 – log(x + a) – log (x + b) – log(x + c)
Differentiating both sides with respect to x,
\(\frac{1}{y}\) \(\frac{dy}{dx}\) = 0 – \(\frac{1}{x + a}\) – \(\frac{1}{x + b}\) – \(\frac{1}{x + c}\)
⇒ \(\frac{dy}{dx}\) = – y [ \(\frac{1}{x + a}\) + \(\frac{1}{x + b}\) + \(\frac{1}{x + c}\) ]
⇒ \(\frac{dy}{dx}\) = \(\frac { 1 }{ (x+a)(x+b)(x+c) } \) × { \(\frac { 1 }{ x+a } +\frac { 1 }{ x+b } +\frac { 1 }{ x+c } \) }

Question 18.
Differentiate log ( \(\sqrt{x}\) + \(\frac { 1 }{ \sqrt { x } } \) ) with respect to x?
Solution:
Let y = log ( \(\sqrt{x}\) + \(\frac { 1 }{ \sqrt { x } } \) ) ⇒ y = log ( \(\frac { x+1 }{ \sqrt { x } } \) )
⇒ y = log (x + 1) – log \(\sqrt{x}\)
⇒ y = log (x + 1) – \(\frac{1}{2}\) log x
Differentiating both sides with respect to x,
\(\frac{dy}{dx}\) = \(\frac{d}{dx}\) log (x + 1) – \(\frac{1}{2}\). \(\frac{d}{dx}\) log x
⇒ \(\frac{dy}{dx}\) = \(\frac{1}{x + 1}\) – \(\frac{1}{2}\).\(\frac{1}{x}\) = \(\frac{2x-x-1}{2x(x+1)}\)
⇒ \(\frac{dy}{dx}\) = \(\frac{x – 1}{2x(x + 1)}\).

Question 19.
Differentiate y = tan^-1 ( \(\frac { sinx }{ 1+cosx } \) ) with respect to x?
Solution:
y = tan^-1 ( \(\frac { sinx }{ 1+cosx } \) )

⇒ y = tan^-1 (tan \(\frac{x}{2}\) ) = \(\frac{x}{2}\)
Differentiating both sides with respect to x,
\(\frac{dy}{dx}\) = \(\frac{d}{dx}\) ( \(\frac{x}{2}\) ) = \(\frac{1}{2}\).

Question 20.
Verify Rolle’s theroem for the function f(x) = x² interval [-1, 1]. (NCERT)
Solution:
Given:
f(x) = x², a = – 1, b = 1.

1. f(x) = x² is a polynomial, hence, f(x) is continous in [-1, 1].
2. f'(x) = 2x exist for every value of x, Hence it is differentiable in (-1, 1).
3. f(-1) = (-1)² = 1, f(1) = (1)² = 1.

∴ f(-1) = f(1)
There exists a value c in (-1, 1) such that:
∴ f'(c) = 0
⇒ 2c = 0, [∵f'(x) = 2x]
⇒ c = 0 ∈ (-1, 1)
Hence, Rolle’s theorem is verified. Proved.

Question 21.
Verify Rolle’s theroem for the function f(x) = x² + 2x – 8, x ∈ [-4, 2]? (NCERT)
Solution:
Given:
f(x) = x² + 2x – 8, a= – 4, b = 2.

1. f(x) = x² + 2x – 8 is a polynomial hence f(x) is continous in [-4, 2].
2. f'(x) = 2x + 2 exist for every value of x, hence it is differentiable in (-4, 2).
3. f(-4) = (-4)² + 2 (-4) – 8

= 16 – 8 – 8 = 0
f(2) = (2)² + 2 × 2 – 8 = 4 + 4 – 8 = 0
∴ f(-4) = f(2).
There exists a value c in (-4, 2),
∴ f'(c) = 0
⇒ 2c + 2 = 0
⇒ c = – 1 ∈ (-4, 2)
Hence, Rolle’s theorem is verified.

Question 22.
Verify Rolle’s theorem for the function f(x) = 2x³ + x² – 4x – 2?
Solution:
Given:
f(x) = 2x³ + x² – 4x – 2 …………………… (1)
We know that polynomial functions are continuous for all real values.
∴ f(x) = o
⇒ 2x³ + x² – 4x – 2 = 0
⇒ x² (2x + 1) – 2(2x + 1) = 0
⇒ (x² – 2) (2x + 1) = 0
⇒ x² = 2, 2x + 1 = 0
⇒ x = ±\(\sqrt { 2 } \), x = – \(\frac{1}{2}\)
⇒ x = – \(\sqrt { 2 } \), \(\sqrt { 2 } \), \(\frac{-1}{2}\)
∴ Interval [-\(\sqrt { 2 } \), \(\sqrt { 2 } \) ].
1. f(x) is continuous in [-\(\sqrt { 2 } \), \(\sqrt { 2 } \) ]
2. f'(x) = 6x² + 2x – 4 is differentiable in [-\(\sqrt { 2 } \), \(\sqrt { 2 } \)].
3. f(-\(\sqrt { 2 } \)) = 2( \(\sqrt { 2 } \) )³ + (-\(\sqrt { 2 } \) ) ² – 4 (- \(\sqrt { 2 } \) ) – 2 = 0
and f ( \(\sqrt { 2 } \) ) = 2( \(\sqrt { 2 } \) )³ + ( \(\sqrt { 2 } \) ) ² – 4( \(\sqrt { 2 } \) ) – 2 = 0
∴ f(- \(\sqrt { 2 } \) ) = f( \(\sqrt { 2 } \) )
There exists a value c in (-\(\sqrt { 2 } \), \(\sqrt { 2 } \) )
∴ f'(c) = 0
⇒ 6c² + 2c – 4 = 0, [∵f'(x) = 6x² + 2x – 4]
∴ c = \(\frac { -2\pm \sqrt { 2^{ 2 }-4\times 6\times (-4) } }{ 2\times 6 } \)
c = \(\frac { -2\pm \sqrt { 4+96 } }{ 12 } \)
⇒ c = \(\frac { -2\pm 10 }{ 12 } \)
⇒ c = \(\frac{-2-10}{12}\) and c = \(\frac{-2+10}{12}\)
⇒ c = -1, \(\frac{2}{3}\) ∈ (- \(\sqrt { 2 } \), \(\sqrt { 2 } \) )
Hence, Rolle’s theroem is verified.

Question 23.
Verify Lagrange’s mean value theorem for the function f(x) = x + \(\frac{1}{x}\) on [1, 3].
Solution:
Given:
f(x) = x + \(\frac{1}{x}\) = \(\frac { x^{ 2 }+1 }{ x } \), x ∈ [1, 3]

1. f(x), x ≠ 0 hence it is a continous function in [1, 3].
2. f'(x) = 1 – \(\frac { 1 }{ x^{ 2 } } \) is differentiable in (1, 3).
3. f(1) = 2 and f(3) = \(\frac{10}{3}\)

Hence, f(1) ≠ f(2)
For mean value theorem,
∴ \(\frac { f(b)-f(a) }{ b-a } \) = f'(c)
⇒ \(\frac { f(3)-f(1) }{ 3-1 } \) = 1 – \(\frac { 1 }{ c^{ 2 } } \)
⇒ \(\frac { \frac { 10 }{ 3 } -2 }{ 2 } \) = 1 – \(\frac { 1 }{ c^{ 2 } } \)
⇒ 1 – \(\frac { 1 }{ c^{ 2 } } \) = \(\frac{2}{3}\)
⇒ \(\frac { 1 }{ c^{ 2 } } \) = \(\frac{3-2}{3}\) = \(\frac{1}{3}\)
⇒ c² = 3
⇒ c = \(\sqrt{3}\) = 1.732 ∈ (1, 3)
Hence, Langrange’s mean value theorem is verified. Proved.

Question 24.
Verify Lagrange’s mean value theorem for the following function f(x) = log x on [1, e]?
Solution:
f(x) = logx, x ∈ [1, e], x > 0.
1. As f(x) = log x, x > 0 is a continuous function, hence f(x) is continuous in [1, e],

2. f'(x) = \(\frac{1}{x}\),
∴ f(x) is differentiable in (1, e).

3. f(1) = log 1 = 0, f(e) = log e = 1.
Now by mean value theorem,
∴ \(\frac{f(e) – f(1)}{e-1}\) = f'(c)
⇒ \(\frac{1-0}{e-1}\) = \(\frac{1}{e}\)
⇒ c = e – 1 ∈ (1, e)
Hence, Langrange’s mean value theorem is verified. Proved.

Question 25.
With the help of Langrange’s value thoerem for the function y = \(\sqrt{x-2}\) in the interval [2, 3]. Find the point where the tangent is parallel to be chord joining the points?
solution:
Given:
f(x) = \(\sqrt{x-2}\), a = 2, b = 3

1. As f(x) = \(\sqrt{x-2}\), x ∈ [2, 3] is defined.
∴ f(x) is continous function for [2, 3].

2. f'(x) = \(\frac { 1 }{ 2\sqrt { x-2 } } \) is defined in interval (2, 3).
∴ f(x) is differentiable in [2, 3]

3. f(2) = 0, f(3) = 1
f(2) ≠ f(3)
Now, by Langrange’s mean value theorem,
∴ \(\frac{f(3)-f(2)}{3-2}\) = f'(c)
⇒ \(\frac{1-0}{1}\) = \(\frac { 1 }{ 2\sqrt { c-2 } } \)
⇒ \(\frac { 1 }{ 2\sqrt { c-2 } } \) = 1
⇒ \(\frac { 1 }{ \sqrt { c-2 } } \) = 2
⇒ \(\sqrt{c-2}\) = \(\frac{1}{2}\)
⇒ c – 2 = \(\frac{1}{4}\)
⇒ c = \(\frac{1}{4}\) + 2 = \(\frac{9}{4}\) = 2.25 ∈ (2,3)
∴ f(c) = \(\sqrt { \frac { 9 }{ 4 } -2 } \) = \(\frac{1}{2}\)
Required points ( \(\frac{9}{4}\), \(\frac{1}{2}\) ).

Differentiation Long Answer Type Questions – II

Question 1.
Differentiate sin^-1 [ \(\frac { 2^{ x+1 } }{ 1+4^{ x } } \) ] with respect to x? (NCERT)
Solution:
y = sin ^-1 [ \(\frac { 2^{ x+1 } }{ 1+4^{ x } } \) ]
⇒ y = sin^-1 [ \(\frac { 2.2^{ x } }{ 1+2^{ 2x } } \) ]
Putting 2^x = tan θ
Then, θ = tan^-1 2^x
⇒ y = sin^-1 [ \(\frac { 2tan\theta }{ 1+tan^{ 2 }\theta } \) ]
⇒ y = sin^-1 [sin 2θ], [∵sin 2θ = \(\frac { 2tan\theta }{ 1+tan^{ 2 }\theta } \) ]
⇒ y = 2θ
⇒ y = 2 tan^-1 (2^x), [θ = tan^-1(2^x)]
∴ \(\frac{dy}{dx}\) = 2 \(\frac{d}{dx}\) tan^-1 (2^x)
Putting 2^x = t
⇒ \(\frac{dy}{dx}\) = 2 \(\frac{d}{dx}\) tan^-1 t
= 2 \(\frac{d}{dt}\) tan^-1 t\(\frac{dt}{dx}\)
⇒ \(\frac{dy}{dx}\) = \(\frac { 2 }{ 1+t^{ 2 } } \) \(\frac{d}{dx}\) (2^x),
= \(\frac { 2 }{ 1+2^{ 2x } } \) × 2^x log 2
⇒ \(\frac{dy}{dx}\) = \(\frac { 2^{ x+1 }log2 }{ 1+4^{ x } } \)

Question 2.
If y = sin^-1 x then prove that: (NCERT)
(1 – x²) \(\frac { d^{ 2 }y }{ dx^{ 2 } } \) – x \(\frac{dy}{dx}\) = 0? (NCERT)
Solution:
Given:
y = sin^-1 x ……………………………. (1)
\(\frac{dy}{dx}\) = \(\frac{d}{dx}\) (sin^-1 x)
\(\frac{dy}{dx}\) = \(\frac { 1 }{ \sqrt { 1-x^{ 2 } } } \)
\(\frac{d}{dx}\) ( \(\frac{dy}{dx}\) ) = \(\frac{d}{dx}\) t^-1/2
Putting 1 – x² = t
\(\frac { d^{ 2 }y }{ dx^{ 2 } } \) = \(\frac{d}{dx}\) t^-1/2
= \(\frac{d}{dt}\) t^-1/2 \(\frac{dt}{dx}\)
= – \(\frac{1}{2}\) t^-1/2-1 \(\frac{d}{dx}\) (1 – x²)

Question 3.
If y = tan x + sec x then prove that:
\(\frac { d^{ 2 }y }{ dx^{ 2 } } \) = \(\frac { cosx }{ (1-sinx)^{ 2 } } \)?
Solution:
y = tan x + sec x (given)
\(\frac{dy}{dx}\) = sec² x + sec x tan x
⇒ \(\frac{dy}{dx}\) = sec x(sec x + tan x)
⇒ \(\frac{dy}{dx}\) = \(\frac{1}{cosx}\) [ \(\frac{1}{cosx}\) + \(\frac{sinx}{cosx}\) ]
= \(\frac { 1+sinx }{ cos^{ 2 }x } \) = \(\frac { 1+sinx }{ 1-sin^{ 2 }x } \)
= \(\frac { 1+sinx }{ (1+sinx)(1-sinx) } \)
⇒ \(\frac{dy}{dx}\) = \(\frac{1}{1-sinx}\)
Again differentiating both sides with respect to x,
\(\frac{d}{dx}\) ( \(\frac{dy}{dx}\) ) = \(\frac{d}{dx}\) ( \(\frac{1}{1-sinx}\)
\(\frac { d^{ 2 }y }{ dx^{ 2 } } \) = \(\frac { (1-sinx).0-1.(0-cosx) }{ (1-sinx)^{ 2 } } \)
⇒ \(\frac { d^{ 2 }y }{ dx^{ 2 } } \) = \(\frac { cosx }{ (1-sinx)^{ 2 } } \)

Question 4.
If y = sin(sinx) then prove that:
y₂ + y₁ tan x + y cos² x = 0? (CBSE 2018)
Solution:
y = sin(sin x)
Differentiating w.r.t. x,
y₂ = cos (sinx) \(\frac{d}{dx}\) (cos x) + cos x \(\frac{d}{dx}\) {cos (sin x)}
= cos (sin x) (- sinx) + (cos x) [-sin(sin x)] cos x
⇒ y₂ = – sin x cos (sin x) – cos₂ x sin (sin x)
⇒ y₂ = -sin x cos(sin x) – y cos₂ x, [from eqn.(1)]
⇒ y₂ = [ \(-\frac { sinx }{ cosx } \). cos x] cos(sin x) – y cos² x
⇒ y₂ = – tan x {cos (sin x) cos x} – y cos²
⇒ y₂ = -tan x {cos(sin x) cos x} – y cos² x [from eqn.(2)]
⇒ y₂ = (-tan x) y₁ – y cos² x, Proved.
⇒ y₂ + y₁ tan x + y cos² x = 0.

Question 5.
If (x² + y²)² = xy then find \(\frac{dy}{dx}\)? (CBSE 2018)
Solution:
(x² + y²)² = xy
Differentiating with respect to x,
2(x² + y²) (2x + 2y \(\frac{dy}{dx}\) ) = x \(\frac{dy}{dx}\) + y.1
⇒ 2(x² + y²). 2x + 2(x² + y²). 2y \(\frac{dy}{dx}\) = x \(\frac{dy}{dx}\) + y
⇒ [4y(x² + y²) – x] \(\frac{dy}{dx}\) = y – 4x (x² + y²)
⇒ \(\frac{dy}{dx}\) = \(\frac { y-4x(x^{ 2 }+y^{ 2 }) }{ 4(x^{ 2 }+y^{ 2 })y-x } \)

Question 6.
If y = 500e^7x + 600e^-7x then prove that:
\(\frac { d^{ 2 }y }{ dx^{ 2 } } \) = 49 y? (NCERT)
Solution:
Given:
y = 500e^7x + 600e^-7x …………………….. (1)

Question 7.
If y = (tan^-1 x)² then prove that:
(x² + 1)² y₂ + 2x (x² + 1) y₁ = 2? (NCERT)
Solution:
Given:
y = (tan^-1 x)²

Question 8.
Differentiate sec^-1 ( \(\frac { 1 }{ 2x^{ 2 }-1 } \) ) with respect to: \(\sqrt { x^{ 2 }-1 } \)?
Solution:
Let y₁ = sec^-1 ( \(\frac { 1 }{ 2x^{ 2 }-1 } \) )
⇒ y₁ = cos^-1 (2x² – 1)

Question 9.
Differentiate tan^-1 ( \(\frac { 2x }{ 1-x^{ 2 } } \) ) with respect to:
sin^-1 ( \(\frac { 2x }{ 1-x^{ 2 } } \) )
Solution:
Let y₁ = tan^-1 \(\frac { 2x }{ 1+x^{ 2 } } \) and y₂ = sin^-1 \(\frac { 2x }{ 1+x^{ 2 } } \)
Let x = tan θ, then θ = tan^-1 x

⇒ y₁ = tan^-1 (tan 2θ) and y₂ = sin^-1 (sin 2θ)
⇒ y₁ = 2θ and y₂ = 2θ
⇒ y₁ = 2 tan^-1 x and y₂ = 2 tan^-1 x

Question 10.
Differentiate tan^-1 ( \(\frac { \sqrt { 1+x^{ 2 }-1 } }{ x } \) ) with respect to x?
Solution:
Let y₁ = tan^-1 ( \(\frac { \sqrt { 1+x^{ 2 }-1 } }{ x } \) )
Put x = tan θ,

Question 11.
If x \(\sqrt { 1+y } \) + y \(\sqrt { 1+x } \) = 0 then prove that:
\(\frac{dy}{dx}\) = -(1 + x)^-2
Solution:
Given:
x\(\sqrt { 1+y } \) + y \(\sqrt { 1+x } \) = 0
⇒ x \(\sqrt { 1+y } \) = -y\(\sqrt { 1+x } \)
Squaring both sides,
x² (1 + y) = y² (1 + x)
⇒ x² + x²y = xy² + y²
⇒ x² – y² + x²y – xy² = 0
⇒ (x – y) (x + y) + xy (x – y) = 0
⇒ (x – y)(x + y + xy) = 0
⇒ x – y = 0
⇒ x = y
But x ≠ y
∴ x + y + xy = 0
⇒ y (l + x) = – x
∴ y = – \(\frac{x}{1+x}\)
Differentiating both sides with respect to x,

Question 12.
If x^y = e^y-x then prove that:
\(\frac{dy}{dx}\) = \(\frac { 2-log_{ e }x }{ (1-log_{ e }x)^{ 2 } } \)
Solution:
Given: x^y = e^y-x
Applying log on both sides,
∴ log_e x^y = log_e(e^y-x)
⇒ y log_e x = (y – x) log_e e
⇒ y log_e x – y = -x
⇒ y(1 – log_e x) = x
⇒ y = \(\frac { x }{ 1-log_{ e }x } \)
Differentiating with respect to x,
Again,

Question 13.
If y\(\sqrt { 1-x^{ 2 } } \) + x \(\sqrt { 1-y^{ 2 } } \) then prove that:
\(\frac{dy}{dx}\) + \($\sqrt{\frac{1-y^{2}}{1-x^{2}}}$\) = 0?
Solution:
Given:
y\(\sqrt { 1-x^{ 2 } } \) + x \(\sqrt { 1-y^{ 2 } } \) = 1.
Let x = sin θ and y = sin ϕ,

Question 14.
(A) If y = x^sin-1x + x^x then find the value of \(\frac{dy}{dx}\)?
Solution:
Given:
y = x^sin-1x + x^x
y = u + v
∴\(\frac{dy}{dx}\) = \(\frac{du}{dx}\) + \(\frac{dv}{dx}\) ……………………. (1)
Where, u = x^sin-1x
∴ log u = sin^-1 x log x, (taking log both sides)
Differentiating both sides with respect to x,


and v = x^x
∴ log v = x log x
Differentiating both sides with respect to x,
\(\frac{1}{v}\). \(\frac{dv}{dx}\) = 1.log x + x. \(\frac{1}{x}\)
⇒ \(\frac{dv}{dx}\) = v(log x + 1)
⇒ \(\frac{dv}{dx}\) = x^x (log x + 1) ………… (3)∴ From eqn.(1),

(B) If y = x^-1x + x^x, then find the value of \(\frac{dy}{dx}\)?
Solution:
Solve like Q.No. 14(A).

Question 15.
If sin y = x sin (a + y) then prove that:
\(\frac{dy}{dx}\) = \(\frac { sin^{ 2 }(a+y) }{ sina } \)?
Solution:
Given:
sin y = x sin (a + y)
⇒ x = \(\frac { siny }{ sin(a+y) } \)
Differentiating with respect to x,

Question 16.
If x^y = e^x-y then prove that:
\(\frac{dy}{dx}\) = \(\frac { logx }{ (1+logx)^{ 2 } } \)?
Solution:
Given: x^y = e^x-y
Applying log on both sides,
y log x = (x – y) log_ea
⇒ y log x = (x – y).1 = x – y
Differentiating both sides with respect to x,

From eqn.(1),
y log x = x – y
⇒ y log x + y = x
⇒ y(logx + 1) = x
Put the value of y in eqn.(2)

MP Board Class 12 Maths Important Questions

MP Board Class 12th Biology Important Questions Chapter 8 Human Health and Disease

 Human Health and Disease Important Questions

 Human Health and Disease Objective Type Questions

Question 1.
Choose the correct answer:

Question 1.
Syphilis is caused by :
(a) Tryponema
(b) Leptospira
(c) Pasturelia
(d) Vibro.
Answer:
(a) Tryponema

Question 2.
AIDS is caused by :
(a) Blood cancer
(b) H1N1
(c) Bacterium
(d)TMV.
Answer:
(b) H1N1

Question 3.
Which one is not cancer :
(a) Leukemia
(b) Glaucoma
(c) Carcinoma
(d) Sarcoma.
Answer:
(b) Glaucoma

Question 4.
First organic acid produced through the process of fermentation :
(a) Acetic acid
(b) Lactic acid
(c) Citric acid
(d) Butyric acid.
Answer:
(d) Butyric acid.

Question 5.
Vaccines produced by genetic engineering is :
(a) Hepatitis B
(b) Herpes virus
(c) Malarial vaccines
(d) Both (a) and (b).
Answer:
(d) Both (a) and (b).

Question 6.
The vitamins produced by activity of microbes are :
(a) Vitamin B₂
(b) Vitamin B₁₂
(c) Both (a) and (b)
(d) Vitamin B₂,B₁₂ and Vitamin C.
Answer:

Question 7.
Enzyme used in manufacture of detergent is :
(a) Proteases
(b) Amylases
(c) Rennet
(d) Lipase.
Answer:
(d) Lipase.

Question 8.
Common human interferons are :
(a) Leukocytic interferon – α
(b) Fibroblastic interferon – β
(c) Immune interferon – γ
(d) All of these.
Answer:
(c) Immune interferon – γ

Question 9.
Which of the following is used in genetic engineering :
(a) DNA – polymerase
(b) Nuclease
(c) Restriction endonuclease
(d) RNA – polymerase.
Answer:
(b) Nuclease

Question 10.
Yeast is used in preparation of:
(a) Acetic acid
(b) Cheese
(c) Curd
(d) Ethyl alcohol.
Answer:
(d) Ethyl alcohol.

Question 11.
Germinating barley seeds are used in the preparation of:
(a) Cheese
(b) Wine
(c) Beer
(d) Lactic acid.
Answer:
(d) Lactic acid.

Question 12.
‘Syphilis’ is a sexually transmitted disease caused by :
(a) Treponema pallidum
(b) Leptospira
(c) Pasturelia
(d) Vibrio.
Answer:
(d) Vibrio.

Question 13.
The immunity obtained after the body has recovered from a disease is :
(a) Active immunity
(b) Passive immunity
(c) Both (a) and (b)
(d) None of these.
Answer:
(b) Passive immunity

Question 14.
Vaccination used for protection from Polio, Diptheria and Tetanus : (MP 2015)
(a) BCG
(b) DPT
(c) MMR
(d) STD.
Answer:
(b) DPT

Question 15.
AIDS test is known us : (MP 2017)
(a) Australian antigen
(b) ELISA
(c) Thyroid test
(d) pH test.
Answer:
(b) ELISA

Question 2.
Fill in the blanks:

1. AIDS is an example of ………………….. transmitted disease.
2. Genes responsible for cancer are called …………………..
3.  ………………….. is known as blood cancer.
4.  ………………….. is first human made insulin by genetic engineering.
5. Hepatitis B disease is caused by …………………..
6. Asthma is a type of …………………..
7.  ………………….. is the transfer of human organs from a donor to a recipient.
8. Nutrient deficiency disease is caused by …………………..
9. Plague vaccine is discovered by …………………..
10.  ………………….. is the full name of AIDS.
11. Gonorrhea disease is caused by …………………..
12. L.S.D. is found by ………………….. fungi.
13. Typhoid is caused by …………………..
14.  ………………….. is found in Klinefelter syndrome.

Answer:

1. Sexually
2. Oncogene
3. Leukemia
4. Humulin
5. Virus
6. Allergy
7. Organ transplantation
8. Less nutrition
9. Dr. Haffkine
10. Acquired Immune Deficiency Syndrome
11. Nesseria gonorrhoeae
12. Clavicepspurpurea
13. Saltnonalatyphi,
14. One extra chromosme.

Question 3.
Match the followings:
I.

Answer:

1. (d)
2. (e)
3. (a)
4. (b)
5. (c)
6. (f)

II.

Answer:

1. (e)
2. (c)
3. (d)
4. (b)
5. (a)

Question 4.
Write answer in one word/sentences:

1. Name the vector of malarial parasite.
2. Give full name of HIV.
3. Give the name of harmful chemical compound of tobacco.
4. Give one example of sedative drugs.
5. Name the disease which is transmitted from one person to another is called.
6. When is AIDS day celebrated?
7. Who prescribed the word AIDS first time?
8. Name the branch that aims at improving the genetic quality of a human population.
9. Write the name of virus which causes cancer.
10. Give the name of one edible yeast.
11. Name the disease which is treated by chemotherapy.
12. What is the name of antiviral protein?
13. Who gave the Germ theory of disease?
14. What is the reason of syphilis?

Answer:

1. Plasmodium
2. Human Immunodeficiency Virus
3. Nicotine
4. Benzodiazopines
5. Infectious disease
6. 1 December
7. Edward Jenner
8. Eugenics
9. Oncogenic virus
10. Ashby a gossypii
11. Cancer
12. Interferon
13. Robert Koch
14. Sexual contact.

Human Health and Disease Very Short Answer Type Questions

Question 1.
What are lymphoid organs?
Answer:
Lymphoid organs are certain organs, in which lymphocytes can differentiate and proliferate.

Question 2.
What is the name of drug which converts thoughts and feelings of human and causes fear?
Answer:
Psychedelic drugs.

Question 3.
Which disease is caused by transmission of HIV?
Answer:
AIDS.

Question 4.
Name the method which is used in the diagnosis of AIDS.
Answer:
ELISA Test.

Question 5.
In different parts of the country Chikungunya is clarified. Name the carrier of this disease.
Answer:
Chikungunya is spread through bites from A. aegypti mosquitoes.

Question 6.
Name the types of Immunity.
Answer:
Immunity is two types:

Innate immunity
Acquired immunity.

Question 7.
Where is Wuchereria found?
Answer:
Filarial worms Wuchereria is found in lymph vessels.

Question 8.
Name the types of tumours.
Answer:
Tumours are of two types : Benign and Malignant.

Question 9.
What harm does AIDS cause in humans?
Answer:
Immune power of the body is decreased by AIDS.

Question 10.
When inability to open the mouth because human chewing areca nuts in betel quid or its variants (gutkha) and jaw muscles become hard. Give the name of possible disease.
Answer:
Submucous fibrasis disease.

Question 11.
Name the full form of DPT.
Answer:
Diphtheria, Pertussis and Tetanus.

Question 12.
What is the side effects of cancer treatment?
Answer:
Hair falling and Anemia.

Question 13.
What is the full form of NAC?
Answer:
National AIDS Control Organization.

Question 14.
Which plant extract is called marijuana?
Answer:
Cannabis sativa.

Question 15.
Name combine form of the poppy, morphine, heroin, pethidine and methedrine.
Answer:
Meconium.

Question 16.
What is the second name of Mary Mallon?
Answer:
The second name of Mary Mallon is Typhoid Mary.

Question 17.
Name the cells which are multiplied by HIV when it enters the human body.
Answer:
Macrophages and helper T – lymphocytes.

Question 18.
Which body organs are affected by Pneumonia?
Answer:
Lungs and Alveolies are affected.

Question 19.
What is the confirmation test of Typhoid?
Answer:
Typhoid fever can be confirmed by Widal test.

Question 20.
Write the full form of LSD.
Answer:
Lysergic Acid Diethylamide.

Question 21.
Which viruses are responsible for cancer?
Answer:
Oncogenic viruses have cancer – causing viral oncogenes.

Human Health and Disease Short Answer Type Questions

Question 1.
What are the various public health measures which you would suggest as safeguard against infectious disease ?
Answer:
The common preventive measures are as follows :

1. Education – People should be educated about communicable diseases to protect themselves from such diseases.
2. Vaccination – People should get vaccination on time to avoid infection.
3. Sanitation – The sanitation condition should be improved to avoid infection from polluted water, contaminated food, etc.
4. Eradication of vectors – The breeding places of vectors should be destroyed and adult vectors should be killed by suitable methods.
5. Sterilisation – The patient’s surroundings and articles of use should be completely sterilised so as to reduce the chances of infection.

Question 2.
Explain what is meant by metastasis?
Answer:
Metastasis is the spread of cancerous cells through migration from one tissue to other tissue and organs resulting in formation of secondary tumour. Malignant tumour is a mass of proliferating cells called neoplastic cells. They grow rapidly and invade surrounding unaffected normal cells assues. Cells get sloughed off from such tumour and migrate to distant sites through blood. A new place of infection is thus, established and a new tumour is formed. This property is called metastasis.

Question 3.
Define the following:

1. Immunity
2. Vaccine
3. Interferon
4. Vaccination.

Answer:
1. Immunity : The capacity of any organism to fight with the disease and causal organisms is known as immunity. The immunity is due to B and T cells.

2. Vaccine : The chemical substances which protect our body by disease causing organisms are called vaccines.

3. Interferon : Interferon is an antiviral protein which is produced within animal cells due to stimulus produced after viral infection and which prevents the infection and multiplication of other viruses.

4. Vaccination : Vaccination is the process by which resistance against specific disease is created in any living organism.

Question 4.
Distinguish between Inborn and Acquired immunity.
Answer:
Differences between Inborn and Acquired immunity are:

Inborn immunity:

• This immunity is present by birth.
• It is a kind of active immunity.

Acquired immunity:

• This immunity helps in the expansion of life span of organism.
• This immunity is of both type active immunity and passive immunity.

Question 5.
What is auto – immunity?
Answer:
This is an abnormality which sometimes develop in the immune system of the body. Instead of destroying foreign molecules, it starts attacking the body’s own cells leading to serious consequence. Such diseases are called autoimmune diseases. Autoimmune diseases depend on the type of self – antigen involved. If the self-antigens are R.B.Cs. then the body destroys its own R.B.Cs. resulting in chronic anaemia. When the self – antigen is a muscle cell, it results in destruction of its own muscles resulting in severe weakness, when the self-antigens are liver cells, it results in chronic hepatitis.

Question 6.
What is allergens? What cause the allergy to produce?
Answer:
Allergy is the condition of hypersensitivity of the body against certain substances or to a physical or chemical agent allergens. When antigen antibody reaction takes place in the body, it results allergy. Sufficient antibodies will not be produced in lacking of proper immune system. The allergens combine with the antibody bound mast cells, which causes the cell to burst releasing histamine. It results inflammatory responses in the body. Allergy may be caused by a medicine, cosmetics and other substances like, pollen grains, dust particles etc.

Question 7.
What is B – cells and T – cells? Explain it.
Answer:
B – lymphocytes or B – cells produce an army of protein called antibodies in blood. In response to pathogens, T – lymphocytes or T – cells help B – cells to produce antibodies, immune response are produced by these two types of lymphocytes.

Question 8.
Which types of diseases are protected by D.P.T. vaccine? Write the name of pathogens for each disease.
Answer:

Question 9.
What is eugenics?
Answer:
Eugenics:
The branch of biology which deals with the study of improvements of human race is called eugenics.

Importance:

1. Development of selective reproduction in similar species
2. Transfer of genetic materials in various organisms
3. Development of GM food and GM crops
4. Gene cloning
5. Gene therapy, etc.

Question 10.
How vaccination is important in immunity?
Answer:
Vacc, nation is the process of introduction of weakened or inactivated pathogens or proteins (vaccine) into a person so, provide protection against the disease. Vaccination provides immunisation after a time gap. Due to immunisation our body produces antibodies against the vaccine and develops the ability to neutralise pathogens during actual infection. Nowadays different types of vaccine which gives in children like polio, tetanus, deptheria, pertusis, small pox etc.

Question 11.
What is drug addiction? What are its causes?
Answer:
Addiction is most common problem of our youths because they start to take different types of drugs and alcoholic beverages due to various reasons. It makes them habitual and dependent on them. Addiction is the habitual, psychological and physiological dependence on a substance or practice which is beyond voluntary control. A person who is habituated to a substance or a practice especially harmful one, is called drug addiction.

Its causes are:

1. Curiosity
2. Fun and Stimulation
3. Will of doing more work
4. Feeling of freeding
5. Temporary escape from the life problems.

Question 12.
Write down the differences between sedative and tranquilizer.
Answer:
Differences between Sedative and Tranquilizer :

Sedative:

• These drugs depress the activities of central nervous system.
• A person sleeps more after taking excess drugs.
• Example: Barbiturates.

Tranquilizer:

• These drugs lessen tension and do not induce sleep.
• They do not sleep.
• Example: Phenothiazines.

Question 13.
Give the name of source of LSD. Give its effects also.
Answer:
LSD (Lysergic Acid Diethylamide):
It is a crystalline amidated alkaloid which is obtained from the sclerotium of ergot fungus Claviceps purpurea, pathogen of ergot disease of rye. LSD causes horrible dreams, hallucinations, chronic psychosis and damage the brain. LSD was tried as treatment for alcoholism, neurosis and cancer patients. LSD brings about chromosomal and foetal abnormalities. Pathological condition caused by LSD abuse or by eating grain affected by ergot is called ergotism.

Question 14.
Describe the effect of alcohol on human body and society.
Answer:
The effects of alcohol on human body and society are :

1. It effects the central nervous system.
2. Persons is incapable of differentiating what is right and what is wrong.
3. Taking excess of alcohol weakens heart, lungs, liver and other parts of the body.
4. Pupil of eye expands on taking excess of alcohol.
5. This increases the criminal activities in human beings.

Question 15.
Write withdrawal symptoms of addiction.
Answer:
Withdrawal symptoms from addiction:
When a drug dependent person fails to get the drug, he feels severe physical and psychological disturbances. These are called withdrawal symptoms. It includes tremors, nausea, vomiting, weakness, insomnia, anxiety run fits, decreased appetite, restlessness, elevated blood pressure, rapid heartbeat and epilepsy. These symptoms indicates that the body of addict person is unable to further use of intoxicant and they should stop it immediately.

Question 16.
Describe about the psychotropic drugs.
Answer:
These drugs effect on thinking power, mental processes, continuous use of these drugs, bring change in human behaviour, consciousness and perception. So, they are called mood altering drugs. The person becomes addict by the use of these drugs and cannot live without these drugs.

Question 17.
What are sedative? What are its types? Write its effect.
Answer:
Sedative:
Drugs which directly depress the brain and central nervous system are included in this group. They make the body free from anxiety and lethargic. The excessive use leads to sleep. Sleep causing drugs are also called Hypnotics.

It is of two types:

1. Barbiturates and
2. Benzodiazepines.

1. Barbiturates : It is a sedative and tranquilizer. It supresses brain’s activity and creates a feeling of relaxation, drowsiness and sleepiness.

2. Benzodiazepines : These drugs are commonly prescribed to help relieve anxiety in people who have anxiety disorder or another mental illness where anxiety is a symptom. They are very addictive.

Question 18.
What is interferon?
Answer:
Interferon:
Interferon is an antiviral protein which is produced within animal cells due to stimulus produced after viral infection and which prevents the infection and multiplication of other viruses.

Question 19.
How is a cancerous cell different from a normal cell?
Answer:
Cancer cell is different from normal cells in the sense that it:

1. Looses the property of contact inhibition.
2. Continues to grow and divide.
3. Produces masses of cells called tumours.

Question 20.
In which way has the study of biology helped us to control infectious diseases?
Answer:
Study of biology helps us to diagnose the pathogen in following ways:

1. The life – cycle of many pathogens studied.
2. Alternate and reservoir hosts are known.
3. The mechanisms of transmission of disease is known.
4. The protective measures are suggested against disease and pathogens based an above studies.
5. Suitable medicines against infectious disease are suggested.
6. The preparation of vaccines against many pathogens also entitle the use and study ofbiology.

Question 21.
How does the transmission of each of the following diseases take place:

1. Amoebiasis
2. Malaria
3. Ascariasis
4. Pneumonia.

Answer:

1. Amoebiasis : Through faecal-oral route.
2. Malaria : Through the bite of female Anopheles mosquito.
3. Ascariasis : Through taking contaminated food and water.
4. Pneumonia : Droplets from the sputum of the patient.

Question 22.
What measure would you take to prevent water – borne diseases?
Answer:
To prevent water borne diseases, following measures are required:

1. Drinking water should he clean, free from contamination. This could be achieved by filtration, boiling or sedimentation and chemical treatment of water.
2. Water resources/ reservoirs should be periodically de – contaminated / disinfected.
3. Water should not be allowed to stand for long to become breeding pools.
4. Standards practices of hygiene should be strictly maintained in public catering.

Question 23.
Discuss with your teacher what does ‘a suitable gene’ mean, in the context of DNA vaccines.
Answer:
The term ‘suitable gene’ refers to that specific segment of DNA which forms immunogenic protein, such genes can be cloned and then integrated with vector for introducing into an individual to be immunised for certain disorder producing a particular vaccine against the pathogens.

Question 24.
Name the primary and secondary lymphoid orgAnswer:
Answer:
Primary lymphoid organs are bone marrow and thymus. Secondarylymphoid organs are spleen, lymph nodes, tonsils, peyer’s patches of small intestine and appendix

Question 25.
The following are some well known abbreviations, which have been used in this chapter. Expand each one to its full form:

1. MALT
2. CMI
3. AIDS
4. NACO
5. HIV.

Answer:

1. MALT : Mucosa Associated Lymphoid Tissue.
2. CMI : Cell Mediated Immunity.
3. AIDS : Acquired Immune Deficiency Syndrome.
4. NACO : National AIDS Control Organisation.
5. HIV : Human Immunodeficiency Virus.

Question 26.
How are allergies related to the body’s immune system?
Answer:
Allergy is the condition of hypersensitivity of the body against certain substances or to a physical or chemical agent allergens. When antigen antibody reaction takes place in the body, it results allergy. Sufficient antibodies will not be produced in lacking of proper immune system. The allergens combine with the antibody bound mast cells, which causes the cell to burst releasing histamine. It results inflammatory responses in the body. Allergy may be caused by a medicine, cosmetics and other substances like pollen grains, dust particles, etc.

Question 27.
Differentiate the following and give examples of each:

1. Innate and Acquired immunity.
2. Active and Passive immunity.

Answer:
1. Differences between innate and acquired immunity:

Innate immunity:

• It is present from birth and is inherited from parents.
• It is non – specific.
• The various physical, physiological cellular and cytokine barriers are the basis of innate immunity.
• The innate immunity remains throughout life.

Acquired immunity:

• It is not present from the birth.
• It is pathogen specific.
• The memory cells formed by B and
• T – cells are the basis of acquired immunity.
• The aquired immunity can be short – lived or life long.

2. Differences between active and passive immunity:

Active immunity:

• It is developed due to contact with pathogen or its antigen that leads to production of antibodies in the host body.
• It has no or only few side effects.
• It is slow but long lasting.
• It takes time to develop its response.

Passive immunity:

• It is developed when readymade antibodies are injected into the body.
• It may cause a reaction.
• It is fast but lasts only for few days.
• It is used when the immune response has to be faster.

Question 28.
Draw a well – labelled diagram of an antibody molecule.
Answer:

Human Health and Disease Long Answer Type Questions

Question 1.
What is cancer? Write the names of two types of cancer and causes of cancer.
Answer:
Cancer:
When tumours are formed due to unorganized and uncontrolled division of cell, then it is called cancer.

Types of Cancer:
Cancer is not a single disease but a complex of many diseases. Today about 200 distinct types of cancer have been recognized. These are grouped into main types:

1. Carcinomas
2. Sarcomas
3. Lymphomas and
4. Leukemias.

1. Carcinomas:
The tumours which are made up of epithelial cells of ectodermal or endodermal origin are called carcinomas, example solid tumours in nerve tissues and in tissues of body surfaces or their attached glands. It includes breast, skin, cervical and brain carcinomas.

2. Sarcomas:
The tumours which are made up of connective tissue cells of mesodermal origin are called sarcomas, example solid tumours growing from connective tissues, bones, cartilages and muscles. It constitutes only about 2% of human cancers.

3. Lymphomas:
Cancers in which there is excessive production of lymphocytes by the lymph nodes and spleen are called lymphomas, example Hodgkin’s disease. It constitutes about 5% of human cancers.

4. Leukemias:
It is cancer of blood characterized by excessive number of W.B.Cs. (or leucocytes) in the blood (neoplastic growth). These cells invade into bone – marrow, lymph nodes and the spleen. It is more frequent in the children of age group 5 to 7 years but it can occur at any age. Acute leukemia causes death. It has no sure remedy. It constitute about 4% of human cancers.

Causes of Cancer:
Physical and Chemical factors which cause cancer are called as carcinogens. Main causes of cancer are as follows:

1. Smoking causes mouth and lung cancer.
2. Radiations, such as X – rays, ultraviolet rays and other ionizing radiations cause cancer.
3. Viruses may cause cancer.
4. Chemical substances such as Nicotine, caffeine, products of combustion of coal and oil, polycyclic hydrocarbons may cause cancer.

Symptoms of Cancer:
There are some symptoms of cancer which must be kept in mind:

1. Any lump or thickening in the tissue especially in breast, tongue or lip.
2. A wound that is not healing.
3. Any sudden change in mole or warts.
4. Persistent indigestion and difficulty in swallowing things.
5. Regular cough and hoarseness in sound.
6. Unusual weight loss.
7. A change in bowel habits.
8. Any ulcer that does not get well.
9. Bleeding in vagina at times other than the menstruation.
10. Non – injury bleeding from the surface of the skin, mouth or any other opening of the body.

Question 2.
What is AIDS? Write down its causes, transmission and symptoms.
Or
Write the name, two symptoms and important preventive measures of today’s dreadening disease spread through blood transfusion.
Or
Where is AIDS reported for the first time ? Describe the causes, method of transmission and control measures of this disease.
Answer:
AIDS (Acquired Immune Deficiency Syndrome) disease is discovered for the first time in America in the year 1981.

Causes of Disease:
This disease is caused by the infection of a vims known as HIV (Human Immunodeficiency Vims).

Transmission:
It is transmitted through sexual contact, homosexuality, contaminated needles, blood transfusion, dmgs, artificial insemination and organ transplantation etc.

Symptoms of Disease:
It is characterized by showing swollen lymph nodes, fever, loss of weight. The person loses the immunity against the infection. In this disease, the number of helper T-cells are reduced.

Treatment:
No suitable drug is available so far against this disease. Only anti – viral cells may increase in the number by immune stimulation method.

Control:
The following measures are advised to prevent spreading of disease:

1. Providing health education and explain the hazardous effects of AIDS.
2. Do not reutilize the used syringe. Throw it away or destroy it.
3. The blood of donor person and organs of transplantation like kidney, liver, cornea of eyes, growth hormones would be carefully examined before use.
4. Sexual contact with many people must be avoided.

Question 3.
What is the mechanism by which the AIDS virus causes deficiency in the immune system of the infected person ?
Answer:
The virus enters macrophages after getting into the body of individual where RNA forms viral DNA by reverse transcription. The viral DNA gets incorporated in the host cell’s DNA and directs the infected cells to produce viral copies. The newly produced virus particles attack helper T – cells and thus, the number of T-cells decrease. Since, the helper T-cel Is are essential for functioning of immune system, the person suffers from various diseases due to dificient immune system.

Question 4.
List the harmful effects caused by alcohol/drug abuse.
Answer:
The adverse effects of drugs and alcohol abuse are:

1. Low to moderate doses can cause reckless behaviour, vandalism and violence depression, fatigue, weight fluctuations, etc.
2. Excessive doses of drugs may lead to coma and death due to respiratory failure, heart failure or cerebral haemorrhage.
3. A combination of different drugs or alcohol mixed with drugs, results in overdosing and even death.

Question 5.
Do you think that friends can influence one to take alcohol/drugs? If yes, how may one protect himself/herself from such an influence?
Answer:
Yes, friends can influence one to take drugs and alcohol. A person can take the following steps for the prevention of themself against drug abuse:

1. By avoiding under peer pressure as everyone has their own field of interest which should be respected by there teachers and family. One should not experiment with alcohol for curiosity and fun.
2. Avoid the company of friends who take drugs.
3. Seek help from parents and peers. A child should not pushed beyond his/her threshold limits.
4. Take proper knowledge and counselling about drug abuse. Devolve your energy in other extra-curricular activities.
5. Seek immediate professional and medical help from psychologists and psychiatrists if symptoms of depression and frustration become apparent.
6. Get rid of the problem completely and lead, perfectly normal life by increasing their will power.

Question 6.
Why is that once a person starts taking alcohol or drugs, it is difficult to get rid of this habit? Discuss it with y.our teacher.
Answer:
It is difficult to get rid of this habit, because these substances are addictive and one starts having unpleasant feelings or withdrawal symptoms like nausea, vomiting, diarrhoea, shivering, muscle twitching, excessive perspiration, muscular and abdominal cramps. Mind loses control and all one can think of is taking the addictive substance. That is why resisting the temptation/pressure for the first time is the only way to avoid getting into the addictive habit and committing a slow suicide.

Question 7.
In your view what motivates youngsters to take to alcohol or drugs and how can this be avoided ? .
Answer:
Probably the ‘motivation’ comes from:

1. Curiosity to experience the effect.
2. Foolishness to try to prove oneself in front of the peers.
3. Wrongly taking it as an excuse to escape from reality.
4. Wrong thinking that one time ‘try’ is not going to do any harm.

But youngsters who are strong willed, who understand its ill effects and who are satisfied with their academic and other achievements and who don’t want to waste their precious life, don’t fall for this kind of ‘Motivation’.

Question 8.
What is immune system? Describe various components of immune system of man and its role.
Answer:
The Immune System or Immunity (A Specific Defence Mechanism):
The ability of an organism to resist the pathogen Or development of disease resistance is known as immunity and the study of immunity is called immunology, while the infected person with no disease is called immune. The most peculiar characteristic of immune system is that it can differentiate the self (body’s own cells) and non-self (foreign microbes).

Cells of the Immune System:
Lymphocytes are the type of W.B.Cs. or Leucocytes which are chief cells of immune system of body. There are two types of lymphocytes that promote cellular immunity and humoral immunity. Both of these types of lymphocytes are derived from lymphocyte stem cells in the bone – marrow in the embryo.

1. T – cells of lymphocytes:
These cells eventually migrate to the lymphoid tissue. Before doing so, the lymphocytes first migrate to thymus gland and are processed in the gland, hence called T – lymphocytes or T – cells. These are responsible for cellular immunity. There are following types of T – cells :

(i) Killer T – cells:
Killer T – cells or KT – cells directly attack and destroy antigen. In doing so, they move to the site of invasion and produce some chemical that attracts and stimulate phagocytes to feed more voraciously on antigen.

(ii) Helper T – cells:
Helper T – cells or HT – cells stimulate B – cells to produce more antibody.

(iii) Suppressor T – cells:
Suppressor T – cells or ST – cells keep entire immune system to attack on the own body cell.

Mode of action of T – cells to antigens:
T – cells are antigen specific (each T – cell recognizes a specific antigen and different types of T – cells are stimulated by different types of antigens). When a T – cell is stimulated by specific antigen, T – lymphocytes divide rapidly to form a clone of T – cells called lymphoblasts. T – cells live for 4 – 5 years or even longer. T – cells of a clone are morphologically similar but they perform different functions. According to their functions, their are three classes of T – cells, i.e., killer T – cells, helper T – cells and suppressor T – cells.

2. B – cells of lymphocytes:
The other population of lymphocytes which produces antibodies are processed in some unknown area, possibly liver or spleen. This population was firstly discovered in birds in which processing occurs in the bursa of fabricus, a structure not found in mammals. For this reason they are called as B – cells or B – lymphocytes. They are responsible for humoral immunity.

Mode of action B – cells to antigens:
Once a B – cells is activated by the antigen, it multiplies very fast and forms a clone of plasma cells. Most of these produce antibody at a tremendous rate of 2,000 molecules per second. These antibodies circulate in the lymph to fight the antigen. So, forming humoral immune system. B – cells are short lived and are replaced by new cells from the bone – marrow after every few days.

The capacity of B – cells to produce specific antibodies is acquired during its development and maturation.

Question 9.
Describe the harmful effects of tobacco smoking.
Answer:
Effect of chewing and smoking tobacco:
The chewing and smoking of tobacco affects us in the following ways:

1. It affects the route of the transfer of nerve impulse and central nervous system. In low concentration nicotine stimulates conduction of nerve impulse but long – term use reduces the activity of nervous system.

2. Nicotine stimulates the release of adrenaline leading to high blood pressure. Increased blood pressure due to smoking enhances the risk of heart diseases.

3. It retards foetal growth in pregnant women.

4. The smoke of tobacco contains aromatic hydrocarbons and tar along with carbon monoxide (CO). Carbon monoxide reduces oxygen carrying capacity of the blood. Hydrocarbons induces cancer. Due to these reasons tobacco chewing person suffer from mouth cancer and smokers suffer from throat and lung cancers.

5. The use of tobacco in any form stimulates the secretion of saliva and gastric juices due to which acidity is increased in stomach. It may cause ulcers in the wall of stomach. The absorption capacity of mucous membrane of stomach also decreases. Thus, person get suffered from hyponutrition, loss of appetite and constipation.

6. Smoking also affects the activity of kidneys.

7. Nicotin relaxes the muscular and skeletal tissues due to which person becomes weak.

8. Long – term smoking may also cause diseases like bronchitis and emphysema.

9. Smoking reduces immunity of the body.

10. Lips of smokers may become dark coloured. Teeth and fingers get stained. The breath becomes foul.

MP Board Class 12th Biology Important Questions

 

MP Board Class 12th Chemistry Important Questions Chapter 16 Chemistry in Everyday Life

Chemistry in Everyday Life Important Questions

Chemistry in Everyday Life Short Answer Type Questions

Question 1.
Why should not medicines be taken without consulting doctors? (NCERT)
Answer:
The drugs or medicines have side effects also. These side effects arise because the drug may bind to more than one type of receptor. Further their wrong choice and over – dose can cause havoc and even may cause death. Therefore, it is must that the medicines should not be given without consulting doctors.

Question 2.
Explain the term, target molecules or drug targets as used in medicinal chemistry. (NCERT)
Answer:
Drugs taken by a patient interact with macromolecules such as proteins, carbo-hydrates, lipids and nucleic acids and these are called drug targets. These macromolecules or drug targets are known to perform several role in the body. The drugs are designed to interact with specific targets so that these have least chances of effecting the other targets. This minimises the side effects and localises the action of the drug.

Question 3.
While antacids and antiallergic drugs interfere with the function of histamines, why do these not interfere with the function of each other? (NCERT)
Answer:
They do not interfere with the functioning of each other because they work on different receptors in the body. Secretion of histamine causes allergy and acidity while ant-acid removes only acidity.

Question 4.
Low level of noradrenaline is the cause of depression. What type of drugs are needed to cure this problem? Name two drugs. (NCERT)
Answer:
Noradrenaline induces a feeling of well being and helps in changing the mood. If the level of noradrenaline is low, then the signal sending activity of the hormone becomes low and the person suffers from depression. In such cases, the patient needs anti – depressant drugs which inhibit the enzymes which catalyses the degradation of noradrenaline. The common drugs used as anti – depressant are iproniazid and phenelzine.

Question 5.
Sleeping pills are recommended by doctors to the patients suffering from sleeplessness but it is not advisable to take its doses without consultation with the doctor. Why? (NCERT)
Answer:
Sleeping pills contain drugs that may be tranquilizers or anti – depressant. They affect the nervous system, relieve anxiety, stress, irritability or excitement. But they should strictly be used under the supervision of a doctor. If not, the uncontrolled and overdose can cause harm to the body and mind because in higher doses, these drugs act as poisons.

Question 6.
With reference to which classification has the statement, “ranitidine is an antacid” been, given? (NCERT)
Answer:
This statement refers to the classification of drugs according to pharmacological effects of the drugs because any drug which is used to neutralise the excess acid present in the stomach will be called an antacid and ranitidine prevents the interaction of histamine with the receptors present in the stomach wall. Histamine stimulates the secretion of pepsin and HCl in the stomach.

Question 7.
What are germicides?
Answer:
Germicides are substances which possess the power Aspirin to destroy germs. Sulphur compounds, mercury compounds (mercuric iodide) and phenolic compounds are used as germicides. Sulphur compounds in soap protect the skin from pimples, dandruff and skin infection. Phenolic compounds are mostly used as germicides. Cresyclic acid which is a mixture of m – cresol and p – cresol is mixed in soap as a germicide.

Question 8.
How are synthetic detergents better than soaps? (NCERT)
Answer:

1. Soaps cannot be used in hard water but detergents can be used.
2. Soaps cannot be used in acidic water but detergents can be used.

Question 9.
Explain the following terms with suitable examples: (NCERT)

1. Cationic detergents
2. Anionic detergents and
3. Non – ionic detergents.

Answer:
1. Cationic detergents are those which have cationic hydrophilic group. These are mostly acetates, chlorides or bromides of quaternary ammonium salts. For example, cetyltrimethyl ammonium chloride.
[CH₃(CH₂)₁₅N(CH₃)₃]⁺+Cl^–

2. Anionic detergents are those which have anionic hydrophilic group. These are of two types:

• Sodium alkyl sulphate example sodium lauiyl sulphate CH₃(CH₂)₁₀CH₃OSO₃^– Na⁺
• Sodium alkyl benzene sulphonate example sodium 4 – (1 – dodecyl) benzene sulphonate (SDS)
  

3. Non – ionic or neutral detergents are esters of high molecular mass alcohols as in fatty acids. For example, polyethylene glycol stearate
CH₃(CH₂)₁₆COO(CH₂CH₂O)_nCH₂CH₂OH
Polyethylene glycol stearate.

Question 10.
What are bio – degradable and non – biodegradable detergents? Give one example of each. (NCERT)
Answer:
1. Bio – degradable detergents are degraded by bacteria. In them, hydrocarbon chain is unbranched. They do not cause water pollution and are bitter.
Example : Sodium lauryl sulphate.

2. Non – biodegradable detergents possess highly branched hydrocarbon chain so bacteria cannot degrade them easily. They cause water pollution.
Example : Sodium 4 – (1, 3, 5, 7 – tetramethyl – actyl) benzene sulphonate.

Question 11.
Why do soaps not work in hard water? (NCERT)
Answer:
Hard water contains calcium and magnesium salts. Therefore, in hard water, soaps get precipitated as insoluble calcium and magnesium soaps which being insoluble stick to the cloth as gummy mass and blocks the ability of soap to move oil or grease from the cloth.

Question 12.
Explain each with an example.

1. Antibiotics
2. Analgesic (Pain Killer).

Answer:
1. Antibiotics:
Chemical substance which are produced by micro – organism and used to destroy micro – organism are called antibiotics.

These are of two types :

• Broad spectrum Antibiotic : Example : Tetracycline, chloramphenicol, Penicillin
• Narrow Spectrum Antibiotic : Example : Niastatin, Penicillin antibiotic medicines are used for the treatment of typhoid, whooping cough, Pneumonia.

2. Analgesic:
Drugs which give relief from pain or reduced pain are called analgesics.
Types and Examples :

• Narcotics : Morphine, Codeine.
• Non – Narcotics : Aspirin, Analgin, Paracetamol.

Question 13.
What is preservative? Give the name and formula of any two preservatives.
Answer:
A preservative is defined as “A substance added to food, capable of retarding the growth of micro – organism which deteriorate the food within no time.
The preservative may be natural compounds such as sugars, salt, acids, etc. as well as they may be synthetic i.e. Sodium benzoate.
Example:

1. Vinegar or acetic acid : CH₃ – COOH
2. Sodium benzoate : C₆H₅COONa.

Question 14.
What are the main differences between soap and detergents?
Answer:
Differences between Soap and Detergents :
Soap:

• Soaps are sodium salts of higher fatty acids.
• These cannot be used with hard water.
• Their aqueous solution is alkaline in nature.
• These contain oil and are not good cleansing agent.
• These cannot be used for soft and delicate cloth.

Detergents:

• Detergents are sodium salt of alkyl benzene sulphonate.
• These can be used with hard water.
• Their aqueous solution is neutral in nature.
• These do not contain oil and are better cleansing agent.
• These can be used for soft and delicate cloth.

Question 15.
What do you understand by antipyretics?
Answer:
These are used to lower down the body temperature in high fever. These drugs are used both as antipyretic and as analgesic, example aspirin (acetylsalicylic acid), paracetamol (4 – acetamido phenol), phenacetin (4 – ethoxy acetanilide), analgin, etc.

Question 16.
What are Antibiotics? Write name of any two antibiotics. (MP 2018)
Answer:
Antibiotics:
are chemical substances which are produced by micro – organisms like bacteria, fungi, actinomycetes and destroy some other micro – organisms are like, virus, ricketsia or obstruct their growth.
Example : Penicillin, Streptomycin etc.

Question 17.
What is Immune system? How does it develop?
Answer:
For the destruction of bacteria or antigen in our body, lymphocytes are developed which are known as Immune. These are a specific type of white blood cells. These prepare and release a special type of protein called globulin to destroy the poison. These proteins destroy the attacking virus, bacteria and poisonous substances. Lymphocyte bind the antigen and themselves divide fast by which immunization increase and effect of antigen is destroyed.

Question 18.
What are antiseptics?
Answer:
Antiseptics:
An antiseptic kills the bacteria or prevents the multiplication of bacteria. These also prevent pus formation. Antiseptics do not harm living tissues. Tincture iodine, phenol (0 – 2%), dettol, chloroxylenol, etc. are applied on skin and bactrim, septran, etc. are taken orally as pills. Bad odour coming out of the wounds due to bacterial decomposition on the body or in the mouth are also reduced by the use of antiseptics. For such purposes, antiseptics are usually incorporated in face powder, breath purifiers, deodorants, etc. to reduce the intensity of bad odour.

Neem soaps containing the extract of neem seeds are also used as antiseptic soaps. Dettol is a mixture of chloroxylenol and terpineol in a suitable solvent is commonly used antiseptic. Bithionol antiseptic is added to soap to provide antiseptic properties to it. Tincture iodine is 2 – 3% solution of iodine in alcohol and water.

Question 19.
What do you mean by Antibiotics? Name the first antibiotic.
Answer:
Chemical substances which are produced by mirco – organism and are used to destroy other micro-organism, are called antibiotics. These chemicals checks the life cycle of bacteria and stop reproduction resulting in release from disease. Antibiotics are almost specific for kinds of illness.

The first antibiotic penicillin was discovered by Alexander Fleming in 1928. He was awarded Nobel prize in 1945 for this important discovery. General formula of penicillin is C₉H₁₁N₂O₄S – R. It is a narrow spectrum drug and used in bronchitis, pneumonia, sore throat and abcesses. Before administration, tolerance has to be tested.

By changing the group R, different penicillin are prepared.

Question 20.
What are artificial sweetening agents? Give two examples. (MP2018)
Answer:
Artificial sweetening agents are the substances produced wholly or partially by chemical synthesis, which are added to food to impart sweet taste.
Example:

1. Sucrose
2. Saccharin.

Question 21.
Give definition of antihistamine drug with name and uses.
Answer:
These are amines which controls the allergy effect produced by histamines. Histamine is found in all body tissue and is also released in allergic conditions due to which allergic responses such as tissue inflammation, asthma, itching etc. are introduced in the body. Drugs which prevent the production of histamine and fight against the allergy effects are called antihistamines.
Example:
1. Entergon : It is used in strong allergic conditions.

2. Benadryl:

Chemistry in Everyday Life Long Answer Type Questions

Question 1.
Write short notes on:

1. Antifertility drugs (MP 2108),
2. Detergents
3. Antacids (MP 2018)
4. Sedatives
5. Sulpha drugs.

Answer:
1. Antifertility drugs:
Drugs which are used to check pregnancy in women are called antifertility drugs. Actually, these drugs control the female menstrual cycle and ovu-lation. The antifertility agent in these drugs are steroids and these drugs are used in the form of oral pills. A mixture of synthetic estrogen and progesterone derivative are used as birth control pill. These are more effective than the natural hormone. Ethynylestradiol and nore- thindrone are the content of common contraceptive pills.

2. Detergents:
Unsaturated hydrocarbon of ethylene type containing 10 to 18 carbon atoms on treatment with sulphuric acid forms organic acid. Sodium salt of organic acid have moisture absorbing and purification property. This compound is called synthetic detergent. Example : Sodium n – dodecyl benzene sulphonate, Sodium n – dodecyl sulphate.

Synthetic detergents have two parts :

• A long chain of hydrocarbon which is hydrophobic (Water repellent).
• Small ionic chain is hydrophilic (Water attracting). Ionic chain is generally of sul- phonate (SO₃Na) or sodium sulphate (SO₄Na).

Detergents are surface active compounds which decreases surface tension of water. When these compounds are dissolved in water they scatter dirt particles leaving the surface clean.

Properties of detergents : Detergents are superior to soap.

• Detergents can be used in hard as well as soft water because they do not form insoluble salt with calcium and magnesium ions of hard water while soap cannot be used in hard water.
• Aqueous solution of detergent is neutral. Therefore, detergents can clean soft fibres without damaging them. Soap solution is alkaline due to hydrolysis and is harmful for washing soft fibres.

Uses of detergents:
Detergensts act as cleansing agent. Like soap it can be used for cleaning cotton, woollen, silky and synthetic fibre cloth and for cleaning other domestic items.

3. Antacids:
Substance which remove the excess acid in the stomach and raise the pH to appropriate level are called antacid Calcium carbonate, Sodium bicarbonate, Magnesium hydroxide or Aluminium hydroxide is used in the form of aqueous suspension or tablets to treats hyperacidity. These substances react with excess hydrochloride acid and neutralizes it partially. Nowadays Omeparazole and Lansoparazole are prescribed as antacids.

4. Sedatives:
These are given to those patients who are violent and mentally agitated.
Example:

1. Equanil
2. Barbituric acid.

5. Sulpha drugs:
Like antibiotics, sulpha drugs are used to kill micro – organism. These are prepared in laboratory. Sulphadiazine, sulphanilamide, sulphathiazole, sulpha guanidine, etc. are important sulpha drugs.

Question 2.
Write notes on the following:

1. Tranquillizers and Hypnotics (MP2018)
2. Antidepressant

Answer:
1. Tranquillizers:
Tranquillizers are the chemical substances which affect higher centres of central nervous systems and reduce anxiety and tension. Tranquillizers are also called psychotherapeutic drugs. These drugs make the patient passive temporarily so that emotional distress or depression is reduced. The patient restores confidence. These drugs if taken for long – time make the person habitual. Luminal, Barbituric acid, seconal, equanil, etc. are the drugs of this class. These are components of sleeping pills.

2. Antidepression:
These are given to patient for boosting their morals in the stage of acute depressions. Some mood elevator drugs are vitellin, methadone, cocaine, etc. These act on the central nervous system. Person becomes healthy by its use and de-velop confidence. These should be taken by the advice of doctor. Tophrenil is one such medicine. The amphetemin group of medicine help to upraise the mental level. Its common example is benzedine.

Question 3.
Write example of the following chemicals :

1. Two Analgesics
2. Two Antiseptic
3. Two Antiseptic chemical
4. Two Antibiotic
5. Two Anaesthetic
6. Two Sulpha drug
7. Two Rocket propellant
8. Two uses of chloramphenicol antibiotic.

Answer:

1. Two Analgesic : (i) Morphine, (ii) Aspirin.
2. Two Antiseptic : (i) Dettol, (ii) Bithional.
3. Two Antiseptic Chemical: (i) Boric acid, (ii) Gention violet.
4. Two Antibiotic : (i) Terramycin, (ii) Streptomycin.
5. Two Anaesthetic : (i) Cyclopropane, (ii) Pelledyne.
6. Two sulpha drug : (i) Sulphonide, (ii) Sulphadyne.
7. Two Rocket Propellant: (i) Polyurethane, (ii) Ammonium perchlorate.
8. Two use of Chloramphenicol Antibiotic : (i) In Typhoid, (ii) High fever and diarrhoea.

Question 4.
Write two differences between Dyes and Pigments.
Answer:
Differences between Dyes and Pigments :
Dyes:

• These are organic substance.
• They colour fibres and food materials also.

Pigments:

• These are inorganic substance.
• Mixed with safeda (white lead) it is used to colour metals and wood.

Question 5.
Give one example of Acidic dye and Basic dye.
Answer:
Acidic dye:
In these, acidic group like phenolic, sulphonic (S03H) are in the form of sodium salts. These colour animal fibre like wool, silk etc. Example : Orange – I and II.

• Acidic dye : Methyl orange , Methyl red.
• Basic dye : Malachite green, Aniline yellow.

Question 6.
What is meant by the term ‘broad spectrum antibiotics’? Explain. (NCERT)
Answer:
The range of bacterias or other micro – organisms that are affected by a certain antibiotic is expressed as its spectrum of action. The term broad spectrum antibiotics means an antibiotic which kills or inhibits a wide range of Gram negative and Gram -positive bacteria.

MP Board Class 12th Chemistry Important Questions

MP Board Class 12th Economics Important Questions Unit 6 National Income and Related Aggregates

Micro Economics National Income and Related Aggregates Important Questions

Micro Economics National Income and Related Aggregates Objective Type Questions

Question 1.
Choose the correct answers:

Question 1.
Macro-economics is the study of:
(a) Principle or Theories of national income
(b) Consumer’s theory
(c) Production theory
(d) None of these.
Answer:
(a) Principle or Theories of national income

Question 2.
Out of the following which is not a flow:
(a) Capital
(b) Income
(c) Investment
(d) Depreciation.
Answer:
(a) Capital

Question 3.
From the following which method is used for measuring national income:
(a) Production method
(b) Income method
(c) Expenditure method
(d) All of the above.
Answer:
(d) All of the above.

Question 4.
Which of the following is included in the primary sector:
(a) Land
(b) Forest
(c) Mines
(d) All of the above.
Answer:
(d) All of the above

Question 5.
Total national income divided by total population is known as:
(a) Private income
(b) Personal income
(c) Personal spendable income
(d) Per capital income.
Answer:
(d) Per capital income

Question 6.
Production enterprises are divided in:
(a) Two sectors
(b) Three sectors
(c) Four sectors
(d) Five sectors.
Answer:
(b) Three sectors

Question 2.
Fill in the blanks:

1. Agriculture is included in sector.
2. Pigou has divided welfare into parts.
3. Chinese product is included in area of the economy.
4. National income in India is calculated by
5. The total value of all final goods and services produced with in the domestic territory of a country during an accounting year is known as
6. is an index of economic development of the country.

Answer:

1. Primary
2. Two
3. Secondary
4. Central statistical organisation
5. GDP
6. National income.

Question 3.
State true or false:

1. As compared to developed countries, India’s per capital income is quite less.
2. Black money has given birth to parallel economy in the country.
3. Major contribution in India’s national income is from the secondary sector.
4. Electricity, LPG and water supply are included in the primary sector.
5. Income from gifts are included in the national income.
6. Sale of second hand goods are not included in the national income.

Answer:

1. True
2. True
3. False
4. False
5. False
6. True.

Question 4.
Match the following:

Answer:

1. (e)
2. (a)
3. (d)
4. (c)
5. (b).

Question 5.
Answer the following in one word/sentence:

1. Which sector contributes maximum in N.I.?
2. Difference between final stock and initial stock is known as.
3. National income is studied under which economics?
4. Increase in national income indicates.
5. How many times national income is calculated in a year?
6. Money value of which goods and services are added in the GNP in a year.

Answer:

1. Tertiary
2. Change in stock
3. Macro-economics
4. Economic progress
5. One time
6. Final.

National Income and Related Aggregates Very Short Answer Type Questions

Question 1.
What is Micro-economics?
Answer:
Micro-economics studies economic actions of individuals e.g., a person, particular firm, individual household, a producer, a unit etc.

Question 2.
What is Macro-economics?
Answer:
Macro-economics is that part of economic theory which deals with the aggregate units of the economy, e.g.,all firms, all industries etc.

Question 3.
What is an Economic unit?
Answer:
Economic unit or Economic agent means those individuals or institutions which take economic decisions. They can be consumer who decide what and how much to consume. They may be producer of goods and services who decide what and how much to produce. They may be entities like the government corporation banks which also take different economic decisions like how much to spend, what interest rate to charge on the credits, how much to tax.

Question 4.
What are consumption goods?
Answer:
Objects that satisfy human needs directly and which are not used for production of other commodities are called consumption goods, e.g., milk, vegetables, wheat, rice etc.

Question 5.
What are capital goods?
Answer:
Capital goods are those goods that are used in producing other goods, rather than being bought by consumers. These goods, are used in production for a long period of time, e.g., machinery, plot, etc.

Question 6.
What are final goods?
Answer:
Final goods are those goods which are out of production line and are ready for use by the user. These goods cannot be resold and are included in estimating national income. There goods cannot be used as raw materials for production of other goods.

Question 7.
What are intermediate goods?
Answer:
Intermediate goods are those goods which are within the production line and are not ready for use by the user. These goods can be used as raw material for production of other goods, and are not included in the estimation of national income.

Question 8.
Explain the concept of Flow and Stock.
Answer:
Stock is related to a point of time. That is, the stock is a quantity measured at a certain point of time which may have accumulated in the past. Flow is an amount to be measured in a specific period of time. Flow is a price fluctuation because they are measured per unit time period, e.g., Interest on capital, Sale of rice, etc.

Question 9.
What do you understand by Gross Investment?
Answer:
Gross Investment refers to the amount invested in the purchase or construction of new capital goods. Capital stock consists of fixed assets and unsold stock. So, gross investment is the expenditure on purchase of fixed assets and unsold stock during the accounting year.

Question 10.
What is Depreciation?
Answer:
Depreciation is the permanent and continuing decrease in the quality, quantity or value of assets. Depreciation may be defined as reduction of recorded cost of a fixed asset in a systematic manner, e.g., building, office equipment, machinery, etc. In order to calculate national income depreciation is deducted from gross national product.

Question 11.
What do you mean by circular flow of income?
Answer:
Circular flow of income refers to the cycle of generation of income in the production process, its distribution among the factors of production and finally, its circulation from households to the production units in the form of consumption expenditure on goods and services produced by these units.

Question 12.
What are the principles on which circular flow of income depend?
Answer:
The circular flow of income involves two basic principles:

1. In any exchange process, the seller receives the same amount which the buyer spends.
2. Goods and services flow in one direction and the money payment to acquire them, flow in the return direction giving rise to a circular flow. Thus, product flows from the seller to the buyer is necessarily a complement of money (income) flow from the buyer to the seller.

Question 13.
What is National income?
Answer:
The national income means the total value of goods and services produced in a year in a country from all the economic activities, in terms of money. According to Prof. Marshall, “ National income is the labor and capital of a country acting on its natural resources, producing annually, a certain net aggregate of commodities, material and immaterial, including services of all kinds.” According to Prof. Pigou, “ National income is that part of the objective income of the community, including of course, income derived from abroad, which can be measured in money.”

Question 14.
What are the different methods of measuring national income?
Answer:
Different methods of measuring national income are:

1. Production method
2. Income method,
3. Expenditure method
4. Combined method,
5. Social accounting method.

National Income and Related Aggregates Short Answer Type Questions

Question 1.
Write difference between National Income and Per Capital Income.
Or
What is national Income and Per Capital Income? Write difference between them.
Answer:
National income refers to total value of goods and services produced by the people of a country in a given year. Per capital income is the average income of the normal resident of a country in a particular year.

Differences between National Income and Per Capital Income:
National Income:

1. National income means the total value of goods and services provided in a year from all the economic activities.
2. National income includes per capital income in it.
3. Active participation of various factors of production is required. .
4. National income is related to macro-economics.
5. It is an absolute concept.

Per Capital Income:

1. The income from various sources of a person is known as per capital income.
2. Per capital income is a part of national ‘income.
3. Active cooperation of the various sources of income is required.
4. Per capital income is related to micro-economics.
5. Per capital income is a relative concept.

Question 2.
Describe the four major sectors in an economy according to the macro-economics point of view.
Answer:
There are four major sectors:

1. Household : By a household we mean a single individual who takes decisions relating to her own consumption or a group of individuals for whom decision relating to consumption are jointly determined.
2. Firms : In macro – economics production units which is organized under capitalist principles are called firms.
3. Government : The role of government includes framing laws, enforcing them and delivering justice.
4. External sector : External sector means the other countries of the world which are engaged with our trade. It consists of import and export.

Question 3.
What is the difference between Micro-Economics and Macro – Economics?
Answer:

Question 4.
What do you mean by Stock and Flow? Write three differences between Stock and Flow.
Answer:
Stock means that quantity of an economic variable which is measured at a particular point of time whereas, flow is that quantity of an economic variable which is measured during a period of time.
Differences between Stock and Flow:
Stock:

1. Stock is measured at a particular point of time.
2. Stock has no dimension.
3. Stock is a static concept.

Flow:

1. Flow is measured during a period of time.
2. Flow has time dimension like how, day,month, year.
3. Flow is a dynamic concept.

Question 5.
Distinguish between National Income and National Wealth.
Answer:
Differences between National Income and National Wealth:
National Income:

1. It refers to the money value of the aggregate of goods and services produced during a particular period of time.
2. National income is measured over a period of time.
3. It is a flow variable.
4. National income is a flow because it is occurring continuously.
5. Increase and decrease of national income affect the standard of life of people.

National Wealth:

1. National wealth is the aggregate of wealth possessed by all the individuals in the country as well as collective or social wealth of the society.
2. National wealth is measured at a point of time.
3. It is a stock variable.
4. National wealth is a stock which is accumulated at a particular time.
5. Its increase and decrease affect the production capacity of goods.

Question 6.
Describe the Great depression of 1929.
Answer:
The ‘Great Depression of 1929’ and the subsequent years saw the output and employment levels in the countries of Europe and North America fall by huge amount. Demand for goods in the market was low. Many factories were lying idle, workers were thrown out of jobs. In USA from 1929 to 1933 unemployment rate rose from 3 percent to 25 percent. Over the same period aggregate output in USA fell by about 33 percent.

Question 7.
How are micro-economics and macro-economics interdependent?
Answer:
Interdependence of macro-economics and micro-economics can be studies as follows:
1. Macroeconomics depend on micro-economics:
Macro-economics and microeconomics depend on each other. Both are interdependent, macro economics contributes to the micro-economics. For example, the theory of investment belongs to micro-economics. It is derived from the behavior of the individual entrepreneur. The theory of aggregate investment function can also be derived from micro-economics theory of investment. Thus, we can say, that macro-economics depends on micro-economics.

2. Microeconomics depend on macro-economics:
Microeconomics depend upon macro-economics to a certain extent. For example, the rate of interest is a subject which belongs to micro-economics, but it is influenced by macro-economics aggregates. Thus, micro-economics depend upon macro-economics.

Conclusion:
Macro and micro-economics both are interdependent On each other. Neither is complete without the other. We must study macro-economics because it deals with average variables, such as national income and national output. We must study micro-economics because national output and national income are eventually the result of decision of millions of business firms and individuals. Thus, we can conclude that both are complementary to each other.

Question 8.
Calculate national income from the given data:

1. Salary –  Rs. 6,000
2. Rent – Rs. 2,000
3. Profit – Rs. 2,000
4. Interest – Rs. 1,000
5. Consumption – Rs. 5,000.

Solution:
N.I. = Salary + Rent + Profit + Interest
= 6,000 + 2,000 + 2,000+ 1,000
N.I. = Rs. 11,000.

Question 9.
Calculate National Income on the basis of the given data by income method: Heads Rs. (in crores)

1. Salary and wages = Rs. 18,000
2. Interest = Rs. 7,000
3. Depreciation = Rs. 4,000
4. Rent = Rs. 6,000
5. Profit = Rs. 25,000.

Solution:
National Income = Salary and wages + Interest +Rent +Profit
= Rs. 18,000 + Rs. 7,000 + Rs. 6,000 + Rs. 25,000 = Rs. 56,000.

Question 10.
On the basis of following data find out National Income by income method:

1. Salary and wages – 30,000
2. Rent – 10,000
3. Prof – 50,000
4. Interest – 10,000
5. Depreciation – 2,000
6. Gross domestic investment – 60,000.

Solution:
National income (N.I.) = Salary and Wages + Rent + Profit + Interest
N.I. = 30,000 + 10,000 + 50,000 + 10,000
N.I. = Rs. 1,00,000.

Question 11.
Calculate National Income from the following data:

1. Salary  =  Rs. 60,000
2. Rent  =  Rs. 20,000
3. Profit  =  Rs. 20,000
4. Interest  =  Rs. 10,000
5. Consumption  =  Rs. 50,000
6. Gross Domestic Product  =  Rs. 8,000.

Solution:
National Income = Salary + Rent + Interest + Profit
= Rs. 60,000 + 20,000 + 10,000 + 20,000
= Rs. 1,10,000
National Income = Salary + Rent + Interest + Profit

Question 12.
Specify the relation of gross domestic product with welfare.
Answer:
Gross domestic product refers to money value of goods and services produced within the territorial boundaries of the country in a given year. With the increase in income consumption expenditure of a person increase which in turn increases material welfare. Therefore, it is not appropriate to relate GNP with welfare or their generalization may not be correct due to. following reasons:

1. GDP shows the total goods and services produced in the country. However, it does not exhibit the structure of the product if increase in GDP is mainly due to increased production of war equipment and ammunition. Then such an increase cannot be associated with any improvement in economic welfare.

2. If increase in GDP is due to rise in prices and not due to increase in physical output, then it will not be a reliable index of economic welfare.

3. GDP does not consider the changes in population of a country. If rate of population growth is higher than the rate of growth of GDP, then it will decrease per capital availability of goods and services, which will adversely affect the economic welfare.

Question 13.
What do you mean by G.D.P.? Write any four characteristics of G.D.P.
Answer:
Meaning of G.D.P:
Gross Domestic Product is defined as “the value of all final goods and services produced by all the enterprises located within the domestic territory of a country during an accounting year. It should be noted that goods and services must be produced within the country.” G.D.P. is always money value of goods and services produced within a year.

Special features of G.D.P:

1. G.D.P. includes the value of all the goods and services produced within the country in a particular year.
2. It includes depreciation value.
3. G.D.P. is measured in terms of market price.
4. G.D.P. includes the value of new goods only i.e., it excludes the value of second hand goods.
5. It includes real capital not financial capital.
6. Consumer and capital goods are classified in durable and non-durable goods.
7. Goods may be from private sector or public sector.
8. To avoid the defect of double counting we include the value of final goods and services.

Question 14.
What precautions should be taken while calculating national income by income method?
Answer:
Precautions taken while calculating national income by income method:

1. Transfer income should not be included.
2. Income from illegal activities should not be included.
3. Imputed rent should be included as it is the part of rental income.
4. Production for self-consumption should be included.
5. Money received by sale of shares/bonds etc. should not be included.
6. Income from sale of second hand goods should not be included.
7. Death duties, wealth tax, gift tax, etc., are not included is national income.
8. Corporation tax should not be recorded separately as it is a part of profit.

Question 15.
What are the difficulties in estimating national income by income method?
Answer:
Estimation of national income by income method passes various difficulties. The major difficulties are:
(i) It is difficult to estimate mixed income. Mixed incomes are earned by an unincorporated sector and it is difficult to get reliable information from such unorganized sector.

(ii) Interest on national debt is not included in national income as per the national income convention on the assumption that government borrowings are used for consumption (unproductive) purposes. However, some economists object to this since, a part of the government borrowing is used for productive purposes.

(iii) Incomes received are generally calculated from income-tax returns. Therefore, income method is of limited used in underdeveloped countries because a very small part of the income earners are tax payers in these countries.
Income method of estimating national income is useful because it provides information about distribution of national income among various factor categories like share of wages profits etc. in national income.

Question 16.
What do you mean by G.D.P. at constant price?
Answer:
Gross Domestic Product at constant prices: Constant price means base year’s price. Base year is an average standard previous year in which major economic changes have not taken place. Goods and services produced during the year are either valued at constant price of the base year or the value of goods and services at current price is converted into the value at constant price.

Modem economies are inflationary economies where prices of goods and services are increasing at faster rates. It is therefore, advisable that the value of goods and services at current price should be converted at constant price, so that real Gross Domestic Product (G.D.P.) could be understood. Calculation at constant price should be referred as real G.D.P. Formula of conversion of G.D.P. at current price into G.D.P at constant price.

Question 17.
Will a profit maximizing firm in competitive market ever produce a positive level of output in the range where the marginal cost is falling? Give and explanation.
Answer:
A profit maximizing firm in a competitive market will produce a positive level at output in the same, where marginal cost is falling. Falling MC means that the cost of producing an additional unit of output trends to reduce. Here, price is constant as the firm is working in a competitive market in this case, the difference between firm’s total revenue and TVC (TVC = Σ MC) tends to increase. It means firm’s profit increases with the increase in the level of output. Then a competitive firm increase output when gross profit is rising.

Question 18.
From the following data, calculate Personal Income and Personal Disposable Income.
Items (₹ In cores )

• Net domestic product at factor cost 8,000
• Net factor income from abroad 200
• Disbursed profit 1,000
• Corporation tax 500
• Interest received by households 1,500
• Interest paid by households 1,200
• Transfer income 300
• Personal tax 500.

Solution:
Personal Income = (a) + (b) + (e – f) + (g) -(d)
= 8000 + 200 +(1500-1200)+ 300 – 500
= 8000 + 200 + 300 + 300 – 500
= 8800 – 500 = ₹ 8,300 Cores.
Personal Disposable Income = Personal Income – Personal Tax
= 8300 – 500 = ₹ 7,800 Croce.

Question 19.
In a single day, Raju, the barber, collects ₹ 500 from hair cuts. Over this day, his equipment depreciates in value by ₹ 50, of the remaining ₹ 450, Raju pays sales tax worth ₹ 30, takes home ₹ 200 and retains ₹ 220 for improvement and buying of new equipment He further pays 120 as income tax from his income. Based on this information, complete Raju’s contribution to the following measures of income:

(a) Gross domestic product
(b) NNP at market price
(c) NNP at factor cost
(d) Personal income
(e) Personal disposable income.

Answer:
(a) GDP = ₹500

(b) NNP_MP=GDP – DeP
₹500 – ₹ 50 = ₹450

(c) NN_fc = NNP – Sales tax
= ₹450 – ₹30 = ₹420

(d) PI = NNP_fc – Retained earnings
= ₹ 420 – ₹ 220
= ₹ 200

(e) PDI = PI – Income tax
=₹ 200 – ₹ 20
= ₹ 180.

National Income and Related Aggregates Long Answer Type Questions

Question 1.
State five points of importance of national income.
Or
Write the importance of national income.
Answer:
Importance of National Income can be explained through the following points:
1. Knowledge about the economic progress of the nation y By collecting the data of the national income of few years the economic progress of any country can be known. Increase in national income is the sign of the progress of the country. By comparing the national income estimates over a period of time, we can know whether economy is growing, or is static or declining.

2. Measure of economic welfare:
The national welfare of a country depends upon its national income. If there is an increase in national income it will bring an increase in economic welfare and a fall in national income will result in fall in economic progress.

3. Formulation of policies:
National income is helpful in the formation of the policies of the country. For example, taxation policy, employment policy etc. National income statics is very useful in formulating the plans and fixing targets.

4. Economic planning:
Economic planning can be easily done on the basis of national income. The national income helps in deciding the area for which planning has to be done. It also helps in deciding the nature of investment. i.e.,the investment should be long-term or short – term.

5. Comparative studies:
The progress of two or more countries can be compared on the basis of the data of national income. It gives the idea of savings, investments, consumption etc. of various countries. Comparative study of the economic progress of various countries can easily be made. We can compare the standards of living and the levels of economic welfare of the people.

Question 2.
Distinction between Gross Domestic Product and Gross National Product. Ans. Differences between Gross Domestic Product and Gross National Product:

Question 3.
Write difference between National Income and Private Income.
Answer:
Differences between National Income and Private Income:
National Income

1. It includes income of both the public
2. It does not include National income.
3. It is not a part of National income.
4. National income is the income of residents of india.
5. National income = Net Domestic Product at factor cost + Net factor income from abroad.

Private Income:

1. It includes the income of private sectors and private sectors. only.
2. It includes both factor income and trans-fer income.
3. It is a part of private income.
4. In private income the income of private idents of India. people are included.
5. Private income = Net Domestic Product at factor cost – Income from the domestic product accruing to public sector+ Transfer income + Net factor income from abroad.

Question 4.
What are the causes of low national income in India?
Or
Give reasons for slow growth rate of national income in India.
Answer:
The following are the causes of low national income in India:

1. Overpopulation:
   At present our population is more than 100 crores. It is the main cause of low national income.
2. Inequality in distribution of national income:
   There is a great disparity in the distribution of national income.The main reason is improper tax policy.
3. Dependence on agriculture:
   Indian economy is mainly agriculture based economy. There is always uncertainty in agricultural product. So, national income is low in India.
4. Illiteracy:
   A major part of the population in our country is uneducated. So, they are not able to understand the latest methods of production and policies. They are also not able to follow them.
5. Old method of production:
   The methods of production that are followed in our country are old and outdated due to which we are not able to utilize our resources to the full extent.

Question 5.
Write five suggestions to increase national income in India.
Or
Write suggestions to increase national income.
Answer:
1. Proper development in the agricultural fields:
Agriculture is the main source of national income in India. So, to increase the national income use of best seeds, fertilizers and tools is very important.

2. Development in the field of technical education:
An educated person can work more efficiently than uneducated one. So, education should be given to maximum number of people.

3. Proper utilization of natural resources:
If natural resources are fully and properly utilized the income of the nation can be increased.

4. Check on population:
Population must be controlled. Special efforts should be made to check population in villages which will increase per capital income.

5. Proper development of transport and communication facilities:
Development of transport and communication should be encouraged. Priority should be given to them. For this proper planning must be done. Development in transport and communication will encourage the export-import also which will increase the national income.

6. Export oriented trade policies:
Trade policies should be made in such a way that it will encourage export. Import should be discouraged so that national income will have a good effect. Five year plans and development programmers must be given stress. Export promotion should be given high priority.

Question 6.
Distinguish between Closed Economy and Open Economy.
Answer:
Differences between Closed Economy and Open Economy:
Closed Economy:

1. When a country does not have any economic relation with other country it is called closed economy.
2. In closed economy GDP and National income is equal.
3. It is an imaginary concept.
4. In this economy, capital formation is negligible.
5. In this economy consumption and investment both are equal to production.

Open Economy:

1. When a country establishes economic relation with other country it is called open economy.
2. There is a difference between GDP and National income.
3. It is a real concept.
4. In this economy, capital formation and investment both take place.
5. In this economy, the total of consumption and investment can be more or may be less than production.

Question 7.
Explain different methods of measuring national income.
Answer:
The various methods of measuring national income are:
1. Census of production method:
The gross national income is calculated by adding up the aggregate values of productions of all the industries and sectors of the economy and net income from abroad. By deducting depreciation from gross income we get national income.

2. Census of Income method:
By summing up the net incomes of all individuals and firms in a country during a year, we get the national income.

3. Expenditure method:
People don’t spend their entire income. They save a part of it as saving. By summing up all expenses and all incomes of all the people during a year, we get the national income.

4. Combined use of production and income method:
This method is also known as ‘mixed method’. In this method, both production and income methods are used together. In any country if due to certain reasons one method cannot be used, there the mixed method can be used.

5. Social accounting method:
This method was propounded by Prof. Richard Stone. In this method, the entire society was divided into various sections such as; producers, consumers, etc. The average income of some people of each section is calculated and then it is multiplied with the total number of people in each section.

Question 8.
A farmer sold cotton of Rs. 500 to cotton mill by producing himself. Cotton mill prepared garments and sold to garment factory at Rs. 600 garment factory sold it to a store on Rs.1000. Store owner sold it to consumer on Rs. 1200. Find out increased value by each.
Solution:
Following is the increased price by Farmer, Cotton mill, Ready made garments factory and store:

1. Price raised by Farmer = Sale of cotton to cotton mill = Rs. 500.
2. Price raised by cotton mill = Sale to garment factory – Sale of cotton from Farmer
   = Rs. 600 – 500 = Rs. 100.
3. By ready made garment = Sale price of dress to store – Price (Sell) of cotton from factory cotton mill
   = Rs. 1000 – 600 = Rs. 400.
4. By Store = Last sell price of consumer – Value of dress by ready made factory
   = Rs. 1200 – 1000 = Rs. 200.
5. Total price rise = Farmer+Cotton mill + Garment factory + Store value
   = Rs. 500 + 100 + 400 + 200 = Rs. 1200.

Question 9.
Write the main characteristics of capitalistic economy.
Or
What are the important features of a capitalist economy?
Answer:
Important features of a capitalist economy:
Following are important features or characteristics of a capitalist economy:

1. There is private ownership of means of production.
2. Production takes place for selling the output in the market.
3. There is sale and purchase of labor services at the price which is called the wage rate.

Question 10.
Explain in short G.D.P. at market price and G.D.P. at factor cost
Answer:
(A) Gross Domestic Product at market price:
It is also called the current price or prevailing price in the market. In order to calculate G.D.P. at current price final goods and services produced during the year are valued in terms of prevailing price of that year. To measure it we multiply the quantity of produced goods with their prices. It can be explained like this:

Here GDP _MP = P₁ (Q) + P₁ (S)
GDP_MP = Gross Domestic Products at market price
P₁ = Market price
Q = Quantity of final goods and services
S = Services

Increase in the value of Gross domestic product (G.D.P.) as compared to the value of previous year shows economic development and happy trend. It should be Carly studied whether the increase is due to increase in the quantity of goods and services produced or increase in price. If the increase has caused due to increase production, it should be taken as real increase. We can calculate per capital Gross Domestic Product (G.D.P) if we divide total G.D.P. with the population of the country.

(B) Gross Domestic Product at factor cost:
Gross Domestic Product at factor cost is the estimate of Gross Domestic Product in terms of earnings of factors of production. It is the sum total of earnings received by various factors of production in terms of wages, interest, rent, profits, etc. within the domestic territory of a country in a year.

It measures factor incomes generated with the domestic territory irrespective of whether generated by residents or non-residents. Being gross it marks no provision for the depreciation. As explained above market value of goods and services differs from the earnings of factors of production because of Net Indirect Taxes. Therefore, if we get gross domestic product at factor cost. Thus,
G.D.P. _FC = G.D.P _MP – Indirect taxes.

MP Board Class 12th Economics Important Questions

MP Board Class 12th Maths Important Questions Chapter 7A Integration

Integration Important Questions

Integration Objective Type Questions:

Question 1.
Choose the correct answer:

Question 1.
The value of \(\int { \frac { sec^{ 2 }x }{ 1+tanx } } \) dx is:
(a) log_e (l + tan x) + c
(b) tan x + c
(c) – cot x + c
(c) – cot x + c
(d) log_e x + c
Answer:
(a) log_e (l + tan x) + c

Question 2.
The value of \(\int { \frac { x }{ 4+x^{ 4 } } } \) dx is:
(a) \(\frac{1}{4}\) x² + c
(b) \(\frac{1}{4}\) tan^-1 \(\frac { x^{ 2 } }{ 2 } \)
(c) \(\frac{1}{2}\) tan^-1 \(\frac { x^{ 2 } }{ 2 } \)
(d) None of these
Answer:
(a) \(\frac{1}{4}\) x² + c

Question 3.
If \(\int \frac{2^{\frac{1}{x}}}{x^{2}}\) dx = k(2)^1/x + c, then find the value of k is:
(a) \(\frac { -1 }{ log_{ e }2 } \)
(b) – log_e 2
(c) -1
(d) \(\frac { 1 }{ 2 } \)
Answer:
(a) \(\frac { -1 }{ log_{ e }2 } \)

Question 4.
The value \(\int \frac{e^{x}(1+x)}{\cos ^{2}\left(x e^{x}\right)}\) dx is:
(a) 2 log_ecos(xe^x) + c
(b) sec(xe^x) + c
(c) tan(xe^x) + c
(d) tan(x + e^x) + c
Answer:
(c) tan(xe^x) + c

Question 5.
If \(\int { xsinxdx } \) = -x cos x + α will be:
(a) sin x + c
(b) cos x + c
(c) c
(d) None of these
Answer:
(a) sin x + c

Question 2.
Fill in the blanks :


Answer:

1. \(\frac{1}{2}\) tan^-1 ( \(\frac{x}{a}\) ) + c
2. log [x + \(\int { \frac { dx }{ \sqrt { x^{ 2 }-a^{ 2 } } } } \) + c
3. log [x + \(\int { \frac { dx }{ \sqrt { a^{ 2 }-x^{ 2 } } } } \) + c
4. \(\frac{x}{2}\) \(\int { \frac { dx }{ \sqrt { a^{ 2 }-x^{ 2 } } } } \) + \(\frac { a^{ 2 } }{ 2 } \) sin^-1 ( \(\frac{x}{a}\) ) + c
5. log(sec x + tan x) + c
6. sin^-1 x + \(\sqrt { 1-x } \) + c
7. tan x + sec x.

Question 3.
Write True/False:

Answer:

1. True
2. True
3. False
4. True
5. False
6. False

Integration Very Short Answer Type Questions

Answer:

1. \(e^{ tan-1x }\) + c
2. – cos x + c
3. sin² x + c
4. \(\frac{1}{2a}\) log \(\frac { a+x }{ a-x } \)
5. \(\frac{1}{2a}\) log \(\frac { x-a }{ x+a } \)
6. \(\frac { e^{ x } }{ x } \) + c
7. x log \(\frac { x }{ e } \) + c
8. 2 tan^-1\(\sqrt{x}\)
9. 1 + log x = t
10. a = – \(\frac { \pi }{ 4 } \), b = 3
11. x = t²
12. – \(\frac{1}{a}\) cos(ax + b)
13. \(\frac{1}{a}\) log (ax + b)
14. tan x – x + c
15. sin^-1 \(\frac{x}{a}\)
16. \(\frac { x^{ 3 } }{ 3 } \) + c
17. \(\frac { x^{ 3 } }{ 2 } \) + c
18. e^xf(x) + c
19. e^x
20. e^x log x + c.

Integration Short Answer Type Questions

Question 1.
Evaluate:
\(\int \frac{\cos 2 x+2 \sin ^{2} x}{\cos ^{2} x} dx\)? (CBSE 2018)
Solution:
Let I = \(\int \frac{\cos 2 x+2 \sin ^{2} x}{\cos ^{2} x} d x\)

= \(\int { sec^{ 2 }xdx } \)
= tan x + c.

Question 2.
Evaluate \(\int { \frac { 1-sinx }{ cos^{ 2 }x } } \) dx? (NCERT)
Solution:
Let I = \(\int { \frac { 1-sinx }{ cos^{ 2 }x } } \)

Question 3.
Evaluate \(\int \frac{2-3 \sin x}{\cos ^{2} x} d x\) dx? (NCERT)
Solution:
Let I = \(\int \frac{2-3 \sin x}{\cos ^{2} x} d x\) dx

Question 4.
Evaluate \(\int \sin ^{-1}(\cos x) d x\) dx? (NCERT)
Solution:
I = \(\int \sin ^{-1}(\cos x) d x\) dx

Question 5.
Evaluate \(\int { \frac { dx }{ 1+cos2x } } \)?
Solution:
Let I =

Question 6.
(A) Evaluate \(\int { tan^{ -1 }xdx } \)?
Solution:
Let

(B) Evaluate \(\int { sin^{ -1 }xdx } \) and \(\int { cos^{ -1 }xdx } \)?
(Do it by yourself)

Question 7.
Evaluate \(\int { sin^{ 2 }xdx } \)?
Solution:
Let

Question 8.
Evaluate \(\int { \frac { cosx }{ cos(x-\alpha ) } } \) dx?
Solution:

Question 9.
(A) Evaluate \(\int { \frac { 1 }{ \sqrt { 1+cosx } } } \) dx?
Solution:
Let

(B) Evaluate \(\int { \sqrt { 1+cos2xdx } } \)?
Solution:
Solve like Q.No 9 (B)

Question 10.
(A) Evaluate \(\int { \frac { e^{ x }(1+x) }{ cos^{ 2 }(xe^{ x }) } } \) dx?
Solution:
Let

(B) Evaluate \(\int { \frac { e^{ tan-1x } }{ 1+x^{ 2 } } } \) dx?
Solution:
Let

Question 11.
Evaluate \(\int { \frac { dx }{ 1-sinx } } \)?
Solution:
Let

Question 12.
Evaluate \(\int { \frac { logx }{ x } } \) dx?
Solution:
Given:

Question 13.
(A) Evaluate \(\int { \frac { dx }{ 1-cosx } } \)?
Solution:
Let

(B) Evaluate \(\int { \frac { logx }{ x } } \) dx?
Solution:
Let

Question 14.
Evaluate \(\int { \frac { dx }{ 1+sinx } } \)?
Solution:
Let

Question 15.
Evaluate \(\int { \frac { cos\sqrt { x } }{ \sqrt { x } } } \) dx?
Solution:
Let

Question 16.
Evaluate \(\int { \frac { 1-cos2x }{ 1+cos2x } } \) dx?
Solution:
Let

Question 17.
Integrate \(\frac { x^{ 4 } }{ x^{ 2 }+1 } \) with respect to x?
Solution:
Let

Question 18.
Find the value of \(\int { \frac { sec^{ 2 }(logx) }{ x } } \) dx?
Solution:
Let I = \(\int { \frac { sec^{ 2 }(logx) }{ x } } \) dx
Put, log x = t
⇒ \(\frac { 1 }{ x } \) dx = dt
∴ I = ∫sec² t dt
⇒ I = tan x + c
⇒ tan(log x) + c

Question 19.
Find the value of \(\int { \frac { sin(logx) }{ x } } \) dx?
Solution:
Let I = \(\int { \frac { sin(logx) }{ x } } \) dx
Put, log x = t
⇒ \(\frac { 1 }{ x } \) dx = dt
∴ I = ∫sin t dt = -cos t + c
⇒ I = – cos (log x) + c

Question 20.
Find the value of \(\int { \frac { cos(logx) }{ x } } \) dx?
Solution:
Solve like Q.No.19

Question 21.
(A) Find the value of \(\int { tan^{ 2 }xdx } \)?
Solution:
Let I = \(\int { tan^{ 2 }xdx } \) = ∫(sec² x – 1) dx
= ∫sec² x dx – ∫1dx = tan x – x.

(B) Find the value of \(\int { cot^{ 2 }xdx } \)?
Solution:
Let I = \(\int { cot^{ 2 }xdx } \) = ∫(cosec² x – 1) dx
= ∫cosec² x dx – ∫1.dx = – cot x – x.

Question 22.
Find the value of \(\int { \frac { sinx }{ 1+cosx } } \) dx?
Solution:
Let I = \(\int { \frac { sinx }{ 1+cosx } } \) dx
= ∫\(\frac { 1 }{ t } \) dt, (Put 1+cos x = dt ⇒ sin x dx = dt)
= log t
= log (1 + cos x).

Question 23.
Find the value \(\int { \frac { sin^{ -1 }x }{ \sqrt { 1-x^{ 2 } } } } \) dx?
Solution:

Integration Long Answer Type Questions – I

Question 1.
Find the value of \(\int { \sqrt { \frac { a+x }{ a-x } } } \) dx?
Solution:
Let I = \(\int { \sqrt { \frac { a+x }{ a-x } } } \) dx
Again let x = a cos θ ⇒ dx = – a sin θ dθ

Question 2.
Evaluate \(\int\left[\frac{1}{(\log x)^{2}}-\frac{2}{(\log x)^{3}}\right]\) dx?
Solution:
Let I = \(\int\left[\frac{1}{(\log x)^{2}}-\frac{2}{(\log x)^{3}}\right]\)
Again let log x = t ⇒ x = e^t ⇒ dx = e^tdt

Question 3.
Evaluate \(\int { sin^{ -1 } } \) xdx?
Solution:
Let

Again let 1 – x² t ⇒ – 2x dx = dt

Question 4.
Evaluate \(\int { cos^{ -1 }xdx } \)?
Solution:
Let

Question 5.
(A) Evaluate \(\int { \frac { x^{ 2 } }{ 1+x } } \) dx?
Solution:
Let

(B) Evaluate \(\int { \frac { x }{ 1+x^{ 4 } } } \) dx?
Solution:
Let

= \(\frac{1}{2}\) tan^-1 t,
= \(\frac{1}{2}\) tan^-1 x²

Question 6.
Evaluate \(\int { \frac { 1 }{ sinx-cosx } } \) dx?
Solution:
Let I = \(\int { \frac { 1 }{ sinx-cosx } } \) dx

Question 7.
Evaluate \(\int { \frac { dx }{ e^{ x }+1 } } \)?
Solution:
Let

Question 8.
Evaluate \(\int { sec^{ 3 }xdx } \)?
Solution:
Let

= sec x tan x – ∫sec x tan x tan x dx
= sec x tan x – ∫sec x tan² x dx
= sec x tan x – ∫sec x (sec² x – 1) dx
= sec x tan x – ∫sec³ xdx +∫sec x dx
⇒ I = sec x tan x – I + log(sec x + tan x)
⇒ 2I = sec x tan x + log (sec x + tan x)
⇒ I = \(\frac{1}{2}\) [sec x tan x + log (sec x + tan x)].

Question 9.
Evaluate \(\int { \frac { dx }{ x^{ 2 }-a^{ 2 } } } \)?
Solution:
Let

We have to break the term with partial fraction,
img

Question 10.
Evaluate \(\int { \frac { 3x }{ (x-2)(x+1) } } \) dx?
Solution:
Let \(\int { \frac { 3x }{ (x-2)(x+1) } } \) = \(\frac { A }{ (x-2) } \) + \(\frac { B }{ (x+1) } \) ………………… (1)
⇒ \(\frac { 3x }{ (x-2)(x+1) } \) = \(\frac { A(x+1)+B(x-2) }{ (x-2)(x+1) } \)
⇒ 3x = A(x + 1) + B (x – 2)
⇒ 3x = (A + B)x + (A – 2B) …………………… (2)
Comparing the coefficient of x from both sides,
3 = A + B
0 = A – 2B
3 = 3B ⇒ B = 1
and A = 2B = 2
image 40 40 40
= 2 log(x – 2) + log (x + 1) + c.

Question 11.
Evaluate \(\int { \frac { x^{ 2 }+1 }{ x^{ 4 }-x^{ 2 }+1 } } \) dx?
Solution:

Question 12.
Evaluate \(\int { \frac { x^{ 2 }+1 }{ x^{ 4 }+x^{ 2 }+1 } } \) dx?
Solution:
Solve like Q.No.11.
Answer:

Question 13.
Evaluate \(\int { \frac { dx }{ \sqrt { x^{ 2 }+2x+3 } } } \)?
Solution:
Let

Question 14.
Integrate \(\frac { 1 }{ 1+sin^{ 2 }x } \) with respect to x?
Solution:
Let

Question 15.
Evaluate \(\int { \frac { cos2x }{ (cosx+sinx)^{ 2 } } } \) dx? (NCERT)
Solution:
Let


Taking cos x + sin x = t
\(\frac { d }{ dx } \) (cosx + sinx) = \(\frac { dt }{ dx } \)
⇒ (-sinx + cos x) = \(\frac { dt }{ dx } \)
∴ I = ∫ \(\frac { dt }{ t } \)
⇒ I = logt + c
⇒ I = log(cos x + sinx) + c.

Question 16.
Evaluate \(\int { \frac { 1+tanx }{ x+logsecx } } \)dx?
Solution:
Let

Question 17.
Evaluate \(\int { \frac { cotx }{ log(sinx) } } \) dx?
Solution:
Let I = \(\int { \frac { cotx }{ log(sinx) } } \) dx
Again let log(sin x) = t
\(\frac{d}{dx}\) log (sin x) = \(\frac{dt}{dx}\)
Taking sin x = u,

⇒ I = log t + c
⇒ I = log log(sin x) + c.

Question 18.
Evaluate \(\int { \frac { 2cosx-3sinx }{ 6cosx+4sinx } } \) dx? (NCERT)
Solution:
Let I = \(\int { \frac { 2cosx-3sinx }{ 6cosx+4sinx } } \) dx
Again let 6 cosx + 4 sin x = t,

Question 19.
Evaluate \(\int { e^{ 3logx } } (x^{ 4 }+1)^{ -1 }\) dx? (NCERT)
Solution:
Let I = \(\int { e^{ 3logx } } (x^{ 4 }+1)^{ -1 }\) dx

Put x⁴ + 1 = t,

Question 20.
Evaluate \(\int { \frac { dx }{ x-\sqrt { x } } } \)? (NCERT)
Solution:
Let I = \(\int { \frac { dx }{ x-\sqrt { x } } } \)

Put \(\sqrt{x}\) – 1 = t

Question 21.
Evaluate \(\int { \frac { dx }{ 1+3sin^{ 2 }x } } \)?
Solution:
Let I = \(\int { \frac { dx }{ 1+3sin^{ 2 }x } } \)

Integration Long Answer Type Questions – II

Question 1.
Evaluate \(\int \sin ^{-1}\left(\frac{2 x}{1+x^{2}}\right) d x\) dx?
Solution:
Let I = \(\int \sin ^{-1}\left(\frac{2 x}{1+x^{2}}\right) d x\) dx
Again let x = tan θ ⇒ dx = sec² θ dθ

Question 2.
Integrate \(\frac{e^{m \tan ^{-1} x}}{\left(1+x^{2}\right)^{\frac{3}{2}}}\) with respect to x?
Solution:
Let tan^-1 x = t ⇒ x = tan t
dx = sec² t dt

= e^mtsin t – m[e^mt(-cos t) – \(\int { me^{ mt } } \) (-cos t) dt]
= e^mtsin t + me^mtcos t – m² \(\int { e^{ mt } } \) cos t dt
= e^mt (sin t + m cos t) – m² I

Question 3.
Evaluate \(\int { \frac { x^{ 2 }tan^{ -1 }x }{ 1+x^{ 2 } } } \) dx?
Solution:
Let I = \(\int { \frac { x^{ 2 }tan^{ -1 }x }{ 1+x^{ 2 } } } \) dx
Let x = tan θ ⇒ θ = tan^-1 x
⇒ dx = sec² θdθ

Question 4.
Evaluate \(\int { tan^{ -1 }\frac { 2x }{ 1+x^{ 2 } } } \) dx?
Solution:
Let I = \(\int { tan^{ -1 }\frac { 2x }{ 1+x^{ 2 } } } \) dx
Let x = tan θ ⇒ dx = sec² θdθ

Question 5.
Evaluate \(\int { \frac { xtan^{ -1 }x }{ (1+x^{ 2 })^{ 3/2 } } } \) dx?
Solution:
Let I = \(\int { \frac { xtan^{ -1 }x }{ (1+x^{ 2 })^{ 3/2 } } } \) dx
Let x = tan θ ⇒ dx = sec² θdθ

Question 6.
Evaluate \(\int { \frac { dx }{ 3+2cosx } } \)?
Solution:
Let I = \(\int { \frac { dx }{ 3+2cosx } } \)

Again let tan \(\frac { x }{ 2 }\) = t,

Question 7.
Evaluate \(\int { \frac { dx }{ 4+5cosx } } \)?
Solution:
Solve like Q.No.6.

Question 8.
Evaluate \(\int { \frac { dx }{ 5-3cosx } } \)?
Solution:
Solve like Q.No.6.

Question 9.
Evaluate \(\int { \frac { 1 }{ 4+5sinx } } \) dx?
Solution:

Let tan \(\frac { x }{ 2 }\) = t ⇒ sec² \(\frac { x }{ 2 }\).\(\frac { 1 }{ 2 }\).dx = dt

Question 10.
Evaluate \(\int { \frac { e^{ x }(1+sinx) }{ (1+cosx) } } \) dx?
Solution:
Let I = \(\int { \frac { e^{ x }(1+sinx) }{ (1+cosx) } } \) dx

Question 11.
Evaluate \(\int { \frac { xe^{ x } }{ (1+x)^{ 2 } } } \) dx?
Solution:
Let I = \(\int { \frac { xe^{ x } }{ (1+x)^{ 2 } } } \) dx = \(\int { \frac { (1+x-1)e^{ x } }{ (1+x)^{ 2 } } } \)

Question 12.
Evaluate \(\int { \frac { 2cosx }{ (1-sinx)(1+sin^{ 2 }x) } } \) dx? (CBSE 2018)
Solution:
Let I = \(\int { \frac { 2cosx }{ (1-sinx)(1+sin^{ 2 }x) } } \) dx
Put sin x = t, cos x dx = dt

⇒ 2 = A(1 + t²) + (1 – t) (Bt + 1)
⇒ 2 = A + At² + Bt – Bt² + 1 – t
⇒ 2 = (A – B)t² + (B – 1) t + (A + 1)
Comparing the cofficient of like terms
∴ A – B = 0
B – 1 = 0
and A + 1 = 2
∴ B = 1, A = 1

Question 13.
Evaluate \(\int { \frac { dx }{ e^{ x }-1 } } \)? (NCERT)
Solution:
Let I = \(\int { \frac { dx }{ e^{ x }-1 } } \) = \(\int { \frac { e^{ x }dx }{ e^{ x }(e^{ x }-1) } } \)
Again let e^x = t, then e^xdx = dt

Question 14.
Evaluate \(\int { \frac { dx }{ x(x^{ n }+1) } } \)? (NCERT)
Solution:
Let I = \(\int { \frac { dx }{ x(x^{ n }+1) } } \)

Put xⁿ = t,

Question 15.
Evaluate \(\int { (\sqrt { tanx } +\sqrt { cotx) } } \) dx? (NCERT)
Solution:
Let

Again let, sin x – cos x = t
(cos x + sin x) dx = dt
(sin x – cos x)² = t²
sin²x + cos²x – 2sinxcos x = t²
⇒ 1 – sin 2x = t²
⇒ sin 2x = 1 – t²

MP Board Class 12 Maths Important Questions

MP Board Class 12th Maths Important Questions Chapter 4 Determinants

Determinants Structure Important Questions

Determinants Structure Objective Type Questions:

Question 1.
Choose the correct answer:

Question 1.
If A is a square matrix of order 3 × 3, then value of |Adj. A| will be:
(a) |A|
(b) |A|²
(c) |A|³
(d) 3|A|
Answer:
(b) |A|²

Question 2.
If a, b, c are in Arithematic series, then value of determinant \(\left|\begin{array}{ccc}
{x+2} & {x+3} & {x+2 a} \\
{x+3} & {x+4} & {x+2 b} \\
{x+4} & {x+5} & {x+2 c}
\end{array}\right|\) will be:
(a) 0
(b) 1
(c) x
(d) 2x
Answer:
(a) 0

Question 3.
Matrix A = \(\begin{bmatrix} 2 & 3 \\ 1 & 2 \end{bmatrix}\), then A^-1 will be:
(a) A^-1 = \(\begin{bmatrix} 2 & -3 \\ -1 & 2 \end{bmatrix}\)
(b) A^-1 = \(\begin{bmatrix} 2 & -3 \\ 1 & -2 \end{bmatrix}\)
(c) A^-1 = \(\begin{bmatrix} -2 & 3 \\ -1 & 2 \end{bmatrix}\)
(d) A^-1 = \(\begin{bmatrix} -2 & 3 \\ 1 & -2 \end{bmatrix}\)
Answer:
(a) A^-1 = \(\begin{bmatrix} 2 & -3 \\ -1 & 2 \end{bmatrix}\)

Question 4.
If ω is the cube roots of unitary, then \(\left|\begin{array}{ccc}
{\mathbf{1}} & {\omega} & {\omega^{2}} \\
{\omega} & {\omega^{2}} & {1} \\
{\omega^{2}} & {1} & {\omega}
\end{array}\right|\) =
(a) 1
(b) 0
(c) ω
(d) ω²
Answer:
(b) 0

Question 5.
Determinat \(\left|\begin{array}{ccc}
{a+b} & {a+2 b} & {a+3 b} \\
{a+2 b} & {a+3 b} & {a+4 b} \\
{a+4 b} & {a+5 b} & {a+6 b}
\end{array}\right|\) =
(a) a² + b² + c² – 3abc
(b) 0
(c) a³ + b³ + c³
(d) None of these
Answer:
(b) 0

Question 2.
Fill in the blanks:

1. If \(\begin{vmatrix} 3 & m \\ 4 & 5 \end{vmatrix}\) = 3, then m = ………………………..
2. In determinant \(\begin{vmatrix} 2 & -3 \\ 1 & -2 \end{vmatrix}\), the cofactor of element – 3 is ………………………..
3. If A = \(\left|\begin{array}{lll}{1} & {0} & {1} \\ {0} & {1} & {2} \\ {0} & {0} & {4}\end{array}\right|\), then the value of |3A| is …………………………..
4. The value of determinant \(\begin{vmatrix} 1 & log_{ b }a \\ log_{ a }b & 1 \end{vmatrix}\) will be ……………………………
5. The value of determinant \(\begin{vmatrix} cos70^{ \circ }\quad & sin20^{ \circ } \\ sin70^{ \circ } & cos20^{ \circ } \end{vmatrix}\) will be ………………………

Answer:

1. 3
2. -1
3. 27A
4. 0
5. 0

Question 3.
Write True/False

1. The value of determinant \($\left|\begin{array}{ccc}{0} & {a} & {-b} \\ {-a} & {0} & {-c} \\ {b} & {c} & {0}\end{array}\right|$\) is abc?
2. The maximum value of determinant
   \(\left|\begin{array}{ccc}
   {1} & {1} & {1} \\
   {1} & {1+\sin \theta} & {1} \\
   {1} & {1} & {1+\cos \theta}
   \end{array}\right|\) is \(\frac{1}{2}\)?
3. If A is the matrix of order 3 × 3, then find the value of |kA| will be k²|A|²?
4. If \(\begin{vmatrix} x\quad & 2 \\ 18 & x \end{vmatrix}\) = \(\begin{vmatrix} 6\quad & 2 \\ 18 & 6 \end{vmatrix}\), then find the value of x is ± 3?
5. The value of the determinant \(\begin{vmatrix} 1\quad & \omega \\ \omega & -\omega \end{vmatrix}\) is 1?

Answer:

1. True
2. True
3. Flase
4. Flase
5. True

Question 4.
Write the answer in one word/sentence:

1. How many number of value k for which the linear equation 4x+ ky + 2z = 0, kx + 4y + z = 0, 2x + 2y + z = 0 passes a non – zero solution?
2. If α, β are the roots of equation 2x² + 3x + 5 = 0, then find the value of \(\left|\begin{array}{lll}
   {0} & {\beta} & {\beta} \\
   {\alpha} & {0} & {\alpha} \\
   {\beta} & {\alpha} & {0}
   \end{array}\right|\)?
3. If area of the traingle with vertices (2, -6), (5, 4) and (k, 4) be 35 square units, then find the value of k?
4. If x ∈ N and A = \(\begin{vmatrix} x+3\quad & -2 \\ -3x & 2x \end{vmatrix}\) = 8, then find the value of x?
5. Find the value of determinant \(\left|\begin{array}{ccc}
   {1^{2}} & {2^{2}} & {3^{2}} \\
   {2^{2}} & {3^{2}} & {4^{2}} \\
   {3^{2}} & {4^{2}} & {5^{2}}
   \end{array}\right|\)?

Answer:

1. 2
2. \(\frac{-15}{4}\)
3. 12
4. 2
5. -8

Determinants Structure Very Short Answer Type Questions

Question 1.
Find the value of \(\begin{vmatrix} 2\quad & 20 \\ 1 & 6 \end{vmatrix}\)?
Answer:
-8.

Question 2.
Find the value of y if \(\begin{vmatrix} -6\quad & 2 \\ 3 & y \end{vmatrix}\) = 24?
Answer:
-5.

Question 3.
Find x if \(\begin{vmatrix} 2\quad & 4 \\ x & 0 \end{vmatrix}\) = -16?
Answer:
4.

Question 4.
If \(\begin{vmatrix} a\quad & b \\ c & d \end{vmatrix}\) = 5, then find the value of \(\begin{vmatrix} 3a\quad & 3b \\ 3c & 3d \end{vmatrix}\)?
Answer:
45.

Question 5.
If \(\begin{vmatrix} a\quad & ω \\ ω & -ω \end{vmatrix}\) = 1, then value of a will be?
Answer:
1.

Question 6.
If \(\begin{vmatrix} 3\quad & m \\ 4 & 5 \end{vmatrix}\) = 3, then find the value of m?
Answer:
3.

Question 7.
If \(\begin{vmatrix} 2\quad & x \\ 4 & 9 \end{vmatrix}\) = 30, then find the value of x?
Answer:
– 3.

Question 8.
If \(\begin{vmatrix} 4\quad & -3 \\ m & m \end{vmatrix}\) = 21, then find the value of x?
Answer:
3.

Question 9.
If \(\begin{vmatrix} 2\quad & 4 \\ 3 & x \end{vmatrix}\) = 0, then find the value of x?
Answer:
6.

Question 10.
If \(\begin{vmatrix} 4\quad & -3 \\ -m & m \end{vmatrix}\), then find the value of m?
Answer:
21.

Question 11.
If \(\begin{vmatrix} -6\quad & 2 \\ 3 & m \end{vmatrix}\) = 12, then find the value of m?
An.swer:
-3.

Question 12.
If \(\begin{vmatrix} 4\quad & -6 \\ -2 & x \end{vmatrix}\) = 20, then find the value of x?
Answer:
8.

Question 13.
If ω, ω² are the cube root of unity, then find the value of \(\begin{vmatrix} 1\quad & \omega \\ \omega & -\omega \end{vmatrix}\)?
Answer:
1.

Question 14.
Find the value of \(\left|\begin{array}{ccc}
{224} & {777} & {32} \\
{735} & {888} & {105} \\
{812} & {999} & {116}
\end{array}\right|\)?
Answer:
0.

Question 15.
If \(\begin{vmatrix} x\quad & 4 \\ 3 & 3 \end{vmatrix}\) = 0 then find the value of x?
Answer:
4.

Question 16.
If \(\begin{vmatrix} 2+3i\quad & 4 \\ 1 & 2-3i \end{vmatrix}\) find its value?
Answer:
9.

Question 17.
In determinants \(\begin{vmatrix} 2\quad & -3 \\ 1 & -2 \end{vmatrix}\) then find the co – factor of element – 3?
Answer:
1.

Question 18.
If \(\begin{vmatrix} 3\quad & -2 \\ -4 & x \end{vmatrix}\) = 16, then find the value of x?
Answer:
8.

Question 19.
The value of \(\begin{vmatrix} 1\quad & log_{ b }a \\ log_{ a }b & 1 \end{vmatrix}\)?
Answer:
0.

Question 20.
Find the value of 2 from determinant \(\begin{vmatrix} 1\quad & 3 \\ 2 & 4 \end{vmatrix}\)?
Answer:
3.

Question 21.
Find the value of \(\begin{vmatrix} 2+5i\quad & 5 \\ 4 & 2-5i \end{vmatrix}\)?
Answer:
9.

Question 22.
Find the value of \(\begin{vmatrix} cot x\quad & cosec x \\ cosec x & cot x \end{vmatrix}\)?
Answer:
-1.

Question 23.
Find the value of \(\begin{vmatrix} cos70^{ \circ }\quad & sin20^{ \circ } \\ sin70^{ \circ } & cos20^{ \circ } \end{vmatrix}\)?
Answer:
0.

Determinants Long Answer Type Questions – I

Question 1.
Prove that:
\(\left|\begin{array}{ccc}
{a+b+2 c} & {a} & {b} \\
{c} & {b+c+2 a} & {b} \\
{c} & {a} & {c+a+2 b}
\end{array}\right|\) = 2 (a + b + c)³?
Solution:
Let ∆ =

= 2 (a + b + c) . 1. [(a + b + c)² – 0]
= 2 (a + b + c)³. Proved.

Question 2.
Prove that:
\(\left|\begin{array}{ccc}
{a^{2}+1} & {a b} & {a c} \\
{a b} & {b^{2}+1} & {b c} \\
{a c} & {b c} & {c^{2}+1}
\end{array}\right|\) = 1 + a² + b² + c²? (NCERT, CBSE 2016)
Solution:
Let ∆ =


= (1 + a² + b² + c²) . 1 \(\begin{vmatrix} 1\quad & 0 \\ 0 & 1 \end{vmatrix}\)
∆ = (1 + a² + b² + c²). Proved.

Question 3.
Prove that \(\left|\begin{array}{ccc}
{a^{2}} & {b c} & {a c+c^{2}} \\
{a^{2}+a b} & {b^{2}} & {a c} \\
{a b} & {b^{2}+b c} & {c^{2}}
\end{array}\right|\) = 4a² b² c² ?(NCERT, CBSE 2015)
Solution:
Let ∆ =

= abc.2c. \(\begin{vmatrix} a-b\quad & -a \\ a+b & -a \end{vmatrix}\)
= 2abc² [-a(a – b) + a (a + b)]
= 2²bc²[-a + b + a + b]
= 2a²bc².2b = 4a²b²c². Proved.

Question 4.
Solve the following determinant:
\(\left|\begin{array}{ccc}
{x+1} & {3} & {5} \\
{2} & {x+2} & {5} \\
{2} & {3} & {x+4}
\end{array}\right|\) = 0?
Solution:


⇒ (x + 9) × 1 \(\begin{vmatrix} x-1\quad & 0 \\ 0 & x-1 \end{vmatrix}\) = 0
⇒ (x + 9) (x – 1)² = 0
∴ (x + 9) = 0 or (x – 1)² = 0
⇒ x = -9 or x = 1, 1.

Question 5.
Prove that:
\(\left|\begin{array}{ccc}
{\alpha} & {\beta} & {\lambda} \\
{\alpha^{2}} & {\beta^{2}} & {\lambda^{2}} \\
{\beta+\lambda} & {\lambda+\alpha} & {\alpha+\beta}
\end{array}\right|\) = (α – β) (β – λ) (λ – α) (α + β + λ)?
Solution:
Let ∆ =

⇒ ∆ = (α + β + λ) (α – β) (β – λ) (β + λ – α – β)
⇒ ∆ = (α – β) (β – λ) (λ – α) (α + β + λ)
= R.H.S. Proved.

Question 6.
Prove that:
\(\left|\begin{array}{ccc}
{1+a} & {1} & {1} \\
{1} & {1+b} & {1} \\
{1} & {1} & {1+c}
\end{array}\right|\) = (abc) (1 + \(\frac{1}{a}\) + \(\frac{1}{b}\) + \(\frac{1}{c}\) )? (NCERT; CBSE 2012, 14)
Solution:
Let



R.H.S. Proved.

Question 7.
Prove that:
\(\left|\begin{array}{ccc}
{-a^{2}} & {a b} & {a c} \\
{a b} & {-b^{2}} & {b c} \\
{a c} & {b c} & {-c^{2}}
\end{array}\right|\) = 4a²b²
c²?
Solution:

= a²b²c²[2 (1 + 1)]
= a²b²c².4 = 4a²b²c². Proved.

Question 8.
Solve the equation:
\(\left|\begin{array}{ccc}
{3 x-8} & {3} & {3} \\
{3} & {3 x-8} & {3} \\
{3} & {3} & {3 x-8}
\end{array}\right|\) = 0?
Solution:

⇒ (3x – 2) (3x – 11) [1. (1 – 0)] = 0
⇒ (3x – 2) (3x – 11) = 0
∴x = \(\frac{2}{3}\), \(\frac{11}{3}\).

Question 9.
Solve the equation \(\left|\begin{array}{lll}
{a+x} & {a-x} & {a-x} \\
{a-x} & {a+x} & {a-x} \\
{a-x} & {a-x} & {a+x}
\end{array}\right|\) = 0?
Solution:

⇒ (3a – x).1.(4x² – 0) = 0
⇒ 3a – x = 0, 4x² = 0
⇒ x = 3a, 0.

Question 10.
Prove that:
\(\left|\begin{array}{ccc}
{a} & {a+b} & {a+b+c} \\
{2 a} & {3 a+2 b} & {4 a+3 b+2 c} \\
{3 a} & {6 a+3 b} & {10 a+6 b+3 c}
\end{array}\right|\) = 0?
Solution:
Let ∆ =


= a² [7a + 3b – 6a – 3b]
= a²(a)
= a³. Proved.

Question 11.
Prove that:
\(\left|\begin{array}{ccc}
{x} & {x+y} & {x+2 y} \\
{x+2 y} & {x} & {x+y} \\
{x+y} & {x+2 y} & {x}
\end{array}\right|\) = 9y² (x + y)? (CBSE 2017)
Solution:
Let ∆


⇒ ∆ = 9y(x + y) [-x – y + x+ 2y]
⇒ ∆ = 9y² (x + y). Proved.

Question 12.
Prove that:
\(\left|\begin{array}{ccc}
{x+4} & {2 x} & {2 x} \\
{2 x} & {x+4} & {2 x} \\
{2 x} & {2 x} & {x+4}
\end{array}\right|\) = (5x + 4) (4 – x)²? (NCERT)
Solution:
Let



= (5x + 4) (x – 4) (2x – x – 4)
= (5x + 4) (x – 4) (x – 4)
= (5x + 4) (x – 4)². [∵(a – b)² = (b – a)²]
⇒ ∆ = (5x + 4) (4 – x)². Proved.

Question 13.
Prove that:
\(\left|\begin{array}{ccc}
{x} & {y} & {x+y} \\
{y} & {x+y} & {x} \\
{x+y} & {x} & {y}
\end{array}\right|\) = -2(x³ + y³). (NCERT)
Solution:
Let ∆ =


= 2 (x + y) (x² – xy + y²)
⇒ ∆ = – 2(x² + y²). Proved.

Question 14.
Prove that:
\(\left|\begin{array}{ccc}
{a^{2}+2 a} & {2 a+1} & {1} \\
{2 a+1} & {a+2} & {1} \\
{3} & {3} & {1}
\end{array}\right|\) = (a – 1)³? (CBSE 2017)
Solution:
Let ∆ =

⇒ ∆ = (a – 1)² (a + 1 – 2)
⇒ ∆ = (a – 1)² (a – 1)
⇒ ∆ = (a – 1)³. Proved.

Question 15.
Prove that:
\(\left|\begin{array}{ccc}
{1} & {1} & {1+3 x} \\
{1+3 y} & {1} & {1} \\
{1} & {1+3 z} & {1}
\end{array}\right|\) = 9(3 xyz + xy + yz + zx)? (CBSE 2018)
Solution:
Let ∆ =


= 9[x{(1 + y) (1 + 3z) – (1 + z)} – z{(x – y) – 0}]
= 9[x{1 + y + 3z + 3yz – 1 – z} – zx + zy]
= 9 [xy + 3xz + 3xyz – xz – zx + zy]
= 9 [3xyz + xy + yz + zx]. Proved.

MP Board Class 12 Maths Important Questions

In this article, we will share MP Board Class 12th Hindi Solutions पद्य Chapter 1 भक्ति काव्य Pdf, These solutions are solved subject experts from the latest edition books.

MP Board Class 12th Hindi Swati Solutions पद्य Chapter 1 भक्ति काव्य

भक्ति काव्य अभ्यास

भक्ति काव्य अति लघु उत्तरीय प्रश्न

प्रश्न 1.
मीरा की भक्ति किस भाव की थी? (2014)
उत्तर:
मीरा की भक्ति दाम्पत्य (प्रेम) भाव की थी। उनके आराध्य श्रीकृष्ण हैं।

प्रश्न 2.
मीराबाई कैसा वेश रखना चाहती हैं? (2015)
उत्तर:
मीराबाई अपने स्वामी श्रीकृष्ण के लिए बैरागिन का वेश धारण करना चाहती हैं। इसके अलावा वह वही वेश धारण करना चाहती हैं, जिससे श्रीकृष्ण प्रसन्न हों।

प्रश्न 3.
‘रामचन्द्रिका’ के रचयिता कौन हैं?
उत्तर:
‘रामचन्द्रिका’ के रचयिता केशवदास हैं।

प्रश्न 4.
गजमुख का मुख कौन देखता है? (2010, 15)
उत्तर:
गजमुख का मुख दसमुख (रावण) देखता है।

भक्ति काव्य लघु उत्तरीय प्रश्न

प्रश्न 1.
मीरा के अनुसार देह का गर्व क्यों नहीं करना चाहिए? (2014)
उत्तर:
मीरा के अनुसार देह का गर्व नहीं करना चाहिए क्योंकि यह शरीर मृत्यु के बाद मिट्टी में मिल जाता है। यह शरीर पाँच तत्वों से निर्मित बताया जाता है-आकाश, वायु, पृथ्वी, अग्नि और जल। यह शरीर मृत्यु के पश्चात् इन्हीं तत्वों में मिल जाता है।

प्रश्न 2.
मीरा को हरि से मिलने में क्या-क्या कठिनाइयाँ हैं? (2010, 17)
उत्तर:
मीरा को हरि से मिलने में निम्नलिखित कठिनाइयाँ हैं-

1. मीरा के चारों मार्ग (कर्म, भक्ति, ज्ञान और वैराग्य) बन्द हैं अर्थात् इनमें से कोई भी मार्ग मीरा के लिए खुला नहीं है।
2. हरि का महल इतना ऊँचा है कि मीरा वहाँ तक चढ़ने में असमर्थ है।
3. मीरा का मार्ग इतना सँकरा है कि चलते हुए डगमगाती है अर्थात् गिरने का डर लगा रहता है।
4. विधाता ने मीरा का गाँव हरि से बहुत दूर बना दिया है।

प्रश्न 3.
भगवान गणेश भक्तों की विपत्तियों को किस प्रकार हर लेते हैं?
उत्तर:
जिस प्रकार एक बालक कमल की डंडी को आसानी से तोड़ देता है उसी प्रकार गणेश जी भक्त के विघ्नों को हर लेते हैं। जिस प्रकार कमलिनी कीचड़ से अलग रहती है उसी प्रकार गणेश जी के भक्त संसार के विघ्नों से दूर रहते हैं। शंकर जी जैसे चन्द्रमा को निष्कलंक कर अपने शीश पर धारण करते हैं उसी प्रकार गणेश जी अपने भक्त को निष्कलंक कर देते हैं।

प्रश्न 4.
माँ सरस्वती की वन्दना कौन-कौन करता है? (2015, 16)
उत्तर:
माँ सरस्वती की वन्दना देवगण, ऋषिगण,श्रेष्ठ तपस्वी, भूत, भविष्य और वर्तमान को जानने वाले,उनके पति ब्रह्मा जी,शंकर जी और कार्तिकेय करते हैं।

भक्ति काव्य दीर्घ उत्तरीय प्रश्न

प्रश्न 1.
“मीरा का सम्पूर्ण काव्य भाव-विह्वलता के गुणों से पूरित है।” सिद्ध कीजिए।
उत्तर:
मीरा के काव्य में भाव-विह्वलता’ कूट-कूटकर भरी है।
(i) विरह-वेदना :
मीराबाई भगवान कृष्ण के प्रेम की दीवानी थीं। उन्होंने आँसुओं के जल से सींच-सींच कर प्रेम की बेल बोई थी। मीरा ने अपने प्रियतम (श्रीकृष्ण) के विरह में जो कुछ लिखा उसकी तुलना कहीं पर भी नहीं की जा सकती।

(ii) रस और माधुर्य भाव :
मीरा के साहित्य में माधुर्य भाव को बहुत ऊँचा स्थान प्राप्त है। उनकी रचनाओं में माधुर्य भाव प्रधान है। उसमें शान्त रस और श्रृंगार रस की अभिव्यक्ति है।

(iii) रहस्यवाद :
मीरा के अधिकतर पदों में उनका रहस्यवाद स्पष्ट रूप से परिलक्षित होता है। इस रहस्यवाद में प्रियतम के प्रति उत्सुकता, मिलन और वियोग के सजीव चित्र हैं।

प्रश्न 2.
मीरा अपने मन को ईश्वर के चरण कमलों में ही क्यों लीन रखना चाहती हैं?
उत्तर:
मीरा श्रीकृष्ण के चरण-कमलों में ही अपने मन को लगाना चाहती हैं। जिस किसी को उनके चरण कमलों के अपनी भृकुटि के मध्य दर्शन हो गए वह संसार से ऊपर उठ गया अर्थात् उसका उद्धार हो गया। तीर्थ एवं व्रत करने, काशी में रहकर मृत्यु प्राप्त करने की इच्छा करने से कुछ नहीं होता और न ही संसार को त्याग करके संन्यासी होने से कुछ होगा। मीरा के अनुसार तो श्रीकृष्ण के चरणों में ध्यान लगाने से ही जीवन सफल होगा। मीरा के प्रभु ही जन्म-मरण के बन्धन को काटने वाले हैं। इसलिए वह श्रीकृष्ण के चरण-कमलों में ही अपने मन को लगाना चाहती हैं।

प्रश्न 3.
‘कठिन क्रूर अक्रूर आयो’ पंक्ति का आशय स्पष्ट कीजिए।
उत्तर:
मथुरा का राजा कंस श्रीकृष्ण का वध करना चाहता था इसलिए उसने नन्दबाबा के मित्र अक्रूर को श्रीकृष्ण को मथुरा लाने के लिए भेजा। उसे विश्वास था कि अक्रूर के साथ नन्दबाबा कृष्ण को मथुरा अवश्य भेज देंगे। अत: वह रथ लेकर श्रीकृष्ण को लेने आया था। अक्रूर का अर्थ यद्यपि दयालु होता है, लेकिन वह कठोर बनकर इस कार्य को करने आया था। श्रीकृष्ण को मथुरा ले जाकर उसने क्रूरता दिखाई है।

प्रश्न 4.
‘बानी जगरानी की उदारता’ का बखान करना क्यों सम्भव नहीं है?
उत्तर:
जगत वन्दनीया सरस्वती की उदारता (दया) का वर्णन संसार में कोई नहीं कर सकता है। देव, सिद्ध मुनि,श्रेष्ठ तपस्वी सभी उनकी उदारता का वर्णन करते-करते थक गए पर उनकी उदारता का वर्णन नहीं कर सके। भूत, भविष्य और वर्तमान के ज्ञाता भी इस बारे में असमर्थ रहे। उनके पति ब्रह्मा जी, पुत्र शिवजी और नाती कार्तिकेय ने भी उनकी उदारता का बखान किया, पर हर बार उन्हें उनमें कुछ नवीनता ही दिखाई दी।

प्रश्न 5.
श्रीराम वन्दना में राम के नाम की क्या महिमा बताई गई है?
उत्तर:
श्रीराम परिपूर्ण परमात्मा हैं। ये पुराण पुरुषोत्तम हैं। भक्त उनका दर्शन पाकर भी उनको नहीं समझ पाता है क्योंकि वेदों में ‘न इति’, ‘न इति’ कहकर उस भेद को वहीं छोड़ दिया है। केशवदास कवि श्रीराम नाम का निरन्तर जाप करते हैं इसलिए उन्हें जन्म-मरण से डर नहीं लगता अर्थात् जन्म-मरण के बन्धन से वह छूट जाएँगे। श्रीराम का रूप अणिमा सिद्धि (सूक्ष्मता) प्रदान करता है,उनका गुण गरिमा सिद्धि प्रदान करता है,उनकी भक्ति महिमा नामक सिद्धि प्रदान करती है और उनका पावन नाम मुक्ति प्रदान करता है।

प्रश्न 6.
केशवदास की काव्यगत विशेषताएँ लिखिए।
उत्तर:
केशव की भाषा के दो रूप हैं-संस्कृतनिष्ठ भाषा और हिन्दी में प्रचलित शब्दों को लिए हुए हिन्दी भाषा। संस्कृत के अतिरिक्त इन्होंने बुन्देलखण्डी,अवधी और अरबी-फारसी के शब्दों का भी पर्याप्त प्रयोग किया है। केशव के काव्य में अलंकारों का प्रचुर मात्रा में प्रयोग हुआ है। इन्होंने जितनी अधिक संख्या में ‘छन्दों का प्रयोग किया है,उतना आज तक किसी भी हिन्दी कवि ने नहीं किया है।

केशव हिन्दी साहित्य के प्रथम एवं सर्वाधिक प्रौढ़ आचार्य हैं। काव्यशास्त्र का जितना व्यापक और प्रौढ़ विवेचन इन्होंने किया है उतना परवर्ती कोई भी आचार्य नहीं कर सका है। केशव की रचनाओं में परिस्थिति और क्रियान्विति के आधार पर सभी रसों की निष्पत्ति हुई है। इन्होंने दोहा, कवित्त, सवैया, चौपाई, सोरठा आदि का प्रयोग किया है। केशव हिन्दी के प्रमुख आचार्य हैं। उच्चकोटि के रसिक होने पर भी वे पूरे आस्तिक थे।

प्रश्न 7.
निम्नलिखित पंक्तियों की सप्रसंग व्याख्या कीजिए
(अ) बाल्हा मैं बैरागिण………..साधाँ संग रहूँगी हो॥
(ब) भज मन चरण………..जनम की फाँसी।
(स) बालक मृणालनि……….गजमुख-मुख को।
(द) भावी भूत वर्तमान…………..नई-नई॥
उत्तर:
(अ) सन्दर्भ :
प्रस्तुत पद्यांश हमारी पाठ्य-पुस्तक के ‘भक्ति काव्य’ के शीर्षक ‘मीरा के पद’ से अवतरित है। इसकी रचयिता मीराबाई हैं।

प्रसंग :
प्रस्तुत पद्यांश में भक्त कवयित्री मीरा ने अपने स्वामी श्रीकृष्ण को प्राप्त करने के लिए वैरागिण होने और शील, सन्तोष आदि गुणों को धारण करके अपनी अनन्य भक्ति का उल्लेख किया है।

व्याख्या :
मीराबाई कहती हैं कि हे स्वामी मैं बैरागिन (संन्यासी) होकर संसार को त्याग दूंगी और जिस भेष (स्वरूप) से मेरे स्वामी कृष्ण प्रसन्न होंगे वैसा ही वेष मैं धारण करूँगी। अपने हृदय में शील और सन्तोष धारण करके सब लोगों के साथ समान व्यवहार करूँगी अर्थात् समता की राह पर चलूँगी। जिसका नाम निरंजन (पवित्र) है,उसी प्रभु का ध्यान मैं हमेशा अपने हृदय में धारण करूंगी। मैं अपने शरीर रूपी वस्त्र को गुरु के ज्ञान रूपी रंग से रंग लूँगी और मन रूपी मुद्रिका (अंगूठी) पहनूंगी। मैं प्रेम से प्रभु के गुणों का वर्णन करूँगी और उन्हीं के चरणों में लिपट कर पड़ी रहूँगी अर्थात् श्रीकृष्ण के चरणों का आश्रय ग्रहण करूँगी। अपने इस शरीर को तन्तु वाद्य बनाकर अपनी जिह्वा से राम नाम को रटती रहूँगी। मेरा शरीर और जिह्वा श्रीकृष्ण के नाम लेने के काम में ही आवे मीरा कहती हैं कि मेरे प्रभु गिरधर गोपाल हैं। मैं उन्हें प्रसन्न करने के लिए और उनका गुणगान करने के लिए साधुओं के साथ रहकर अपना जीवन सफल बनाऊँगी।

(ब) सन्दर्भ :
पूर्ववत्।

प्रसंग :
प्रस्तुत पद में मीरा श्रीकृष्ण के चरण-कमलों का भजन करने के लिए अपने आपको प्रस्तुत करने के लिए प्रेरित कर रही है।

व्याख्या :
मीराबाई कहती है कि हे मन ! तू श्रीकृष्ण के चरण-कमलों का भजन कर। जिसने भी गिरधर के चरणों के दर्शन अपनी भृकुटि के बीच में कर लिए उसको तो संसार फीका लगता है। जब तक प्रभु श्रीकृष्ण के चरणों के दर्शन नहीं हुए तो तीर्थ करने,व्रत करने और काशी में शरीर त्यागने से भी कोई लाभ नहीं होता। मनुष्य को इस शरीर का गर्व नहीं करना चाहिए क्योंकि यह शरीर एक दिन मिट्टी में मिल जाएगा। इस संसार का आनन्द तो हार जीत की शर्त के समान है जो शाम होते ही उठ जाता है। जैसे बाजार की चहल-पहल दिन में ही रहती है,शाम होते ही समाप्त हो जाती है। गेरुए वस्त्र धारण कर और घर त्याग कर संन्यासी होकर यदि ईश्वर को प्राप्त करने की युक्ति नहीं जानी तो फिर यह सब व्यर्थ है। फिर दोबारा संसार के जन्म-मरण के चक्कर में फंसना पड़ता है। मीरा के प्रभु तो गिरधर गोपाल हैं,वही उनके जन्म-मरण की रस्सी को काटकर उसे जन्म-मरण के बन्धन से मुक्त करेंगे।

(स) सन्दर्भ :
प्रस्तुत पद्यांश केशवदास द्वारा रचित ‘वन्दना’ के शीर्षक ‘गणेश वन्दना’ से उद्धृत है।

प्रसंग :
यहाँ पर कवि केशवदास ने विघ्नहारी गणेश जी की वन्दना की है।

व्याख्या :
कवि कहता है कि जैसे बालक कमल की डाल को किसी भी समय आसानी से तोड़ डालता है। उसी प्रकार गणेश असमय में आए विकराल दुःख को भी दूर कर देते हैं। जैसे कमल के पत्ते पानी में फैली कीचड़ को नीचे भेज देते हैं और स्वयं स्वच्छ होकर ऊपर रहते हैं, उसी प्रकार गणेश हर विपत्ति को दूर कर देते हैं। जिस प्रकार चन्द्रमा को निष्कलंक कर शिवजी ने अपने शीश पर धारण किया उसी प्रकार गणेश जी अपने दास को कलंक रहित कर पवित्र कर देते हैं। गणेश जी बन्धन से अपने दास को मुक्त कर देते हैं। रावण भी गणेश जी के मुख की तरफ देखकर अपनी बाधाओं को दूर करने की आशा रखता है।

(द) सन्दर्भ :
प्रस्तुत पद ‘केशवदास’ द्वारा रचित ‘वन्दना’ के शीर्षक ‘सरस्वती वन्दना’ से उद्धृत है।

प्रसंग :
यहाँ पर कवि ने सरस्वती की उदारता का वर्णन किया है।

व्याख्या :
कवि कहता है कि जगत में पूज्य सरस्वती की उदारता का वर्णन नहीं किया जा सकता। संसार में ऐसी श्रेष्ठ बुद्धि किसी में नहीं है जो उनकी उदारता का वर्णन कर सके देवता, सिद्ध मुनि,श्रेष्ठ तपस्वी सभी कह-कह कर हार गये, लेकिन कोई भी उनकी उदारता का वर्णन नहीं कर सका। भूत, वर्तमान और भविष्य बताने वाले सभी ने वर्णन किया, लेकिन केशवदास कहते हैं कि कोई भी सरस्वती की दया (उदारता) का वर्णन नहीं कर सका। उनके पति ब्रह्माजी ने, पुत्र शंकर जी ने और उनके नाती कार्तिकेय ने भी सरस्वती की उदारता का वर्णन किया लेकिन वे भी उनकी उदारता का पार नहीं पा सके। (शंकर जी का जन्म ब्रह्माजी की भौंहों से होने के कारण उनको पुत्र कहा गया है और कार्तिकेय शिवजी के पुत्र होने के नाते सरस्वती के नाती हुए।)

भक्ति काव्य काव्य सौन्दर्य

प्रश्न 1.
निम्नलिखित शब्दों के हिन्दी मानक रूप लिखिए।
उत्तर:

प्रश्न 2.
‘म्हारों’, ‘सूँ’ आदि राजस्थानी शब्दों का प्रयोग मीरा के पदों में हुआ है। ऐसे ही अन्य शब्दों का चयन कर उनका अर्थ लिखिए।
उत्तर:

प्रश्न 3.
निम्नलिखित शब्दों के पर्यायवाची शब्द लिखिए।
उत्तर:
रसना – जिह्वा,जीभ,रसना।
पथ – मार्ग,पथ,राह।
गगन – नभ, आकाश, व्योम।
देह – तन,बदन,शरीर।
जगत – संसार,जग, दुनिया।
मुख – मुँह, वदन, आनन।
भव – जन्म,उत्पत्ति,संसार।

प्रश्न 4.
निम्नलिखित पंक्तियों में अलंकार पहचान कर लिखिए
(क) ‘सोच सोच पग धरूँ जतन से, बार-बार डिग जाइ।’
(ख) भज मन चरण कँवल अविनासी।’
(ग) ‘बालक मृणालनि ज्यों तोरि डारै सब काल।’
(घ) विपति हरत हठि पद्मिनी के पात सम।’
(ङ) पूरण पुराण अरु पुरुष पुराण परिपूरण ‘
(च) ‘दरसन देत जिन्हें दरसन सुमुझै न।’
उत्तर:
(क) अनुप्रास, पुनरुक्तिप्रकाश अलंकार
(ख) रूपक अलंकार
(ग) उत्प्रेक्षा अलंकार
(घ) उपमा अलंकार
(ङ) अनुप्रास अलंकार
(च) यमक अलंकार।

प्रश्न 5.
रस की परिभाषा दीजिए।
उत्तर:
विभाव, अनुभाव और संचारी भावों की सहायता से पुष्ट होकर स्थायी भाव जब परिपक्व अवस्था को प्राप्त होता है, तो रस कहलाता है।

प्रश्न 6.
‘केशवदास’ की संकलित वन्दनाओं में कौन-सा रस है?
उत्तर:
शान्त रस।

प्रश्न 7.
निम्नलिखित पंक्तियों में निहित रस तथा उसके विभिन्न अंगों को समझाइए-
बानी जगरानी की उदारता बखानी जाइ,
ऐसी मति उदित उदार कौन की भई।
देवता प्रसिद्ध सिद्ध रिषिराज तपबृद्ध,
कहि कहि हारे सब कहि न काहू लई।
उत्तर:
उक्त पंक्तियों में शान्त रस है। इसका स्थायी भाव निर्वेद है। यहाँ आलम्बन विभाव सरस्वती जी हैं तथा आश्रय भक्त, गुणों का गान, अनुभव, धृति, मति आदि संचारी भाव हैं।

मीरा के पद भाव सारांश

‘मीरा के पद’ नामक कविता की रचयिता ‘मीराबाई हैं। उन्होंने इन पदों में श्रीकृष्ण को पति रूप में स्वीकार कर प्रेमभाव से समन्वित भक्ति को ही अपनी साधना का आधार बनाया।

भक्तिकाल में भक्ति का लक्ष्य ईश्वर प्राप्ति के साथ-साथ समाज कल्याण की भावना की परिपुष्टि भी रही है। संकलित पदों में मीरा का दृढ़ संकल्प,उनकी सत्संग की प्रबल-चाह, उनकी भक्ति-यात्रा में आने वाले विघ्न, उन पर सद्गुरु की असीम कृपा तथा कृष्ण-कृपा की एकनिष्ठ आकांक्षा का उल्लेख है। मीरा के अनुसार, वह अपने प्रभु को प्रसन्न करने के लिए कोई भी वेष धारण कर सकती हैं। पिय से मिलने में कठिनाई है। संसार के काम, क्रोध, लोभ, मोह आदि बाधाएँ प्रभु के पास जाने से रोकते हैं। मीरा के सतगुरु ने गिरधर नागर को ही उनका प्रभु बताया है। लाज के कारण मीरा कृष्ण के साथ मथुरा नहीं जा सकीं। श्याम के बिछड़ने से हृदय में पीड़ा हुई। संसार से उद्धार पाने के लिए देह का गर्व छोड़कर श्रीकृष्ण के चरण कमलों की वन्दना करनी चाहिए। श्रीकृष्ण से मीराबाई की यही प्रार्थना है कि वे उनका जन्म-मरण के बन्धन से उद्धार कर दें।’

मीरा के पद संदर्भ-प्रसंग सहित व्याख्या

(1) बाल्हा मैं बैरागिण हूँगी हो।
जो-जो भेष म्हाँरो साहिब रीझै, सोइ-सोइ भेष धरूँगी, हो।
सील सन्तोष धरूँ घट भीतर, समता पकड़ रहूँगी, हो।
जाको नाम निरजण कहिये, ताको ध्यान धरूँगी, हो।
गुरु ज्ञान रंगू, तन कपड़ा, मन मुद्रा पेरूँगी, हो।
प्रेम प्रीत सँ हरि गुण गाऊँ चरणन लिपट रहँगी, हो।
या तन की मैं करूँ कीगरी, रसना नाम रदूँगी, हो।
मीरा कहे प्रभु गिरधर नागर, साधाँ संग रहूँगी, हो।

शब्दार्थ :
बाल्हा = स्वामी; म्हाँरो = मेरे; साहिब = आराध्य (कृष्ण); सील = शील, लज्जा; घट = हृदय; समता = बराबरी; निरजण = निरंजन (दोष रहित); या तन = यह शरीर; कीगरी = तंतु वाद्य; रसना = जिह्वा (जीभ); गिरधर नागर = गिरिराज पर्वत को धारण करने वाले श्रीकृष्ण; साधौँ = साधुओं के।

सन्दर्भ :
प्रस्तुत पद्यांश हमारी पाठ्य-पुस्तक के ‘भक्ति काव्य’ के शीर्षक ‘मीरा के पद’ से अवतरित है। इसकी रचयिता मीराबाई हैं।

प्रसंग :
प्रस्तुत पद्यांश में भक्त कवयित्री मीरा ने अपने स्वामी श्रीकृष्ण को प्राप्त करने के लिए वैरागिण होने और शील, सन्तोष आदि गुणों को धारण करके अपनी अनन्य भक्ति का उल्लेख किया है।

व्याख्या :
मीराबाई कहती हैं कि हे स्वामी मैं बैरागिन (संन्यासी) होकर संसार को त्याग दूंगी और जिस भेष (स्वरूप) से मेरे स्वामी कृष्ण प्रसन्न होंगे वैसा ही वेष मैं धारण करूँगी। अपने हृदय में शील और सन्तोष धारण करके सब लोगों के साथ समान व्यवहार करूँगी अर्थात् समता की राह पर चलूँगी। जिसका नाम निरंजन (पवित्र) है,उसी प्रभु का ध्यान मैं हमेशा अपने हृदय में धारण करूंगी। मैं अपने शरीर रूपी वस्त्र को गुरु के ज्ञान रूपी रंग से रंग लूँगी और मन रूपी मुद्रिका (अंगूठी) पहनूंगी। मैं प्रेम से प्रभु के गुणों का वर्णन करूँगी और उन्हीं के चरणों में लिपट कर पड़ी रहूँगी अर्थात् श्रीकृष्ण के चरणों का आश्रय ग्रहण करूँगी। अपने इस शरीर को तन्तु वाद्य बनाकर अपनी जिह्वा से राम नाम को रटती रहूँगी। मेरा शरीर और जिह्वा श्रीकृष्ण के नाम लेने के काम में ही आवे मीरा कहती हैं कि मेरे प्रभु गिरधर गोपाल हैं। मैं उन्हें प्रसन्न करने के लिए और उनका गुणगान करने के लिए साधुओं के साथ रहकर अपना जीवन सफल बनाऊँगी।

काव्य सौन्दर्य :

1. भगवान श्रीकृष्ण के प्रति मीरा की भक्ति भावना और श्रद्धा व्यक्त हुई है।
2. अनुप्रास, रूपक अलंकार का प्रयोग हुआ है।
3. दास्य भाव की प्रधानता है।
4. राजस्थानी मिश्रित ब्रजभाषा का प्रयोग हुआ है।
5. शान्त रस का प्रयोग।

(2) गली तो चारों बन्द हुई, मैं हरि से मिलूँ कैसे जाइ।
ऊँची नीची राह रपटीली, पाँव नहीं ठहराइ।
सोच-सोच पग धरूँ जतन से, बार-बार डिग जाइ।
ऊँचा नीचा महल पिया का, हमसे चढ्या न जाइ।
पिया दूर पथ म्हारो झीणों, सूरत झकोला खाइ।
कोस कोस पर पहरा बैठ्या, पैड़ पैड़ बटमार।
हे विधना कैसी रच दीन्हीं, दूर बस्यौ म्हाँरो गाँव।
मीरा के प्रभु गिरधर नागर, सतगुरु दई बताय।
जुगन जुगन से बिछड़ी मीरा, घर में लीन्हीं लाय॥

शब्दार्थ :
गली = रास्ता; राह = मार्ग; रपटीली = चिकनी;जतन से = प्रयास से; डिग जाय = फिसल जाता है; झीणों = पतला, सँकरा; सूरत = शरीर;झकोला = हिल जाना; कोस = दो मील की दूरी;पैड़ = जगह; बटमार = राह का कर लेने वाले विधना = विधाता; बस्यौ = स्थित; म्हाँरो = मेरा; जुगन-जुगन = युग-युग से (युग चार होते हैं-सतयुग, त्रेता, द्वापर, कलयुग); बिछड़ी = बिछड़ गई है; लाय = अग्नि।

सन्दर्भ :
पूर्ववत्।

प्रसंग :
प्रस्तुत पद्यांश में मीराबाई ने अपने स्वामी श्रीकृष्ण से मिलने में संसार में आने वाली कठिनाइयों का वर्णन किया है।

व्याख्या :
मीराबाई कहती हैं कि प्रभु से मिलने के चारों रास्ते (कर्म, भक्ति,ज्ञान, वैराग्य) बन्द हैं तो फिर वह कैसे प्रभु से मिलें अर्थात् न तो कर्म अच्छा है,न भक्ति है,न ज्ञान है और न ही वैराग्य है जिससे कि प्रभु के पास जाया जा सकता है। उनसे मिलने का मार्ग ऊँचा-नीचा और रपटीला है जिस पर पैर ठहर नहीं पाते हैं अर्थात् चलने के लिए खड़े होते ही गिर जाते हैं। यहाँ पर प्रभु-मार्ग में आने वाली कठिनाइयों की ओर संकेत किया गया है। मन में बार-बार सोच-विचार कर आगे बढ़ने का प्रयत्न करती हूँ फिर भी पैर आगे नहीं बढ़ पाते। मेरे प्रिय श्रीकृष्ण का महल बहुत ऊँचा है जिसमें चढ़ने में मैं अपने को असमर्थ पाती हूँ। मेरे प्रियतम दूर बसे हैं और उन्हें प्राप्त करने का मार्ग बहुत सँकरा है जिस पर चलते ही शरीर डगमगाता है और नीचे गिरने का भय बना रहता है। हर कोस पर पहरेदार बैठे हैं और जगह-जगह पर कर वसूल करने वाले (लूटने वाले लुटेरे-काम, क्रोध,लोभ,मोह) बैठे हुए हैं जो हमारे आगे बढ़ने में बाधा उत्पन्न करते हैं। विधाता ने कुछ ऐसा नियम बनाया है जिसके कारण मेरा गाँव मेरे पिया से बहुत दूर है। मीरा को उसके सद्गुरु ने यह बताया है कि उसके प्रभु (स्वामी) तो गिरधर नागर श्रीकृष्ण हैं। उनसे बिछड़े हुए कई युग बीत गये हैं। मीरा के घर में आग लगी हुई है जिसके कारण न तो घर में रह सकती है और बाहरी संसार उसे रहने नहीं देता। ऐसे में प्रभु श्रीकृष्ण ही उसे अपना कर उसकी रक्षा कर सकते हैं।

काव्य सौन्दर्य :

1. ब्रजभाषा, पद गेय एवं लालित्यपूर्ण है।
2. अनुप्रास अलंकार।
3. गुण माधुर्य।
4. शान्त रस है।

3. सखी री लाज बैरन भई।
श्री लाल गोपाल के संग काहे नाहिं गई।।
कठिन क्रूर अक्रूर आयो, साजि रथ कह नई।
रथ चढ़ाय गोपाल लैगो, हाथ मीजत रही।।
कठिन छाती स्याम बिछुरत, बिरह में तन तई।
दासी मीरा लाल गिरधर, बिखर क्यों न गई।

शब्दार्थ :
लाज = लज्जा; बैरन = दुश्मन; काहे = क्यों; क्रूर = कठोर; साजि = सजाकर; हाथ मीजत रही = पछता कर रह गई; बिरह = वियोग; तन = शरीर;तई = कढ़ाई; बिखर = नष्ट होना।

सन्दर्भ :
पूर्ववत्।

प्रसंग :
प्रस्तुत पद्यांश में मीराबाई ने विरह जनित पीड़ा का बड़ा ही मार्मिक वर्णन किया है। लोकलाजवश वह श्रीकृष्ण के साथ नहीं जा पाईं और उनके मथुरा चले जाने पर पछता कर रह गई।

व्याख्या :
मीराबाई कहती हैं कि हे सखी ! मेरी लाज ही मेरी दुश्मन हो गई। उसने मुझे गोपाल श्रीकृष्ण के साथ नहीं जाने दिया। मथुरा से कठोर हृदय वाला अक्रूर आया और अपने साथ सुन्दर रथ सजाकर लाया जिसमें कि श्रीकृष्ण को बिठाकर मथुरा ले गया और मैं अपने मन में पश्चाताप करती हुई रह गई। श्रीकृष्ण के वियोग में मेरा हृदय कठोरता का अनुभव करने लगा और मेरा शरीर उनके विरह में कढ़ाई के समान जलने लगा। मीरा तो गोपाल श्रीकृष्ण की दासी है। उन्होंने ही भक्तों के हित में गोवर्धन पर्वत उठाया था। मीरा को इस बात का दुःख है कि वह श्रीकृष्ण के विरह में नष्ट क्यों नहीं हो गई।

काव्य सौन्दर्य :

1. ब्रजभाषा,पद गेय है एवं लालित्यपूर्ण है।
2. रस वियोग शृंगार।
3. अनुप्रास व उपमा अलंकार।
4. विरह का अनूठा वर्णन।

4. भज मन चरण कँवल अविनासी।
जे ताई दीसे धरण गगन बिच, ते ताइ सब उठि जासी।
कहा भयो तीरथ ब्रत कीन्हें, कहा लिए करवत कासी।
इस देही का गरब न करणा, माटी में मिल जासी।।
यो संसार चहर की बाजी, साँझ पड्यो उठ जासी।
कहा भयो है भगवा पहरयाँ, घर तज भये संन्यासी।।
जोगी होइ जुगत नहि जाणी, उलटि जनम फिर आसी।
मीरा के प्रभु गिरधर नागर, काटो जनम की फाँसी।। (2009)

शब्दार्थ :
कँवल = कमल; अविनासी = जिसका नाश न हो; करवत कासी = काशी में मृत्यु होने पर; देही = शरीर; गरब = घमण्ड; चहर = रौनक; बाजी = हार जीत पर कुछ लेन-देन की शर्त; भगवा = गेरुए कपड़े; जुगत = युक्ति।

सन्दर्भ :
पूर्ववत्।

प्रसंग :
प्रस्तुत पद में मीरा श्रीकृष्ण के चरण-कमलों का भजन करने के लिए अपने आपको प्रस्तुत करने के लिए प्रेरित कर रही है।

व्याख्या :
मीराबाई कहती है कि हे मन ! तू श्रीकृष्ण के चरण-कमलों का भजन कर। जिसने भी गिरधर के चरणों के दर्शन अपनी भृकुटि के बीच में कर लिए उसको तो संसार फीका लगता है। जब तक प्रभु श्रीकृष्ण के चरणों के दर्शन नहीं हुए तो तीर्थ करने,व्रत करने और काशी में शरीर त्यागने से भी कोई लाभ नहीं होता। मनुष्य को इस शरीर का गर्व नहीं करना चाहिए क्योंकि यह शरीर एक दिन मिट्टी में मिल जाएगा। इस संसार का आनन्द तो हार जीत की शर्त के समान है जो शाम होते ही उठ जाता है। जैसे बाजार की चहल-पहल दिन में ही रहती है,शाम होते ही समाप्त हो जाती है। गेरुए वस्त्र धारण कर और घर त्याग कर संन्यासी होकर यदि ईश्वर को प्राप्त करने की युक्ति नहीं जानी तो फिर यह सब व्यर्थ है। फिर दोबारा संसार के जन्म-मरण के चक्कर में फंसना पड़ता है। मीरा के प्रभु तो गिरधर गोपाल हैं,वही उनके जन्म-मरण की रस्सी को काटकर उसे जन्म-मरण के बन्धन से मुक्त करेंगे।

काव्य सौन्दर्य :

1. ब्रजभाषा है,पद गेय एवं लालित्यपूर्ण है।
2. अनुप्रास एवं उपमा अलंकार है।
3. गुण-माधुर्य
4. शान्त रस है।

वन्दना भाव सारांश

‘वन्दना’ नामक कविता के रचयिता नीतिनिपुण एवं स्पष्टवादी ‘केशवदास’ हैं। इसमें उन्होंने प्रथम पूज्य गणेश, विद्या की देवी सरस्वती एवं मर्यादा पुरुषोत्तम राम की वन्दना की है।

भक्ति केवल भक्तिकाल तक सीमित भाव नहीं है, यह काव्य के लिए एक शाश्वत-भाव भी है। इसलिए अन्य काल के कवियों में भी भक्ति-तत्व के दर्शन होते हैं; जैसे’केशवदास’-वे रीतिकाल के कवि माने जाते हैं, किन्तु उनकी कविता में भी भक्ति-भावना का निदर्शन हुआ है। प्रस्तुत काव्यांश में केशवदास द्वारा की गई देव वन्दना परक पंक्तियाँ दृष्टव्य हैं। भक्ति’ के अन्तर्गत ‘इष्ट’ के वन्दन-अर्चन की प्रक्रिया है। वे गणेश, सरस्वती और श्रीराम की वन्दना करते हुए इनकी महिमा का वर्णन करते हैं। वे गणेश की कष्ट निवारक क्षमता,सरस्वती की उदारता और श्रीराम की मुक्ति प्रदायिनी क्षमता का विशेष रूप से उल्लेख करते हैं।

वन्दना संदर्भ-प्रसंग सहित व्याख्या

1. गणेश वन्दना
बालक मृणालनि ज्यों तोरि डारै सब काल,
कठिन कराल त्यों अकाल दीह दुःख को।
बिपति हरत हठि पद्मिनी के पात सम,
पंक ज्यों पताल पेलि पठवै कलुष को।
दूरि कै कलंक-अंक भव-सीस-ससि सम,
राखत है केशोदास दास के बपुष को।
साँकरे की साँकरनि सनमुख होत तोरै,
दसमुख मुख जोवै गजमुख-मुख को।।

शब्दार्थ :
मृणालनि = कमल की नाल; कराल = विकराल; अकाल = असमय; दीह = बड़ा,लम्बा; पद्मिनी = कमलनी; पात = पत्ता;पंक = कीचड़; पेलि = हठपूर्वक; पठवै = भेज देता है; कलुष = पाप; अंक = गोद; वपुष = देह; सनमुख = सामने दसमुख = रावण; गजमुख = गणेश।

सन्दर्भ :
प्रस्तुत पद्यांश केशवदास द्वारा रचित ‘वन्दना’ के शीर्षक ‘गणेश वन्दना’ से उद्धृत है।

प्रसंग :
यहाँ पर कवि केशवदास ने विघ्नहारी गणेश जी की वन्दना की है।

व्याख्या :
कवि कहता है कि जैसे बालक कमल की डाल को किसी भी समय आसानी से तोड़ डालता है। उसी प्रकार गणेश असमय में आए विकराल दुःख को भी दूर कर देते हैं। जैसे कमल के पत्ते पानी में फैली कीचड़ को नीचे भेज देते हैं और स्वयं स्वच्छ होकर ऊपर रहते हैं, उसी प्रकार गणेश हर विपत्ति को दूर कर देते हैं। जिस प्रकार चन्द्रमा को निष्कलंक कर शिवजी ने अपने शीश पर धारण किया उसी प्रकार गणेश जी अपने दास को कलंक रहित कर पवित्र कर देते हैं। गणेश जी बन्धन से अपने दास को मुक्त कर देते हैं। रावण भी गणेश जी के मुख की तरफ देखकर अपनी बाधाओं को दूर करने की आशा रखता है।

काव्य सौन्दर्य :

1. भक्ति रस का प्रयोग हुआ है।
2. अनुप्रास, उत्प्रेक्षा अलंकार का प्रयोग।
3. गुण-माधुर्य।

2. सरस्वती वन्दना
बानी जगरानी की उदारता बखानी जाइ
ऐसी मति उदित उदार कौन की भई।
देवता प्रसिद्ध सिद्ध रिषिराज तपवृद्ध
कहि-कहि हारे सब कहि न काहू लई।
भावी भूत वर्तमान जगत बखानत है,
केशोदास क्योंहू ना बखानी काहू पै गई।
पति बनें चार मुख पूत बर्ने पाँच मुख,
नाती बनें घटमुख तदपि नई-नई। (2009)

शब्दार्थ :
बानी = सरस्वती;जगरानी = जगत् की पूज्य; उदारता = दयालुता; बखानी = वर्णन करना;मति = बुद्धि; उदित = उदय होना; तपवृद्ध = श्रेष्ठ तपस्वी; भावी भूत वर्तमान = भूत, वर्तमान और भविष्य; चारमुख = ब्रह्मा; पाँच मुख = शिवजी; षटमुख = कार्तिकेय; तदपि = फिर भी।

सन्दर्भ :
प्रस्तुत पद ‘केशवदास’ द्वारा रचित ‘वन्दना’ के शीर्षक ‘सरस्वती वन्दना’ से उद्धृत है।

प्रसंग :
यहाँ पर कवि ने सरस्वती की उदारता का वर्णन किया है।

व्याख्या :
कवि कहता है कि जगत में पूज्य सरस्वती की उदारता का वर्णन नहीं किया जा सकता। संसार में ऐसी श्रेष्ठ बुद्धि किसी में नहीं है जो उनकी उदारता का वर्णन कर सके देवता, सिद्ध मुनि,श्रेष्ठ तपस्वी सभी कह-कह कर हार गये, लेकिन कोई भी उनकी उदारता का वर्णन नहीं कर सका। भूत, वर्तमान और भविष्य बताने वाले सभी ने वर्णन किया, लेकिन केशवदास कहते हैं कि कोई भी सरस्वती की दया (उदारता) का वर्णन नहीं कर सका। उनके पति ब्रह्माजी ने, पुत्र शंकर जी ने और उनके नाती कार्तिकेय ने भी सरस्वती की उदारता का वर्णन किया लेकिन वे भी उनकी उदारता का पार नहीं पा सके। (शंकर जी का जन्म ब्रह्माजी की भौंहों से होने के कारण उनको पुत्र कहा गया है और कार्तिकेय शिवजी के पुत्र होने के नाते सरस्वती के नाती हुए।)

काव्य सौन्दर्य :

1. सरस्वती वन्दना में उनके प्रति आस्था का निष्पादन हुआ है।
2. ब्रजभाषा में रचना है।
3. अनुप्रास, पुनरुक्तिप्रकाश अलंकार।
4. भाषा में मधुरता का गुण है।
5. शान्त रस का प्रयोग।

3. श्रीराम वन्दना
पूरण पुराण अरु पुरुष पुराण परिपूरण,
बतावै न बतावै और उक्ति को।
दरसन देत जिन्हें दरसन सुमुझैं न,
नेति-नेति कहैं वेद छाँड़ि भेद जुक्ति को।
जानि यह केशोदास अनुदिन राम-राम,
स्टत रहत न डरत पुनरुक्ति को।
रूप देहि अणिमाहि गुन देई गरिमाहि
भक्ति देई महिमाहि नाम देई मुक्ति को।

शब्दार्थ :
पूरण पुराण = पूर्ण ब्रह्म; परिपूरण = पूरे; पुरुष पुराण = पुरुषोत्तम; उक्ति = उपाय; दरसन = दर्शन; नेति-नेति = इतना ही नहीं; वेद = वेद चार हैं-सामवेद, यजुर्वेद, अथर्ववेद, ऋग्वेद, भेद जुक्ति = भेद करने की युक्ति; अनुदिन = प्रतिदिन; पुनरुक्ति = बार-बार संसार में आना; अणिमाहि = सूक्ष्मता, अणिमा सिद्धि; गुन = गुण; गरिमा = अष्ट सिद्धियों में से एक; गुरुत्व,महिमा = आठ सिद्धियों में से एक (महिमा); मुक्ति = जन्म मृत्यु से छुटकारा।

सन्दर्भ :
प्रस्तुत पद्यांश ‘केशवदास’ द्वारा रचित ‘वन्दना’ के शीर्षक ‘श्रीराम वन्दना’ से लिया गया है।

प्रसंग :
यहाँ पर कवि ने श्रीराम की वन्दना का वर्णन किया है।

व्याख्या :
केशवदास कहते हैं कि और कोई उक्ति बताये या न बताये श्रीराम पूर्ण ब्रह्म पुरुषोत्तम हैं। उनका दर्शन पाकर भी कोई उन्हें समझ नहीं पाता है क्योंकि वेद भी ‘न इति’ ‘न इति’ कहकर उस भेद को वहीं छोड़ देते हैं। यह जानकर केशवदास प्रतिदिन राम-राम रटते रहते हैं जिसके कारण उन्हें जन्म-मरण का डर नहीं रहता,क्योंकि राम-राम रटने से जन्म-मरण से मुक्ति मिल जाती है। श्रीराम का रूप अणिमा सिद्धि (सूक्ष्मता) प्रदान करता है, उनका गुण गरिमा सिद्धि (गुरुत्व) प्रदान करता है, उनकी भक्ति महिमा (बड़प्पन) सिद्धि प्रदान करती है और उनका नाम मुक्ति प्रदान करता है।

काव्य सौन्दर्य :

1. श्रीराम की महानता का बड़ा विशद वर्णन है।
2. भक्ति रस समाया हुआ है।
3. अनुप्रास, श्लेष, पुनरुक्तिप्रकाश अलंकारों का प्रयोग।
4. ब्रजभाषा में मधुरता का गुण है।

MP Board Class 12th Biology Important Questions Chapter 12 Biotechnology and its Applications

Biotechnology and its Applications Important Questions

Biotechnology and its Applications Objective Type Questions 

Question 1.
Choose the correct answer:

Question 1.
Restriction endonuclease is employed for cutting :
(a) A single stranded DNA
(b) Double stranded DNA
(c) RNA fregment
(d) m – RNA.
Answer:
(d) m – RNA.

Question 2.
Which enzyme is helpful in genetic engineering:
(a) RNA polymerase
(b) DNA polymerase
(c) Restriction endonuclease
(d) Nuclease.
Answer:
(c) Restriction endonuclease

Question 3.
Extrachromosomal DNA used as vector in gene cloning is :
(a) Transposon
(b) Intron
(c) Exon
(d) Plasmid.
Answer:
(d) Plasmid.

Question 4.
The most extensively used bacteria in genetic engineering is :
(a) Bacillus
(b) Clostridium
(c) Escherichia
(d) Salmonella.
Answer:
(c) Escherichia

Question 5.
Hybridomas are:
(a) Antibodies
(b) Hybrid swarms
(c) Hybrid cultures
(d) Hybrid zone.
Answer:
(c) Hybrid cultures

Question 6.
Vaccine can not protect us from :
(a) Malaria
(b) Polio
(c) Small pox
(d) Tuberculosis.
Answer:
(a) Malaria

Question 7.
Humulin is:
(a) A type of chitin
(b) New digestive enzyme
(c) Powerfull antibiotic
(d) Human insuline
Answer:
(a) A type of chitin

Question 8.
Which is not used in the form of bio weapons :
(a) Bacillus anthrasis
(b) Bacillus thuringiensis
(c) Botulinum toxin
(d) Small pox.
Answer:
(b) Bacillus thuringiensis

Question 9.
Super bug is called :
(a) Pseudomonas pulida
(b) Xanthomonas citrae
(c) Bacillus anthresis
(d) Streptococcus pneumoniae
Answer:

Question 10.
Biopiracy affected plants are :
(a) Neem
(b) Basmati rice
(c) Turmeric
(d) All of these.
Answer:
(d) All of these.

Question 11.
Golden rice will help in :
(a) Producing petrol like fuel
(b) Pest resistance
(c) Herbicide tolerance
(d) Alliviation of Vit – A deficiency
Answer:
(d) Alliviation of Vit – A deficiency

Question 12.
During gene cloning which is called as “gene taxi” :
(a) Vaccine
(b) Plasmid
(c) Bacterium
(d) Protozoa.
Answer:
(b) Plasmid

Question 13.
In transgenics, expression of transgene in target tissue is determied by.
(a) Transgene
(b) Promoter
(c) Reporter
(d) Enhancer.
Answer:
(b) Promoter

Question 2.
Fill in the blanks :

1. Bt is a ………………………..
2. Bt toxin is formed from ……………………….. by the bacillus.
3. The prooduct of Cry – 1 gene is used for ………………………..
4. RNA interpritation is the method of cellular conservation in ……………………….. genes.
5. Both peptide chains are joined by the ……………………….. in insuline.
6.  ……………………….. is the found in proinsuline which is not found in muture insulin.
7.  ……………………….. is found in transgenic cow ‘Rosi’, it is not found in commen cow’s milk.
8. Flavr savr tomato is a transgenic veriety of ………………………..
9.  ……………………….. has two polypeptide chain and 51 amino acids.
10.  ……………………….. gene which found in Rhizobium is converted from nitrogen into nitrates.
11.  ……………………….. is the reason of male infertility in maize.
12. First transgenic organism is petant in ………………………..
13. Monoclsonal antibody is produce with the help of ……………………….. technology.

Answer:

1. Bio Toxin
2. Protoxin
3. Corn bores
4. Eukaryotic
5. Three sulphaid bundles
6. Peptide ‘c’
7. Human α – heredity lectalbumen
8. Tomato
9. Insulin
10. Nif gene
11. Cytoplasmic heredity
12. 1989
13. Hybridoma.

Question 3.
Match the followings:
I.

Answer:

1. (e)
2. (d)
3. (a)
4. (b)
5. (c)

II.

Answer:

1. (d)
2. (a)
3. (b)
4. (c)

Question 4.
Write the answer in one word/sentances:

1. Write the full name of RNAi.
2. Bt Toxic is encrypted by this gene.
3. Is our blood has proteoses and nucleases.
4. Who produce Bt toxin protein?
5. What is humulin?
6. What is SCID (Severe Combined Immunodeficienay)?
7. Which is controled by Trycoderma?
8. Name the organism which bear the other organism obtained gene?
9. Bt. cotton and Golden rice is the examples of.
10. Name the gene which controles the cell cycle?

Answer:

1. RNA interference
2. By Cry genes
3. No
4. Bacillus thuringiensis
5. Human insulin
6. Hereditary disease
7. Biological fungal disease
8. Transgenic organism
9. Transgenic crop
10. p53 gene.

Biotechnology and its Applications Important Questions Very Short Answer Type Questions

Question 1.
Can you suggest a method to remove oil (hydrocarbon) from seeds based on your understanding of r – DNA technology and chemistry of oil?
Answer:
To remove oil from seeds using recombinat DNA technology would involve:

1. Identifying the genes that code for oil production.
2. Deleting these genes from the seed genome.
3. Splicing back together the remaining DNA.
4. Putting it back into the cell.

It will be not be very easy because the oils are made up of fatty acids and glycerol. Since, fatty acids are important components of cell membrane system, deleting or switching off of its genes might affect the cell structure itself.

Question 2.
Find out from internet what is golden rice?
Answer:
Golden rice is a variety of rice produced through genetic engineering to biosynthesize β – carotene, a precursor of vitamin ‘A’ in the edible parts of rice. It is intended to produce a fortified food to be grown and consumed in areas with a shortage of dietary vitamin ‘A’.

Question 3.
Does our blood have proteases and nucleases?
Answer:
No.

Question 4.
Name the organism whose genetic material has been altered using genetic engineering techniques.
Answer:
Genetically Modified Organisms (GMO).

Question 5.
Name the crops which are prepaired with the help of biotechnology.
Answer:
Bt cotton, Bt maize, paddy, tomato, potato and soyabeen.

Question 6.
Through whom Bt toxin protein originates?
Answer:
By Bacillus thuringiensis.

Question 7.
By which Bt toxin is coded?
Answer:
By Cry genes Bt toxin is coded.

Question 8.
Full form ofRNAi.
Answer:
RNA interference (RNAi).

Question 9.
Name the therapy which is help of missing of defective ones in order to correct genetic disorders.
Answer:
Gene therapy.

Question 10.
Name the scientific name of bacteria in which be form organism toxin.
Answer:
Bacillus thuringiensis.

Biotechnology and its Applications Important Questions Short Answer Type Questions

Question 1.
What is genetically modified (GM) food? Give two examples.
Answer:
Genetically Modified (GM) food:
The food substances produced from genetically modified crops or transgenic crops is called GM food. This food differ from conventionally developed varieties in the following aspects :

1. GM food contains antibiotic resistance gene itself.
2. It contains protein produced by transgene, example Cry protein in insect resistance varieties.
3. These GM foods contain enzyme produced by the antibiotic resistance gene that was used during gene transfer by recombinant DNA technology.

Examples of GM Crops, Food and Fruits:

1. Flavr Savr Tomato:
It is the first food containing genetically engineered DNA. These tomatoes contain genes for antibiotic resistance for kanamycin.

2. Maize:
GM maize has a bacterial gene which increases its resistance to pests and diseases. It also has a gene for ampicillin resistance which is harmful for us, therefore introduction of GM maize is opposed by many European countries.

3. Rape oil seed:
It is a new type of plant that contain genes for resistance to the herbicide Basta. It has for more potential, dangers and can become a weed and would be impossible to control with Basta. It could cross fertilize with relatives such as wild mustard, thus, spreading the resistance to wild plants. Such type of environmental risks could occur with genetically modified rapeseed crop. They might also effect food chains in unpredictable ways.

Question 2.
Write down the advantage of GM Crops.
Answer:
Advantages of GM Crops:

• Genetic modification has made crops more tolerant to abiotic stresses (cold, drought, heat, salt.)
• Viral resistance can be introduced.
• Over ripening losses can be reduced. Example : Flavr Savr Tomato.
• Enhanced nutritional value of food. Example : Golden Rice.
• Reduced reliance on chemical pesticides.

Disadvantages of GM crops:

• Transgenes in crop plants can endanger native species. Example : The gene for Bt toxin expressed in pollen may end natural pollinators such as honeybees.
• Weeds also become resistant.
• Products of transgenes may be allergic or toxic.
• They cause damage to the natural environment.

Question 3.
What is perfect agriculture? How is this method better than traditional method? Explain.
Answer:
Perfect agriculture is a method of agriculture which is sustainable, perfect and harmless. Green revolution and there after the production of agricultural crops has definately increased due to use of new and high yielding varieties, development of irrigation facilities, increased irrigated area, use of fertilizers etc. but it results many problems such as loss of soil fertility, pollution of food and water and diseases. The resistance power of plants and human beings falls slowly.

Food and water borne diseases affecting the health of human beings and animals. All of these conditions and events taking place due to the modem commercial agriculture. (MPBoardSolutions.com) Therefore, it would become necessary to develop a method of agriculture which would be free from above mentioned demerits. This kind of agriculture is called to be as perfect or sustainable agriculture. Organic agriculture is the best example of perfect agriculture.

Question 4.
What is organic cropping? What are its basis?
Answer:
Organic agriculture:
Organic agriculture is a method of agriculture which does not allow the use of synthetic fertilizers, pesticides, insecticides, weedicides, plant growth regulators, substances of animal origin and genetically modified bacteria. In this method biofertilizers, crop rotation methods are used to increase crop production and biopesticides are used to control insects and weeds. Thus, organic farming is a holistic way of agriculture which tries to bridge the widening gap between man and nature.

If has the commitment of meeting production needs on one hand and sustaining resources and ecosystem function on the other hand. Thus, organic farming is an alternative agriculture production system which avoid or largely excludes the use of synthetic chemicals, fertilizers, pesticides and growth regulating hormones and live stock additives.

Basics of organic agriculture:

1. Organic agriculture is based on improvement of soil, plants, animals, man and global scinery and make it sustainable.
2. Organic agriculture is based on those ecosystems and biocycles which utilize that organisms which would be promoted.
3. It is based on the principle which are related with making pollution free environment and possibilities of life.
4. It is also based on saving environment and health of present and future generations.

Question 5.
What is eugenics? Write importance of eugenics.
Answer:
Eugenics: The branch of biology which deals with the study of improvements of human race is called eugenics.

Importance:

1. Development of selective reproduction in similar species.
2. Transfer of genetic materials in various organisms.
3. Development ofGM food and GM crops.
4. Gene cloning.
5. Gene therapy, etc.

Question 6.
Crystals of Bt toxin produced by some bacteria do not kill the bacteria themselves because:
(a) Bacteria are resistant to the toxin,
(b) Toxin is immature
(c) Toxin is inactive
(d) Bacteria enclose toxin in a special sac.
Answer:
(c) Toxin is inactive : In bacteria, the toxin is present in an inactive form called prototoxin. This gets converted into the active form when it enters the salivary gland of insects having alkaline medium.

Question 7.
What are transgenic bacteria ? Illustrate using any one example.
Answer:
The becteria whose DNA is manipulated to carry and express a foreign DNA is called transgenic bacteria. These microbes are used for producing important bio – chemicals. They have been synthesizing alcohol, enzymes, steroids and antibiotics. Example  Bacillus thuringiensis for Bt cotton, hirudin from transgenic Brassica napus seed. Hirudin is a protein which prevents blood clotting. Its gene was chemically synthesized and introduced in Brassica napus, in which hirudin accumulates in the seed from where it is extracted, purified and used as a medicine.

Question 8.
Compare and contrast the advantages and disadvantages of production of genetically modified crops.
Answer:
Advantages of GM Crops:

1. Genetic modification has made crops more tolerant to abiotic stresses (cold, drought, heat, salt.)
2. Viral resistance can be introduced.
3. Over ripening losses can be reduced. Example : Flavr Savr Tomato.
4. Enhanced nutritional value of food. Example : Golden Rice.
5. Reduced reliance on chemical pesticides.

Disadvantages of GM crops :

1. Transgenes in crop plants can endanger native species. Example : The gene for Bt toxin expressed in pollen may end natural pollinators such as honeybees.
2. Weeds also become resistant.
3. Products of transgenes may be allergic or toxic.
4. They cause damage to the natural environment.

Question 9.
What are Cry proteins? Name an organism which produces it. How has man exploited this protein for his benefit?
Answer:
Cry proteins are toxic proteins (insecticidal proteins) secreted by Bacillus thuringiensis in crystal form during a particular phase of their growth. The toxin is coded by a gene called Cry. The genes encoding cry proteins called Bt toxin genes were isolated from B. thuringiensis and incorporated into several crop plants such as Bt cotton, Bt com etc. to provide resistance against insect pests.

Question 10.
What is gene therapy? Illustrate using the example of adenosine deaminase deficiency (ADA).
Answer:
It is a collection of methods which allows correction of a gene defect that has been diagnosed in a child or embryo. In gene therapy, normal genes are inserted into a person’s cells or tissues to treat a hereditary defect. Gene therapy is being tried for sickle cell anaemia and Severe Combined Immuno Deficiency (SCID).

In some children, ADA deficiency can be cured by bone marrow transplantation. In others, it can be treated by enzyme replacement therapy, in which functional ADA is given to the patient by injection. (MPBoardSolutions.com) However, both of these approaches are not completely curative. In gene therapy, lymphocytes from the blood of the patient are grown in culture outside the body.

A functional ADA cDNA (using a retroviral vector) is then introduced into these lymphocytes, which are subsequently returned to the patient. Because these cells are not immortal, the patient requires periodic infusion of such genetically engineered lymphocytes. However, if the gene isolated from marrow cells producing ADA is introduced into cells at early embryonic stages, the disease could be cured permanently.

Question 11.
Consult internet and find out how to make orally active protein pharma – eeutical What is the major problem to be encountered?
Answer:
For making any oral drug or nutritional supplement, the action of digestive enzymes has to be taken into account. Most of the antibiotics and vitamin supplements are made in capsule form to prevent the action of HC1 in the stomach. For protein preparation, the major source is groundnut shells. The protein extracted from the source is predigested so, as to make it absorbable by the digestive system.

Biotechnology and its Applications Important Questions Long Short Answer Type Questions

Question 1.
Diagrammatically represent the experimental steps in cloning and expressing a human gene (say the gene for growth hormone) into a bacterium like E. coli.
Answer:

Question 2.
Explain the following in brief:

1. Biopiracy
2. Biopatent

Answer:
1. Biopiracy:
Some organisations and multinational companies exploid biological resources and genetical resources indegenous to a country without proper authorisation. This is called biopiracy. In fact it is illegal removal of biological material. The process of biopyracy involves collection of samples of biological sources, which can be done unnoticed. This biological material is then subjected to product development for use on a commercial scale.

Today a range of biological resources are facing biopiracy. It includes plants and animals, microorganisms genetic materials etc. Western companies are getting great benefits from using the knowledge and biological resources of the third world communities. (MPBoardSolutions.com) While the companies stand to make huge revenue from this process, the local communities are unrewarded and infact, may have to buy the products of these companies at high prices.

To check illegal exploitation of biological resources Government of India has signed the General Agreement on Tariffs and Trade (GATT), which opens country natural resources for foreign exploitation.

2. Biopatent:
The protection given by government to an inventor of biological material to secure him for a specific time the exclusive right of manufacturing, exploiting, using and selling of an invention is called biopotent.

Today manufacturing companies are being granted patents for products and technologies that make of biological resources, such as plants and animals, genetic materials which was identified developed and used by farmers and indegenous peoples.

There is growing worldwide opposition to the granting of patents on biological materials such as genes, plants, animals and human. Farmers and indegenous peoples are outaged that plants that they developed are being ‘hijacked’ by companies. Groups are diverse as religious leaders, parliamentarians and environment NGOs are intensifying campaign against corporate patenting of living things.

Question 3.
What is gene library?
Answer:
Gene library:
Several clones of cells, each clone containing one or a few foreign genes representing almost all the genes of an organism is referred to as genes library. From this gene library it is possible to identify a clone containing gene of interest. In order to obtain gene library of an organism, its genome is first cut into smaller DNA fragments containing one or a few genes such as fragments can be cloned into a cell which may be that of bacteria, yeast, insects, plant or animal cell.

When such a cell multiplies to form a group of cells, all cells will contain the same foreign DNA fragment which was introduced initially. (MPBoardSolutions.com) These cells which have similar foreign DNA fragment are referred to as a clone of cells. Several clones of cells each clone containing one or a few foreign genes are finally obtained and is called gene library.

Question 4.
What is genetic engineering? Describe the application of genetic engineering in the field of Agriculture and Medicine.
Answer:
The branch of biology by which important and permanent changes are created in plants and animals by increasing or decreasing manipulation and transplantation of genetic units is called genetic engineering.

(A) Application of Genetic engineering or Biotechnology in Agriculture: Genetic engineering is found to be very beneficial in agriculture. Its important use in agriculture are:

1. Increase in photosynthetic efficiency:
An increase in photosynthetic efficiency of crop plants can be achieved by introducing suitable Carbon dioxide Fixation Gene (cfx) from any plant into the crop plants.

2. Transfer of nitrogen fixing ability:
Number of symbiotic and non-symbiotic micro¬organism have capacity of fixing atmospheric nitrogen. Nitrogen fixers are found to possess nitrogen fixing gene (nif genes) which are located on chromosomes or plasmids. Introduc¬tion of nif gene in crop plants results in ability in crop plants to fix atmospheric nitrogen and reduction in the use of chemical nitrogen fertilizers.

3. Disease resistance in crop plants:
Plant breeders at present are developing high yield varieties by transferring gene for disease resistance through conventional breeding.

4. Plant tissue in crop improvement:
Some of the areas of plant improvement where tissue culture has been applied with success are as follows :

• Rescuing hybrids through embryo culture.
• Multiplication of germplasm.
• Production of disease free plants.
• Production of haploid through another culture.
• Somaclonal variation.
• Somatic hybridization.
• Cryopreservation of germplasm.

5. VAM (Vesicular – Arbuscular Mycorrhiza) fungi with Rhizobium can boost the yields: Recently there has been a new dimension to this farm practice by the way of increasing Rhizobium inoculation effect by simultaneous inoculating seeds with VAM as well as Rhizobium culture.VAM are structural modification of hyphae helping in absorption and storage of phosphorus.

(B) Application of Genetic engineering in Medical field:

1. The hereditary diseases like colour – blindness, haemophilia which are caused by recessive genes and also many inborn metabolic disorders due to defective genes as alkaptonuria, phenylketonuria can be cured with the gene therapy.

2. Substances like vitamins, hormones, amino acids and antibodies can be synthesized in bacteria by introducing the genes which code these substances. In this way bacteria can be used as biofactories for the synthesis of these substances.

3. Production of insulin: Insulin is medicine used for the treatment of diabetes.
Initially it is derived from animals (pig and cows) but today it is produced by gene splicing.

4. Hepatitis-B vaccine : Hepatitis-B is a viral disease of liver. Today this vaccine is prepared with the help of genetic engineering.

Question 5.
What is forensic science? Explain DNA fingerprinting method of forensic science.
Answer:
Forensic science : Forensic science is the application of scientific knowledge and methodology to criminal investigations and legal problems.

DNA figerprinting : DNA fingerprinting is a hybridization technique used to identify the similarities of DNA molecule of two individuals.

Procedure of DNA fingerprinting : The DNA fingerprinting involves the following steps:

1. First of all, the DNA of the organism which has to be tested in isolated. It is host DNA. The DNA may be obtained from blood, semen, vaginal swabs and bone marrow. The amount of DNA needed for developing fingerprints is very small.

2. The isolated host DNA is then digested with a suitable restriction enzyme (example Restriction endonucleases) and the digest is subjected to gel electrophoresis (Southern hybridization). This enzyme cut the host DNA into small fragments.

3. The fragments of double stranded DNA (ds DNA) are denatured to produce single stranded DNA’by alkali treatment.

4. The DNA fragments are separated by gel electrophoresis.

5. The electrophoresed DNA is then transferred from gel into a nitrocellulose filter paper where it is fixed by baking the filter at 80°C for 2 hours.

6. A known sequence of single stranded DNA is prepared. It is called probe – DNA. The probe is obtained from organisms or prepared by DNA preparation method.

7. The probe DNA is labelled with radioactive isotopes such as P32 and then probe is added to the nitrocellulose filter paper containing host DNA.

8. The single stranded probe DNA base pair with complementary strands of the host DNA. As a result DNA – DNA hybrids are formed on nitrocellulose paper.

9. The nitrocellulose paper is then washed to remove unbound DNA probes from the paper.

10. The nitrocellulose filter paper is photographed on X-ray film through autoradiography. The film is analyzed to determine the presence of hybrid nucleic acid.

A schematic representation of DNA fingerprinting of a person accused of rape, and of the semen stain recovered from the clothes of rape victim. The fingerprints match perfectly; the probabillity of this being due to chance is extremely low. DNA samples from a close relative of the accused and from an unrelated person are also included for comparisons (not shown here).

In case of disputed parentage, the DNA fingerprints of the child, the mother and the suspected father are compared. As a rule, the bands present in a child’s fingerprint must be accounted for by those in the mother’s and the fathers’s fingerprints. (MPBoardSolutions.com) Therefore, the child’s fingerprint is compared with that of the mother and their common bands are marked. The remaining bands in the child’s fingerprint must be present in that of the child’s father.

Applications of DNA Fingerprinting:

1. Identification of criminals in forensic laboratories and legal pursuits.
2. Settlement of disputed paternity i.e., who is the biological father or mother of the child.
3. It is useful in restoring health of patients suffering from leukemia or blood cancer.
4. It can explore the evolutionary pathway of a species.
5. It can verify the kinship of an individuals with another.

On the basis of DNA fingerprints, the killer of Shri Rajiv Gandhi, the former Prime Minister of India was identified as ‘Dhanu’. The sexual relationship of Bill Clinton, the former President of USA with Monika Levinski, a working staff of White House was also concluded to be true on the basis of DNA fingerprinting.

Question 6.
Explain stem cell technique with example and give its uses.
Answer:
Stem Cell Technology:
Stem cell technology is a rapidly developing field that combines the efforts of cell biologists, geneticists, and clinicians and offers hope of effective treatment for a variety of malignant and non-malignant diseases using stem cells.

Stem cell:
A stem cell is a non – specialized,undifferentiated generic cell which can make exact copies of itself indefinitely and can differentiate and produce specialized cells such as a liver cells, muscle cells, blood cells, and other cells with specific functions. The process of changing into a specific cell type is known as differentiation. Stem cells are found in multicellular organisms.
Stem cells divide regularly to renew and repair the existing tissue.

Example:
The bone marrow and gastrointestinal tract in which stem cells function to renew and repair tissue.

Uses of stem cell:

1. Due to capacity of regeneration it is useful for treatment of injured cells by replacement of deflective tissue, teeth, retina, cochlear cells.
2. It is used to treat diseases including spinal cord injury, stroke, bums, heart disease, diabetes, osteoarthritis and rheumatoid arthritis.
3. Treatment of diabetes.

MP Board Class 12th Biology Important Questions

MP Board Class 12th Biology Important Questions Chapter 10 Microbes in Human Welfare

Microbes in Human Welfare Important Questions

Microbes in Human Welfare Objective Type Questions 

Question 1.
Choose the correct answer:

Question 1.
Name the place from which viruses entered into the plant:
(a) From lenticels
(b) From wound
(c) From stomata
(d) From root.
Answer:
(b) From wound

Question 2.
Fertilizer elements are :
(a) Nitrogen
(b) Phosphorus
(c) Potassium
(d) All of these.
Answer:
(d) All of these.

Question 3.
Fertilizer that supplies least % of nitrogen is :
(a) Urea
(b) (NH₄)SO₄
(c) (NH₄)NO₃
(d) Organic nitrogen fertilizer.
Answer:
(d) Organic nitrogen fertilizer.

Question 4.
VAM is:
(a) Bacteria
(b) Yeast
(c) Fungi
(d) Virus.
Answer:
(b) Yeast

Question 5.
Nitrifying bacteria converts :
(a) N₂ into nitrates
(b) Ammonia into nitrates
(c) Nitrates into N₂
(d) CO₂ into carbohydrates.
Answer:
(b) Ammonia into nitrates

Question 6.
Who discovered the virus :
(a) Stanley
(b) Ivanowski
(c) Herel
(d) Beijerinck.
Answer:
(b) Ivanowski

Question 7.
Name the virus which has double helical stranded DNA :
(a) Hepatits A
(b) Hepatits B
(c) Hepatits C
(d) Flepatits D.
Answer:
(b) Hepatits B

Question 8.
Spirally coiled bacteria is known as :
(a) Spirilla
(b) Cocci
(c) Bacilli
(d) Vibrio.
Answer:
(a) Spirilla

Question 9.
Name the bacteria in which flagella are found in whole body :
(a) Peritrichous
(b) Atrichous
(c) Monotrichous
(d) Cephalotrichous
Answer:
(a) Peritrichous

Question 10.
Useful activities of microbes is :
(a) Nitrogen fixation
(b) Nitrification
(c) Biogeochemical cycle
(d) All of the above.
Answer:
(d) All of the above.

Question 11.
Which of the following is prokaryotes :
(a) Chlorella
(b) Clamydomonas
(c) Protomyces
(d) Ossiletoria.
Answer:
(d) Ossiletoria.

Question 12.
Yeast is used in the production of :
(a) Ethyl alcohol
(b) Acetic acid
(c) Cheese
(d) Curd.
Answer:
(a) Ethyl alcohol

Question 13.
B.T. cotton provides immunity from :
(a) Pest
(b) Weeds
(c) Salt
(d) Animal.
Answer:
(a) Pest

Question 14.
Which is the used for making bread :
(a) Lactobacillus
(b) Straptobacillus
(c) Aspergillus
(d) S. cerevisiace.
Answer:
(c) Aspergillus

Question 2.
Fill in the blanks:

1. Rhizobium, Azolla and Anabaena are the example of …………………….. fertilizers.
2. …………………….. bacterium is found in the roots of leguminous plants.
3. Nostoc and Anabaena are called ……………………..
4. …………………….. is nitrogen fixing bacteria.
5. …………………….. is the fungal resistant, bacterial antibody component.
6. …………………….. is the other name of mycoplasma.
7. …………………….. is the other name of Archaebacteria.
8. …………………….. type of ribosome is found in Moneran.
9. Bacterial cell wall is made by ……………………..
10. …………………….. is the meaning of word virus.
11. Butter milk is obtained from the activation of ……………………..
12. Ethanol is produced in a large scale through …………………….. yeast.
13. …………………….. bacteria is helpful in vinegar production.

Answer:

1. Bio
2. Rhizobium
3. Cyanobacteria
4. Rhizobium
5. Polymixin
6. PPLO
7. Living fossils
8. 70S type
9. Mucopeptides
10. Poison
11. Streptococcus lactis
12. Saccharomyces cerevisiae
13. Azotobacter aceti.

Question 3.
Match the followings :
I.

Answer:

1. (d)
2. (a)
3. (e)
4. (b)
5. (c).

II.

Answer:

1. (e)
2. (d)
3. (a)
4. (b)
5. (c)

Question 4.
Write answer in one word/ sentences:

1. Name the bacteria which is used in making swiss cheese.
2. Write the name of the microorganism which converted milk into curd.
3. Name the fish which control mosquito.
4. Write the name of two bacteria which are found in soil in free state.
5. Write the full name of IPM.
6. What is yogurt?
7. What is interferon?
8. Write the full name of B.O.D.
9. Write the name of an autotrophic nitrogen fixing microorganism.
10. Which microbes are used in industries for making citric acid?
11. Who discovered the penicillin?
12. Write the name of an alcoholic drink which is made by without distillation.
13. Microbes which is respire without oxgyen is called?
14. Synibiotic relationship which is found between fungi and higher plant root.

Answer:

1. Propionibacterium shermanii
2. Lactobacillus
3. Gambussia
4. Azotoba – cterium and Clostridium
5. Integrated Pest Management
6. Milk product
7. Antiviral protein
8. Biochemical Oxygen Demand
9. Anabaena
10. Aspergillus niger
11. Alexander Fleming
12. Beer
13. Anaerobic
14. Micorrhiza.

Microbes in Human Welfare Very Short Answer Type Questions

Question 1.
Name the fungus which produce these products:

1. Citric acid
2. Vitamin B₂

Answer:

Question 2.
What is yoghurt?
Answer:
Yoghurt is a semi – solid sourish food prepared from milk fermented by added bacteria.

Question 3.
Why does the river Ganga water not spoil even kept for long – time?
Answer:
Bacteriophages are present in Ganga river which feed on bacteria which spoil water. So, this water does not get spoil for long –   time.

Question 4.
Who discover penicillin?
Answer:
Alexander Fleming.

Question 5.
Name the microorganism/fungi which gave penicillin.
Answer:
Penicillium notatum.

Question 6.
Which organism is used for making citric acid in industries?
Answer:
Aspergillus niger.

Question 7.
Write the name of methanogen bacteria.
Answer:
Methano bacterium species.

Question 8.
Which bacteria is found in anaerobic sludge?
Answer:
Methanogen.

Question 9.
What is lady bird?
Answer:
It is an insect which is used as biocontroller for Aphid control.

Question 10.
Give the name of autotrophic nitrogen fixing microbes.
Answer:
Anabaena.

Question 11.
Name the mineral absorbed by mycorrhiza, which is not absorbed by plant roots.
Answer:
Phosphorus.

Question 12.
Name the microorganism which changes to milk into curd.
Answer:
Lactobacillus spp.

Question 13.
Which fungi is used in treatment of plant due to biological control?
Answer:
Trichoderma spp.

Question 14.
Which bacteria is used in swiss paneer?
Answer:
Propionibacterium shermanii.

Question 15.
Which paneer is completed by the growth of fungus?
Answer:
Roquefort cheese.

Question 16.
Name two alcoholic drink which are formed without distillation.
Answer:
Beer and Wine.

Question 17.
Name two alcoholic drink which are formed by distillation.
Answer:
Whiskey and Rum.

Question 18.
What is the full form of BOD?
Answer:
Biochemical or Biological Oxygen Demand.

Microbes in Human Welfare Short Answer Type Questions

Question 1.
Bacteria cannot be seen with the naked eyes, but these can be seen with the help of a microscope. If you have to carry a sample from your home to your biology laboratory to demonstrate the presence of microbes under a microscope, which sample would you carry and why?
Answer:
Curd can be used as a sample for the study of microbes. Curd contains numerous Lactic Acid Bacteria (LAB) or Lactobacillus. These bacteria produce acids that coagulate and digest milk proteins. A small drop of curd contains million of bacteria, which can be easily observed under a microscope.

Question 2.
Give example to prove that microbes release gases during metabolism.
Answer:
The examples of bacteria that release gases during metabolism are :

1. Bacteria and fungi carry out the process of fermentation and during this process, they release carbon dioxide.
2. The dough used for making idli and dosa gives a puffed appearance. This is because of the action of bacteria which releases carbon dioxide. This CO₂ released from the dough gets trapped in the dough, thereby giving it a puffed appearance.

Question 3.
In which food would you find lactic acid bacteria? Mention some of their useful applications.
Answer:
Lactic acid bacteria can be found in curd. It is this bacterium that promotes the formation of milk into curd. The bacterium multiplies and increases its number, which converts the milk into curd. They also increase the content of vitamin B₁₂
in curd. Lactic acid bacteria are also found in our stomach where it keeps a check on the disease causing microorganisms.

Question 4.
Name some traditional Indian foods made of wheat, rice and Bengal gram (or their products) which involve use of microbes.
Answer:

1. Wheat product: Bread, Cake etc.
2. Rice product: Idli, Dosa.
3. Bengal gram product: Dhokla, Khandvi.

Question 5.
In which way have microbes played a major role in controlling diseases caused by harmful bacteria?
Answer:
Several microorganisms are used for preparing medicines. Antibiotics are medicines produced by certain microorganisms to kill other disease causing microorganisms. These medicines are commonly obtained from bacteria and fungi. They either kill or stop the growth of disease causing microorganisms. (MPBoardSolutions.com) Streptomycin, tetracycline and penicillin are common antibiotics. Penicillium notatum produces chemical penicillin, which checks the growth of staphylococci bacteria in the body. Antibiotics are designed to destroy bacteria by weakening their cell walls.

Question 6.
Name any two species of fungus, which are used in the production of the antibiotics.
Answer:
Antibiotics are medicines that are produced by certain microorganisms to kill other disease causing microorgainsms. These medicines are commonly obtained from bacteria and fungi. The species of fungus used in the production of antibiotics are:

Antibiotic:

• Penicillin
• Cephalosporin

Fungus source:

• Penicillium notatum
• Cephalosporium acremonium

Question 7.
What is sewage? In which way can sewage be harmful to us?
Answer:
Sewage is the municipal waste – water collected from city or town homes, that contains toilet, bathroom and kitchen waste.
It contains large amounts of organic matter and many pathogenic microbes which are harmful to humans as they can cause many diseases like cholera, typhoid, polio.

Question 8.
What is the key difference between primary and secondary sewage treatment?
Answer:
Differences between Primary and Secondary sewage treatment:

Primary sewage treatment:

• It is a physical process.
• Primary treatment involves the removal of large sized floating and suspended solids.
• BOD is not affected in this treatment.

Secondary sewage treatment:

• It is a biological process.
• Secondary treatment involves decomposition of organic matter by microbial action which produce methane, hydrogen sulphide and carbon dioxide.
• BOD is less by secondary treatment.

Question 9.
Do you think microbes can also be used as source of energy? If yes, how?
Answer:
Yes, microbes can be used as a source of energy. Bacteria such as; Methane bacterium is used for the generation of gobar gas or biogas. The generation of biogas is an anaerobic process in a biogas plant, which consists of a concrete tank (10 – 15 feet deep) with sufficient outlets and inlets. The dung is mixed with water to form the slurry and thrown into the tank. The digester of the tank is filled with numerous anaerobic methane producing bacteria, which produce biogas from the slurry. Biogas can be removed through the pipe which is then used as a source of energy, while the spent slurry is removed from the outlet and is used as a fertilizer.

Question 10.
Microbes can be used to decrease the use of chemical fertilizers and pesticides. Explain how this can be accomplished.
Answer:
Microbes play an important role in organic farming which is done without the use of chemical fertilizers and pesticides. Biofertilizers are living organisms which help in increasing the fertility of soil. It involves the selection of beneficial microorganisms that help in improving plant growth through the supply of plant nutrients. Biofertilizers are introduced in seeds, roots or soil to mobilize the availability of nutrients. Thus, they are extremely beneficial in enriching the soil with organic nutrients.

Many species of bacteria and cyanobacteria have the ability to fix free atmospheric nitrogen, Rhizobium is a symbiotic bacteria found in the root nodules of leguminous plants. (MPBoardSolutions.com) Azospirilhum and Azotobacter are free living nitrogen – fixing bacteria, whereas Anabena, Nostoc and Oscillitoria are examples of nitrogen – fixing cyanobacteria. Biofertilizers are cost effective and eco – freindly. Microbes can also act as biopesticides to control insect pest in plants. An example of biopesticides is Bacillus thuringiensis, which produces a toxin that kills the insect pests.

Dried bacterial spores are mixed in water and sprayed in agricultural fields. When larvae of insects feed on crops, these bacterial spores enter the gut of the larvae and release toxins, thereby it. Similarly, Trichoderma are free living fungi. They live in the roots of higher plants and protect them from various pathogens. Baculoviruses is another bio – pesticides that is used as a biological control agent against insects and other arthropods.

Question 11.
Three water samples namely river water, untreated sewage water and secondary effluent discharged from a sewage treatment plant were subjected to BOD test. The samples were labelled A, B and C; but the laboratory attendant did not note which was which. The BOD values of the three samples A, B, and C were recorded as 20mg/L, 8 mg/L and 400mg/L, respectively. Which sample of the water is most polluted ? Can you assign the correct label to each assuming the river water is relatively clean?
Answer:
The BOD values of the three samples A, B and C were recorded as 20 mg/L, 8 mg/L and 400 mg/L. Greater the BOD of waste water more is its polluting potential. So, sample C is more polluting as compared to sample A. Hence, sample A is the secondary effluent, sample B is river water and sample C is untreated sewage water.

Question 12.
What is paneer? Give its preparation method.
Answer:
Paneer is a milk product, which has 20 – 30% protein first filtered and the milk in thin cloth than heat on 60°C at 30 minutes and heat on 75°C at 15 second later it cold till 30°C. Add some quantity of lactic acid bacteria Streptococcus lactis, Streptococcus cremoris and enzyme renin. By this fat and casein protein is detached from milk after 45 minutes this mixture became solid. Now, they are cut into small pieces and boild in hot water, when it starts floating, they are separated and squeezed. Then they are put in salt water for treating. Paneer is now ready.

Question 13.
What is the utilization of bacteria in agriculture?
Answer:
Uses of Bacteria : Uses of bacteria for agriculture are as follows :

1. They increase soil fertility due to decomposition of dead organisms.
2. They increase soil fertility through nitrogen fixation in soil.
3. Blue – green algae is used the form of fertilizers.
4. They balance the quantity of mineral salts.

Question 14.
How are the bacteria used in vinegar industry?
Answer:
Fermentation of sugar by yeast in vinegar industry. Due to this manner, wine is prepared. This ethyl alcohol abandoned in direct air for much time now, it is changed in vinegar.

Question 15.
Name live fungi which give antibiotics.
Answer:
The fungi which give antibiotics are as follows:

Question 16.
Name five bacteria which produce antibiotics.
Answer:
The bacteria which produce antibiotics are as follows:

Microbes in Human Welfare Long Answer Type Questions

Question 1.
Write seven useful activities of Bacteria.
Answer:
Useful activities of bacteria :

1. N₂ fixation : Some bacterias play an important role in nitrogen fixation example Azo – tobacter, Clostridium, Rhizobium. These bacterias increase the fertility of soil by the fixation of atmospheric nitrogen.
2. Lactic acid synthesis : Lactobacillus lacti converts the milk sugar into lactic acid.
3. Acetic acid synthesis: Acetobacter aceti takes part in synthesis of acetic acid or vinegar.
4. Rating of fibres: Isolation of wood fibres from the stem of plants is called rating. Clostridium butyricum is used in rating of fibres.
5. Tobacco and Tea industry : Some bacteria like Micococcus candisens is used to increase the flavour of the leaves of tobacco and tea. This process is called as seasoning.
6. Medicine production : Bacteria are the chief source of antibiotics, hence, they are used to extract antibiotics, example Streptomyces gresius (Streptomycine).
7. As symbionts: Bacteria presents in our body, helps in the various metabolic reactions example E.coli.

Question 2.
Write economic importance of fungi.
Answer:
Following are the economic importance of fungi:

1. As food : Mushrooms like Agaricus, Lycoperdon, Romaria, Clavasia are used as food. These mushrooms contain about 50% protein. Morchella is also used as food.
2. As medicine : Fungi provides various types of antibiotics as example Penicillin, Griseofulvine, Citrinine, Clavicine, Gliotoxine, etc. which are used in the treatment of disease.
3. Fertility of soil: Many fungi species increase the soil fertility by decomposition of dead organic matter.
4. Nitrogen fixation : Many fungus like Rhodotorula increases the soil fertility by nitrogen fixation.
5. In bakery industry : Yeast cells are used in bakery to produce spongy breads.
6. In wine industry : Yeast cells contain enzyme zymase which ferment sugar into alcohol.
7. In chemical industry : Many fungi species are used in the production of various types of acid like citric acid.
8. In cheese industry : Fungus Penicillium roqueforti is used in the preparation of camembert type of cheese from milk.

Question 3.
Explain the uses and types of virus.
Answer:
Uses of Viruses:

1. As it forms a link between non – living and living thus, it helps us to understand organic evolution.
2. Cyanophage (Blue – green algae) viruses are used to destroy blue – green algae grown in different areas.
3. Bacteriophages are used as biocides to destroy many harmful bacterias present in polluted area.

For example : Water of the river Ganga always remain pure and clean in bottles year after year due to presence of bacteriophage in it.

Nucleic acids of viruses : Viruses generally contain only one type of nucleic acid DNA or RNA. DNA is found in animal viruses, whereas RNA is found in plant viruses.

Human Immuno Virus (HIV):
It causes AIDS disease in human. Full form of AIDS is Acquired Immune Deficiency Syndrome. This virus destroys immune system of the body, thus, the patient of AIDS suffers from number of diseases at a time and at last he dies. This virus is found surrounded by protein and a ring of RNA is found at the centre. Whole body of virus is surrounded by a covering of glycoprotein.

Type of viruses:
On the basis of host infected, viruses are grouped into following four groups:

1. Animal viruses : Viruses which infect animals are called animal viruses. These viruses contain DNA as genetic material.
2. Plant viruses : Viruses which infect plants are called plant viruses. These viruses contain RNA as genetic material.
3. Cyanophages : Viruses that infect blue – green algae are called cyanophages. These viruses contain RNA as genetic material.
4. Bacterial viruses or Bacteriophages : Viruses that infect bacteria are called as bacteriophages. They contain DNA as genetic materials.

Question 4.
Find out the role of microbes in the following and discuss it with your teacher:

1. Single Cell Protein (SCP)
2. Soil.

Answer:
1. Single Cell Protein (SCP):
It refers to harmless microbial cells that can be used as an alternate source of good protein. Just like mushrooms (a fungus) is eaten by many people and yeast is used by athletes as a protein source; similarly, other forms of microbial cells can also be used as food rich in protein, minerals, fats, carbohydrate and vitamins. (MPBoardSolutions.com) Microbes like Spirullina and Methylophilus methylophus are being grown on an industrial scale on materials containing starch like waste water from potato processing plants, straw, molasses, animal manure and even sewage. These single cell microbes can be used as source of proteins.

2. Role of microbes in soil:
Microbes play an important role in organic farming which is done without the use of chemical fertilizers and pesticides. Biofertilizers are living organisms which help in increasing the fertility of soil. It involves the selection of beneficial microorganisms that help in improving plant growth through the supply of plant nutrients.

Biofertilizers are introduced in seeds, roots or soil to mobilize the availability of nutrients. Thus, they are extremely beneficial in enriching the soil with organic nutrients. Many species of bacteria and cyanobacteria have the ability to fix free atmospheric nitrogen, Rhizobium is a symbiotic bacteria found in the root nodules of leguminous plants. Azospirilhum and Azotobacter are free living nitrogen-fixing bacteria, whereas Anabena, Nostoc and Oscillitoria are examples of nitrogen – fixing cyanobacteria. Biofertilizers are cost effective and eco – freindly.

Microbes can also act as biopesticides to control insect pest in plants. An example of biopesticides is Bacillus thuringiensis, which produces a toxin that kills the insect pests. Dried bacterial spores are mixed in water and sprayed in agricultural fields. When larvae of insects feed on crops, these bacterial spores enter the gut of the larvae and release toxins, thereby it. Similarly, Trichoderma are free living fungi. (MPBoardSolutions.com) They live in the roots of higher plants and protect them from various pathogens. Baculoviruses is another bio – pesticides that is used as a biological control agent against insects and other arthropods.

Question 5.
Arrange the following in the decreasing order (most important first) of their importance, for the welfare of human society. Give reasons for your answer. Biogas, Citric acid, Penicillin and Curd.
Answer:
The order of arrangement of products according to their decreasing importance is:
Penicillin – Biogas – Citric acid – Curd.

Penicillin is the most important product for the welfare of human society. It is an antibiotic, which is used for controlling various bacteral diseases. The second most important product is biogas. It is an eco – friendly source of energy. The next important product is citric acid, which is used as a food preservative. The least important product is curd, a food item obtained by the action of lactobacillus bacteria on milk. Hence, the products in the decreasing order of their importance are as follows :
Penicillin – Biogas – Citric acid – Curd.

Question 6.
How do biofertilizers enrich the fertility of the soil?
Answer:
Biofertilizers are living orgainsms which help in increasing the fertility of soil. It involves the selection of beneficial microorganisms that help in improving plant growth through the supply of plant nutrients. These are introduced to seeds, roots, or soil to mobilize the availability of nutrients by their biological activity. Thus, they are extremely beneficial in enriching the soil with organic nutrients. (MPBoardSolutions.com) Many species of bacteria and cyanobacteria have the ability to fix free atmopheric nitrogen. Rhizobium is a symbiotic bacteria found in the root nodules of leguminous plants. Azospirillium and Azotobacter are free living nitrogen – fixing bacteria, whereas Anabaena, Nostoc and Oscillitoria are examples of nitrogen – fixing cyanobacteria. Biofertilizers are cost effective and eco – friendly.

Question 7.
Describe role of microorganisms in biogas production.
Answer:
The gas produced by anaerobic fermentation of waste biomass or waste bi – product is called as biogas.

Role of microorganisms in biogas production:
In biogas production under anaerobic condition, microorganism including methanogenes convert the bio – degradable organic waste into biogas and humus. The whole process is completed in three stages:

1. Solubilization
2. Acidogenesis
3. Methanogenesis.

1. Solubilization : In this step methanogenic bacteria hydrolyse the complex polymers into organic acids, alcohol by hydrolytic fermentation.

2. Acidogenesis : It is a biological reaction where simple monomers are Converted into volatile fatty acids, then into acetic acid, CO₂ and hydrogen.

3. Methenogenesis: Anaerobic digestion occurs in which acetate and CO₂ are converted into methane.

MP Board Class 12th Biology Important Questions