Prasanna

MP Board Class 8th Maths Solutions Chapter 11 क्षेत्रमिति Ex 11.2

प्रश्न 1.
एक मेज के ऊपरी पृष्ठ (सतह) का आकार समलंब जैसा है। यदि इसकी समांतर भुजाएँ 1 m और 1.2 m हैं तथा इन समांतर भुजाओं के बीच की दूरी 0.8 m है, तो इसका क्षेत्रफल ज्ञात कीजिए।

हल:
यहाँ समान्तर भुजाएँ a = 1.2 मी
b = 1 मी
समान्तर भुजाओं के बीच की दूरी h = 0.8 मी
मेज के ऊपरी पृष्ठ का क्षेत्रफल = समलम्ब का क्षेत्रफल
= \(\frac{1}{2}\) समान्तर भुजाओं का योग x उनके बीच की दूरी
= \(\frac{1}{2}\)(a + b) x h
= \(\frac{1}{2}\) (1.2 मी. + 1 मी.) x 0.8 मी
= \(\frac{1}{2}\) x 2.2 x 0.8 वर्ग मी.
= 0.88 वर्ग मीटर।
अत: मेज के ऊपरी पृष्ठ का क्षेत्रफल = 0.88 वर्ग मीटर।

प्रश्न 2.
एक समलम्ब का क्षेत्रफल 34 cm² है और इसकी ऊँचाई 4 सेमी है। समान्तर भुजाओं में से एक की 10 cm लम्बाई है। दूसरी समान्तर भुजा की लम्बाई ज्ञात कीजिए।
हल:
समलम्ब का क्षेत्रफल = 34 सेमी²
ऊँचाई = 4 सेमी
समलम्ब की एक समान्तर भुजा = 10 सेमी
माना कि दूसरी समान्तर भुजा = a सेमी
समलम्ब का क्षेत्रफल = \(\frac{1}{2}\) x समान्तर भुजाओं का योग x ऊँचाई
34 सेमी² = \(\frac{1}{2}\) (10 + a) x 4
10 + a = \(\frac{34×2}{4}\) = 17
a = 17 – 10 = 7 सेमी
अतः समलम्ब की दूसरी समान्तर भुजा की लम्बाई = 7 सेमी।

प्रश्न 3.
एक समलम्ब के आकार के खेत ABCD की बाड़ की लम्बाई 120 m है। यदि BC = 48 m, CD = 17 m और AD = 40 m है, तो इस खेत का क्षेत्रफल ज्ञात कीजिए। भुजा AB समान्तर भुजाओं AD तथा BC पर लंब है।

हल:
खेत ABCD की बाड़ की लम्बाई = 120 मी.
BC = 48 मी
CD = 17 मी और
AD = 40 मी
खेत की बाड़ की लम्बाई = AB + BC + CD + DA
120 मी = AB + 48 मी + 17 मी + 40 मी
120 मी = AB + 105 मी
AB = 120 मी – 105 मी = 15 मी
∴ समलम्ब का क्षेत्रफल = \(\frac{1}{2}\) समान्तर भुजाओं का योग x उनके बीच की दूरी।
∴ समलम्ब का क्षेत्रफल = \(\frac{1}{2}\) x (48 + 40) x 15 वर्ग मीटर
= \(\frac{1}{2}\) x 88 x 15
= 660 वर्ग मीटर।
अतः खेत ABCD का क्षेत्रफल = 660 वर्ग मीटर।

प्रश्न 4.
एक चतुर्भुज आकार के खेत का विकर्ण 24 m है और शेष सम्मुख शीर्षों से इस विकर्ण पर खींचे गए लम्ब 8 m एवं 13 m हैं। खेत का क्षेत्रफल ज्ञात कीजिए।
हल:
यहाँ d= 24 मी
h₁ = 13 मी, h₂ = 8 मी

∴ खेत का क्षेत्रफल = \(\frac{1}{2}\) x d (h₁ + h₂)
∴ खेत का क्षेत्रफल = \(\frac{1}{2}\) x 24 x (13 + 8) मीटर²
\(\frac{1}{2}\) x 24 x 21 मीटर² = 252 मीटर²
अतः चतुर्भुज आकार के खेत का क्षेत्रफल = 252 मीटर

प्रश्न 5.
किसी समचतुर्भुज के विकर्ण 7.5 cm एवं 12 cm हैं। इसका क्षेत्रफल ज्ञात कीजिए।
हल:
यहाँ, समचतुर्भुज के विकर्ण = 7.5 सेमी और 12 सेमी हैं।
∴ समचतुर्भुज का क्षेत्रफल= \(\frac{1}{2}\) x विकर्णों का गुणनफल
समचतुर्भुज का क्षेत्रफल = \(\frac{1}{2}\) x (7.5 x 12) वर्ग सेमी
= 45 वर्ग सेमी।
अतः समचतुर्भुज का क्षेत्रफल = 45 वर्ग सेमी।

प्रश्न 6.
एक समचतुर्भुज का क्षेत्रफल ज्ञात कीजिए जिसकी भुजा 6 cm और शीर्ष लम्ब 4 cm है। यदि एक विकर्ण की लम्बाई 8 cm है तो दूसरे विकर्ण की लम्बाई ज्ञात कीजिए।
हल:
समचतुर्भुज की भुजा = 6 सेमी
शीर्ष लम्ब = 4 सेमी
एक विकर्ण की लम्बाई =8 सेमी
दूसरे विकर्ण की लम्बाई =d सेमी
समचतुर्भुज का क्षेत्रफल = आधार x शीर्ष लम्ब
= 6 x 4वर्ग सेमी = 24 वर्ग सेमी।
∴ समचतुर्भुज का क्षेत्रफल = \(\frac{1}{2}\) x विकर्णों का गुणनफल
∴ 24 वर्ग सेमी = \(\frac{1}{2}\) x 8 x d
∴ d = \(\frac{24×2}{2}\) = 6 सेमी
अतः समचतुर्भुज का क्षेत्रफल = 24 वर्ग सेमी
दूसरे विकर्ण की लम्बाई = 6 सेमी।

प्रश्न 7.
किसी भवन के फर्श में समचतुर्भुज के आकार की 3000 टाइलें हैं और इनमें से प्रत्येक के विकर्ण 45 cm और 30 cm लम्बाई के हैं। ₹ 4 प्रति वर्ग मीटर की दर से इस फर्श को पॉलिश करने का व्यय ज्ञात कीजिए।
हल:
टाइल के विकर्ण = 45 सेमी और 30 सेमी
टाइलों की संख्या = 3000
पॉलिश का व्यय = ₹ 4 प्रति वर्ग मीटर
∴ 1 टाइल का क्षेत्रफल = \(\frac{1}{2}\) x विकर्णों का गुणनफल
= \(\frac{1}{2}\) x 45 x 30 वर्ग सेमी।
= 675 वर्ग सेमी
∴ 3000 टाइलों का क्षेत्रफल = 3000 x 675 वर्ग सेमी
= 2025000 वर्ग सेमी
= \(\frac{2025000}{100×100}\) वर्ग मीटर
= 202.5 वर्ग मीटर।
∴ फर्श का क्षेत्रफल = 202.5 वर्ग मीटर।
फर्श पर पॉलिश करने का व्यय = ₹ 4 x 202.5
= ₹ 810
अतः फर्श पर पॉलिश करने का व्यय = ₹ 810

प्रश्न 8.
मोहन एक समलम्ब के आकार का खेत खरीदना चाहता है। इस खेत की नदी के साथ वाली भुजा सड़क के साथ वाली भुजा के समान्तर है और लम्बाई में दुगुनी है। यदि इस खेत का क्षेत्रफल 10,500 m हैं और दो समांतर भुजाओं के बीच की लम्बवत् दूरी 100 m है, तो नदी के साथ वाली भुजा की लम्बाई ज्ञात कीजिए।

हल:
खेत का क्षेत्रफल = 10,500 m²
माना कि सड़क के साथ वाली भुजा की लम्बाई = x मीटर
नदी के साथ वाली भुजा की लम्बाई = 2x मीटर
दोनों भुजाओं के बीच की दूरी = 100 मीटर
खेत का क्षेत्रफल = \(\frac{1}{2}\)
\(\frac{1}{2}\) x समान्तर भुजाओं का योग x उनके बीच की दूरी
10500 मी² = \(\frac{1}{2}\) x (x + 2x) x 100
3x = \(\frac{10500×2}{100}\)
x = \(\frac{10500×2}{3×100}\)
= 70 मीटर
अतः नदी के साथ वाली भुजा की लम्बाई = 2x = 2 x 70
=140 मीटर।

प्रश्न 9.
एक ऊपर उठे हुए चबूतरे का ऊपरी पृष्ठ अष्टभुज के आकार का है जैसा कि आकृति में दर्शाया गया है। अष्टभुजी पृष्ठ का क्षेत्रफल ज्ञात कजिए।

हल:
अष्टभुजी पृष्ठ ABCDEFGH का क्षेत्रफल = समलम्ब ABGH का क्षेत्रफल + आयत BCFG का क्षेत्रफल + समलम्ब CDEF का क्षेत्रफल = \(\frac{1}{2}\) x (5 + 11) x 4 + 11 x 5 + \(\frac{1}{2}\) x (11 + 5) x 4 वर्ग मीटर
= 32 + 55 + 32 वर्ग मीटर
= 119 वर्ग मीटर।
अतः अष्ठभुजी पृष्ठ का क्षेत्रफल = 119 वर्ग मीटर।

प्रश्न 10.
एक पंचभुज आकार का बगीचा है जैसा कि आकृति में दर्शाया गया है। इसका क्षेत्रफल ज्ञात करने के लिए ज्योति और कविता ने इसे दो विभिन्न तरीकों से विभाजित किया। दोनों तरीकों का उपयोग करते हुए इस बगीचे का क्षेत्रफल ज्ञात कीजिए। क्या आप इसका क्षेत्रफल ज्ञात करने की कोई और विधि बता सकते हैं?

हल:
ज्योति के आरेख द्वारापंचभुज आकार के बगीचे का क्षेत्रफल = 2 x समलम्ब ARCLका क्षेत्रफल
यहाँ, समलम्ब की समान्तर भुजाएँ = 30 मी और 15 मी
समान्तर भुजाओं के बीच की दूरी = \(\frac{15}{2}\) मी = 7.5 मी
अतः बगीचे का क्षेत्रफल = 2 x समान्तर भुजाओं का योग x उनके बीच की दूरी
= 2 x \(\frac{1}{2}\) (30 + 15) x 7.5 वर्ग मी
= 45 x 7.5 वर्ग मी
= 337.5 वर्ग मीटर।
अत: ज्योति के आरेख द्वारा पंचभुज आकार के बगीचे का क्षेत्रफल = 337.5 वर्ग मीटर।

कविता के आरेख द्वारा:

पंचभुज आकार के बगीचे का क्षेत्रफल = ∆ का क्षेत्रफल + वर्ग का क्षेत्रफल
यहाँ, त्रिभुज का आधार = 15 मीटर
त्रिभुज की ऊँचाई = 15 मीटर
वर्ग की भुजा = 15 मीटर

अतः बगीचे का क्षेत्रफल = \(\frac{1}{2}\) x आधार x ऊँचाई + वर्ग की भुजा
= \(\frac{1}{2}\) x 15 x 15 + (15)² वर्ग मीटर
= \(\frac{225}{2}\) + 225 वर्ग मीटर
= 112.5 + 225 वर्ग मीटर
= 337.5 वर्ग मीटर।
अतः कविता के आरेख द्वारा बगीचे का क्षेत्रफल = 337.5 वर्ग मीटर।

अन्य विधि:

अभीष्ट क्षेत्रफल = आयत BDEG का क्षेत्रफल – 2 x ∆ABC का क्षेत्रफल
= 15 x 30 – 2 x \(\frac{1}{2}\) = \(\frac{15}{2}\) x 15 वर्गमीटर
= 450 वर्ग मी – 112.5 वर्गमीटर
= 337.5 वर्ग मीटर
अतः बगीचे का अभीष्ट क्षेत्रफल = 337.5 वर्ग मीटर

प्रश्न 11.
संलग्न पिक्चर फ्रेम के आरेख की बाहरी एवं अंतः विमाएँ क्रमशः 24 cm x 28 cm एवं 16 cm x 20 cm हैं। यदि फ्रेम के प्रत्येक खंड की चौड़ाई समान है, तो प्रत्येक – खंड का क्षेत्रफल ज्ञात कीजिए।

हल:

खण्ड ABQP का क्षेत्रफल = खण्ड CDSR का क्षेत्रफल
= \(\frac{1}{2}\) x (AB + PQ) x 4 सेमी
= \(\frac{1}{2}\) ( 28 + 20) x 4 सेमी²
= 48 x 2 वर्ग सेमी
= 96 वर्ग सेमी।
खण्ड BCRQ का क्षेत्रफल = खण्ड APSD का क्षेत्रफल
= \(\frac{1}{2}\) (BC + QR) x 4 वर्ग सेमी
= \(\frac{1}{2}\) (24 + 16) x 4 वर्ग सेमी
= 40 x 2 = 80 वर्ग सेमी। उत्तर

पाठ्य-पुस्तक पृष्ठ संख्या # 187

ठोस आकार

प्रश्न 1.
ध्यान दीजिए कि कुछ आकारों में दो या दो से अधिक समरूप (सर्वांगसम) फलक हैं। उनको नाम दीजिए। कौन से ठीसों में सभी फलक सर्वांगसम हैं?

हल:
ठोस आकारों में घनाभ, बेलन, घन और पिरामिड में दो या दो से अधिक फलक समरूप सर्वांगसम हैं। घन में सभी फलक सर्वांगसम हैं।

पाठ्य-पुस्तक पृष्ठ संख्या # 188

सोचिए, चर्चा कीजिए और लिखिए (क्रमांक 11.2)

प्रश्न 1.
संलग्न आकृति में दर्शाए गए ठोस को बेलन कहना क्यों गलत है?

हल:
बेलन में दो वृत्ताकार सर्वांगसम फलक होते हैं। लेकिन इस आकृति के फलक सर्वांगसम नहीं है।
अतः दिए गए ठोस को बेलन कहना गलत है। उत्तर

पाठ्य-पुस्तक पृष्ठ संख्या # 189

प्रयास कीजिए (क्रमांक 11.7)

प्रश्न 1.
निम्नलिखित घनाभों (आकृति 11.32) का कुल पृष्ठीय क्षेत्रफल ज्ञात कीजिए –

हल:
(i) लम्बाई l = 6 सेमी
चौड़ाई b = 4 सेमी
ऊँचाई R = 2 सेमी
∵ कुल पृष्ठीय क्षेत्रफल = 2(lb + bh + hl)
∵ कुल पृष्ठीय क्षेत्रफल = 2 (6 x 4 + 4 x 2 + 2 x 6) वर्ग सेमी
= 2 (24 + 8 + 12) वर्ग सेमी
= 2 x 44 वर्ग सेमी
= 88 वर्ग सेमी।

(ii) लम्बाई l = 4 सेमी
चौड़ाई b = 4 सेमी
ऊँचाई h = 10 सेमी
∵ कुल पृष्ठीय क्षेत्रफल = 2(lb + bh + hl)
∵ कुल पृष्ठीय क्षेत्रफल = 2 (4 x 4 + 4 x 10 + 10 x 4) वर्ग सेमी
= 2 (16 + 40 + 40) वर्ग सेमी
= 2 (96) वर्ग सेमी
= 192 वर्ग सेमी।

पाठ्य-पुस्तक पृष्ठ संख्या # 190

इन्हें कीजिए (क्रमांक 11.3)

प्रश्न 1.
1. एकघनाभाकार डस्टर (जिसे आपके अध्यापक कक्षा में उपयोग करते हैं। के पार्श्व पृष्ठ को भूरे रंग के कागज़ की पट्टी से इस प्रकार ढकिए कि यह डस्टर के पृश्ठ के चारों ओर बिल्कुल ठीक बैठे। कागज़ को हटाइए। कागज़ का क्षेत्रफल मापिए। क्या यह डस्टर का पार्श्व पृष्ठीय क्षेत्रफल है?
2. अपनी कक्षा के कमरे की लम्बाई, चौड़ाई और ऊँचाई मापिए और निम्नलिखित को ज्ञात कीजिए

(a) खिड़कियों और दरवाजों के क्षेत्रफल को छोड़कर कमरे का कुल पृष्ठीय क्षेत्रफल।
(b) इस कमरे का पार्श्व पृष्ठीय क्षेत्रफल।
(c) सफेदी किए जाने वाला, कमरे का कुल क्षेत्रफल।

हल:
1. हाँ, कागज का क्षेत्रफल डस्टर के पार्श्व पृष्ठीय क्षेत्रफल के बराबर है।

2. कक्षा के कमरे की लम्बाई, चौड़ाई तथा ऊँचाई मापने पर,
लम्बाई = 6 मी
चौड़ाई = 5 मी तथा
ऊँचाई = 4 मी

(a) कमरे का कुल पृष्ठीय क्षेत्रफल = 2(lb + bh + hl)
= 2(6 x 5 + 5 x 4 + 4 x 6) वर्ग मीटर।
= 2 (30 + 20 + 24) वर्ग मीटर
= 2 (74) वर्ग मीटर
= 148 वर्ग मीटर।

(b) कमरे का पार्श्व पृष्ठीय क्षेत्रफल = 2 (l + b)h
= 2 (6 + 5) x 4 वर्ग मीटर
= 2 x 11 x 4 वर्ग मीटर
= 88 वर्ग मीटर।

(c) सफेदी किए जाने वाला कमरे का कुल क्षेत्रफल = कमरे का पार्श्व पृष्ठीय क्षेत्रफल + छत का क्षेत्रफल
= 88 वर्ग मीटर + 6 x 5 वर्ग मीटर
= 88 + 30 वर्ग मीटर
= 118 वर्ग मीटर।

सोचिए, चर्चा कीजिए और लिखिए (क्रमांक 11.3)

प्रश्न 1.
क्या हम कह सकते हैं कि घनाभ का कुल पृष्ठीय क्षेत्रफल = पार्श्व पृष्ठीय क्षेत्रफल + 2 x आधार का क्षेत्रफल।
हल:
हाँ, हम कह सकते हैं कि घनाभ का कुल पृष्ठीय क्षेत्रफल = पार्श्व पृष्ठीय क्षेत्रफल + 2 x आधार का क्षेत्रफल
2 (l + b)h + 2 x lb = 2 (hl + bh + lb)
= 2 (1b + bh + hl)

प्रश्न 2.
यदि हम किसी घनाभ [ आकृति 11.33 (i)] की ऊँचाई और आधार की लम्बाई को परस्पर बदलकर एक दूसरा घनाभ [(आकृति 11.33 (ii)] प्राप्त करलें तो क्या = पार्श्व पृष्ठीय क्षेत्रफल बदल जाएगा?

हल:
घनाभ (i) का पार्श्व पृष्ठीय क्षेत्रफल
= 2 (l + b)h ….(1)
तथा घनाभ (ii) का पार्श्व पृष्ठीय क्षेत्रफल
= 2 (h + b)l …(2)
स्पष्ट है कि दोनों पार्श्व पृष्ठीय क्षेत्रफल भिन्न हैं।
अतः ऊँचाई और आधार की लम्बाई को बदलने पर पार्श्व पृष्ठीय क्षेत्रफल बदल जाएगा।

इन्हें कीजिए (क्रमांक 11.4)

प्रश्न 1.
एक वर्गांकित कागज पर दर्शाए गए पैटर्न को खींचिए और उसे काटिए [ आकृति 11.34 (i)]। आप जानते हैं कि यह पैटर्न घन का जाल (नेट) है। इसे रेखाओं के अनुदिश मोडिए[आकृति 11.34 (ii)]और घन बनाने के लिए किनारों पर टेप लगाइए [ आकृति 11.34 (iii) ]।

(a) इस घन की लम्बाई, चौड़ाई और ऊँचाई क्या है? ध्यान दीजिए घन के सभी फलक वर्गाकार हैं। = इसलिए घन की लम्बाई, चौड़ाई और ऊँचाई समान होती है (आकृति 11.35)।

(b) प्रत्येक फलक का क्षेत्रफल लिखिए। क्या सभी फलकों के क्षेत्रफल समान हैं?
(c) इस घन का कुल पृष्ठीय क्षेत्रफल लिखिए।
(d) यदि घन की प्रत्येक भुजा है, तो प्रत्येक फलक का क्षेत्रफल क्या होगा [ आकृति 11:35 (ii)]। क्या हम कह सकते हैं कि । भुजा वाले घन का कुल पृष्ठीय क्षेत्रफल 612 है?
हल:
(a) क्योंकि घन के सभी फलक वर्गाकार आकृति के होते हैं।
अत: घन की लम्बाई = चौड़ाई = ऊँचाई = प्रत्येक 3 इकाई।

(b) प्रत्येक फलक का क्षेत्रफल = (भुजा)²
= (3)² = 9 वर्ग इकाई।
हाँ, सभी फलकों के क्षेत्रफल समान हैं।

(c) घन का कुल पृष्ठीय क्षेत्रफल = 612 वर्ग इकाई
= 6 x (3)²
= 54 वर्ग इकाई।

(d) घन की प्रत्येक भुजा = l
∴ प्रत्येक फलक का क्षेत्रफल = l x l x l²
भुजा वाले घन का पृष्ठीय क्षेत्रफल = 2 (l x l + l x l + l x l)
= 2(l² + l² + l²)
= 2 x 3l² = 6l²
हाँ, हम कह सकते हैं कि ! भुजा वाले घन का कुल पृष्ठीय क्षेत्रफल 612 है।

पाठ्य-पुस्तक पृष्ठ संख्या # 191

प्रयास कीजिए (क्रमांक 11.8)

प्रश्न 1.
घन A का पृष्ठीय क्षेत्रफल और घन B का पार्श्व पृष्ठीय क्षेत्रफल ज्ञात कीजिए।

हल:
घन A की लम्बाई = चौड़ाई = ऊँचाई = 10 सेमी घन का पृष्ठीय क्षेत्रफल = 6l²
= 6 x (10)² = 6 x 100
= 600 वर्ग सेमी
अतः घन A का पृष्ठीय क्षेत्रफल = 600 वर्ग सेमी।
घन B की लम्बाई = चौड़ाई = ऊँचाई = 8 सेमी घन B का पार्श्व पृष्ठीय क्षेत्रफल = 2(l + l) x l
= 2 (8 + 8) x 8 वर्ग सेमी
= 2 x 16 x 8 वर्ग सेमी।
= 256 वर्ग सेमी।
अतः घन B का पार्श्व पृष्ठीय क्षेत्रफल = 256 वर्ग सेमी।

सोचिए, चर्चा कीजिए और लिखिए (क्रमांक 11.4)

प्रश्न 1.
1. b भुजा वाले दो घनों को मिलाकर एक घनाभ बनाया गया है (आकृति 11.37) । इस घनाभ का पृष्ठीय क्षेत्रफल क्या है? क्या यह 1252 है? क्या ऐसे तीन घनों को मिलाकर बनाए गए घनाभ का पृष्ठीय क्षेत्रफल 1862 है? क्यों?

2. न्यूनतम पृष्ठीय क्षेत्रफल का घनाभ निर्मित करने के लिए समान भुजा वाले 12 घनों को किस प्रकार व्यवस्थित करेंगे?

3. किसी घन के पृष्ठीय क्षेत्रफल पर पेंट करने के पश्चात् उस घन को समान विमाओं वाले 64 घनों में काटा जाता है (आकृति 11.38)। इनमें से कितने घनों का कोई भी फलक पेंट नहीं हुआ है? कितने घनों का 1 फलक पेंट हुआ है? कितने घनों के 2 फलक पेंट हुए हैं ? कितने घनों के तीन फलक पेंट हुए हैं?

हल:
1. b भुजा वाले दो घनों को मिलाकर बने घनाभ की लम्बाई l = b + b = 2b इकाई, चौड़ाई = b इकाई तथा ऊँचाई = b इकाई इस घनाभ का पृष्ठीय क्षेत्रफल = 2 (lb + bh + hl)
= 2 (2b x b + b x b + b x 2b)
= 2 (2b² + b² + 2b²)
= 2 x 5b² = 10b² वर्ग इकाई
अत: घनाभ का पृष्ठीय क्षेत्रफल = 10b² वर्ग इकाई उत्तर नहीं, यह 12b² नहीं है।
जब ऐसे तीन घनों को मिलाकर घनाभ बनाया जाता है, तब घनाभ की लम्बाई l = 3b, चौड़ाई = b, ऊँचाई = b इस घनाभ का पृष्ठीय क्षेत्रफल = 2 (3b x b + b x b + b x 3b)
= 2 (3b² + b² + 3b²) वर्ग इकाई
= 2 x 7b² = 14b² वर्ग इकाई
नहीं, इस प्रकार बने घनाभ का पृष्ठीय क्षेत्रफल 18b2 नहीं है। क्योंकि घनाभ की चौड़ाई और ऊँचाई में कोई परिवर्तन नहीं हुआ है।

2. प्रथम स्थिति:
घनाभ निर्मित करने के लिए समान भुजा वाले 12 घनों को लम्बाई में व्यवस्थित करने पर

इस स्थिति में, l = 12b
b = b
h = b
पृष्ठीय क्षेत्रफल = 2 (12b x b + b x b + b x 12b)
= 2(12b² + b² + 12b²)
= 2 x 25b² = 50b²

द्वितीय स्थिति:

इस स्थिति में,
l = 6b
b = b
h = 2b
∴ इस घनाभ का पृष्ठीय क्षेत्रफल = 2(6b x b + b x 2b + 2b x 6b)
= 2(66² + 2b² + 12b²)
= 2 x 20b² = 40b²

तृतीय स्थिति:

इस स्थिति में,
l = 4b
b = b
h = 3b
∴ इस घनाभ का पृष्ठीय क्षेत्रफल = 2 (4b x b + b x 3b + 3b x 4b)
= 2(4b² + 3b² + 12b²)
= 2 x 19b² = 38b²
अतः न्यूनतम पृष्ठीय क्षेत्रफल का घनाभ निर्मित करने के लिए समान भुजा वाले 12 घनों को तृतीय स्थिति के अनुसार व्यवस्थित करना चाहिए।

3. घनों की संख्या जिनके कोई भी फलक पेंट नहीं हुए = 16
घनों की संख्या जिनका 1 फलक पेंट हुआ = 16
घनों की संख्या जिनके 2 फलक पेंट हुए = 24
घनों की संख्या जिनके 3 फलक पेंट हुए = 8

पाठ्य-पुस्तक पृष्ठ संख्या # 193

प्रयास कीजिए (क्रमांक 11.9)

प्रश्न 1.
निम्नलिखित बेलनों का कुल पृष्ठीय क्षेत्रफल ज्ञात कीजिए (आकृति : 11.39)

हल:
(i) त्रिज्या r = 14 सेमी
ऊँचाई h = 8 सेमी
बेलन का कुल पृष्ठीय क्षेत्रफल = 2πr (r + h)
= 2 x \(\frac{22}{7}\) 14 (14 + 8)
= 2 x 22 x 2 x 22 वर्ग सेमी
= 1936 वर्ग सेमी
अतः कुल पृष्ठीय क्षेत्रफल = 1936 वर्ग सेमी

(ii) यहाँ, त्रिज्या r = \(\frac{2}{2}\) मी = 1 मी
ऊँचाई h = 2 मी
बेलन का पृष्ठीय क्षेत्रफल = 2πr (r + h)
= 2 x \(\frac{22}{7}\) x 1 (1 + 2) वर्ग मी
= \(\frac{44}{7}\) x 3 वर्ग मी.
= \(\frac{132}{7}\) वर्ग मी.
= 186 वर्ग मी.
अत: बेलन का कुल पृष्ठीय क्षेत्रफल = 18\(\frac{6}{7}\) वर्ग मी

सोचिए, चर्चा कीजिए और लिखिए (क्रमांक 11.5)

प्रश्न 1.
नोट कीजिए कि किसी बेलन का पार्श्व पृष्ठीय (वक्र पृष्ठीय क्षेत्रफल) आधार की परिधि x बेलन की ऊँचाई के समान होता है। क्या हम घनाभ के पार्श्व पृष्ठीय क्षेत्रफल को आधार का परिमाप x घनाभ की ऊँचाई के रूप में लिख सकते हैं?
हल:
माना कि घनाभ की लम्बाई, चौड़ाई और ऊँचाई क्रमशः l, b तथा h हैं, तब
घनाभ का पार्श्व पृष्ठीय क्षेत्रफल = 2 (l + b) x h
= आधार का परिमाप x ऊँचाई
अतः हम घनाभ के पार्श्व पृष्ठीय क्षेत्रफल को आधार का परिमाप – घनाभ की ऊँचाई के रूप में लिख सकते हैं।

MP Board Class 8th Maths Solutions

MP Board Class 6th Social Science Solutions Chapter 12 The Mauryan Empire

MP Board Class 6th Social Science Text Book Exercise

Answer the following questions in (short answer type):

Question 1.
Question (a)
How was Ashoka’s attitude changed?
Answer:
Ashoka was saddened by the wounded and dying soldiers and the unhappiness that Kalinga war had caused to the women and children. When he saw so much bloodsheel, he was very disturbed. He vowed never to go to war again. He then decided that he would not fight any more.

Question (b)
Which Architecture of Ashoka was adopted as our National symbol?
Answer:
We got the Architecture of our National Symbol from the pillar at Sarnath. It was made by Ashoka.

Question (c)
In what scirpt are Ashoka’s petrographs found?
Answer:
Ashoka gave many messages to the people, which are still found in the form of petrographs. These petrographs were inscribed on such places that people could read them and learn something. The petrograph of Ashoka were inscribed in Bramhi, Kharosthi and Aremaic. They all belong to the language Prakrat. The Bramhi script in India, Khorashti in Bangladesh and Pakistan, and Aremic was in Afganistan.

The language and script of common people was used in the petrographs so that they could understand the thoughts of the Emperor.

Question (d)
What was the work of Dharma Mahamatyas?
Answer:
After the war of Kalinga the feelings of remorse and misery led Ashoka to embrace the Buddhist religion. After twelth year of his reign, he began issuing edicts. From that time he exerted himself energetically to propagate Buddhism. He visited the holy places of Buddhism.

He instructed his high officials to proceed oh circuit every five years and to spread the dharma among the people. He instituted a special class of the officers called Dharma Mahamatras whose sole business was to propagate dhamma among the people. Moreover, he enacted a code of morality for his people to lead a peaceful and virtuous life. This he called dharma.

The edicts were written in Prakrit, the language spoken by the common people. In those days, Sanskrit was the language of the learned. To spread the essential features of his dharma he engraved them on rocks, pillars, and caves, throughout his vast dominions.

In Afghanistan Greek was spoken by the common people at that time. So some of Ashoka’s edicts were also composed in Greek and inscribed in Afghanistan.

Question (e)
Who used to give advise to the emperor?
Answer:
There was a council of people called Mantri Parishad to advise the king. The heads of all the departments lived in Patliputra. The empire was divided into four provinces. Each province was governed by a governor. Most of the governers were the princes. Every province was further divided into districts and in districts, villages were also included. There were various officers to look after the law and order.

Answer the following questions in details:

Question 2.
Question (a)
Describe the expansion of the empire of Chandragupta?
Answer:
Chandragupta raised an army and dethroned king Nanda. He himself became the king. The people welcomed the new king. He established his power in Magadah. He turned his eyes towards the Punjab in the northwest. He Soon won over the Punjab. In 305 B.C. after a long compaign in the far north he defeated Alexander’s general Seleucus Nicator, crossed the river Indus and conquered Afghanistan. In this way Chandragupta established his empire over the whole of northern India.

Question (b)
Give the cause of decline of the Mauryan Empire?
Answer:
The vast Mauryan empire established by Emperor Ashoka and his ahcestors lasted for a little over a hundred years It began to break up after the death of Ashoka. It was difficult to maintain contact and to administer such a large empire. The successors of Ashoka were not as capable as him. Adequate taxes needed to run the empire could not be collected.

The several rulers under Ashoka now became independent. Thus, the empire became weak. As a result of this disunity the Greek ruler of Bactria attacked India from the north west but since he did not get help from any other king, he was defeated. After twenty years, in 185 B.C. Pushymitra Shungha murdered the last Mauryan ruler. The Mauryan dynasty thus came to an end.

Question (c)
What did Ashoka do for the public welfare?
Answer:
Ashoka looked upon his subjects as his own children and did all he could to make them lead better and happier life. He writes in his edicts, “Men are my children.” He did the following welfare for the good of his people:

1. He built many hospitals both for men and animals.
2. He made roads, lined with trees and rest houses at regular intervals.
3. He gave sums of money in charity to the poor.
4. He apointed a special group of officers called the dhamma mahamatras to listen to the people and hear their complaints.

MP Board Class 6th Social Science Very short answer type questions:

Question 3.
Question (a)
What is called an empire?
Answer:
When the kings expand the limits of their states, then those states are called empire.

Question (b)
Who established the Maurya empire?
Answer:
Chandragupta Maurya established the Maurya empire.

Question (c)
What religion did Ashoka believe?
Answer:
Ashoka became the follower of Buddhism. He believed in the high human ideals so that people live in peace and follow moral conduct. He named them Dhamma.

Question (d)
What country did Ashoka send his son and daughter?
Answer:
Ashoka sent his son Mahendra and daughter Sanghmitra to Sri Lanka for preaching Buddhism.

Question 4.
Fill in the blanks:

1. The capital of Maurya Empire was …………………..
2. Ashoka was the follower of religion …………………..
3. The guru of Chandragupta was ………………..
4. ………………. was the greek ambassador in the state of Chandragupta.

Answer:

1. Patliputra
2. Buddhism
3. Chanakya (Kautilya)
4. Megasthnese

Question 5.
Make Pairs:

Answer:

Project work

Question 1.
Write down what you see on the currency notes and postage stamps?
Answer:
Do yourself.

MP Board Class 6th Social Science Solutions

MP Board Class 6th Social Science Solutions Chapter 22 The Local Self-Governing Bodies in Cities

MP Board Class 6th Social Science Chapter 22 Text Book Exercise

MP Board Class 6th Social Science Chapter 22 Short Answer Type Question

Question 1.
Question (a)
What are the local self – governing bodies in cities called?
Answer:
The local self – governing bodies in cities and towns are called Nagar Panchayat, Municipal Committees and Municipal Corporation.They are also called local bodies.

Question (b)
What is the population for which Nagar Panchayats can be formed?
Answer:
Nagar Panchayat forms in town where the population is lying between 5,000 to 20,000.

Question (c)
What is the work of Aldermen?
Answer:
The members of the Nagar Panchayat nominate some experienced people for advice, who are called Alderman. Aldermen can only suggest the Nagar Panchayat but they do not have the right to vote in passing any resolution.

MP Board Class 6th Social Science Chapter 22 Long Answer type Question

Question 2.
Question (a)
What are the compulsory functions of the local bodies in cities? Mention any five.
Answer:
Following are the main functions of the local bodies:

1. Plan a systematic development of the town/city and give permission for constructions and land utilization.
2. Plan for a social, and economic development of the area.
3. Ensure maintenance of roads, bridges and regular power supply.
4. Work for people’s good health and ensure supply of pure, drinking water and removal of waste material.
5. Provide social security.
6. Plant trees and protect them.
7. Provide security to weaker sections of the society, especially the mentally or the physically challenged.
8. Provide appropriate facilities in slums.
9. Work towards removal of poverty.
10. Work towards beautification of the town/city by developing parks, gardens, play grounds, etc.

Question (b)
What are the optional functions of the local bodies in cities?
Answer:
Besides compulsory works, the municipalities also maintain the fire services for extinguishing fire, construct the parks, museums and toilets etc.

Question (c)
Mention the sources of income of the local bodies in cities.
Answer:
The local bodies function with the help of income from the following sources:

1. Property tax on house, land etc.
2. Tax on trade and business.
3. Fees on water facilities.
4. Fees on electricity facilities.
5. Income and rent earned from the institutions, property like the buildings, markets, etc.
6. Grants from the state government.
7. Income from various kinds of fine on pets or stray animals etc.

Question (d)
What is meant by Ward, Mayor, President and Vice – president?
Answer:
Ward:
Nagars or towns are divided into smaller areas called the wards.

Mayor:
The president of the Municipal Corporation is called the Mayor. The mayor is directly elected and deputy – mayor is elected by the elected corporators.

President of Municipality:
The President of municipality is elected by the people. The meetings of the municipality take place regularly, chaired by the President. In his/ her absence the Vice-President, chairs the meeting.

Vice-President of Municipality:
The vice-president is elected by the elected councellers.

Question (e)
How are Nagar Panchayats and Municipalities constituted? Explain.
Answer:
Constitution of Nagar Panchayat:

1. To be able to become a member, a person has to be atleast 21 years old.
2. The voters elect these members, the voters must be at least 18 years old.
3. Some seat are kept reserved for the schedule caste, schedule tribes, backward class and female members.
4. Once constituted, these bodies have a term period of 5 years.
5. If the period gets over or is dissolved mitlway then a fresh election has to take place within six months.

Constitution of Municipalities:
The municipality is formed on the basis of population of a city. It consists of the elected representatives of the local people. This number is generally between fifteen and sixty, depending upon population of the city. Apart from this some other experienced members known as Eldermen, are elected by the members of the Municipality.

The elected-officer-bearers of the municipality are:

1. The Chairman and
2. The Vice – chairman.

Besides these elected officer bearers there are some salaried officials of the high rank who formed the municipality. They are the Executive Officer, the Secretary, the Sanitary Officer etc,

Question 3.
Fill in the blanks:

(a) Plantation of trees and looking after them ……………. function of the local bodies in cities.
(b) The work of the Commissioner, Municipal Corporation is to implement …………….
(c) The members of a Municipality are called …………………..
(d) Local bodies get ………… from the state government.

Answer:

(a) compulsory
(b) the works on the decisions taken by the corporation
(c) counselor
(d) their grants

Question 4.
Match the following:

Answer:

Project Work:

Question 1.
Find out the, names of the President, Vice President, Chief Executive Officer and Commissioner of a local body in your city or village.
Answer:
Do with the help of your teacher.

MP Board Class 6th Social Science Solutions

MP Board Class 9th Social Science Solutions Chapter 7 India: Population

MP Board Class 9th Social Science Chapter 7 Text Book Questions

Choose the Correct Answer:

Questions 1.
in which of the following period did the growth of population increase steadily?
(a) 1901-21
(b) 1921-51
(c) 1951-81
(d) 1981-2001
Answer:
(b) 1921-51

Questions 2.
According to 2001 census which is the most densely populated state?
(a) Uttar Pradesh
(b) Bihar
(c) Kerala
(d) West Bengal
Answer:
(a) Uttar Pradesh

Questions 3.
Which state has highest percentage of literacy?
(a) Uttar Pradesh
(b) Kerala
(c) Goa
(d) Delhi
Answer:
(b) Kerala

Questions 4.
Which is the most densely populated Union Territory?
(a) Chandigarh
(b) Pondicherry
(c) Delhi
(d) Lakshadweep
Answer:
(c) Delhi

Fill in the blank:

1. Population density is ……………. in India.
2. ………………. has the highest percentage of literacy in India.
3. The president of national population commission is ……………
4. World population day is celebrated on ………………. every year.
5. Population wise India is the country in the world.
6. In India the female population is ………….. ! ………….. then male population.

Answer:

1. 382
2. Kerala
3. Prime Minister
4. 17 July
5. Second
6. Less.

MP Board Class 9th Social Science Chapter 7 Very Short Answer Type Questions

Question 1.
What is birth rate?
Answer:
The number of live births for every thousand persons is called birth rate.

Question 2.
What is death rate?
Answer:
The number of deaths per thousand population in a year is called death rate.

Question 3.
What was the density of population in India in 2011?
Answer:
In the year 2011 population density of India was 382 persons per square km.

Question 4.
What was the sex – ratio in India in 2011?
Answer:
According to census 2011 the sex – ratio of the country was 943 (there are 943 females per thousand males) meaning that the number of females is less than number of males.

Question 5.
Population – wise and Area – wise what is the position of India in the world?
Answer:
Population – wise India is the second largest and area – wise the seventh largest country in the world.

MP Board Class 9th Social Science Chapter 7 Short Answer Type Questions

Question 1.
Write about any three problems resulting from population growth.
Answer:
Due to the population growth many problems are coming up in our country. Among many problems, there are given below:

• Poverty
• Unemployment
• Decline of standard of living

Question 2.
Why is the rate of sex – ratio declining in India? Give reasons.
Answer:
The rate of sex – ratio is declining in India due to the following reasons –

• Literacy is low among females.
• High maternal mortality rate.
• Desire of male child in a male dominating society.
• Increasing female foeticide.
• Neglecting girl child and considering girl child as a liability.
• Dowry system in the society causes female foeticide and encourage females towards suicide.

Question 3.
What do you understand by National Population Commission?
Answer:
Following National Population Policy 2000, National Commission on Population has been established. The Prime Minister is the President of this commission. Chief ministers of all States and Union Territories, administrators and ministers, in charge of all related departments and central ministers, renowned demographers and the representatives of public health and professional organizations and non – government organization are its members.

Following the National Population Policy 2000, state level population commissions like the National level population commission have also been formed. The chief ministers of the respective states are their .presidents.

Question 4.
What do you mean by sex – ratio? Explain its distribution in the country.
Answer:
Sex – ratio means number of females per thousand males. According to census 2001 the sex – ratio for the country was 933 (there are 933 females per thousand males) meaning that the number of females is less than number of males. This means that the sex – ratio in India is adverse. When the number of females is more than males the sex – ratio is said to be favorable.

There are wide regional disparities in sex – ratio in India. When we will go through the map of distribution of male-female ratio we find that Kerala records favorable sex – ratio (1058).whereas in Chandigarh it is adverse (773)
The distribution of male – female ratio are as under:

MP Board Class 9th Social Science Chapter 7 Long Answer Type Questions

Question 1.
Give the main causes of population growth in India and the measures being taken to control it.
Answer:
The main causes of population growth in India are:

1. Birth – rate and death – rate:
During 1911 to 1921 birth – rale and death – rate were 48.1 and 47.2 respectively, meaning that both were quite high. From 1921 to 1951 though birth – rate decreased slowly but, death rate decreased rapidly. Between 1991 and 2001 difference between the two increased to 17.4 resulting in continuous growth of population. The cause of decline in death – rate was increase in health facilities and adequacy of facilities of livelihood.

2. Increase in Life Expectancy:
The difference between birth – rate and death-rate is called natural growth rate. The average age of life is known as life expectancy. In our country, life expectancy (average age) was 50 years in 1921 which increased to 62 years in 1991. Hence due to longevity population kept on increasing.

3. Lack of Education:
In education gives birth to superstition.. Most of the uneducated people believe that children are gift of God. Believing this they keep on begetting children and hence population also increases. Desire for son is also responsible for many children in one family. The lower class hesitate from adopting family welfare programmer.

4. Other Causes:
Poverty, lack of means of entertainment, low standard of living, child marriage and migration etc. are among the other causes of population growth. Due to population growth many problems are coming up in our country, such as poverty, unemployment, decline of standard of living, hunger, increasing crimes, housing problem, transport problems, lack of medical facilities and increasing pollution etc.

5. Measures to Control Population Growth:
If the population growth is not checked immediately, flow of development will be hampered in the future. Following measures are essential to control the growth of population.

• Family welfare programmer should be accepted.
• Spread of education especially women education should be increased.
• Child marriage should be prevented.
• Standard of living should be improved.
• Social security should be rapidly extended.

Question 2.
Explain with examples the factors affecting the density of population in India.
Answer:
The factors affecting the density of population in India are –

1. Physical factors.
2. Socioeconomic and cultural factors.

1. Physical Factors:
Terrain, climate, soil and minerals are main physical factors. Terrain affects distribution of population the most. On one hand, dense population is found in the plains of Ganga – Yamuna and coastal areas, whereas on the other hand in the hilly state of Arunachal Pradesh density of population is the lowest. Climatic condition also influences density and distribution of population.

Suitable climate is helpful to the health and efficiency of man. The dry deserts of western Rajastan and Arunachal Pradesh are sparsely population due to bad climate. Fertile soil is ideal for agricultrue. The agriculture crops are the fundamental bases of livelihood and sustenance.

Therefore, population clusters around the fertile plains of rivers. Availability of minerals and industrial development based on them has attracted population in the mineral areas of Chottanagpur Plateau. Thus population has become very dense in Chottanagpur Plateau region.

2. Socioeconomic and Cultural Factors:
Socioeconomic and cultural factors also play important role in the distribution and density of population. The cultural, social, historical and political factors have together raised the size and density of Do population in the Mumbai-Pune industrial area.

Many years from today Mumbai area was non – significant, but after the advent of Europeans its importance kept increasing and gradually it turned into commercial and industrial center, as a result its population increased. Today a large group of people go to stay from one place to another and from one country to another. This is called population migration. Population migration also affects a country’s population growth.

Question 3.
On the basis of population density, in how many parts India can be divided?
Answer:
India can be divided in four parts on the basis of density.
1. High Density Areas:
If we look at the population density map of India, we find that more than 501 persons reside in per square km. area in Uttar Pradesh, Bihar, West Bengal and Kerala. The fertile land and availability of water provide enough facilities of sustenance. In these areas urbanization and industrialization have provided people with sufficient employment opportunities and services.

2, Medium Density Areas:
These include areas having population density of 251 to 500 persons per sq. km. Andhra Pradesh, Assam, Goa, Maharashtra, Tamilnadu, Jharkhand, Punjab, Haryana, Tripura, Dadra and Nagar Haveli fall under this category. Developed agriculture, availability of minerals and industrial development are some of the reasons for high (medium) population density in these areas.

3. Areas of Normal Density:
These include all those states which have population density ranging from 101 to 250 persons per sq. km. The States included in this category are M.P., Rajasthan, Orissa, Chhattisgarh, Uttaranchal, Meghalaya, Manipur and Nagaland. These are hilly and dissected semi arid, forest covered regions. Here the means of livelihood are quite limited.

4. Low Density Areas:
These include Jammu and Kashmir, Arunachal Pradesh, Mizoram, Sikkim and Andaman and Nicobar Islands. Hilly areas, lack of transport facilities, under – development of agriculture and industries are the responsible factors for low density. The means of livelihood are very limited here. In Arunachal Pradesh, density of population is as low as 13 persons per sq. km.

Question 4.
What is National Population Policy 2000?
Answer:
According to the new population policy, qualitative change of life is essential for socioeconomic development. This will ensure use of man as productive capital for the society. The policy has three objectives.

1. Short term objective:
To develop health and basic infra – structure for the extension of contraceptive measures.

2. Mid term objective:
To reduce the total rate of reproduction till 2010 and onward.

3. Long term objective:
To achieve the target of stable population for sustainable economic development till 2045.
In order to meet the above objectives following socio demographic aims were also declared under the new policy.

1. To pay attention to the incomplete needs related to basic reproduction and health services, supplies and basic infrastructure.
2. To impart free and compulsory school education till the age of 14 years. To reduce the number of dropouts among primary and middle standard boy and girl students up to 20%.
3. To bring down the infant mortality rate below 100 per one lakh live births.
4. To implement universal vaccination against diseases which are preventive.
5. To encourage late marriage among girls. To stress the significance of marriage at the age of 20 plus.
6. To ensure presence of trained midwives at all institutions.
7. To find out expensive alternatives of contraception.
8. 100% registration of birth, death, marriage and conception.
9.  To check the spread of AIDS, encourage integration between Aids control organizations with regards Reproductive Track Infection (RTI) and Venereal Diseases (VD).
10. To make, ample efforts for prevention’ and control of infectious diseases!
11. To integrate various types of Indian medicinal systems for providing’ reproductive and child health services at doorstep.
12. To solidly ‘encourage the norm of small family in order to reduce’ fertility rate.
13. To develop family welfare as people – oriented programmer.

Question 5.
What is the status of growth in literacy rate in India? Suggest your views to increase female literacy.
Answer:
After independence we had fast development in ail fields hut in the field of literacy continuous efforts are still needed.

The Status of Growth in Literacy Rate in India:
Literacy rate has increased in last hundred years. It is evident from the table of status.’of literacy’ in India given on the next page that in the. beginning of the century in 1911 the literacy rate was about .6%. After Independence in’ 1951 it’has increased to 18.13%. It has increased . from 52.21% in 1991 to 65.38% in 2001 in female Literacy rate was 1.1% in 1911 which has increased to 54.16% in 2001. It is out come of the policy of Central Government aiming at providing free primary education to all.

Disparities in Literacy Rates:
There are wide regional dis – parities in literacy rate. See the state – wise distribution of literacy in the map. It varies from 47.5% in Bihar to 90.9 in Kerala. Kerala is closely followed by Lakshadweep (87.5 percent) and Mizoram (88.4 per cent). Bihar ranks last in literacy among the states and union territories of India.

Male – female differentials are also wide. Only 54.16 per cent of the females are literate as against 75.85 per cent of males. There is much difference in the literacy rate of rural and urban population. In 2001 the literacy rate in urban areas was 79.9 per cent, whereas in rural areas it was only 58.7 per cent.

MP Board Class 9th Social Science Chapter 7 Other Important Questions

Choose the correct answer:

Question 1.
(i) India is the second most popular country of the world after –
(a) Australia
(b) China
(c) Japan
(d) None of the above
Answer:
(b) China

Question 2.
The population of Sikkim is –
(a) 2.2 crores
(b) 3.4.crores
(c) 5.4 lacs
(d) 6 crores
Answer:
(c) 5.4 lacs

Question 3.
In our country, life expectancy was 62 in the year –
(a) 1981
(b) 1991
(c) 2001
(d) 1987
Answer:
(b) 1991

Question 4.
Which states ranks first in literacy rate?
(a) West Bengal
(b) Madhya Pradesh
(c) Kerala
(d) Utter Pradesh
Answer:
(c) Kerala

Question 5.
On the basis of population density India can be divided into –
(a) Four Categories
(b) Three Categories
(c) Two Categories
(d) Six Categories
Answer:
(a) Four Categories

Fill in the blank:

1. The first census of India was held in …………….
2. Population census is released in ……………. year.
3. The 500 croreth child was born in ………………..
4. The state with lowest population density in India is …………….
5. The density of population in 2011 was ……………. in Madhya Pradesh.

Answer:

1. 1872
2. 10
3. Yugoslavia
4. Arunachal Pradesh
5. 236.

MP Board Class 9th Social Science Chapter 7 Very Short Answer Type Questions

Question 1.
Where do we find more population – in the plains or in the hilly or desert – areas?
Answer:
We find more population in the plains.

Question 2.
What is the population of Uttar Pradesh?
Answer:
The population of Uttar Pradesh is 19.9 crores.

Question 3.
Define ‘density of population’?
Answer:
The ratio of population of a country or state and its per unit area (square km.) is called its density.

Question 4.
What is the formula used to calculate density of population of a country or state?
Answer:
The formula is:

Question 5.
What was the population density of India in 2001?
Answer:
It was 324 persons per square km.

Question 6.
Divide India into four categories on the basis of population density.
Answer:
The four categories are:

• Areas of high density.
• Areas of medium density.
• Areas of normal density.
• Areas of low density.

Question 7.
Name the areas of high density.
Answer:
Uttar Pradesh, Bihar, West Bengal and Kerala.

Question 8.
Name the areas of low density?
Answer:
Jammu and Kashmir, Arunachal Pradesh, Mizoram, Sikkim and Andman and Nicobar Islands.

Question 9.
What is the natural growth rate?
Answer:
The difference between the birth – rate and tire death – rate is called the natural growth rate per year,

Question 10.
Name the state where we find favorable sex – ratio
Answer:
Kerala.

Question 11.
What was the literacy rate in urban areas in 2001?
Answer:
It was 79.9 per cent.

Question 12.
What will happen if the population growth is not checked?
Answer:
If the population growth is not checked flow of development will be hampered in the future.

Question 13.
Give one term for the number of women per thousand of population.
Answer:
Sex – ratio.

Question 14.
What is the life expectancy in India now?
Answer:
67 years.

Question 15.
Which state has the highest sex – ratio in India?
Answer:
Kerala. It is 1058 females to 1000 males.

Question 16.
What is the main cause of rapid population growth in India after independence?
Answer:
There has been – sharp fall in death – rate but very slow fall in birth – rate.

MP Board Class 9th Social Science Chapter 7 Short Answer Type Questions

Question 1.
What is density of population? How can density of population be calculated?
Answer:
Density of population is the number of people living per square kilometer of area. It represents the land man ratio. It can be calculated by dividing the total population of a region or country or state by its total area. It is expressed as the number of persons per square kilometer as 180 persons per square kilometer.

The distribution of population of India is extremely uneven. The average density for the country as a whole as per the census 1991 in India is 267 persons per sq. km. The density of population in India can be calculated by dividing total population with total area. Thus density of population = Total population s ÷ Total area.

Question 2.
Describe the areas m normal density.
Answer:
These include all the e states which have population density ranging from 101 to 250 persons per sq. km. The states included in this category are M.P. Rajastan, Orissa, Chhattisgarh, Uttaranchal, Meghalaya, Manipur, and Nagaland.

Question 3.
What measures can be taken to control population growth?
Answer:
Following measures can be taken to control the growth of population:

• Family welfare programmer should be accepted.
• Spread of education especially women education should be increased.
• Child marriage should be prevented.
• Standard of living should be improved.
• Social security should b’e rapidly extended.

Question 4.
‘Literacy’ rate has increased in last hundred years. Justify it.
Answer:
In the beginning of the century in 1911 the literacy rate was about 6%. After independence in 1951 it has increased to 18.3%. It has increased from 52.21% in 1991 to 65.38% in 2001. Female literacy rate was 1.1% in 1911 which has increased to 54.16% in 2001. Thus we can say that literacy rate has increased in last hundred years.

Question 5.
Mention the objectives of the National Population Policy 2000.
Answer:
The National Population Policy 2000 has three objectives –

• Short term objectives – To develop health and basic infrastructure for the extension of the contraceptive measures.
• Mid term objective – To reduce the total rate of reproduction till 2010.
• Long term objective – To achieve the target of stable population for sustainable economic development till 2045.

MP Board Class 9th Social Science Chapter 7 Long Answer Type Questions

Question 1.
Define birth and death rate. Explain growth rate. Also make a table to show growth rate in India (1901-2001).
Answer:

1. The birth – rate is calculated in terms of number of live birth per thousand population per year.
2. The death – rate is known as number of deaths per thousand population per year in a given area.
3. The difference between these two is called the natural growth rate per year.

Growth rate in India (1901-2001):

The growth rate of a population may be positive or negative. Positive growth rate means growth in the number of people living in an area, whereas negative growth means the number of people living in that area declines. Find out the population growth rate m India from the table given above and see whenever the growth was negative.

Question 2.
What are the main features of population situation in India?
Answer:
The main features of India’s population can be summarized as below:

1. Size of India’s Population:
India is the second largest populated country in the world, after China. Population of India has been constantly rising since 1921. The following figures indicate the size, of India’s population.
Population of India

It will be seen from the above table that in just 34 years after independence another India was added while the territorial limit of the country remained unchanged. It is estimated that if we grow with this number, we will be more than 100 crore mark at the end of this century.

2. Second Largest Populated Country:
India has 2.4 per cent of the total land area of the world, India caters to the needs of 15% of the total world population. This means every seventh person in the world is an Indian.

3. Population Increasing at a Fast Rate:
It is not the overall absolute size of population which is the cause of concern, equally important is the fact that India’s population has been rising at a relatively very fast rate. It has gone up by a little over 2.0 per cent annum during the period 1951 to 1991 and about 2.1% presently.

4. Density of Population:
The density of population of India in 1961 was 216 persons per.sq. km. It rose to 267 in 1991. Thus the land man has been declining fast which indicates that the land will fall short for the in habitation of mankind of the population grow in this rate.

5. Uneven Distribution of Population:
The population is unevenly distributed. The northern plains, coastal plains and some river valley in lower Himalayas are densely populated while other areas of scanty rainfall or desert plateau and mountainous areas are sparsely populated. Thus there are areas which have great population pressure while other rare less inhabited.

MP Board Class 9th Social Science Solutions

MP Board Class 9th Social Science Solutions Chapter 6 India: Natural Vegetation and Wild Life

MP Board Class 9th Social Science Chapter 6 Text Book Questions

Choose the Correct Answer:

Question 1.
State with the minimum forest area in India is –
(a) Assam
(b) Rajastan
(c) Jharkhand
(d) Haryana.
Answer:
(d) Haryana.

Question 2.
Sundari trees are found in –
(a) Tropical forests
(b) Himalayan forests
(c) Mangrove forests
(d) Tropical deciduous forests
Answer:
(c) Mangrove forests

Question 3.
Natural vegetation of Rajastan is –
(a) Tropical moist evergreen forests
(b) Tropical moist semi-evergreen
(c) Tropical thorny forest
(d) Alpine forests
Answer:
(c) Tropical thorny forest

Question 4.
Natural habitat reserved for Indian Loin is –
(a) Gujarat Gir forest
(b) Kaziranga forest area of Assam
(c) Sundarban of West Bengal
(d) Nilgiri forest area
Answer:
(a) Gujarat Gir forest

MP Board Class 9th Social Science Chapter 6 Very Short Answer Type Questions

Question 1.
What do you mean by natural vegetation?
Answer:
Plants, trees, grasses and bushes that grow naturally without man’s interference is called natural vegetation.

Question 2
What is a forest?
Answer:
A large area covered by plants and shrubs is called a forest.

Question 3.
What are mangrove forests?
Answer:
Mangrove is a type of vegetation with submerged roots. It is found on the coastal areas of India where the tides occur.

Question 4.
What is the meaning of Endemic and Exotic vegetation?
Answer:

1. Endemic Vegetation:
The vegetation which is basically Indian is known as Endemic Vegetation.

2. Exotic Vegetation:
Plants which are brought from out of India are called Exotic Plants.

Question 5.
What is a sanctuary?
Answer:
A sanctuary is dedicated to protect, wild life and conserve species. Without permission hunting is restricted in a sanctuary.

Question 6.
Classify the forests on the basis of administration.
Answer:
Forests are classified in three categories from the administrative viewpoint:

• Reserved forests
• Protected forests
• Unclassified forests.

MP Board Class 9th Social Science Chapter 6 Short Answer Type Questions

Question 1.
What are migratory birds?
Answer:
Birds coming from North Asia to India for a short period of time are called migratory birds.

Question 2.
What is the meaning of forest conservation?
Answer:
Forest is a national wealth. Looking to.the problems originated due to decreasing forest resources, their conservation is very necessary. Human needs are unlimited whereas the natural resources are limited. Hence, efforts for forestation have been encouraged so that forest may be conserved.

Question 3.
Describe the vegetation of Himalayan region of India.
Answer:
Oak and chestnut are found on eastern Himalayas and pine on western Himalayas. At an altitude of 2000 to 3000 meters forests of deodar, silver, fur, and spruce are sparsely attributed. Sal is mainly found at low altitudes. On the slopes of high altitude mountains, where temperatures are low and rain is less than 100 cm dry temperate vegetation is found.

Question 4.
Differentiate between National Park and Sanctuary.
Answer:
A National Park is relatively a large area where different ecosystems exist. Exploitation and acquisition could not change this region. For special scientific, educative and re-creative interests plant and animal species, with their geomorphological sites and habitats are persevered here. Hunting, grazing and human interference are totally banned in national parks.

A Sanctuary is similar to a national park, but is medicated to protect wild-life and conserve species. Without permission hunting is restricted in a Sanctuary but grazing and regular movement of cow and other animals is permitted. Human activities are allowed in a Sanctuary.

Question 5.
Distribution of plants and vegetation depends on which factors in India? Explain.
Answer:
The geographical factors or elements affect the development of vegetation of a particular area. The important elements are rainfall, temperature, humidity, soil, altitude and geological structure.

Question 6.
Differentiate between Evergreen and Deciduous Forest.
Answer:
Differences between Evergreen Forests and Deciduous Forest.

Evergreen Forests:

1. The forests having trees which remain green throughout the year. This means that seasonal shed – ding of leaves does not take place.
2. Shedding of leaves and growth of new leaves is continuous process and it goes side by side throughout the year.
3. Ever green forests are found mainly in equatorial regions where rainfall is very heavy and where there is no dry season.
4. Trees like eucalyptus, oak, wattle, Mahagony, Man – grove and Rosewood are common in these forests.

Deciduous Forests:

1. The forests consisting of trees which loose their leaves at some season of the year are called deciduous forests.
2. Tropical deciduous forests are found in sub – tropical regions with a distinct dry season such as Monsoon regions of Asia, parts of central America, Brazil and North Australia.
3. These forests have fewer than tropical evergreen forests.
4. In case of Monsoon forests, the trees shed their leaves during the. hot season. Teak, Oak, Elm and Beach are important timber products.

Question 7.
Explain the chief characteristics of tropical moist ever green forests.
Answer:
The chief characteristics of tropical moist evergreen forests are:

1. These forests thrive in areas having annual rainfall above 300 cm and dry season is short.
2. These forests are very dense, length of the trees in 60 m or more.
3. Layers of different height can be seen in these forests. Shrubs, climbers and creepers are found under tall trees.
4. Grass is generally not found in this region.
5. The wood of these trees are hard and heavy,
6. These forests do not have a distinct season of shedding of leaves, so these forests appear to be evergreen.
7. The main trees found here are rubber, mahogany, cinchona, bamboo and palm.

Question 8.
Describe how forests are useful to man?
Answer:
Forest is a natural wealth. It has various uses for humans. Forests contribute in the economic development of the country by functioning in two ways production and conservation. we have two types of benefits from the forests – Direct benefit and Indirect benefit.

Direct Benefits:
They give us timber, fuel wood, fodder, raw material for small and cottage industries, valuable minor products (fruits, flower, grass and leaves) and raw material for medicines. It is a main source of livelihood for many people.

Indirect Benefits:

1. Indirect benefits of forests are more important than direct benefits. They are the essential part of our nature and culture. They increase human values, provide spiritual strength and are the habitat of entertainment ancL recreation.
2. Forests affect the temperature of the air control the speed of wind and control the climate by rainfall.
3. Forests control floods and the soil erosion by controlling the flow of rivers.
4. Forests increase the fertility of soil by adding humus formed due to the decomposition of the leaves and branches of the trees.
5. Forests are the natural habitat of birds and animals.
6. Forests are the symbol of natural beauty.
7. Forests are the source of natural balance.

Question 9.
How are the indirect benefits of forests more important as compared to the direct benefits? Explain.
Answer:
Indirect benefits of forests are more important than direct benefits. We know that forests are the essential part of our nature and culture. They increase human values, provide spiritual strength and are the habitat of entertainment and recreation. Forests affect the temperature of the air. They control the speed of wind. They also control the climate by rainfall. Forests control floods and soil erosion by controlling the flow of rivers. They increase the fertility of soil by adding humus.

MP Board Class 9th Social Science Chapter 6 Long Answer Type Questions

Question 1.
Describe various types of vegetation in India.
Answer:
1. Tropical Evergreen Forests:
These are of two types.

(A) Tropical wet evergreen forests:
The forests thrive in areas having annual rainfall above 300 cm. and dry season is short. These forests are very dense, length of the trees is 60 m or more. Layers of different height can be seen in these forests. Shrubs, climbers and creepers are found under tall trees.

Grass is generally not found in this region. The wood of these trees is hard and heavy’. These forests do not have a distinct season of shedding of leaves, so these forests appear to be evergreen. The main trees found here are Rubber, Mahogony, Cinchona, Bamboo and Palm.

(B) Tropical wet semi-evergreen forests:
These forests are restricted to the areas where annual rainfall is between 200 to 300 cm. So these evergreen forests are found in the Central parts of temperate moist deciduous forests. These forests are found in Mehgalaya, Mizoram and Andaman and Nicobar Islands. They are less dense than wet evergreen forests. The important plants here are Rosewood, Ebony’, Telsur, Champa, Jun, Gurjan, Ice-wood and Laurel.

2. Tropical Deciduous Forests:
This is the largest belt of India, these forests are also known as Monsoon forests. They cover 39% of the total forest area. (See the distribution of these forests in the Vegetation Map) On the basis of availability of water these forests are classified into two parts Moist deciduous forests and Dry deciduous forests.

Moist deciduous forests are found in the area of 100 to 200 cm. rainfall in India, North-east states, foot – hills of Himalayas, Jharkhand, Western Orissa, Chhattisgarh and the eastern slopes of Western Ghats. Teak is the main species of these forests. Other trees are Bamboo, Sal, Shesham, Chandan, Khair, Kusum, Ar-jun and Mulbery.

Trees of these forests shed their leaves during the dry season for 6 to 8 weeks. To fulfill the demand of wood these forests have been exploited and cleared for cultivation. The areas with 70 to 100 cm. rainfall have Dry deciduous forests. The main areas of these forests are Peninsular Plateau, Uttar Pradesh and Bihar. Main trees are Teak, Sal, Pee-pal, Neem and Mango.

3. Mountainous Forests:
(A) Peninsular mountain forests:

• On the high altitudes of Peninsular Plateau open wavy grasslands are found with the shrubs or undeveloped forests.
• Dense vegetation is found under tall trees in these forests. Heterotrophic plants, mosses and plants with small leaves are found in these areas.
•  Maglonia, Laurel, Elm are the common trees whereas Cinchona and Eucalyptus are brought from foreign countries and planted here.
• There forests are found in Nilgiri, Palni, Annamalai, Western Ghats, Mahabaleshwar and Satpura and Maikal ranges.

(B) Mountainous forests of Himalayan Ranges:
In Himalayan mountainous region due to increasing altitude and decreasing temperature a difference in natural vegetation is seen. In Shivalik ranges, at an altitude of 1000 meters in the foothill region, Bhabar and Tarai tropical deciduous forests are found.

It is then succeeded by temperate moist evergreen forests between 1000 and 20000 meters. These are the dense forests with tall trees. Oak and Chestnut are found on eastern Himalayas and Pine on western Himalayas.

At an altitude of 2000 to 3000 meters forests of Deodar, Silver fur, and Spruce are sparsely distributed. Sal is mainly found at low altitudes. On the slopes of the high altitude mountains, where temperatures are low and rainfall is less than 100 cm dry temperate vegetation similar to that of Mediterranean vegetation, is found. Olive,. Babool and hard Savanna grass is found with Oak and Deodar trees.

Alpine vegetation is found between the altitude of 3000 to 4000 meters. These are less dense forests and the height of the trees decreases towards Snowline. At higher altitudes alpine pastures are found. Silver fur, Juniper, Birch and Pine are the main species of these forests.

4. Mangrove Forests or Tidal Forests:
Mangrove or Tidal vegetation is found on the coastal areas of India where the tides occur. Mangrove is a type of vegetation with submerged roots. This vegetation is found in the delta region of the Ganga, Bhahmaputra, Mahanadi, Godavari, Krishna and Kaveri rivers. Sundari is a well – known mangrove tree found in the delta region of Ganga-Bhrahmaputra. Coconut, Palm and Agar trees are also found in this region.

Wild Life of Mangrove Forests:
Royal Bengal Tiger is famous in these forests. Tortoise, Crocodile, Alligators and different types of snake are found here.

5.  Tropical Thorny Forests:
The areas with less than 70 cm annual rainfall have thorny forests and shrubs. This type of vegetation is found in the northwestern parts of the Country. It includes Gujarat, Rajasthan, Madhya Pradesh, Uttar Pradesh and semi-arid regions of Haryana. Date, Palms, Babul, Cactus is the main vegetation here. These plants have long roots spread in a radial pattern in search of water.’ Leaves are small to reduce evaporation.

Question 2.
Why is conservation of forest resources necessary? Give examples of different measures for their conservation.
Answer:
Forest conservation is necessary because our life is dependent on it. Forests provide us food. They help in the maintenance of ecosystem. They give oxygen which is necessary for survival of our life. Forests contribute in the economic development of the country. Different measures for their conservation.

Forest is a national wealth. Looking to the problems originated due to decreasing forest resources, their conservation is very necessary. Human needs are unlimited whereas the natural resources are limited. So, efforts for afforestation has been encouraged by the government.

Following measures have been taken for the conservation of forests:

1. Dangerous tendency of the destruction of forests should be immediately controlled. The main objective of the National Forest Policy is the maintenance of environmental stability and restoration of ecological balance.
2. Forest Conservation Act, 1980 is to prevent the destruction of forests and to prevent use of forest land for other purposes.
3. The main objective of Social Forestry and Agro – forestry is to provide fuel wood and minor wooden resources to the farmers. Farmers are encouraged for plantation.
4. Afforestation and development of waste and degraded land.
5. Reforestation in the existing forest areas.
6. Controlled cutting of forests and by scientific method.
7. Establishment of Watch Towers and surveying to prevent forest fire.
8. Ban on grazing, poaching and cutting trees and shrubs for fuel wood.
9. Controlled and limited trade of timber.
10. Controlled jhuming agriculture.
11. Controlling harmful insects like termites, cockroaches and gubrela.
12. Creating awareness in people regarding Agro – forestry, extensive forestry, development of social forestry and forest conservation, Chipko Movement and Van Mahotsava are all included as the measures of forest conservation.

Question 3.
Write about the different measures taken for wild-life conservation.
Answer:
Out of 5 lakh animal species of the world 75,000 are found in India. Similarly about 12,000 species and 900 sub-species of birds are available in India. Beginning of wild – life conservation was an effort of ecologists movement.

1. In 1972 Wild Life Conservation Act was passed in India. This act gives protection and preservation to endangered species of wild – life and ban the trading of related species.

2. Tiger Development Programmer Project was launched in 1973. Today there are 27 Tiger Reserves in 14 slates of the country.

3. Crocodile Breeding and Management Project was started in 1975 to conserve Crocodiles.

4. To increase the number of elephants, Elephant Project was launched-. Economic and scientific assistance was made available for this project.

5. Project Tiger movement was started to conserve the endangered species of Tiger. 17 Tiger Reserves were established for this purpose. The natural habitat of lion in the country is the Gir forest of Gujarat.

6. For the management and upkeep of zoos Central Zoo Authority is established. Responsibility of 200 zoos established in India is given to this authority.

7. There are 14 Biosphere Reserves set up in different regions of the .country. Out of which Sunderbans (West Bengal), Nanda Devi (Uttaranchal), Gulf of Mannar (Tamilnadu), Nilgiri (Kerala, Karnataka and Tamilnadu) are included in the Biosphere Reserves of the world. Other Biosphere Reserves are Nakrak, Great Nicobar, Manas, Simlipal, Dihang – Dibang, Dibru – Saikhova, Augustmalai, Kanchanjunga, Pachmarhi, Achnakmar – Amarkantak. .

Map Work:
Show the following areas in the outline Map of India.

1. Tropical evergreen forests and tidal forest.
2. Bharatpur Bird Sanctuary and Silent Valley.
3. Kanha Kesli and Corbett National Park.
4. Nanda Devi, Nilgiri and Sundarban Biosphere Reserve.

Project Work
Collect the medicinal herbs from your surroundings and prepare a list and write the uses of medicinal herbs.
Answer:
Do yourself.

MP Board Class 9th Social Science Chapter 6 Other Important Questions

Question 1.
Choose the correct answer:
(1) What is the percentage of total area of forest in Tripura?
(a) 44%
(b) 55%
(c) 66%
(d) 48%
Answer:
(b) 55%

Question 2.
Highest forest area found in –
(a) North – East India
(b) South – West India
(c) East – West India
(d) None of the above
Answer:
(a) North – East India

Question 3.
Which one is not medicinal herb?
(a) Tulsi
(b) Neem
(c) Sarpgandha
(d) Teak
Answer:
(d) Teak

Question 4.
Wild life Conservation Act was passed in India in –
(a) 1975
(b) 1972
(c) 1980
(d) 1985
Answer:
(b) 1972

Question 6.
From administrative viewpoint forests are classified in –
(a) Four categories
(b) Three categories
(c) Two categories
(d) None of the above.

Fill in the blank:

1. …………….. % are is under forest in Madhya Pradesh and Chhatitisgarh.
2. In …………….. year Wild-Life Conservation Act was passed in India.
3. A large area covered by plants, shrubs etc. growing naturally is called a …………….
4. Tulsi is used in ……………… and ………………..
5. Out of 5 lakh animal species of the world …………….. are found in India.

Answer:

1. 30
2. 1972
3. Forest
4. cold, cough
5. 75,000.

MP Board Class 9th Social Science Chapter 6 Very Short Answer Type Questions

Question 1.
What is water hyacinth called in West Bengal?
Answer:
Water hyacinth in West Bengal is called the terror of Bengal.

Question 2.
In which areas do we find plants with long roots?
Answer:
In desert areas we find plants with long roots.

Question 3.
Which is the most dominant and widespread natural vegetation belt in India?
Answer:
The tropical deciduous forest or the monsoon forest provide the most dominant and widespread natural vegetation belt of India.

Question 4.
In what part of the country are the evergreen forests confined?
Answer:
The evergreen forests are confined to altitudes ranging form 500 – 1500 meters along the windward side of the Western Ghats and up to 1100 meters in the north eastern part of the country.

Question 5.
Name two important products of Tropical deciduous forests.
Answer:
Sal and Sagon.

Question 6.
Name the most important species of tree found in the Western Ghat regions.
Answer:
Teak.

Question 7.
Which forests are called the monsoon forests?
Answer:
The tropical deciduous forests are also called the monsoon forests.

Question 8.
Where are the moist deciduous forests found?
Answer:
They are found along the Shivaliks, the Piedmont plains of the Bhabar and Tarai regions in the north, the Chhotanagpur,  the South East Deccan Plateau and along north – south strip on the coast on the east of Western Ghats.

Question 9.
Name the few species of the vegetation in the Himalayan Region.
Answer:
Sal, chir, chil, pine, cedar, silver fir and spruce.

Question 10.
What are two important trees of the thorn forests?
Answer:
Babul and Kikar.

Question 11.
Name the type of forests in which the following trees are grown mahogany, chestnut; shisham, chir, sal, sundari, cam phor, rubber, kikar, teak, lawrel, sandal wood, oak, fur, spurce, palm.
Answer:

Question 12.
Where are the elephants found in India?
Answer:
Elephants in India are found in the Jungles of Assam and those of Kerala and Karnataka.

Question 13.
Name the most endangered species in India?
Answer:
The tiger, the rhino, the bustard and the lion.

Question 14.
Which is the first biological reserve in India?
Answer:
The first biological reserve was set up in the Nilgiries.

Question 15.
Where is the Gulf of Mannar?
Answer:
Tamilnadu.

Question 16.
How many national parks have been established is our country to protect wild – life?
Answer:
Eighty – nine national parks have been established in our country to protect wild – life.

Question 17.
Where is the natural habitat of lion in India?
Answer:
The natural habitat of lion in India is the Gir forest of Gujarat.

Question 18.
Why are national parks and wild-life sanctuaries developed?
Answer:
They are developed to provide safe habitat and to secure species of the wild – life.

MP Board Class 9th Social Science Chapter 6 Short Answer Type Questions

Question 1.
What is bio-reserve?
Answer:
Efforts are being made to protect and preserve every plant and animal species found in India so that this natural heritage can be transmitted to, the future generation in all its natural vigor and glory. With these objectives in mind the biosphere reserve or bio-reserve has been set up.

First such reserve was set up in the Nilgiries consisting of 5500 sq km at the tri junction of the Karnataka, Tamilnadu, and Kerala. Thus protection and conservation of the great biological diversity in its natural form is ‘bio-reserve’. After Nilgiri Bio – reserve, the one at Nanda Devi in U.P., Himalaya was set up in 1988. The other Noktek in Meghalaya was set up in this year itself.

Question 2.
Describe the administrative classification of forests.
Answer:
Forests are classified in three categories from the administrative viewpoint.

1. Reserved Forests:
The forest which are permanently reserved for timber or other forest produce and agriculture and grazing is strictly banned are called Reserved Forests.

2. Protected Forests:
The forests where local inhabitants are allowed to graze their animals and permission of agriculture with normal restrictions is given are called Protected Forests.

3. Unclassified Forests:
The forests, which are neither reserved nor protected, are Unclassified Forests.

Question 3.
Write a short note on medicinal herbs.
Answer:
From the ancient times India is famous for medicinal herbs. 2000 Plants species are described in Ayurveda, out of which at least 500 are in continuous use. Some of important plant species used as medicine are Sarpgandha, Tulsi, Neem, Jamun, Babul, Kachnar, and Arjun, etc.

Sarpgandha is used to control blood pressure, Tulsi is used when we are caught cough and cold, Neem is used as an antibiotic, Jamun is used to improve digestion. It is also useful is diabetes Babul is useful in boils. It is also used to increase physical strength. Kachnar is useful in boils and Asthma and Arjun is used to control blood pressure and ear pain.

Question 4.
Explain the characteristics of tropical deciduous forests.
Answer:
The characteristics of tropical deciduous forests are:

• They shed leaves seasonally.
• They are comparatively open with lesser under growth.
• Teak is the most important species. Others are sandal wood rose wood, shisham and mahua.
• Trees are of economic significance and well exploited.

MP Board Class 9th Social Science Chapter 6 Long Answer Type Questions

Question 1.
Write a short note on conservation of wild – life
Answer:
The wild-life of a country is a part of its heritage. Every effort should therefore be made to protect – and preserve the wild life. Today there are man – endangered species of wild – life birds and animals. The Indian bustard of Rajasthan and Malwa, number of lions and tigers are some of the endangered species.

In order to conserve this resource, government of India has been taking time-to-time suitable measure, to maintain this great biological diversity of our land. Periodic census undertaken to find out the latest position and trends in this regard. The project tiger has been a great success. Now there are 16 tiger reserves in various parts of the country.

Likewise Rhino Project is being implemented in Assam, The Biosphere Reserves have been set up in the Nilgiries. It consists of 5500 km and is spread at the trijunction of Karnataka, Tamilnadu and Kerala. The other bio – reserves have been set up as Nanda Devi in U.P., Noktek in Meghalaya, Andaman and Great Nicobar etc. The country has 63 national parks, 358 wild life sanctuaries and 35 zoological gardens covering 130000 km² of area.

Question 2.
Describe the factors affecting vegetation.
Answer:
The geographical factors or elements affect the development of vegetation of a particular area. The important elements are rainfall, temperature, humidity, soil, altitude and geological structure.

1. Earth Surface:
It includes relief features and nature of soil.

Land:
Land affects vegetation directly and indirectly. Mountains, Plateaus and Plains do not have same type of vegetation. Plain surface is useful for agriculture. Forests and grasslands are found on rugged and uneven surface, which are the habitat of wild – life.

Soil:
Different type of soil is found on different places which is a base for different type of Vegetation. Mangrove forests are found in delta region of rivers. Whereas conical forests on the slope of high mountains plain areas are favorable for agriculture – and deciduous forests are found on plateau region normally.

2. Climate:
Temperature Favorable temperature is required for the germination, growth and reproduction of the plants. Variety of plants grow in the tropical zone because of high temperatures and humidity. Increase in temperature by 6°C to 9°C results in the stunted of the plants. Temperatures are low on high mountains therefore the growth period of the vegetation is short

Sunlight:
Duration of sunlight at any place depends on latitude altitude from sea level and the season. Plants grow rapidly in summer season because in Summers the duration of day light is more. As the Southern slopes of the Himalaya mountainous regions receives more sunlight as compare to northern slopes, dense vegetation is found here.

Rainfall:
In the areas of heavy rainfall the forests are very dense with tall trees. In the areas of low rainfall dwarf trees, grasses and shrubs are found sparsely. In desert areas plants have long roots. To prevent the loss of moisture due to transpiration some plants have wax-coated and thorny leaves. Vegetation of Thar desert is thorny due to scanty water.

MP Board Class 9th Social Science Solutions

MP Board Class 7th Sanskrit Solutions Surbhi Chapter 17 राज्ञी दुर्गावती

MP Board Class 7th Sanskrit Chapter 17 अभ्यासः

प्रश्न 1.
अधोलिखित प्रश्नों के उत्तरों को एक शब्द में लिखो
(क) महाराज्ञी दुर्गावती कुत्र जाता? [महारानी दुर्गावती का जन्म कहाँ हुआ?]
उत्तर:
मण्डलाक्षेत्रे

(ख) दुर्गावत्याः विवाहः केन सह जातः? [दुर्गावती का विवाह किसके साथ हुआ?]
उत्तर:
दलपतशाहेन सह

(ग) दुर्गावती कृपाणेन किम् अकरोत्? [दुर्गावती ने तलवार से क्या किया?]
उत्तर:
प्राणघातम्

(घ) दुर्गावत्या पुत्र कः आसीत्? [दुर्गावती का पुत्र कौन था?]
उत्तर:
वीरनारायणः

(ङ) दुर्गावतीविश्वविद्यालयः कुत्र स्थितः? [दुर्गावती विश्वविद्यालय कहाँ स्थित है?]
उत्तर:
जबलपुरनगरे।

प्रश्न 2.
अधोलिखित प्रश्नों के उत्तर एक वाक्य में लिखो
(क) दुर्गावत्याः समाधिः कुत्र अस्ति? [दुर्गावती की समाधि कहाँ है?]
उत्तर:
जबलपुरमण्डलामार्गे तस्याः समाधिः अस्ति। [जबलपुर और मण्डला के मार्ग पर उसकी समाधि है।]

(ख) प्रजासु दुर्गावत्याः कीदृशः स्नेहः आसीत्? [प्रजा पर दुर्गावती का कैसा स्नेह था?]
उत्तर:
प्रजासु तस्याः पुत्रवत् स्नेहः आसीत्। [प्रजा पर उसका पुत्र के समान स्नेह था।]

(ग) कः दुर्गावत्याः उपरि आक्रमणम् अकरोत्? [किसने दुर्गावती पर आक्रमण किया?]
उत्तर:
अकबरस्य सेनापतिः आसफखानः तस्याः उपरि आक्रमणम् अकरोत्। [अकबर के सेनापति आसफखान ने उसके ऊपर आक्रमण किया।]

प्रश्न 3.
अधोलिखित शब्दों के मूल शब्द, विभक्ति और वचन लिखो
(क) मण्डलाक्षेत्रे
(ख) दलपतशाहेन
(ग) राजकार्येषु
(घ) राजधान्याम्
(ङ) रक्षायै
(च) तस्याः।
उत्तर:
(क) ‘मण्डलाक्षेत्र’ शब्द, सप्तमी विभक्तिः, एकवचनं।
(ख) ‘दलपतशाह’ शब्द, तृतीया विभक्तिः, एकवचनं।
(ग) ‘राजकार्य’ शब्द, सप्तमी विभक्तिः, बहुवचनं।
(घ) ‘राजधानी’ शब्द, सप्तमी विभक्तिः, एकवचनं।
(ङ) ‘रक्षा’ शब्द, चतुर्थी विभक्तिः, एकवचनं
(च) ‘सा’ शब्द, चतुर्थी विभक्तिः, एकवचनं।

प्रश्न 4.
अधोलिखित शब्दों का मूलधातु-लकार-पुरुषवचन लिखो
(क) न्यवसत्
(ख) अकरोत्
(ग) आसीत्
(घ) अपश्यत्
(ङ) प्राप्नोत्
(च) अत्यजत्।।
उत्तर:
(क) ‘वस्’ धातु, लङ् लकार, अन्य पुरुषः, एकवचनम्।
(ख) ‘कृ’ धातु, लङ् लकार, अन्य पुरुषः, एकवचनम्।
(ग) ‘अस्’ धातुः, लङ् लकारः, अन्य पुरुषः, एकवचनम्।
(घ) ‘दृश्’ धातुः, लङ् लकारः, अन्य पुरुषः, एकवचनम्।
(ङ) ‘आप्’ धातुः, लङ् लकारः, अन्य पुरुषः, एकवचनम्।
(च) ‘त्यज्’ धातुः, लङ् लकारः, अन्य पुरुषः, एकवचनम्।

प्रश्न 5.
कोष्ठक में उचित शब्द चुनकर रिक्त स्थानों को पूरा करो
(क) सा चन्देलराज्यपुत्री …………। (आसीत्/आस्ताम्)
(ख) प्रजाः अपि तां मातेव …………. (पश्यत्/अपश्यन्)
(ग) सा रणचण्डी भूत्वा युद्धम् …………। (अकरोत्/अकुर्वन्)
(घ) तस्याः बलिदानम् अधुनापि जनाः ………। (स्मरतः/स्मरन्ति)
(ङ) सा अद्यापि यशः शरीरेण ……….। (जीवति/जीवन्ति)
उत्तर:
(क) आसीत्
(ख) अपश्यन्
(ग) अकरोत्
(घ) स्मरन्ति
(ङ) जीवति।

प्रश्न 6.
अधोलिखित तालिका से वाक्य बनाओ

उत्तर:
(क) वीरनारायणः बालकः एव आसीत्।
(ख) दुर्गावती चातुर्येण शौर्यण च राज्यमकरोत्।
(ग) राज्ञी दुर्गावती धीरा वीरा च आसीत्।
(घ) प्रजासु तस्याः पुत्रवत् स्नेहः आसीत्।
(ङ) प्रजाः अपि तां माता इव अपश्यन्।

प्रश्न 7.
लङ्लकार में निम्नलिखित धातुओं के रूप लिखो
(वस्, लिख्, भू(भव), क्रीड्, धाव, खाद्, गम् (गच्छ))
उत्तर:

प्रश्न 8.
अधोलिखित वाक्यों के शुद्ध रूप लिखो
(क) सा “महाराज्ञी” उपाधिना विभूषितः।
(ख) महिला अगच्छन्।
(ग) वीरनारायणः जाता।
(घ) आसफखानः आक्रमणम् अकुर्मः।
(ङ) बालकाः अक्रीडत।
उत्तर:
(क) विभूषिता
(ख) अगच्छत्
(ग) जातः
(घ) अकरोत्
(ङ) अक्रीडन्।

राज्ञी दुर्गावती हिन्दी अनुवाद

दीक्षा :
भ्रात! त्वं कुत्र पठसि?

रमण :
अहं जबलपुरनगरे पठामि। दीक्षा-तत्र कस्यां संस्थायाम् अध्ययनं करोषि?

रमणः :
अहं “राज्ञीदुर्गावतीविश्वविद्यालये” अध्ययनं करोमि।

दीक्षा :
महाराज्ञी दुर्गावती का आसीत् यस्याः नाम्ना विश्वविद्यालयः प्रचलित।

रमणः :
महाराज्ञी दुर्गावती मध्यप्रदेशस्य मण्डलाक्षेत्रस्य वीराङ्गना आसीत्। सा चन्देलराज्यपुत्री आसीत्। तस्याः विवाहः गोंडराजदलपतशाहेन सह अभवत्। दलपतशाहः गोंडवानाराजस्य राजधान्यां मण्डलानगरे न्यवसत्। विवाहात् चतुर्वर्षाणाम् अनन्तरं दलपतशाहः दिवङ्गतः।

अनुवाद :
दीक्षा:
भाई! तुम कहाँ पढ़ते ह?

रमण :
मैं जबलपुर नगर में पढ़ता हूँ।

दीक्षा :
वहाँ किस संस्था में अध्ययन करते हो?

रमण :
मैं “रानी दुर्गावती विश्वविद्यालय में” अध्ययन करता हूँ।

दीक्षा :
महारानी दुर्गावती कौन थी, जिसके नाम से विश्वविद्यालय चलता है।

रमण :
महारानी दुर्गावती मध्य प्रदेश के मण्डला क्षेत्र की वीरांगना (वीर स्त्री) थी। वह चन्देल राज्य की पुत्री थी। उसका विवाह गौंडराज दलपतशाह के साथ हुआ था। दलपतशाह गौंडवाना राज की राजधानी में मण्डला नगर में रहते थे। विवाह के चार वर्षों के बाद ही दलपतशाह का स्वर्गवास हो गया।

दीक्षा :
तदा दलपतशाहस्य पुत्रः नृपः अभवत् किम्?

रमण: :
आम्! राज्ञः मरणोपरान्तं तस्य अल्पवयस्कपुत्रः। वीरनारायणः राजा अभवत्।

दीक्षा :
केन कारणेन सा इयती प्रसिद्धा?

रमणः :
वीरनारायणः बालक एव आसीत्। अतः सा दुगा. ‘वती चातुर्येण शौर्यण च राज्यमकरोत्। अतएव सा “महाराज्ञी” इति उपाधिना विभूषिता।

दीक्षा :
तस्याः राज्यस्य वैशिष्ट्यं किम् आसीत्?

रमणः :
राज्ञी दुर्गावती धीरा वीरा च आसीत्। राजकार्येषु युद्धविद्यायां च प्रवीणा आसीत्। प्रजासु तस्याः पुत्रवत् स्नेहः आसीत्। प्रजा अपि तां माता इव अपश्यन्। लोककल्याणमेव तस्याः आदर्शः। तस्याः राज्यकाले सर्वत्र सम्पन्नता आसीत्।।

अनुवाद :
दीक्षा :
क्या तब दलपतशाह का पुत्र राजा हो गया था?

रमण :
हाँ! राजा की मृत्यु के बाद उनका अल्पवयस्क पुत्र वीरनारायण राजा हो गया था।

दीक्षा :
वह किस कारण से इतनी प्रसिद्ध हो गयी?

रमण :
वीरनारायण बालक ही था। इसलिए उस दुर्गावती ने चतुराई से और शूरवीरता से राज्य किया। इसलिए वह महारानी’ इस उपाधि से विभूषित हुई।

दीक्षा :
उसके राज्य की क्या विशेषता थी?

रमण :
रानी दुर्गावती धैर्यवान और वीर थी। राजकार्यों में और युद्धविद्या में चतुर थी। प्रजा पर उसका पुत्र के समान प्रेम था। प्रजा भी उसे माता की तरह देखती थी। लोककल्याण ही उसका आदर्श था। उसके राज्य काल में सर्वत्र सम्पन्नता थी।

दीक्षा :
केनापि सह तस्याः युद्धः अभवत् किम्?

रमण :
आम्! अवश्यमेव, तस्याः राजस्य सुखसमृद्धिम् असहमानः अकबरस्य सेनापतिः आसफखान: तस्याः उपरि आक्रमणम् अकरोत्। सा रणचण्डी भूत्वा युद्धं कृतवती, प्रथमदिवसे विजयं प्राप्नोत्।

दीक्षा :
तदन्तरं दुर्गावत्याः पूर्णविजयः अभवत् किम्?

रमण: :
न, पराजित: आसफखानः द्वितीयदिवसे शतघ्नीनां प्रयोगं कुर्वन् प्रचण्डाक्रमणम् अकरोत्। तस्य प्रतिरोधे असमर्थाः बहवः गौंडसैनिकाः हताः। अस्मिन् युद्धे एकः बाणः तस्याः नेत्रे, द्वितीयश्च कण्ठे लग्नः, तथापि सा युद्धं कृतवती अन्ते मृत्यु समीपम् अवलोक्य स्वसम्मानरक्षायै सा स्वयमेव कृपाणघातेन प्राणान् अत्यजत्।

अनुवाद :
दीक्षा :
क्या उसका किसी के साथ युद्ध हुआ?

रमण :
हाँ! अवश्य ही, उसके राज्य की सुखसमृद्धि को न सह सकने वाले अकबर के सेनापति आसफखान ने उसके ऊपर आक्रमण कर दिया। उसने रणचण्डी होकर युद्ध किया, पहले दिन विजय प्राप्त की।

दीक्षा :
क्या उसके बाद दुर्गावती की पूर्ण विजय हो गयी?

रमण :
नहीं, पराजित आसफखान ने दूसरे दिनशतघ्नीयों का (तोपों का) प्रयोग करते हुए भयंकर आक्रमण किया। उसका प्रतिरोध करने में असमर्थ बहुत से गौंड सैनिक मारे गये। इस युद्ध में एक बाण उसके नेत्र में और दूसरा कण्ठ में लग गया था फिर भी वह युद्ध करती रही। अन्त में मृत्यु को समीप ही देखकर अपने सम्मान की रक्षा के लिए उसने स्वयं ही तलवार के प्रहार से प्राणों को त्याग दिया।

दीक्षा :
इदं तु बहुकष्टकारकम्।

रमणः :
आम्, तस्याः, बलिदानम् अधुनापि जनाः स्मरन्ति। जबलपुरमण्डलामार्गे तस्या समाधिः अस्ति। काव्येषु लोकगीतेषु इतिहासे च सा अद्यापि यशः शरीरेण जीवति।

दीक्षा :

सत्यम्! दुर्गावती दुर्गा इव आसीत्।

अनुवाद :
दीक्षा :
यह तो बहुत ही कष्ट देने वाली बात है।

रमण :
हाँ, उसके बलिदान को तो आज भी लोग याद करते हैं। जबलपुर और मण्डला के मार्ग पर उसकी समाधि है। काव्यों में और लोकगीतों में तथा इतिहास में वह आज भी यशरूपी शरीर से जीवित है।

दीक्षा :
सत्य है। दुर्गावती दुर्गा की भाँति थी।

राज्ञी दुर्गावती शब्दाथा:

सह = साथ में। न्यवसत् = निवास करते थे। दिवङ्गतः = स्वर्गवास होना। प्रतिरोधः विरोध करना।

MP Board Class 7th Sanskrit Solutions

MP Board Class 7th Sanskrit Solutions Surbhi Chapter 21 सूक्तयः

MP Board Class 7th Sanskrit Chapter 21 अभ्यासः

प्रश्न 1.
एक शब्द में उत्तर लिखो
(क) कः परमो धर्म:? [परम धर्म कौन-सा है?]
उत्तर:
आचारः

(ख) विपरीत बुद्धिः कदा भवति? [बुद्धि किस समय विपरीत हो जाती है?]
उत्तर:
विनाशकाले

(ग) कूपखननं कदा न युक्तम्? [कुएँ का खोदना कब उचित नहीं है?]
उत्तर:
प्रदीप्तेवह्निकागृहे

(घ) केन कार्याणि सिद्धयन्ति? [कार्य किससे सिद्ध हो जाते हैं?]
उत्तर:
उद्यमेन

(ङ) किं सर्वत्र वर्जयेत्? [सभी स्थानों पर क्या वर्जनीय है?]
उत्तर:
अति।

प्रश्न 2.
एक वाक्य में उत्तर लिखो-
(क) कानि परेषां न समाचरेत्? [कौन-से कार्य दूसरों के लिए नहीं करने चाहिए?]
उत्तर:
आत्मनः प्रतिकूलानि परेषां न समाचरेत्। [जो काम अपने लिए विपरीत हों, उन्हें दूसरों के लिए नहीं करना चाहिए।]

(ख) संसर्गजाः के भवन्ति? [संगति से क्या हो जाते हैं?]
उत्तर:
संसर्गजा दोषगुणाः भवन्ति। [संगति से दोष भी गुण हो जाते हैं।]

(ग) सर्वोत्तम भूषणं किम् अस्ति? [सबसे अच्छा आभूषण क्या है?]
उत्तर:
वाग्भूषणं सर्वोत्तमं भूषणं अस्ति। [वाणी का आभूषण ही सबसे अच्छा आभूषण है।]

प्रश्न 3.
रिक्त स्थानों की पूर्ति करो
(क) ……… वसुधैव कुटुम्बकम्।
(ख) हितं मनोहारि च ………. वचः।
(ग) आत्मनः ……….. परेषां न समाचरेत्।
(घ) न ……… युक्तं प्रदीप्ते वह्निकागृहे।
(ङ) विनाशकाले ……….
उत्तर:
(क) उदारचरितानां तु
(ख) दुर्लभम्
(ग) प्रतिकूलानि
(घ) कूपखननं
(ङ) विपरीतबुद्धिः।

प्रश्न 4.
उचित शब्दों का मेल करो

उत्तर:
(क) → (3)
(ख) → (4)
(ग) → (1)
(घ) → (5)
(ङ) → (2)

प्रश्न 5.
समानार्थक शब्द लिखो
(1) वह्निना
(2) युक्तम्
(3) उद्यमेन
(4) वसुधा।
उत्तर:
(1) अग्निना
(2) सहितम्
(3) परिश्रमेन
(4) पृथिवी।

प्रश्न 6.
अधोलिखित शब्दों के विलोम शब्द पाठ से चुनकर लिखो
(क) अनुदारचरितानाम्
(ख) अनुकूलानि
(ग) सुलभम्
(घ) आलस्येन
(ङ) समृद्धिकाले।
उत्तर:
(क) उदारचरितानाम्
(ख) प्रतिकूलानि
(ग) दुर्लभम्
(घ) उद्यमेन
(ङ) विनाशकाले।

प्रश्न 7.
शुद्ध वाक्यों के समक्ष ‘आम्’ तथा अशुद्ध वाक्यों के समक्ष ‘न’ लिखो
(क) संसर्गजा दोषगुणाः न भवन्ति।
(ख) आत्मनः प्रतिकूलानि परेषां समाचरेत्।
(ग) वाग्भूषणं भूषणं न अस्ति।
(घ) अति सर्वत्र न वर्जयेत्।
(ङ) कार्याणि मनोरथैः सिध्यन्ति।
उत्तर:
(क) न
(ख) न
(ग) न
(घ) न
(ङ) न

प्रश्न 8.
संस्कृत वाक्यों में प्रयोग करो
(क) खलु
(ख) सततं
(ग) गृहे
(घ) बृद्धिः
उत्तर:
(क) सः खलुः अत्र आगच्छेत्.
(ख) सततम् श्रम करणेन साफल्यं भवति।
(ग) गृहे सति कः मित्रम् भवति।
(घ) विपत्तिकाले बद्धिः विपरीतम् भवति।

प्रश्न 9.
रेखांकित शब्दों के आधार पर प्रश्न बनाओ
(क) अति सर्वत्र वर्जयेत्।
(ख) आचारः परमो धर्मः।
(ग) उद्यमेन हि सिध्यन्ति कार्याणि।
(घ) उदारचरितानां तु वसुधैव कुटुम्बकम्।
उत्तर:
(क) का सर्वत्र वर्जयेत्?
(ख) कः परमो धर्मः?
(ग) केन हि सिध्यन्ति कार्याणि?
(घ) केषाम् तु वसुधैव कुटुम्बकम्?

सूक्तयः हिन्दी अनुवाद

1. आचारः परमोधर्मः।
2. संसर्गजाः दोषगुणाः भवन्ति।
3. उदारचरितानां तु वसुधैव कुटुम्बकम्।
4. हितं मनोहारि च दुर्लभं वचः।।
5. उद्यमेन हि सिध्यन्ति कार्याणि न मनोरथैः।
6. अति सर्वत्र वर्जयेत्।
7. विनाशकाले विपरीतबुद्धिः।
8. न कूपखननं युक्तं प्रदीप्ते वह्निना गृहे।
9. आत्मनः प्रतिकूलानि परेषां न समाचरेत्।
10. क्षीयन्ते खलु भूषणानि सततं वाग्भूषणं भूषणम्।

अनुवाद :

1. आचरण सबसे बड़ा धर्म है।
2. संगति से दोष भी गुण हो जाया करते हैं।
3. उदार चरित्र वाले लोगों के लिए तो सारी पृथ्वी ही कुटुम्ब के समान होती है।
4. हितकारी और मनोहारी वचन दुर्लभ होते हैं।
5. परिश्रम करने से ही कार्य हुआ करते हैं, इच्छाओं से नहीं।
6. किसी काम की अति सभी जगह रोक लेनी चाहिए।
7. जब विनाशकाल आता है, तो बुद्धि भी उल्टी हो जाती है अर्थात् मनुष्य का आचरण भी विपरीत होने लगता है।
8. घर में आग लगने पर कुएँ का खोदना उचित नहीं होता है।
9. जो काम अपने लिए विपरीत हो, वह दूसरों के लिए नहीं करना चाहिए।
10. आभूषण तो नष्ट हो जाते हैं परन्तु वाणी का आभूषण सदा आभूषण रूप में बना रहता है।

सूक्तयः शब्दार्थाः

उद्यमेन = मेहनत से। संसर्गजाः = साथ रहने से। प्रदीप्ते = जलने पर। कूपखननं = कुआँ खोदना। आत्मनः = अपने। क्षीयन्ते = नष्ट हो जाते हैं। भूषणानि = गहने।

MP Board Class 7th Sanskrit Solutions

MP Board Class 6th Maths Solutions Chapter 5 प्रारंभिक आकारों को समझना Ex 5.5

पाठ्य-पुस्तक पृष्ठ संख्या # 110

प्रश्न 1.
निम्नलिखित में से कौन लम्ब रेखाओं के उदाहरण हैं ?
(a) मेज के ऊपरी सिरे की आसन्न भुजाएँ
(b) रेलपथ की पटरियाँ
(c) अक्षर L बनाने वाले रेखाखण्ड
(d) अक्षर V बनाने वाले रेखाखण्ड
उत्तर-
(a) हाँ,
(b) नहीं,
(c) हाँ,
(d) नहीं।

प्रश्न 2.
मान लीजिए रेखाखण्ड PQ रेखाखण्ड XY पर लम्ब है। मान लीजिए ये परस्पर बिन्दु A पर प्रतिच्छेद करते हैं। ∠PAY की माप क्या है?
हल :
∵\(\overline{P Q} \perp X Y\)
∴उनके बीच कोण = 90°
अतः ∠PAY = 90°

प्रश्न 3.
आपके पास ज्यामिति बक्स में दो सेट स्क्वेयर हैं। इनके कोनों पर बने कोणों की माप क्या है ? क्या इनमें से कोई ऐसी माप है, जो दोनों में उभयनिष्ठ है ?
हल :
एक सेट स्क्वे यर पर बने कोणों की माप 30°, 60° और 90° है तथा दूसरे पर बने कोणों की माप 45°, 45° और 90° है।
दोनों में उभयनिष्ठ कोण 90° है।

प्रश्न 4.
इस आकृति को ध्यान से देखिए। रेखा l रेखा m पर लम्ब है।
(a) क्या CE = EG है ?
(b) क्या रेखा PE रेखाखण्ड CG को समद्विभाजित करती है ?

(c) कोई दो रेखाखण्डों के नाम लिखिए जिनके लिए PE लम्ब समद्विमाजक है।
(d) क्या निम्नलिखित सत्य हैं?
(i) AC > FG
(ii) CD = GH
(iii) BC < EH
हल :
(a) CE = 2 इकाई, EG = 2 इकाई
∴ हाँ, CE = EG
(b) हाँ, रेखा PE रेखाखण्ड CG को समद्विभाजित करती है।
(c) \(\overline{B H}\) और \(\overline{D F}\)
(d) (i) सत्य, (ii) सत्य, (iii) सत्य।

पाठ्य-पुस्तक पृष्ठ संख्या # 111

इन्हें कीजिए

प्रश्न 1.
नीचे दिए हुए त्रिभुजों के कोणों और भुजाओं को क्रमशः चाँदे और रूलर से मापें। दी हुई सारणी में इनकी मापों को भरिए :
हल :

पाठ्य-पुस्तक पृष्ठ संख्या # 112

उपर्युक्त कोण, त्रिभुज और उनकी भुजाओं की मापों को ध्यानपूर्वक देखिए। क्या इनके बारे में कोई बात कही जा सकती है?
उत्तर-
हाँ, त्रिभुज में समान कोणों की भुजाएँ समान होती हैं। यदि किसी त्रिभुज में दो कोण समान हैं तो उनकी सम्मुख भुजाएँ भी समान होती हैं। किसी त्रिभुज में कोण असमान होने पर उनकी भुजाओं की लम्बाइयाँ भी असमान होंगी।

आप क्या प्राप्त करते हैं ?
(i) यदि किसी त्रिभुज के सभी कोण बराबर हैं तो इसकी भुजाएँ भी ……. हैं।
(ii) यदि एक त्रिभुज की सभी भुजाएँ बराबर हैं, तो उसके कोण भी …… हैं।
(iii) यदि किसी त्रिभुज की दो भुजाएँ बराबर हैं, तो उसके ……. कोण बराबर होते हैं।
(iv) यदि किसी त्रिभुज की तीनों भुजाएँ बराबर नहीं हैं, तो उसके तीनों कोण भी ……. नहीं हैं।
उत्तर-
(i) समान,
(ii) समान,
(iii) दो,
(iv) समान।

पाठ्य-पुस्तक पृष्ठ संख्या # 113

इन्हें कीजिए

प्रश्न 1.
निम्न के रफ चित्र खींचने का प्रयत्न कीजिए :
(a) एक विषमबाहु न्यून कोण त्रिभुज
(b) एक अधिककोण समद्विबाहु त्रिभुज
(c) एक समकोण समद्विबाहु त्रिभुज
(d) एक विषमबाहु समकोण त्रिभुज।
हल :
(a) विषमबाहु न्यून कोण त्रिभुज
(b) अधिकोण समद्विबाहु त्रिभुज
(c) समद्विबाहु समकोण त्रिभुज
(d) विषमबाहु समकोण त्रिभुज

प्रश्न 2.
क्या आप सोचते हैं कि निम्न आकृति खींचना सम्भव है:
(e) एक अधिककोण समबाहु त्रिभुज?
(f) एक समकोण समबाहु त्रिभुज?
(g) एक त्रिभुज जिसमें दो समकोण हों?
सोचिए, चर्चा कीजिए और फिर अपने निष्कर्षों को लिखिए।
उत्तर-
(e) सम्भव नहीं है। क्योंकि समबाहु त्रिभुज का प्रत्येक कोण 60° (न्यून कोण) होता है।
(f) सम्भव नहीं है। क्योंकि समबाहु त्रिभुज में समकोण असम्भव है।
(g) सम्भव नहीं है। क्योंकि त्रिभुज में केवल एक ही समकोण हो सकता है।

MP Board Class 6th Maths Solutions

MP Board Class 6th Maths Solutions Chapter 5 प्रारंभिक आकारों को समझना Ex 5.4

पाठ्य-पुस्तक पृष्ठ संख्या # 107-109

प्रश्न 1.
निम्न के क्या माप हैं :
(i) एक समकोण?
(ii) एक ऋजुकोण ?
हल :
(i) एक समकोण = 90°
(ii) एक ऋजुकोण = 180°

प्रश्न 2.
बताइए सत्य (T) या असत्य (F):
(a) एक न्यून कोण का माप < 90° है।
(b) एक अधिक कोण का माप < 90° है।
(c) एक प्रतिवर्ती कोण का माप < 180° है।
(d) एक सम्पूर्ण घूर्णन का माप = 360° है।
(e) यदि m∠A = 53° और m∠B = 35° है तो m∠A > M∠B है।
उत्तर-
(a) सत्य
(b) असत्य
(c) असत्य
(d) सत्य,
(e) सत्य

प्रश्न 3.
निम्न के माप लिखिए :
(a) कुछ न्यून कोण
(b) कुछ अधिक कोण। (प्रत्येक के दो उदाहरण दीजिए।)
हल :
(a) न्यूनकोण : 60° और 72°
(b) अधिक कोण : 100° और 162°

प्रश्न 4.
निम्न कोणों को चाँदे से मापिए और उनके माप लिखिए :

हल :
(a) → 45°,
(b) → 120°,
(c) → 90°,
(d) x = 60°, y = 135°, z = 90°

प्रश्न 5.
किस कोण का माप बड़ा है ? पहले आकलन (estimate) कीजिए और फिर मापिए।
कोण A का माप
कोण B का माप

हल :
आकलन से ∠B का माप बड़ा है
मापने पर : ∠A = 40° ; ∠B = 65°
∴ ∠B > ∠A

प्रश्न 6.
निम्न दो कोणों में से किस कोण का माप बड़ा है ? पहले आकलन कीजिए और फिर मापन द्वारा पुष्टि कीजिए।

हल :
आकलन से ∠B का माप बड़ा है।
मापने पर : ∠A = 40° ; ∠B = 60°
∴ ∠B > ∠A

प्रश्न 7.
न्यूनकोण, अधिक कोण, समकोण या ऋजुकोण से रिक्त स्थानों को भरिए :
(a) वह कोण, जिसका माप एक समकोण के माप से कम है, ………. होता है।
(b) वह कोण, जिसका माप एक समकोण के माप से अधिक हो, ……….. होता है।
(c) वह कोण जिसका माप दो समकोण के योग के बराबर है,………. होता है।
(d) यदि दो कोणों के मापों का योग समकोण के माप के बराबर है, तो प्रत्येक कोण …….. होता है।
(e) यदि दो कोणों के मापों का योग एक ऋजुकोण के माप के बराबर है, और इनमें से एक कोण न्यून कोण है, तो दूसरा कोण ……… होना चाहिए।
उत्तर-
(a) न्यून कोण
(b) अधिक कोण (यदि 180° से कम है)
(c) ऋजुकोण
(d) न्यूनकोण
(e) अधिक कोण।

प्रश्न 8.
नीचे दी आकृति में दिए प्रत्येक कोण का माप ज्ञात कीजिए (पहले देखकर आकलन कीजिए और फिर चाँदे से मापिए):

हल :
(a) आकलन से 350° (a) कोण का माप = 40°
(b) आकलन से 120° (b) कोण का माप = 130°
(c) आकलन से 60° (c) कोण का माप = 65°
(d) आकलन से 130° (d) कोण का माप = 135°

प्रश्न 9.
नीचे दी प्रत्येक आकृति में घड़ी की सुइयों के बीच के कोण का माप ज्ञात कीजिए :

हल :
कोणों की माप
(i) प्रात: 9 : 00 बजे = 90° ;
(ii) दोपहर 1 : 00 बजे = 30° ;
(iii) सायं 6 : 00 बजे = 180°

प्रश्न 10.
खोज कीजिए : दी हुई आकृति में चाँदा 30° दर्शा रहा है। इसी आकृति को एक आवर्धन शीशे (magnifying glass) द्वारा देखिए, क्या यह कोण बड़ा हो जाता है ?

क्या कोण का माप बड़ा हो जाता है ?
उत्तर-
आवर्धन शीशे द्वारा देखने पर कोण के माप में कोई अन्तर नहीं आता है। न तो यह कोण बड़ा होता है और न कोण का माप बड़ा हो जाता है।

प्रश्न 11.
मापिए और प्रत्येक कोण को वर्गीकृत कीजिए :

उत्तर-

पाठ्य-पुस्तक पृष्ठ संख्या # 109-110

सोचिए, चर्चा कीजिए एवं लिखिए

प्रश्न 1.
यदि AB ⊥ CD है, तो हमें क्या यह भी कहना चाहिए कि CD ⊥ AB है?
हल :
यदि CD ⊥ AB हो, तो ∠COB = 90° जो कि सत्य है। क्योंकि
AB ⊥ CD
अतः AB ⊥ CD = CD ⊥ AB
अतः हम यह कह सकते हैं कि CD ⊥ AB

प्रश्न 2.
क्या कोई और अक्षर (T अतिरिक्त) भी है, जो लम्बों का उदाहरण है ?
हल :
हाँ, है; अंग्रेजी अक्षर L अन्य अक्षर है जो लम्ब का उदाहरण है।

प्रश्न 3.
एक पोस्टकार्ड को लीजिए। क्या इसके किनारे परस्पर लम्ब हैं ?
उत्तर-
हाँ, पोस्टकार्ड के किनारे परस्पर लम्ब हैं।

MP Board Class 6th Maths Solutions

MP Board Class 7th Sanskrit Solutions Surbhi Chapter 20 योगः स्वास्थ्यस्य साधनम्

MP Board Class 7th Sanskrit Chapter 20 अभ्यासः

प्रश्न 1.
एक शब्द में उत्तर लिखिए
(क) कः योगस्य प्रवर्तकः? [योग के प्रवर्तक कौन थे?]
उत्तर:
पतञ्जलिः

(ख) केन शरीरं स्वस्थं भवति? [किससे शरीर स्वस्थ होता है?]
उत्तर:
योगेन

(ग) श्वासनियंत्रणम् केन भवति? [श्वास नियंत्रण किससे होता है?]
उत्तर:
श्वासोच्छ्वसनं

(घ) कः कालः योगाय उचितः? [योग के लिए कौन-सा समय उचित होता है?]
उत्तर:
प्रातः

(ङ) योगनिद्रा किमर्थं क्रियते? [योगनिद्रा किसलिए की जाती है?]
उत्तर:
मनः शान्त्यर्थं।

प्रश्न 2.
एक वाक्य में उत्तर लिखो
(क) आद्यं धर्मसाधनं किम् अस्ति? [प्रारम्भिक धर्म का साधन क्या है?]
उत्तर:
शरीरमाद्यम् खलु धर्मसाधनम् अस्ति। [शरीर ही धर्म का प्रारम्भिक साधन है।]

(ख) योगेन किं स्वस्थं भवति? [योग से क्या स्वस्थ होता है?]
उत्तर:
योगेन शरीरं स्वस्थं भवति। [योग से शरीर स्वस्थ होता है।]

(ग) स्वस्थ शरीरे किं सुकरम्? [स्वस्थ शरीर से क्या आसान है?]
उत्तर:
स्वस्थ शरीरे अध्ययनं सुकरम् भवति। [स्वस्थ शरीर से अध्ययन आसान है।]

(घ) योगशास्त्रम् किमर्थं प्रवर्तितम्? [योगशास्त्र का प्रवर्तन किसलिए हुआ?]
उत्तर:
योगशास्त्रम् शरीरस्वास्थ्यार्थम् प्रवर्तितम्। [योगशास्त्र का प्रवर्तन शरीर के स्वास्थ्य के लिए हुआ।]

(ङ) सुलभा कस्य मूर्तिम् अपश्यत्? [सुलभा ने किसकी मूर्ति को देखा?]
उत्तर:
सुलभा मुनेः पतञ्जलेः मूर्तिम् अपश्यत्। [सुलभा ने मुनि पतञ्जलि की मूर्ति को देखा।]

प्रश्न 3.
उचित विकल्प से रिक्त स्थानों को भरो (व्याकरणम्, आयुर्वेदम्, नास्ति, अस्ति, करिष्यति, कारयिष्यति)
(क) सम्यग् अन्नपचनं …………।
(ख) सदैव क्षुधाभावः ………..।
(ग) सुलभा योगं ………….।
(घ) शारदा योगं ……………।
(ङ) पतञ्जलिः शरीरस्वास्थ्यार्थम् ………….अरचयत्।
(च) पतञ्जलिः वाणीशुद्धयर्थं …………. अरचयत्।।
उत्तर:
(क) नास्ति
(ख) अस्ति
(ग) करिष्यति
(घ) कारयिष्यति
(ङ) आयुर्वेदम्
(च) व्याकरणम्।

प्रश्न 4.
अधोलिखित पदों को लकार के अनुसार लिखो (आसीः, भवति, करिष्यति, अपश्यत्, अकरोत्, सम्भवन्ति, इच्छामि, उन्मूलयन्ति, ज्ञास्यामि, आगमिष्यामि)
उत्तर:
(क) लङ् (भूतकालिकः) = आसीः, अपश्यत्, अकरोत्।
(ख) लट् (वर्तमाने) = भवति, सम्भवन्ति, इच्छामि, उन्मूलयन्ति।
(ग) लुट (भविष्यत्) = करिष्यति, ज्ञास्यामि, आगमिष्यामि।

प्रश्न 5.
अधोलिखित भूतकालिक कृदन्त शब्दों को देखो और रिक्त स्थानों को भरो [लिखितम्, आगतः, पीडिता, प्रयुक्तम्]
(क) बालकः पत्रम् लिखति। तेन पत्रं ………..।
(ख) रोगः सुलभां पीडयति। सुलभा रोगेन ………..।
(ग) बालकः गृहम् आगच्छत्। बालकः गृह ………..।
(घ) शारदा आसनं प्रायुक्त। शारदया आसनं ………..।
उत्तर:
(क) लिखितम्
(ख) पीडिता
(ग) आगतः
(घ) प्रयुक्तम्।

प्रश्न 6.
रेखांकित पदों के लिए प्रश्न निर्माण करो
(क) योगाभ्यासेन कार्ये कौशलं जायते।
(ख) आसनानि सन्धि रोगान् उन्मूलयन्ति।
(ग) सुलभा शारदाम् अमिलत्।
(घ) सर्वं गुरोः निर्देशने करणीयम्।
उत्तर:
(क) योगाभ्यासेन कस्मिन् कौशलं जायते?
(ख) आसनानि कान् रोगान् उन्मूलयन्ति?
(ग) का शारदाम् अमिलत्?
(घ) सर्वम् कस्य निर्देशने करणीयम्?

प्रश्न 7.
उचित शब्दों को मिलाओ-

उत्तर:
(क) → (3)
(ख) → (4)
(ग) → (5)
(घ) → (6)
(ङ) → (1)
(च) → (2)

प्रश्न 8.
अधोलिखित रूपों का लकार, वचन और पुरुष लिखो
(क) आसीः
(ख) आसम्
(ग) अस्ति
(घ) सन्ति
उत्तर:
(क) आसी: = लङ् लकार, अन्य पुरुषः, एकवचनम्।
(ख) आसम् = लङ् लकार, उत्तम पुरुषः, एकवचनम्।
(ग) अस्ति = लट् लकार, अन्य पुरुषः, एकवचनम्।
(घ) सन्ति = लट् लकार, अन्य पुरुषः, बहुवचनम्।

योगः स्वास्थ्यस्य साधनम् हिन्दी अनुवाद

(संस्कृतशिक्षिका विद्यावती स्वछात्रां सुलभाम् अपृच्छत्)

विद्यावती :
सुलभे! ह्यः त्वं कक्षायाम् उपस्थिता न आसीः। किं कारणम्?

सुलभा:
महोदये! रात्रौ मम उदरपीडा आसीत्। गतसप्ताहे अपि अनेनैव कारणेन पीडिता आसम्। कदाचित् ज्वरः वर्तते। अन्नपचनं सम्यग् नास्ति। क्षुधाभावः सदैव अस्ति।

विद्यावती :
एतत् चिन्तनीयम्। वैद्यस्य किम् अभिमतम्?

सुलभा:
वैद्यः औषधयोजनां करोति। किन्तुस्थगिते औषधे पुनः पीडा प्रादुर्भवति। न जाने किं कर्त्तव्यमिति। धिगस्तु रुग्णजीवनम्।

विद्यावती:
यदा औषधसेवनं रोगान् न उन्मूलयति, तदा योगोपचारः कर्त्तव्यः। योगकक्षां गत्वा योगशिक्षिकायाः मार्गदर्शनं स्वीकुरु। सा चिकित्सां करिष्यति।

अनुवाद :
(संस्कृत की अध्यापिका विद्यावती ने अपनी छात्रा सुलभा से पूछा)

विद्यावती :
हे सुलभा! कल तुम कक्षा में उपस्थित नहीं थीं। क्या कारण था?

सुलभा :
हे महोदया! रात को मेरे पेट में दर्द था। बीते सप्ताह भी इसी कारण से (मैं) पीड़ित थी। शायद ज्वर है। अन्न का पाचन ठीक तरह से नहीं होता है। भूख की कमी सदा ही बनी रहती है।

विद्यावती :
यह चिन्ता का विषय है। वैद्य की क्या राय है?

सुलभा :
वैद्य औषधि की योजना करता है। किन्तु औषधि के बन्द कर देने पर पीड़ा फिर से उत्पन्न हो जाती है। क्या करना चाहिए? नहीं जानते हैं। रोगयुक्त जीवन के लिए धिक्कार है।

विद्यावती :
जब औषधि सेवन करने पर भी रोग नष्ट नहीं होता है, तब योग से उपचार (इलाज) करना चाहिए। योग की कक्षा में जाकर योग की शिक्षिका का मार्गदर्शन स्वीकार करो। वह चिकित्सा (इलाज) करती है।

सुलभा :
महोदये! योगमार्गः तु संन्यासिनां मार्गः। संसारत्यागं न इच्छामि। अहं छात्रा अस्मि।

विद्यावती :
न एतत्। योगेन शरीरं चित्तम् अपि स्वस्थं भवति। “शरीरमाद्यं खलु धर्मसाधनम्” इति प्रसिद्धं वचनम्। स्वस्थे शरीरे अध्ययनं सुकरं भवति। तेन चित्तस्य एकाग्रता भवति। कार्ये कौशलं जायते। योगस्य अभ्यासेन अनेके लाभाः सम्भवन्ति।

(अन्यस्मिन् दिने सुलभा योगकक्षां गत्वा योगशिक्षिकां शारदां मिलितवती।)

अनुवाद :
सुलभा-हे महोदया! योगमार्ग (योग का उपाय) तो संन्यासियों का मार्ग है। संसार को त्यागना नहीं चाहती। मैं एक छात्रा हूँ।

विद्यावती :
ऐसा नहीं है। योग से शरीर (और) चित्त भी स्वस्थ होता है। ‘शरीर ही धर्म का साधन होता है’, यह कहावत प्रसिद्ध है। शरीर के स्वस्थ रहने पर अध्ययन आसान होता है। उससे चित्त की एकाग्रता होती है। कार्य में कुशलता पैदा हो जाती है। योग के अभ्यास से अनेक लाभ सम्भव हैं।

(दूसरे दिन सुलभा योग की कक्षा में जाकर योग की शिक्षिका शारदा से मिलती है।)

सुलभा :
नमस्ते भगवति। अहं सुलभा। मम शिक्षिका विद्यावती भवती मेलितुं मां समादिशत्। अहम् उदररोगेण पीडिता अस्मि। अत: योगोपचारम् इच्छामि।

शारदा :
स्वागतं। प्रविश कक्षाम्। (सुलभा कक्षां प्रविश्य एका मूर्तिम् अपश्यत्) सुलभा-भगवति! एषः ऋषिः कः?

शारदा :
एषः भगवान् पतञ्जलिः। एषः योगविद्यायाः प्रवर्तकः। अनेन मुनिना शरीरार्थम् आयुर्वेदे, वाणीशुद्धयर्थं व्याकरणे, मनोनिग्रहार्थं च योगशास्त्रे ग्रन्थाः लिखिताः।।

अनुवाद :
सुलभा :
हे भगवति! नमस्ते। मैं सुलभा हूँ। मेरी शिक्षिका विद्यावती ने आपसे मिलने के लिए मुझे आदेश दिया था। मैं पेट के रोग से पीड़ित हूँ। अत: योग का उपचार चाहती हूँ।

शारदा :
स्वागत है। कक्षा में प्रविष्ट हो जाइए। (सुलभा ने कक्षा में प्रवेश करके एक मूर्ति को देखा।)

सुलभा :
हे भगवति! ये कौन से ऋषि हैं?

शारदा :
ये भगवान पतञ्जलि हैं। ये ही योगविद्या के प्रवर्तक थे। इन मुनि महोदय के द्वारा शरीर के लिए आयुर्वेद में, वाणी की शुद्धता के लिए व्याकरण में और मन का निग्रह करने के लिए योगशास्त्र पर ग्रंथों को लिखा।

सुलभा :
वन्दे पतञ्जलिम्। योगकक्षायाम् अहं किं करिष्यामि?

शारदा :
आदौ स्वस्तिकासनं सिद्धासनं पद्मासनं च कारयिष्यामि एतेषाम् अभ्यासेन एकस्थितौ उपवेशनं स्थिरं भवति। तदा अध्ययने, कार्ये, प्राणायामे लेखने च काठिन्यं न स्यात।

सुलभा:
रोगनिवारणार्थं कः उपायः?

शारदा :
कानिचित् आसनानि उदररोगोपचारे प्रयुक्तानि। कानिचित् हस्तपादयोः सञ्चालने सहायकानि। कानिचित् सन्धिरोगम् उन्मूलयन्ति।

अनुवाद :
सुलभा-पतञ्जलि को नमस्कार। योग की कक्षा में मैं क्या करूँगी?

शारदा :
पहले स्वास्तिक आसन, सिद्ध आसन और पद्म आसन कराऊँगी। इनके अभ्यास से एक स्थिति में उपवेशन स्थिर होता है। तब अध्ययन करने में, काम करने में, प्राणायाम करने में और लेखन कार्य करने में कठिनाई नहीं होती है।

सुलभा :
रोग दूर करने के लिए क्या उपाय है?

शारदा :
पेट के रोग के उपचार में कुछ आसनों का प्रयोग किया जाता है। कुछ हाथ और पैरों के संचालन में सहायक होते हैं। कुछ जोड़ों के दर्द को जड़ से नष्ट कर देते हैं।

सुलभा :
कः एषः प्राणायामः? किम् एतद् अपि आसनम्?

शारदा :
न। प्राणायामेन श्वासोच्छ्वसनं नियन्त्रितं भवति। अनेन हृदयरोगे, नासिकारोगे श्वासरोगे च लाभः भवति। शवासनं योगनिद्रा च मनः शान्त्यर्थं क्रियते। ततः उत्साहलाभः भवति। भवती शनैः शनैः सर्वं ज्ञास्यसि। सर्वम् एतत् गुरोः निर्देशने करणीयम्।

अनुवाद :
सुलभा :
यह कौन-सा प्राणायाम है? क्या यह भी आसन है?

शारदा :
नहीं। प्राणायाम से श्वास का छोड़ना नियन्त्रित होता है। इसमें हृदय रोग में, नासिका रोग में और श्वास रोग में लाभ होता है। शव-आसन और योगनिद्रा आसन मन की शान्ति दे लिए किया जाता है। उसके बाद उत्साह लाभ होता है। आप धीरे-धीरे सब कुछ जान जायेंगी। यह सब गुरु के निर्देशन में किया जाना चाहिए।

सुलभा :
योगकक्षा किमर्थं प्रातः एव आयुज्यते?

शारदा :
प्रातः सूर्यः शान्तः, वायुः शीतलः, शरीरं च निर्मलं भवति। प्रात:काल सुखकरः भवति। योगः प्राकृतिक उपचारः। अतः प्रात:कालः योगाय उचितः।

सुलभा :
तहिं अहं योगाभ्यासाय श्वः आगमिष्यामि। शारदा-पुनरागमनाय गच्छतु भवती।

अनुवाद :
सुलभा :
योग की कक्षा प्रातः ही क्यों आयोजित होती है?

शारदा :
प्रातः सूर्य शान्त रहता है, वायु शीतल होती है और शरीर भी स्वच्छ होता है। प्रातः का समय सुखकर (सुख देने वाला) होता है। योग प्राकृतिक उपचार (इलाज) है। अतः प्रातः का समय योग के लिए उचित होता है।

सुलभा :
तो मैं योग के अभ्यास के लिए कल आऊँगी।

शारदा :
फिर से आने के लिए आप जाएँ।

योगः स्वास्थ्यस्य साधनम् शब्दार्थाः

ह्यः = भूतकालिक कल (बीता हुआ)। श्वः = भविष्यकालिक कल (आने वाला)। करिष्यामि = (मैं) करूँगी/करूँगा। कारयिष्यामि = मैं कराऊँगी/कराऊँगा। प्रादुर्भवति = उत्पन्न होती है। उन्मूलयति = मिटाती है। प्रवर्तकः = आरम्भकर्ता। ज्वरः = बुखार। वैद्यः = डॉक्टर, चिकित्सक। क्षुधाभावः = (क्षुधा + अभाव) भूख न लगना। अभिमतम् = मत, सलाह। समादिशत् = सलाह दी। सम्यक् = ठीक।

MP Board Class 7th Sanskrit Solutions