MP Board Class 12th Maths Solutions Chapter 8 Application of Integrals Ex 8.1

In this article, we share MP Board Class 12th Maths Book Solutions Chapter 8 Application of Integrals Ex 8.1 Pdf, These solutions are solved by subject experts from the latest MP Board books.

MP Board Class 12th Maths Solutions Chapter 8 Application of Integrals Ex 8.1

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MP Board Class 9th Maths Solutions Chapter 2 Polynomials Ex 2.1

MP Board Class 9th Maths Solutions Chapter 2 Polynomials Ex 2.1

Question 1.
Which of the following expressions are polynomials in one variable and which are not? State reasons for your answer.

  1. 4x2 – 3x + 7
  2. y2 + √2
  3. 3√t + t√2
  4. y + \(\frac{2}{y}\)
  5. x10 + y3 + t50.

Solution:
1. 4x2 – 3x + 7
This expression is a polynomial in one variable .r because in the expression there is only one variable (x) and all the indices of x are whole numbers.

2. y2 + √2
This expression is a polynomial in one variable y because in the expression there is only one variable (y) and all the indices of y are whole numbers.

3. 3√t + t√2
This expression is not a polynomial because in the term 3√t, the exponent of t is \(\frac{1}{2}\), which is not a whole number.

4. y + \(\frac{2}{y}\)
This expression is not a polynomial because in the term \(\frac{2}{y}\) the exponent of y is (-1) which is not a whole number.

5. x10 + y3 + t50
This expression is not a polynomial in one variable because in the expression, three variables (x, y and t) occur.

Given a polynomial function, identify the degree and leading coefficient calculator…. the following exercises, graph the polynomial functions using a calculator.

Question 2.
Write the coefficients of x2 in each of the following:

  1. 2 + x2 + x
  2. 2 – x2 + x3
  3. \(\frac{π}{2}\)x2 + x
  4. \(\sqrt{2x}\) – 1

Solution:
1. 2 + x2 + x
Coefficient of x2 = 1

2. 2 – x2 + x3
Coefficient of x2 = – 1

3. \(\frac{π}{2}\)x2 + x
Coefficient of x2 = \(\frac{π}{2}\)

4. \(\sqrt{2x}\) – 1
Coefficient of x2 = 0.

Question 3.
Give one example each of a binomial of degree 35, and of a monomial of degree 100.
Solution:
One example of a binomial of degree 35 is 3x35 – 4.
One example of a monomial of degree 100 is √2y100

Question 4.
Write the degree of each of the following polynomials:

  1. 5x3 + 4x2 + 7x
  2. 4 – y2
  3. 5x3 – √7
  4. 3

Solution:
1. 5x3 + 4x2 + 7x
Term with the highest power of x = 5x3
Exponent of x in this term = 3
∴ Degree of this polynomial = 3.

2. 4 – y2
Term with the highest power of y = – y2
Exponent of y in this term = 2
∴ Degree of this polynomial = 2.

3. 5t – √7
Term with the highest power of t = 5t
Exponent of t in this term = 1
∴ Degree of this polynomial = 1.

4. 3
It is a non-zero constant. So the degree of this polynomial is zero.

Square polynomial root calculator. grade 10 math linear algebra substitution word problems.

Question 5.
Classify the following as linear, quadratic and cubic polynomials:

  1. x2 + x
  2. x – x3
  3. y + y2 + 4
  4. 1 + x
  5. 3t
  6. r2
  7. 7x3

Solution:

  1. Quadratic
  2. Cubic
  3. Quadratic
  4. Linear
  5. Linear
  6. Quadratic
  7. Cubic.

Zero’s of a Polynomial:
1. A zero of a polynomial p(x) is a number c such that p(c) = 0. Here p(x) = 0 is a polynomial equation and c is the root of the polynomial equation.

2. A non-zero constant polynomial has no zero. Every real number is a zero of the zero polynomial.

Some Observations:

  1. A zero of a polynomial need not be 0.
  2. 0 may be a zero of a polynomial.
  3. Every linear polynomial has one and only one zero.
  4. A polynomial can have more than one zero.

MP Board Class 9th Maths Solutions

MP Board Class 12th Maths Solutions Chapter 9 Differential Equations Ex 9.2

In this article, we share MP Board Class 12th Maths Book Solutions Chapter 9 Differential Equations Ex 9.2 Pdf, These solutions are solved by subject experts from the latest MP Board books.

MP Board Class 12th Maths Solutions Chapter 9 Differential Equations Ex 9.2

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MP Board Class 12th Maths Solutions Chapter 1 Relations and Functions Ex 1.4

In this article, we share MP Board Class 12th Maths Book Solutions Chapter 1 Relations and Functions Ex 1.4 Pdf, These solutions are solved by subject experts from the latest MP Board books.

MP Board Class 12th Maths Solutions Chapter 1 Relations and Functions Ex 1.4

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MP Board Class 8th Social Science Solutions Chapter 6 Lithosphere and Land Forms

In this article, we will share MP Board Class 8th Social Science Solutions Chapter 6 Lithosphere and Land Forms Pdf, These solutions are solved subject experts from the latest edition books.

MP Board Class 8th Social Science Solutions Chapter 6 Lithosphere and Land Forms

MP Board Class 8th Social Science Chapter 6 Text Book Exercise

Choose the correct option of the following.

Question 1.
How much area of earth is covered by hydrosphere?
(a) 61 percent
(b) 71 percent
(c) 81 percent
(d) 51 percent
Answer:
(b) 71 percent

Question 2.
Which country is world renowned for earthquakes?
(a) India
(b) France
(c) Japan
(d) Srilanka
Answer:
(c) Japan

Fill up the blanks:

  1. ………….. area or earth is surrounded by lithosphere.
  2. The outer layer of earth is called …………….
  3. Sal contains silicon and ………… metals mostly.
  4. At the depth of every 32 meter ………….. Celsius temperature increases.

Answers:

  1. 29 percent
  2. lithosphere
  3. Magnesium

MP Board Solutions

find the Kbps full form of acronym or get information about Kilobits per second to read full article that has number of abbreviations.

MP Board Class 8th Social Science Chapter 6 Very Short Answer Type Questions

Question 1.
Which are the elementary rocks of the earth?
Answer:
The elementary rocks are Igneous rocks.

Question 2.
Write names of three prominent land forms?
Answer:
The three land forms are Mountains, Plateaus, Plains.

Question 3.
What do you call when rocks curve like waves?
Answer:
When rocks curve like waves are called Metamorphic rocks.

Question 4.
Where volcanoes are mostly dominant in the world?
Answer:
The volcanoes are mostly dominant near the coastal area of pacific ocean and in the continental regions.

MP Board Solutions

MP Board Class 8th Social Science Chapter 6 Short Answer Type Questions

Question 1.
What is difference between a fold mountain and a rift mountain?
Answer:
Fold Mountain are formed by the horizontal land movement in earth which causes wave like bends in rocks. Rift mountains are formed by breaking of rocks with pressure and tension of the horizontal land movement which causes few part of land lift and few part go down.

Question 2.
How Sedimentary rocks are formed?
Answer:
Sedimentary rocks are formed due to the deposits of sediments brought by wind, running water or moving ice.

Question 3.
What is Volcano? Give two causes of eruption?
Answer:
Volcano is an opening on the earth crust, in the form of lava which emits molten magma, rock pieces, gases and steam on the surface of the earth. The two causes of eruptions are, the break up of radioactive minerals under die bottom of earth and the movement of plates due to eternal heat.

Question 4.
Mention the merits and demerits of earthquakes?
Answer:
Earth quakes are useful when we get fertile lands, formation of new land areas, valuable minerals come upon the surface and lakes are formed in low-lying areas. Earthquakes brings loss of life, material, devastating floods and few areas go down of land.

MP Board Solutions

MP Board Class 8th Social Science Chapter 6 Long Answer Type Questions

Learn what volume percent or volume/volume percent concentration means and how to calculate volume percent when preparing a solution.

Question 1.
What is Rock? Explain the type of Rocks?
Answer:
The earth’s crust is made up of rocks. A rock is a mixture of minerals which forms the earths upper part called crust. These rocks are composed of all types of material which may be hard and resistant substance like granite, marble etc. and of soft and loose substance like salt, sand, mud, chalk etc. The difference between rock and mineral is that the rocks contain in them various types of minerals. Rocks do not have definite chemical composition while minerals have definite chemical properties.

There are three kinds of rocks:
1. Igneous Rock
2. Sedimentary Rock
3. Metamorphic Rock

1. Igneous Rock:
Igneous rocks are formed due to the solidification of molten magma. The high temperature inside the earth causes rock masses to melt. The molten material due to heavy pressure inside tries to come out on the surface or to low pressure areas.

In this process some of its material cools down under the earth surface itself and solidifies in the form of solid rocks. Some of it comes out on tire surface as lava and gas hardened. These solidified rocks are called igneous rocks. Basalt and Granite are the other examples. Basalt is formed above the earth surface and Granite below the earth.

2. Sedimentary Rock:
Sedimentary rocks are formed due to the deposits of sediments brought by wind, running water or moving ice. These deposits or sediments lay down on the floor of the river beds, lakes, sea etc. forming one layer over the other. These layers contain fossils also. Fossils are the remains of animals embedded in the rocks. They are also called stratified rocks. Sandstone, Limestone, Clay, Coal, Gravels etc. are the examples of Sedimentary rocks.

3. Metamorphic Rocks:
When main rocks change in appearance and composition losing their original identity, they are called metamorphic rocks. In other words, when Igneous rocks and Sedimentary rocks change their original form due to intense heat and pressure, they are called metamorphic rocks.

The chemical composition of minerals present in the rocks get transformed into new type minerals. For example Limestone gets transformed into Marble, Sandstone changes into granite. Other examples of metamorphic rocks are slate and gneiss etc.

Question 2.
Define the formation of earth by Diagram?
Answer:
The structure of earth can be divided into three distinct parts. They are Crust, Mantle, Core.
1. The Crust:
The outer most part of the earth is crust. It is also known as lithosphere. It has thickness of 60 kms. It forms the continents, islands and lands underlying seas and oceans. The outer crust is made of silicates and aluminum and is called SIAL.

MP Board Class 8th Social Science Solutions Chapter 6 Lithosphere and Land Forms img 1

2. The Mantle:
The next layer that underlies Sial is Mantle. It has two parts:

  •  inner silicate layer made of silica and magnesium called SIMAL.
  • Transitional layer of mixed metals and silicate: This is about 2900 km in thickness, and is made of solid heavy rocks containing mixture of silicates and other metals. The average density of his layer varies between 45 to 5.5.

3. The Core:
The innermost part of the earth is known as Core it extends beyond the depth of 2900 kilometers. It is made up of heavy meta like iron and nickel generally expressed as Nife. They believed to be source of earth magnetism its thickness is 3467 kms. The temperature inside the earth increases at an average rate of 1°C for 32 meters of depth This is also called bray sphere

Question 3.
Explain the impact of volcanoes on! human life?
Ans. The volcanoes create formations of various land forms like plains, plateaus, mountain etc. We get valuable minerals from these The Java which spreads forms a fertile land after Sometimes. The dead volcanoe smouth filled with rain water creates lakes. The eruption of volcanoes destroy human lives. Cattles. vegetation, Agricultural land cities.

Question 4.
What is earthquake? Describe the causes of the carthquake?
Answer:
Earthquake is sudden shaking of the earth by sudden tectonic or external movement. The place where earthquake occurs is earthquake epicenter (focus). The place exactly over focus where waves of earthquakes are felt is called carthquake center
The causes of earthquake are as follows:

  • Sudden movement within earth.
  • The eruption of volcano
  • The gases or vapors, formed under the bottom of the earth breaks earth crust to come out and thus earthquake happens.

Question 3.
Mention the following rocks in the table given below?

  1. Marble
  2. Coal
  3. Granite
  4. limestone
  5. basalt
  6. Diamond

Answer:
types of rocks
1. Ligneous Rock:          Granite         basalt
2. Sedimentary Rock:     limestone     Coal
3. Metamorphic Rock:    Marble         Diamond

Project Work.

Question 1.
Draw a diagram of the formation of the earth?
Answer:

MP Board Class 8th Social Science Solutions Chapter 6 Lithosphere and Land Forms img 1

Question 2.
Draw a sketch of volcano?
Answer:

MP Board Class 8th Social Science Solutions Chapter 6 Lithosphere and Land Forms img 3

Question 3.
Collect samples of granite, coal and sand stone?
Answer:
Do your self.

MP Board Class 12th Maths Solutions Chapter 9 Differential Equations Ex 9.1

In this article, we share MP Board Class 12th Maths Book Solutions Chapter 9 Differential Equations Ex 9.1 Pdf, These solutions are solved by subject experts from the latest MP Board books.

MP Board Class 12th Maths Solutions Chapter 9 Differential Equations Ex 9.1

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MP Board Class 12th Maths Solutions Chapter 7 Integrals Ex 7.11

In this article, we share MP Board Class 12th Maths Book Solutions Chapter 7 Integrals Ex 7.11 Pdf, These solutions are solved by subject experts from the latest MP Board books.

MP Board Class 12th Maths Solutions Chapter 7 Integrals Ex 7.11

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MP Board Class 12th Hindi Swati Solutions पद्य Chapter 5 प्रकृति चित्रण

In this article, we will share MP Board Class 12th Hindi Solutions पद्य Chapter 5 प्रकृति चित्रण Pdf, These solutions are solved subject experts from the latest edition books.

MP Board Class 12th Hindi Swati Solutions पद्य Chapter 5 प्रकृति चित्रण

प्रकृति चित्रण अभ्यास

प्रकृति चित्रण अति लघु उत्तरीय प्रश्न

प्रश्न 1.
प्रस्तुत गीत में ‘तारागण’ को किस रूप में चित्रित किया गया है?
उत्तर:
प्रस्तुत गीत में ‘तारागण’ को घट के रूप में चित्रित किया गया है।

प्रश्न 2.
कवि ने पनघट किसे कहा है? (2009)
उत्तर:
कवि ने पनघट आसमान को कहा है।

प्रश्न 3.
बिजली की चमक देखकर कवि सखी को क्या सलाह देता है? (2014, 16)
उत्तर:
बिजली की चमक देखकर कवि सखी को परामर्श देता है कि हे सखी ! तू भाग, बिजली चमक रही है,पानी आने वाला है।

प्रश्न 4.
‘अरी सुहागिन’ सम्बोधन किसके लिए आया है?
उत्तर:
‘अरी सुहागिन’ सम्बोधन वैसे तो विवाहित स्त्री के लिए किया गया है, लेकिन प्रकृति की ओर भी संकेत है।

प्रश्न 5.
सहज रंगीली नायिका किसके रंग में रंगी हुई है ?
उत्तर:
सहज रंगीली नायिका इन्द्रधनुषी रंगों से रंगी हुई है।

MP Board Solutions

प्रकृति चित्रण लघु उत्तरीय प्रश्न

प्रश्न 1.
विभावरी’ के बीतने पर ‘उषा नागरी’ क्या कर रही है? (2009, 17)
उत्तर:
‘विभावरी’ यानी रात्रि के बीत जाने पर उषा रूपी स्त्री अम्बर रूपी पनघट में तारे रूपी घड़ों को डुबो रही है। इस दृश्य को कवि ने बड़े मनोहारी ढंग से मानवीय भावनाओं और कार्यों से जोड़ा है।

प्रश्न 2.
‘आँखों में भरे विहाग री’ सम्बोधन किसके लिए आया है?
उत्तर:
प्रस्तुत कविता में ‘आँखों में भरे विहाग री’ सम्बोधन उस स्त्री के लिए आया है जिसकी आँखें अभी उनींदी हैं और प्रभात का गीत उसकी आँखों में भरा हुआ है। दूसरी ओर रजनी रूपी स्त्री की आँखों में अभी तक नींद भरी है और उसके उठते ही खग अपने गीत गाने लगेंगे।

प्रश्न 3.
खगकुल ‘कुल-कुल सा’ क्यों बोलने लगा?
उत्तर:
पक्षियों का समूह प्रभात की किरण के साथ आमोद-प्रमोद में भर जाते हैं और नभमण्डल में उड़ान भरते हुए मधुर गीत गाने लगते हैं। प्रभात ही उनके गीत प्रारम्भ करने का संकेत देता है।

प्रश्न 4.
आसमान में बादलों के आते ही धरती पर क्या प्रतिक्रिया होती है?
उत्तर:
आसमान में बादलों के आते ही धरती पर प्यार के अंकुर फूटने लगते हैं। धरती प्रसन्न हो जाती है। बिजली आकाश में चमकती है और दादुर अपनी बोली से वर्षा का स्वागत करते हैं। मोर वन में नाचने लगता है और गाँवों में स्त्रियों के हिंडोले सज जाते हैं और किसान की पलियाँ ‘कजरी’ नामक गीत गाती हैं। सभी वर्षा का स्वागत करने को तत्पर रहते हैं।

MP Board Solutions

प्रकृति चित्रण दीर्घ उत्तरीय प्रश्न

प्रश्न 1.
निम्न पद्यांशों का आशय स्पष्ट कीजिये
(अ) अधरों में राग अमंद…………विहाग री।
(आ) ‘फिसली-सी पगडण्डी…………सरग-नसैनी री !’
(इ) बिजली चमकी भाग………..पानी बरसा री।
उत्तर:
(अ) सन्दर्भ :
महाकवि जयशंकर प्रसाद का यह गीत हमारी पाठ्यपुस्तक के ‘प्रकृति चित्रण’ के ‘गीत’ नामक शीर्षक से उद्धृत है जो ‘लहर’ नामक काव्य संकलन में से संकलित है।

प्रसंग :
इस गीत में प्रकृति के प्रातःकालीन सौन्दर्य का नवयौवना नायिका के रूप में चित्रण किया है। एक सखी रात्रि व्यतीत हो जाने पर दूसरी सखी को जगाती है और कहती है।

व्याख्या :
री सखि ! चाँदनी से युक्त रात्रि अब व्यतीत हो रही है। अतः तु अब जाग जा। अपनी आँखों को खोल और देख कि आकाशरूपी पनघट में उषारूपी चतुर नायिका तारारूपी घड़े को डुबो रही है। भाव यह है कि उषाकाल हो गया है, जिससे तारे धीरे-धीरे विलुप्त हो रहे हैं। जल में घड़ा डुबोने का कुलकुल स्वर पक्षियों की कलरव ध्वनि के रूप में हो रहा है। उषारूपी नायिका का हिलता हुआ आँचल कोमल कोपलों के कम्पन में दिखाई देता है और देखो वह लतिका नाम की सखी भी अपनी गगरी को परागयुक्त पुष्पों के नवीन रस से भर लायी है। अर्थात् लताएँ सरस कलियों से पूर्ण हो गयी हैं।

प्रातःकालीन शोभा का चित्रण करते हुए एक सखी दूसरी सोती हुई सखी से कहती है कि तेरे रक्तिम ओठों से प्रतीत होता है कि तूने रात को प्रेम मदिरा का पान किया है जिससे तेरे ओंठ रक्तिम हो गये हैं। भाव यह है कि तेरे ओठों पर प्रेम दिखायी देता है। तेरे काले केशों में चन्दन जैसी सुगन्ध, स्निग्धता और कोमलता बढ़ गयी है। हे सखी ! तू अब तक सोई हुई है। देख, प्रातःकाल हो गया है और तू अपनी आँखों में विहाग राग की सी खुमारी भरे हुए है, जो तेरे रात्रिकालीन जागरण और आलस्य की सूचना दे रही है।

(आ) सन्दर्भ :
पूर्ववत्।

प्रसंग :
प्रस्तुत पंक्तियों में कवि वर्षा के आगमन पर प्रकृति में होने वाले परिवर्तनों और पेड़ों पर पड़ने वाले झूलों के बारे में वर्णन कर रहा है।

व्याख्या :
पानी के आने से पगडण्डियों पर फिसलन हो गई है। आँखें लज्जावश झुक गई हैं। प्रकृति मानो इन्द्रधनुषी रंगों से रंग गई हो। ऐसे ही कामिनियाँ रंग-बिरंगे वस्त्रों से सुसज्जित होकर इन्द्रधनुष की शोभा को फीका कर रही हैं। स्त्रियों के बीछिया रुनझुन बज रहे हैं और मदित मन से चलने से उनकी बेणी इधर-उधर हिल रही है। हिंडोले पड़े हुए हैं उन पर स्त्रियाँ ऊँचे पेंग बढ़ा रही हैं।

एक सखी दूसरी सखीं से कहती है कि हे सखी ! सुन, ये मोर जो सूने स्थान पर रहते हैं उन्हें भी वह वन घर जैसा प्रतीत हो रहा है,वर्षा के आने पर। वर्षा के आने पर प्यार के अंकुर फूटने लगे हैं। धरती पर उगते हुए अंकुर भी बड़े प्यारे लगते हैं।

(इ) शब्दार्थ :
पीके = अंकुर; दादुर = मेंढक। सन्दर्भ-प्रस्तुत पंक्तियाँ पं. भवानी प्रसाद मिश्र द्वारा रचित ‘मंगल वर्षा’ से उद्धृत हैं।

प्रसंग :
इस कविता में मिश्र जी ने सावन में वर्षा के आने के सुन्दर दृश्य का वर्णन किया है। बादलों के आसमान में आने पर प्रकृति के सभी उपादान और स्त्री-पुरुष प्रसन्न हो जाते हैं।

व्याख्या :
कवि कहता है कि पानी के बरसने से प्रकृति में प्यार के अंकुर फूटने लगे हैं। चारों तरफ हरियाली छा गई है और सावन हरा-भरा हो गया है। आकाश में बादल छा गये हैं और सम्पूर्ण धरती प्रफुल्लित हो रही है। एक सखी दूसरी सखी से कहती है कि तेरी माँग भरी हुई है और ऐसा लगता है कि इस मनोरम मौसम में तू कुछ भूली-भूली सी लगती है। आसमान में बिजली चमक रही है और बादलों को देख मेंढक भी हर्षित होकर बोलने लगे। हवा के चलने से सुन्दर पक्षी भी उड़ने लगे। पक्षियों के उड़ने का दृश्य मनोरम है। मन में उमंग उठ रही है,मन मानो पागल जैसा मस्त हो गया हो। पानी के बरसने से आज प्यार के अंकुर फूटने लगे हैं।

प्रश्न 2.
भोर होते ही प्रकृति में कैसी-कैसी चेतनता आ जाती है? प्रसाद की कविता के आधार पर स्पष्ट कीजिये।
उत्तर:
भोर होते ही सम्पूर्ण प्रकृति चैतन्य दृष्टिगत होती है। एक स्त्री दूसरी स्त्री से कहती है-हे सुन्दरी ! तू जाग रात्रि समाप्त हो गई है और भोर की बेला ने दस्तक दे दी है। ऊषा रूपी सुन्दर स्त्री अम्बर रूपी पनघट में अपने तारे रूपी घड़े को डुबो रही है। यहाँ प्रातः होते ही रमणियों का घड़े लेकर पानी भरने का दृश्य चित्रित किया है। प्रातः होते ही तारे डूबने लगते हैं। पक्षियों के समूह अपनी मधुर बोली में गीत गा रहे हैं और सुगन्धित पवन के चलने से मुलायम पत्तियाँ हिल रही हैं। लता भी अपने पुष्प रूपी घड़े में मधु भर लाई है। तेरे होठों पर राग बन्द है और तेरी अलकों में सुगन्धित वायु भरी हुई है तू अभी तक क्यों सो रही है,जाग।।

प्रश्न 3.
“किसलय का अंचल डोल रहा” कहकर कवि क्या कहना चाहता है? स्पष्ट कीजिये।
उत्तर:
प्रातः के सुहावने मौसम में नमी लिए हुए सुगन्धित समीर बहने लगता है। इसके चलने से धरती के मुलायम किसलय (नयी कोपलें या घास के पत्ते) प्रसन्नता लिए हुए झूमने लगते हैं। प्रातःकाल होते ही प्रकृति के सभी उपादान अपनी प्रमोदता प्रकट करने के लिए मानवीय भावों जैसे दिखाई देते हैं। दिन सुख का प्रतीक है इसलिए प्रकृति भी मानव और अन्य पशु-पक्षियों के साथ अपने सुख बाँटती है। प्रातः समीर के साथ किसलय का इधर-उधर झूमना उसकी प्रसन्नता का प्रतीक है। धरती भी अपने मन के भावों को किसलय के साथ बाँटने लगती है। किसलय का हिलना ऐसे लगता है मानो धरती के हृदय में खुशी की लहर उठ रही हो।

MP Board Solutions

प्रश्न 4.
सावन में ग्रामवधू के उल्लास का वर्णन कवि के शब्दों में कीजिये।
उत्तर:
सावन के महीने में अति उल्लासपूर्ण वातावरण रहता है। पानी के बरसते ही स्नेह के अंकुर पृथ्वी पर उग आये हैं। चारों तरफ हरियाली छा गई है। ग्रामवधू वर्षा के आगमन पर अति हर्षित दिखाई दे रही है। बिजली आसमान में चमक रही है। वर्षा की आस में मेंढक अपनी बोली में प्रसन्नता प्रकट कर रहे हैं। मन पागल की तरह आसमान में घूम रहा है। पगडण्डी पानी के गिरने से फिसलन भरी हो गई हैं। ग्रामवधू इन्द्रधनुषी रंगों से सजी हुई है। ग्राम में चारों तरफ पेड़ों पर झले पड़ गये हैं। उस स्त्री के बीछिया रुनझन बज रहे हैं और चलने से बेणी इधर-उधर हिल रही है। वन में मोर बोलने लगे हैं। वर्षा के आगमन पर मयूरों की मधुर बोली हमारे मन को आकर्षित कर रही है। खेतों के बीच में खड़ी हुई किसानिन ‘कजरी’ गीत गा रही है। रात रूपी सुहागिन के शरीर को जैसे उसके वर्षारूपी साजन ने स्पर्श करके उसे आल्हादित कर दिया हो। झरने के झरने के साथ हमारा मन श्रीहर्षित हो गया है। पानी के आने से प्यार के अंकुर फूटने लगे हैं। कहने का तात्पर्य है कि ग्रामवधू प्रकृति की मनोहारी छवि पर मोहित हो गई हैं।

प्रकृति चित्रण काव्य सौन्दर्य

प्रश्न 1.
निम्नलिखित पंक्तियों में से अलंकार पहचान कर लिखिए
बीती विभावरी जाग री।
अम्बर-पनघट में डुबो रही
तारा-घट ऊषा-नागरी।
खग-कुल कुल-कुल सा बोल रहा,
किसलय का अंचल डोल रहा।
उत्तर:
(i) अम्बर-पनघट, तारा-घट, ऊषा-नागरी में रूपक अलंकार और प्रकृति का मानवीकरण।
(ii) कुल-कुल में पुनरुक्तिप्रकाश।
(iii) किसलय का अंचल डोल रहा-मानवीकरण।

प्रश्न 2.
निम्नलिखित शब्दों के पर्यायवाची शब्द लिखिए
विभावरी, अम्बर, ऊषा, मलयज, खग।
उत्तर:
(i) विभावरी – रात्रि, रजनी, यामिनी।
(ii) अम्बर – आकाश,नभ, आसमान।
(iii) ऊषा – प्रातः बेला, सुबह, अरुणोदय।
(iv) मलयज – मलय,समीर, बयार।
(v) खग – पक्षी,नभचर, पखेरू।

प्रश्न 3.
निम्नलिखित पंक्तियों का भाव सौन्दर्य स्पष्ट कीजिए
(1) अधरों में राग अमन्द पिये।
अलकों में मलयज बंद किये।
फिसली-सी पगडण्डी।
खिसली आँख लजीली री।
उत्तर:
(1) भाव सौन्दर्य-
(i) किसी सोती हुई सुन्दरी के अधरों में कोई मधुर गीत बन्द है-इसमें भावों का सुन्दर सामंजस्य है।
(ii) प्रकृति के रूप में मानवीकरण का सुन्दर उदाहरण है।
(iii) अलकों में सुगन्धित हवा बन्द है-कितनी सटीक और अद्भुत कल्पना की उड़ान है।

(2) (i) पगडण्डी की फिसलन का सुन्दर शब्द चित्र संजोया है।
(ii) खिसकने के लिए खिसली शब्द लिखकर ग्रामीण परिवेश का चित्रण किया गया है।
(iii) सुन्दरी की आँख में लज्जा होना उसकी शोभा है।

MP Board Solutions

प्रश्न 4.
निम्नलिखित शब्दों में से तत्सम एवं तद्भव शब्द छाँटकर लिखिए
अम्बर, धरती, दादुर,खग, नवल, अधर, अलक, मोती, सरग।
उत्तर:
MP Board Class 12th Hindi Swati Solutions पद्य Chapter 5 प्रकृति चित्रण img-1

प्रश्न 5.
कविता में आए पुनरुक्तिप्रकाश के उदाहरण छाँटकर लिखिए।
उत्तर:
(1) खग-कुल कुल-कुल सा बोल रहा।

(2) छन-छन उठी हिलोर,मगन मन पागल दरसा री।
ऊँचे-ऊँचे पेंग, हिंडोला सरग नसैनी री।
फुर-फुर उड़ी फुहार अलक हल मोती छाए रो।
झर-झर झरना झरे, आज मन प्राण सिहाये री।

प्रश्न 6.
कविता में आए मानवीकरण के उदाहरण छाँट कर लिखिये।
उत्तर:
(1) अम्बर-पनघट में डुबो रही
तारा-घट ऊषा-नागरी।
किसलय का अंचल डोल रहा,
लो यह लतिका भी भर लायी
मधु-मुकुल नवल रस-गागरी।

(2) हरियाली छा गयी, हमारे सावन सरसा री
बादल आए आसमान में, धरती फूली री।

प्रश्न 7.
कविता में आयी ‘प्रसाद गुण’ सम्पन्न पंक्तियाँ छाँटकर लिखिए।
उत्तर:
पीके फूटे आज प्यार के, पानी बरसा री।
हरियाली छा गयी,हमारे सावन सरसा री।
बादल आए आसमान में, धरती फूली री,
बिजली चमकी भाग सखी री,दादुर बोले री,
अन्ध प्राण ही बहे,उड़े पंछी अनमोले री॥

प्रश्न 8.
माधुर्य गुण के दो उदाहरण लिखिए।
उत्तर:
(1) बीती विभावरी जाग री।
अम्बर-पनघट में डुबो रही
तारा-घट ऊषा-नागरी।

(2) पीके फूटे आज प्यार के, पानी बरसा री।
हरियाली छा गयी, हमारे सावन सरसा री।
बादल आए आसमान में, धरती फूली री।
अरी सुहागिन, भरी माँग में भूली-भूली री।
बिजली चमकी भाग सखी री,दादुर बोले री।
अन्द प्राण ही बही, उड़े पंछी अनमोले री।

प्रश्न 9.
पाठ में आए विभिन्न रसों की पंक्तियाँ छाँट कर स्थायी भाव सहित रस का उल्लेख कीजिये।
उत्तर:
(1) बीती विभावरी जाग री।
अम्बर-पनघट में डुबो रही
तारा-घट ऊषा-नागरी।

खग-कुल कुल-कुल सा बोल रहा,
किसलय का अंचल डोल रहा,
लो लतिका भी भर लायी
मधु-मुकुल नवल रस-गागरी।

रस – श्रृंगार रस।
स्थायी भाव – रति।

MP Board Class 12th Hindi Swati Solutions पद्य Chapter 5 प्रकृति चित्रण img-2
रस – श्रृंगार।
स्थायी भाव – रति।

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गीत भाव सारांश

संकलित कविता ‘गीत’ के रचयिता छायावादी कवि ‘जयशंकर प्रसाद’ हैं। इसमें कवि ने ऊषा रूपी सुन्दरी को तारा रूपी घट को आकाश रूपी सरोवर में डुबोते हुए चित्रित किया है।

मनुष्य के जीवन में प्रकृति की भूमिका अत्यन्त महत्त्वपूर्ण है। प्रकृति का अनुकरण करके ही मनुष्य ने अपने परिगत भाव-संसार और कला-संसार की सृष्टि की है। काव्य का सम्पूर्ण इतिहास प्रकृति के प्रकाश से जगमगा रहा है। छायावाद के जयशंकर प्रसाद का काव्य प्रकृति को केन्द्र मानकर ही प्रारम्भ होता है। ‘गीत’ नामक रचना में प्रातःकाल के परिवर्तन को मानवीकरण के रूप में चित्रित किया है। इसमें रूपक अलंकार का प्रयोग किया है। रात बीत गई है और ऊषा रूपी कामिनी आकाश रूपी पनघट में तारों रूपी घड़ों को डुबो रही है। तारे अस्त होते जा रहे हैं। सुबह का प्रकाश फैल रहा है। पक्षियों,लताओं और कलिकाओं का बड़ा ही सजीव और सुन्दर वर्णन किया गया है।

गीत संदर्भ-प्रसंग सहित व्याख्या

(1) बीती विभावरी जाग री
अम्बर-पनघट में डुबो रही
तारा-घट ऊषा-नागरी।
खगकुल कुल-कुल सा बोल रहा,
किसलय का अंचल डोल रहा,
लो यह लतिका भी भर लायी।
मधु-मुकुल नवल रस-गागरी। (2010)

अधरों में राग अमन्द पिये,
अलकों में मलयज बन्द किये
तू अब तक सोयी है आली !
आँखों में भरे विहाग री।

शब्दार्थ :
विभावरी = ज्योत्स्नामयी रात्रि अम्बर = गगन, आकाश; घट = घड़ा; उषा = प्रातःकाल; नागरी = चतुर स्त्री; खग = पक्षी; किसलय = कोमल कोपलें; अंचल = आँचल; लतिका = लता; मधु-मुकुल = परागयुक्त पुष्प; नवल रस = नवीन पराग; गागरी = गगरी; अधर = होठ; अमंद = पर्याप्त; अलक = केशराशि; मलयज = शीतल सुगन्धित पवन,चन्दन,सर्प; आली = सखी; विहाग = राग विशेष,जो रात्रि के अन्तिम प्रहर में गाया जाता

सन्दर्भ :
महाकवि जयशंकर प्रसाद का यह गीत हमारी पाठ्यपुस्तक के ‘प्रकृति चित्रण’ के ‘गीत’ नामक शीर्षक से उद्धृत है जो ‘लहर’ नामक काव्य संकलन में से संकलित है।

प्रसंग :
इस गीत में प्रकृति के प्रातःकालीन सौन्दर्य का नवयौवना नायिका के रूप में चित्रण किया है। एक सखी रात्रि व्यतीत हो जाने पर दूसरी सखी को जगाती है और कहती है।

व्याख्या :
री सखि ! चाँदनी से युक्त रात्रि अब व्यतीत हो रही है। अतः तु अब जाग जा। अपनी आँखों को खोल और देख कि आकाशरूपी पनघट में उषारूपी चतुर नायिका तारारूपी घड़े को डुबो रही है। भाव यह है कि उषाकाल हो गया है, जिससे तारे धीरे-धीरे विलुप्त हो रहे हैं। जल में घड़ा डुबोने का कुलकुल स्वर पक्षियों की कलरव ध्वनि के रूप में हो रहा है। उषारूपी नायिका का हिलता हुआ आँचल कोमल कोपलों के कम्पन में दिखाई देता है और देखो वह लतिका नाम की सखी भी अपनी गगरी को परागयुक्त पुष्पों के नवीन रस से भर लायी है। अर्थात् लताएँ सरस कलियों से पूर्ण हो गयी हैं।

प्रातःकालीन शोभा का चित्रण करते हुए एक सखी दूसरी सोती हुई सखी से कहती है कि तेरे रक्तिम ओठों से प्रतीत होता है कि तूने रात को प्रेम मदिरा का पान किया है जिससे तेरे ओंठ रक्तिम हो गये हैं। भाव यह है कि तेरे ओठों पर प्रेम दिखायी देता है। तेरे काले केशों में चन्दन जैसी सुगन्ध, स्निग्धता और कोमलता बढ़ गयी है। हे सखी ! तू अब तक सोई हुई है। देख, प्रातःकाल हो गया है और तू अपनी आँखों में विहाग राग की सी खुमारी भरे हुए है, जो तेरे रात्रिकालीन जागरण और आलस्य की सूचना दे रही है।

काव्य सौन्दर्य :

  1. इस गीत में प्रकृति का मार्मिक एवं सजीव अंकन हुआ है।
  2. वियोग शृंगार से अनुप्राणित इस गीत में गेयता तथा चित्रोपमता सर्वत्र विद्यमान है।
  3. सांगरूपक, उपमा, मानवीकरण, अनुप्रास तथा रूपकातिशयोक्ति, अलंकारों का सौन्दर्य दृष्टव्य है।
  4. विषयानुरूप परिमार्जित खड़ी बोली का प्रयोग हुआ है।

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मंगल वर्षा भाव सारांश

संकलित कविता ‘मंगलवर्षा’ के रचयिता ‘भवानी प्रसाद मिश्र’ हैं। इस कविता में कवि ने वर्षा के आगमन पर प्रकृति और मानव की प्रफुल्लता का सजीव वर्णन किया है।

भवानी प्रसाद मिश्र छायावादोत्तर काल के प्रतिनिधि कवि हैं। उनकी कविताओं में प्रकृति भावों के उद्दीपन का आधार बनती है। प्रस्तुत कविता में उन्होंने वर्षा का मनोहारी वर्णन किया है। बादलों का आसमान में घिरना, बिजली का चमकना,फिसलती पगडण्डियाँ,रंगीला इन्द्रधनुष, झरनों का झरना ये सब मानवीय भावनाओं के अनुरूप दृष्टिगोचर होते हैं। वर्षा के माध्यम से जीवन की प्रसन्नता कविता के माध्यम से प्रकट हो रही है। लोक छबियों और लोक जीवन की अनुभूतियों का सुन्दर वर्णन इस कविता में दिखाई देता है। इस कविता में लयात्मकता है और शब्दों में प्रवाह है। प्रकृति चित्रण के रूप में यह कविता एक अनूठी रचना है।

मंगल वर्षा संदर्भ-प्रसंग सहित व्याख्या

1. पीके फूटे आज प्यार के, पानी बरसा री,
हरियाली छा गयी हमारे, सावन सरसा री।
बादल आये आसमान में, धरती फूली री,
अरी सुहागिन, भरी माँग में भूली-भूली री,
बिजली चमकी भाग सखी री, दादुर बोले री,
अन्य प्राण ही बही, उड़े पंछी अनमोले री,
छन-छन उठी हिलोर, मगन मन पागल दरसा री।
पीके फूटे आज प्यार के, पानी बरसा री।

शब्दार्थ :
पीके = अंकुर; दादुर = मेंढक। सन्दर्भ-प्रस्तुत पंक्तियाँ पं. भवानी प्रसाद मिश्र द्वारा रचित ‘मंगल वर्षा’ से उद्धृत हैं।

प्रसंग :
इस कविता में मिश्र जी ने सावन में वर्षा के आने के सुन्दर दृश्य का वर्णन किया है। बादलों के आसमान में आने पर प्रकृति के सभी उपादान और स्त्री-पुरुष प्रसन्न हो जाते हैं।

व्याख्या :
कवि कहता है कि पानी के बरसने से प्रकृति में प्यार के अंकुर फूटने लगे हैं। चारों तरफ हरियाली छा गई है और सावन हरा-भरा हो गया है। आकाश में बादल छा गये हैं और सम्पूर्ण धरती प्रफुल्लित हो रही है। एक सखी दूसरी सखी से कहती है कि तेरी माँग भरी हुई है और ऐसा लगता है कि इस मनोरम मौसम में तू कुछ भूली-भूली सी लगती है। आसमान में बिजली चमक रही है और बादलों को देख मेंढक भी हर्षित होकर बोलने लगे। हवा के चलने से सुन्दर पक्षी भी उड़ने लगे। पक्षियों के उड़ने का दृश्य मनोरम है। मन में उमंग उठ रही है,मन मानो पागल जैसा मस्त हो गया हो। पानी के बरसने से आज प्यार के अंकुर फूटने लगे हैं।

काव्य सौन्दर्य :

  1. प्रकृति चित्रण अनूठा बन पड़ा है।
  2. अनुप्रास अलंकार का प्रयोग सुन्दर है।
  3. मानवीकरण की छटा सुन्दर है।

MP Board Solutions

2. फिसली-सी पगडण्डी खिसली आँख लजीली री,
इन्द्रधनुष-रंग-रंगी, आज मैं सहज रंगीली री,
रुनझुन बिछिया आज, हिला-डुल मेरी बेनी री,
ऊँचे-ऊँचे पेंग, हिंडोला, सरग-नसैनी री,
और सखी सुन ! मोर विजन वन दीखे घर-सारी,
पीके फूटे आज प्यार के, पानी बरसा री।

शब्दार्थ :
हिंडोला = झूला; सरग-नसेनी = स्वर्ग की सीढ़ी (बहुत ऊँचे जाना); विजन = जन रहित।

सन्दर्भ :
पूर्ववत्।

प्रसंग :
प्रस्तुत पंक्तियों में कवि वर्षा के आगमन पर प्रकृति में होने वाले परिवर्तनों और पेड़ों पर पड़ने वाले झूलों के बारे में वर्णन कर रहा है।

व्याख्या :
पानी के आने से पगडण्डियों पर फिसलन हो गई है। आँखें लज्जावश झुक गई हैं। प्रकृति मानो इन्द्रधनुषी रंगों से रंग गई हो। ऐसे ही कामिनियाँ रंग-बिरंगे वस्त्रों से सुसज्जित होकर इन्द्रधनुष की शोभा को फीका कर रही हैं। स्त्रियों के बीछिया रुनझुन बज रहे हैं और मदित मन से चलने से उनकी बेणी इधर-उधर हिल रही है। हिंडोले पड़े हुए हैं उन पर स्त्रियाँ ऊँचे पेंग बढ़ा रही हैं।

एक सखी दूसरी सखीं से कहती है कि हे सखी ! सुन, ये मोर जो सूने स्थान पर रहते हैं उन्हें भी वह वन घर जैसा प्रतीत हो रहा है,वर्षा के आने पर। वर्षा के आने पर प्यार के अंकुर फूटने लगे हैं। धरती पर उगते हुए अंकुर भी बड़े प्यारे लगते हैं।

काव्य सौन्दर्य :

  1. प्रकृति का मनोहारी वर्णन किया है।
  2. रूपक, उपमा और मानवीकरण की शोभा निराली है।
  3. वर्षा के आगमन से मोर का प्रसन्न होना प्रसिद्ध उक्ति है।

3. फुर-फुर उड़ी फुहार अलक हल मोती छाए री,
खड़ी खेत के बीच किसानिन कजरी गाये री,
झर-झर झरना झरे, आज मन प्राण सिहाये री,
कौन जन्म के पुण्य कि ऐसे शुभ दिन आये री,
रात सुहागिन गात मुदित मन, साजन परसा री।
पीके फूटे आज प्यार के, पानी बरसा री॥ (2009)

शब्दार्थ :
अलक = बाल; परसा = स्पर्श किया,कजरी = गीत; सिहाये = प्रसन्न हुए; गात = शरीर; मुदित = प्रसन्न।

सन्दर्भ :
पूर्ववत्।

प्रसंग :
प्रस्तुत पंक्तियों में कवि ने फुहारों के पड़ने,खेत में किसानिन के कजरी गाने का बड़ा ही सुहावना वर्णन किया है।

व्याख्या :
वर्षा की फुहारों के पड़ने से कामिनी के बालों पर बूंदें मोती जैसी शोभित हो रही हैं। अपने खेत के बीच में खड़ी किसान की पत्नी वर्षा ऋतु में गाये जाने वाला कजरी गीत गा रही है। वर्षा के आने से झरने झर-झर कर नीचे गिर रहे हैं। इस सबको देखकर मन-प्राण हर्षित हो जाते हैं। स्त्रियाँ मन में सोचने लगीं कि किसी जन्म के पुण्य रहे होंगे जो इतने सुहावने दिन आये हैं। सावन के महीने में किसी सुहागिन के शरीर को उसके पति ने स्पर्श किया हो तो वह कितना मंगलमय लगता है। ऐसा लगता है मानो प्रकृति रूपी सुहागिन के तन को वर्षा रूपी उसके साजन ने स्पर्श किया हो। पानी के बरसने से चारों ओर प्यार के अंकुर फूटने लगे हैं। सभी ओर सम्पूर्ण वातावरण प्रसन्नता से भरा हुआ है।

काव्य सौन्दर्य :

  1. प्रकृति चित्रण अनूठा है।
  2. कविता में अनुप्रास, पुनरुक्तिप्रकाश अलंकार की छटा दर्शनीय है।
  3. किसानिन का कजरी गाने का भाव हृदय में आनन्द भर देता है।

MP Board Solutions

MP Board Class 10th Social Science Solutions Chapter 15 Economic Development and Planning

In this article, we will share MP Board Class 10th Social Science Book Solutions Chapter 15 Economic Development and Planning Pdf, These solutions are solved subject experts from the latest edition books.

MP Board Class 10th Social Science Solutions Chapter 15 Economic Development and Planning

MP Board Class 10th Social Science Chapter 15 Text book Exercises

Objective Type Questions

Question 1.
Multiple Choice Questions
(Choose the correct answer from the following)

Question (i)
Economic planning results in –
(a) Improvement in living standard
(b) Increase in economic welfare
(c) Increase in life expectancy
(d) All of above
Answer:
(d) All of above

Question (ii)
The per capita income of the country is calculated on the basis of –
(a) That country’s population
(b) The world’s population
(c) States population
(d) Other country’s population
Answer:
(a) That country’s population

Question (iii)
Prof. Amratya Sen has considered basis of development as – (MP Board, 2009, 2013)
(a) Prosperity
(b) Self – dependency
(c) Public Welfare
(d) Foreign Trade.
Answer:
(c) Public Welfare

Question (iv)
Developed countries utilise natural resources –
(a) Very little
(b) Do not use
(c) Little bit
(d) On a large extent.
Answer:
(c) Little bit

Question (v)
How many five years plans have been completed in India till now – (MP Board, 2010)
(a) 5
(b) 10
(c) 15
(d) 11
Answer:
(d) 11

MP Board Solutions

Question 2
Fill in the blanks:

  1. The standard of …………… increases by economic development.
  2. India Vision 2020 was published in the year ……………
  3. …………… constructed physical quality of life index.
  4. According to World Bank that country is developed country whose per capita income is …………… rupees or more per year.
  5. The period of tenth plan was from …………… to ……………

Answer

1. Living
2. 2003
3. Prof. Morris
4. 4,53,000
5. 2002, 2007

MP Board Class 10th Social Science Chapter 15 Very Short Answer Type Questions

Question 1.
What is the meaning of economic development according to Mercantilism?
Answer:
For the mercantile economists an economic development is based on the previous metals like gold or silver.

Question 2.
During which period of time is national income calculated?
Answer:
National income is calculated from 1st April to 31st March every year.

MP Board Solutions

Question 3.
What are the basis of calculating human Development Index?
Answer:
Basis for calculating human Development Index are:

  1. Life expectancy at time of birth for measuring a long and healthy life.
  2. Rate of adult literacy and total enrolment ratio.
  3. Per Capital Gross Domestic Product.

Question 4.
According to the World Bank, what must be per capita income of the developed countries?
Answer:
The World Bank in its development report of 2006 has used the measure of per capita income to distinguish between developed countries and developing countries. According to this report those countries having per capita income Rs. 4,53,000 or more are considered as developed countries and countries having per capita income Rs. 37,000 or less are considered as developing (low income) country.

Question 5.
What are the main measurement of measuring economic development?
Answer:
Actually facilities of health, education, housing, nutritive food, drinking water etc., provided to common people should be included in the development. Therefore as an alternative for the national and per capita income, importance is given to human development indicators for measuring economic development.

MP Board Class 10th Social Science Chapter 15 Short Answer Type Questions

Question 1.
What is national income? How is it calculated? Write. (MP Board 2009, 2011)
Answer:
National income is the income of a country. It is obtained by adding the monetary values of the commodities and services produced in a country’ in a year. One of the methods of measuring economic development is in terms of an increase in country’s real national income over a long period of time. National income refers to the total value of all the final goods and services produced within a country plus income earned from other country.

Question 2.
What is per capita income? Write the formula of calculating it. (MP Board 2010)
Answer:
When the National income of a country is divided by its total population then we get its per capita income.
The following formula is used to calculate the per capita income of a country:
MP Board Class 10th Social Science Solutions Chapter 15 Economic Development and Planning img 1a
Per capita income gives us an idea of the standard of living of the peopl of country. If the per capita income is increasing in a country it means that the lives of the people of that country are becoming happier It means their standard of living is improving.

Question 3.
What is the main objective of making Human Development Index? (MP Board 2009)
Answer:
Human development is index term. It consists of economic and social development. Human development is the end of all human activities, whereas social development is mean to it. Economic development consists of structures which support indirectly the economic system. It consists of education, health, environment, housing and civic amenities, etc.

Question 4.
Which are the developed and developing states of India?
Answer:
In India some states are comparatively developed states and some states are developing states. We can classify 15 big states of India on the ground of per capita income into two classes i.e. developed states and developing states. Punjab, Maharashtra, Haryana, Gujarat, West Bengal, Karnataka, Kerala, Tamil Nadu and Andhra Pradesh, are included in list of developed states while Madhya Pradesh, Assam, Uttar Pradesh, Rajasthan, Orissa and Bihar etc. states are in list of developing states.

According to the census of 2001, 90% of total population of the country resides in these states. Out of this 48% population resides comparatively in developed states and 42% population resides in the developing or backward states.

Question 5.
What is India Vision 2020?
Or
What is Vision India 2020? Write. (MP Board 2009, 2011, 2013)
Answer:
In January 2003, The Planning Commission of India has issued an important document named India Vision 2020. According to this document till the year 2020, India will be included in the category of developed countries. As a result of this, unemployment, poverty, illiteracy will be completely eradicated from the country.

The Planning Commission has estimated that by the year 2020, 135 crore of country’s population will be better nourished, will have good living standard and be completely healthy. Average age of the population will increase.

The Age Calculator can determine the age or interval between two dates. The calculated age will be displayed in years, months, days.

MP Board Class 10th Social Science Chapter 15 Long Answer Type Questions

Question 1.
Explain old and new concepts of Economic Development? (MP Board 2009)
Answer:
In ancient time a special place was given to materialistic prosperity under economic development at global level. The mercentile thinkers of Germany and France considered gold and silver as the basis of development. The concept of development kept on changing with time.

According to classical economist Adam Smith, economic development is the increase in. goods and services of a country. Karl Marks considered economic development as the establishment of socialism J.S. Mill’s opinion about economic development is totally different. He considered economic development as to follow the principle of cooperation for welfare of people and economic development.

Among the new economists Paul Albert considers economic development as the increase in real national income by use of all productive resources by a country. While in the opinion of Williamson and Bustricks development is the increase in the per capita income of the people of a country. The opinion of D. Bright Singh is different from all these, in that economic development involves not only increase in money income but also improvement in social welfare. Prof. Amirtya Sen, honored by Nobel Prize has also given special importance to social welfare.

Meir and Baldwin has defined economic development as “Economic development is a process whereby an economy’s real national income increases over a long period of time.”

MP Board Solutions

Question 2.
State the meaning of Human Development Index and discuss its components?
Answer:
The quality of life index prepared and published by United Nations Development Programme (UNDP) is termed as Human Development Index. The United Nations was the first to prepare and publish Human Development Index in the year 1990. Human Development Index studies the following three basic hurrtan capabilities:

  1. Living a long life (Longevity)
  2. Being knowledgeable (Educational Attainment)
  3. Enjoying decent standard of living (Red per capita GDP).

Question 3.
Distinguish between developed and developing economies?
Answer:
Developed Economy:

  • This economy is economically sound. Its people have higher standard of living.
  • The main occupation of people is industry.
  • Modern technology is used.

Developing Economy:

  • This economy is not financially sound. The standard of living of general masses is lower.
  • The main occupation of people is agriculture.
  • Generally old techniques of production are used.

Question 4.
Explain the meaning of Economic planning in India anc state the main objectives of planning in India?
Answer:
After the independence, in order to make plans for the country the Planning Commission was set up on 15th March, 1950 for the country. By now 11 five – year plans have been prepared by this commission and implemented by Government of India. At present the Eleventh Five Year Plan has been started from 1st April, 2007.

The main guiding principles of the five – year plans in India are economic equality, social justice, self – dependence, improvement in efficiency and productivity. In different plans out of above directive principles, emphasis has been laid on. different facts due to changes in situations and problems. In brief the basic objectives of Indian plans are as below:

  1. To obtain high rate of development
  2. To obtain self – dependency
  3. To obtain economic stability
  4. To increase social welfare
  5. To obtain social and economic justice
  6. To increase the opportunities of employment
  7. To increase the standard of living
  8. Poverty eradication.

MP Board Solutions

Question 5.
State the success and failures of planning of India? (MP Board, 2010)
Answer:
The following are the factors of success:

1. Increase in National and Per Capita Income:
At the current prices the national income of India was only 9142 crore in 195051 which rose up to 28,46,762. In similar manner, during this period the per capita income increased from Rs. 255 to Rs. 25,716. Thus it is clear that the national income as well as per capita income both increased rapidly during the period of the planning.

2. Increase in Rate of Saving and Investment:
Some portion of the national income is invested (used for production) for the economic development. In each plan high targets of saving and investments were fixed for this which have nearly been achieved too. The gross saving and investment rates in the year 1950 – 51 (on current prices) were only 8.9 and 8.7 per cent of gross national product which increased to 32.4 and 33.8 percent in the year 2005 – 06.

3. Development in Agriculture Sector:
Agricultural production has increased extensively due to economic planning. The production of food grains increased to 2083 lakh tonnes in the year 2005-06 which was only 508 lakh tonnes in 1950 – 51. During this period as a result of green revolution high yielding seeds, chemical, fertilizer, pesticides, irrigation facilities etc. were expanded. Along with this in agricultural sector infrastructure developed too.

4. Industrialisation:
There has been a remarkable increase in industrial sector through five years plAnswer:Today India has become the tenth largest industrial country of the world. India’s progres can be estimated by the fact that the contribution of India b manufactured goods in the foreign trade is gradually increasing. Iro: and steel, engineering, goods, chemical and cement etc.

5. Education and Health:
At the beginning of planning, there were 27 universities, but now they are 389 in number, the literacy rate of the country in 1950-51 was 16.6 per cent which increased upto 64.8 percent in 2001.

Failures are as follows:

1. Slow Progress in per Capita Income:
In spite of economic planning in India, the growth in per capita income has been very slow. Still today 21 per cent of population in India is living below poverty line.

2. Regional Imbalance:
As a result of planning, the regional imbalance in the country should have decreased, but there has been no significant change. Uttar Pradesh, Orrisa, Bihar, etc. states are still backward states while the states of Maharashtra, Tamil Nadu, West Bengal, Punjab, Haryana, etc. are included under the category of comparatively developed states.

3. Increase in Prices:
The prices are continuously increasing since the period of planning. On the basis of 1993-94, the whole sale price index, number has risen to 2079 in December 2006. It is estimated that during the period of planning the prices increased near about 27 times.

4. Increase in Unemployment:
An important objective of economic planning was to reduce unemployment. But the unemployment kept on increasing a.t the end of each plan. In the beginning of first five year plan, where 33 lakh people were unemployed which is now estimated to about 4 crore.

MP Board Class 10th Social Science Chapter 15 Additional Important Questions

Objective Type Questions

Question 1.
Multiple Choice Questions:
(Choose the correct answer from the following) (MP Board 2009)

Question (i)
In ancient time India was called –
(a) Golden Triangle
(b) Golden Bird
(c) Golden Ring
(d) Golden Country
Answer:
(b) Golden Bird

Question (ii)
International Bank for Reconstruction and Development is known as –
(a) IMF
(b) World Bank
(c) RBI
(d) UNO
Answer:
(b) World Bank

Question (iii)
The peroid of 10th plan is –
(a) 2002 – 2007
(b) 2001 – 2008
(c) 2003 – 2008
(d) 2004 – 2009
Answer:
(a) 2002 – 2007

Question (iv)
How many persons were unemployed in beginning of first plan – (MP Board 2009, Set B)
(a) 25 lac
(b) 33 lac
(c) 43 lac
(d) 35 lac.
Answer:
(b) 33 lac

Question 2.
Fill in the blanks:

  1. The writer of the famous book Arthshastra is ……………..
  2. The First Five Year Plan was started in ……………..
  3. Shri Mannarayan was related to the ……………..

Answer:

  1.  Kautilya
  2. 1951
  3. Gandhiyan plan

Question 3.
True and False type questions:

  1. The years 1966-67, 1967 – 68 and 1968 – 69 are known as the Rolling Plan.
  2. Indian Planning is based on the Russian model.
  3. Prof. Amartya Sen is related to the Planning Commission of India.

Answer:

  1. True
  2. True
  3. False

Question 4.
Match the column:
MP Board Class 10th Social Science Solutions Chapter 15 Economic Development and Planning 2
Answer:

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

Answer in One – Two Words or One Sentence

Question 1.
Mention three objectives of planning in India.
Answer:

  1. Self – Sufficiency
  2. Social Justice
  3. Higher rate of growth.

Question 2.
How many five – year plans have been completed so far after independence?
Answer:
Ten five – year plans have been completed.

MP Board Solutions

Question 3.
Name the sector which was given top priority during the First Five Year Plan?
Answer:
Agriculture was accorded top priority.

Question 4.
What are the essential things for analysing the economic planning?
Answer:
Two things are essential in economic planning such as:

  1. Pre – decided aims which have to be accomplished.
  2. Description of the use of available resources to obtain the pre – determined aims.

Question 5.
Name any three types of economics?
Answer:

  1. Capitalist Economy
  2. Socialist Economy
  3. Mixed Economy.

Question 6.
What are the three sectors of enterprises on the basis of ownership?
Answer:

  1. Private sector
  2. Public sector and
  3. Joint sector

Question 7.
Define national income?
Answer:
It is defined as the total value of all the goods and services produced within a country plus income coming from abroad.

MP Board Solutions

Question 8.
What does consumption mean?
Answer:
The use of goods and services is called consumption. In other words, reduction in utilities is termed as consumption.

Question 9.
What are primary activities of an economy?
Answer:
Activities that are associated with land and water such as farming, cattle rearing, fishing and mining are called primary activities.

Question 10.
What is per capita income?
Answer:
National income divided by the total population of the country is termed as per capita income.

Question 11.
What is Human Development Index?
Answer:
The quality of life index prepared and published by United Nation’s Development Programme (UNDP) is termed as Human Development Index.

MP Board Solutions

Question 12.
Mention the formula for the calculation of Human?
Development Index.
Answer:
Human Development Index = Life expectancy index + Educational attainment
MP Board Class 10th Social Science Solutions Chapter 15 Economic Development and Planning 225

Question 13.
Define longevity?
Answer:
Life expectancy at birth as known as longevity. It means the number of years a newly born baby is expected to live. Longevity in India at present is 63 years.

Question 14.
Identify different thrust areas of human development.
Answer:
Health, Gender Equity and Gender Empowerment are the thrust areas of human development?

Question 15.
What basis of development has considered by Prof. Amartya Sen? (MP Board 2009)
Answer:
Social Welfare.

MP Board Class 10th Social Science Chapter 15 Very Short Answer Type Questions

Question 1.
State briefly the main features of capitalist economy?
Answer:

  1. Factors of production are owned by the individuals.
  2. Economic activities are carried out with the sole motive of project.
  3. Producers are to choose occupation of their own choice.

Question 2.
State briefly the features of socialist economy?
Answer:

  1. Government is the sole producer of goods and services.
  2. All properties belong to the government.
  3. Economic decision are taken by the central planning authority.

MP Board Solutions

Question 3.
Define national income in the words of Professor Marshall?
Answer:
According to Professor Marshall, the labour and capital of country, acting on its natural resources produce annually a certain net aggregate of commodities, material and immaterial including services of all kinds. This is the true net annual income or revenue of the country or the national dividend.

Question 4.
What are the advantages of a capitalist economy?
Answer:

  1. Economic freedom.
  2. Maximum utilisation of resources.
  3. Higher standard of living.
  4. Increase production.

MP Board Class 10th Social Science Chapter 15 Short Answer Type Questions

Question 1.
How is planning useful for economic development?
Answer:
It is rightly said that India is rich country inhabited by pocrs. We have got abundance of resources lying undiscovered, untapped and unexploited. This is due to the fact that we did not formulate plans to make the best possible utilisation of these resources. After independence we adopted planned developmental economy aiming at higher rate of growth self – reliance and balanced economic development. Planning creates employment opportunities, economic stability and allround economic development of the country.

Question 2.
Give any two objectives of economic planning?
Answer:
Two objectives of economic planning are as under:

(a) High Growth Rate:
It was felt after independence that we were an undeveloped economy. It was necessary to accelerate the pace of agricultural and industrial growth for the rapid economic development of the country. This is why, we adopted planned developmental economy to attain high growth rate.

(b) Social Justice:
Our society has been victim of social injustice and inequality of income. There is wide disparity in income and wealth of individual. There are regional imbalances resulting in social tensions. Under these circumstances the planner formulated our five
year plans with an aim towards social justice.

MP Board Solutions

Question 3.
What is a Socialistic Pattern of society?
Answer:
Socialist pattern of society means that the basic criterion of determining the lines of advance must not be private profit but social gain and the pattern of development and the structure of socioeconomic relations should be so planned that they result not. only in appreciable increase in national income and employment but also greater equality in income and wealth. The benefits of economic development must accure more and more to the relatively less privileged class of society, and there should be progressive reduction in the concentration of economic power.

Question 4.
Distinguish between:

  1. A Capitalist Economy and a Socialist Economy
  2. Economic and Non – economic Activities.

Answer:
1.
A Capitalist Economy:

  • Private ownership on means of production.
  • Freedom of enterprise.
  • Profit is the main motive.
  • Efficient use of resources.
  • Free working of price mechanism.

A Socialist Economy:

  • Government ownership on means of production.
  • No freedom of enterprise.
  • The main motive is social welfare and service.
  • Inefficient use of resources.
  • Interference by the government in the economy.

2.
Economic Activities:

  • Activities which contribute to the flow of goods and services.
  • These activities are included in national income.
  • Examples: Farmers, doctors, technicians etc.

Non – economic Activities:

  • Activities which do not contribute to the flow of goods and services.
  • These activities are not included in national income.
  • Examples: Religious activities, social works etc.

MP Board Class 10th Social Science Chapter 15 Long Answer Type Questions

Question 1.
Discuss the contribution of agriculture in National Income?
Answer:
Contribution of Agriculture to National Income. About 45% of our national income is earned through agriculture. Nearly 67% of our people earn livelihood through agriculture and its allied activities.

1. Contribution of Agriculture to Employment:
About 67% of our working population is engaged directly or indirectly with agriculture.

2. Agriculture is Source of Government Revenue:
State government earn land revenue and some states have taxed agricultural income.

3. Contribution of Agriculture to Industry:
Agriculture lays down sound foundation of our industries in the following ways

  • Agriculture supplies us food and fodder.
  • Agriculture contributes to trade also. Trading in food grains is all based on agriculture.
  • Agriculture is main source of our exports.
  • Agriculture is the foundation stone for economic development.
  • Agriculture is major source of raw material for industry. Jute Cotton, Sugar, tea, Coffee, oil, Silk, Tobacco etc. are based on agricultural product.
  • Agriculture is the source of capital formation.
  • Agriculture supplies healthy manpower.
  • Agriculture sector purchase goods of industrial sector.

MP Board Solutions

Question 2.
Give any five suggestions for increasing the growth of national income?
Answer:
In order to increase the national income following measures should be adopted:

1. Increase in the Rate of Savings and Investment:
In order to increase the national income productive activities must be increased. Modem large scale industrial venture requires huge amount of capital. It requires that there must be sufficient savings and investment in the productive activities.

2. Improvement in the Technique of Production:
In case we want to increase our production at faster rates we will have to introduce new technology in the field of production. It will increase the production and consequently national income will be multiplied.

3. Discouraging Increase in Populations:
Our economic development is eaten up by exploding population. It reduces our per capita income also. If we want to increase our national income we will have to check population explosion.

4. Discouraging Price Rise:
After independence inflationary pressure is Jbeing continuously felt. The commodities have become very costly, so savings are very little. Low savings and lesser capital formation is adversaliy affecting our national income.

5. Increasing Exports:
In order to increase our industrial production we will have to import latest machines equipments and technology. It requires foreign exchange, which can be earned by exporting our surplus agricultural.

MP Board Solutions

Question 3.
Describe the construction of Human Development Index. What are its levels ?
Answer:
Construction of Human Development Index Three basic factors of life are utilised in the construction of Human Development Index. These factors are:

  1. Life expectancy at time of birth for measuring a long and healthy life.
  2. Rate of adult literacy and total enrolment ratio.
  3. Per Capita Gross Domestic Product.

First of all indicators of these three factors are prepared separately to calculate Human Development Index. Then after their average is calculated whose value is presented between 0 to 1. The indicator of most developed country stands near 1 and most undeveloped country’s indicator stands near 0. On this basis, the countries of the world are classified into the following three classes according to their level of development.

1. Highly Human Developed Countries:
Those countries whose indicator is measured 0.8 or more are considered highly developed.

2. Medium Human Developed Countries:
Those countries are considered to be medium human developed countries whose indicator is measured from 0.5 to 0.8.

3. Low Human Developed Countries:
Those countries are considered to be low human developed countries whose measure of Index is below 0.5. Under the development programme of United Nations Organisation Human Development Index has been published for 177 countries. According to these indexes 63 countries are high human developed, 83 are medium and 31 are low human developed.

MP Board Class 9th Maths Solutions Chapter 12 Heron’s Formula Ex 12.1

MP Board Class 9th Maths Solutions Chapter 12 Heron’s Formula Ex 12.1

Question 1.
A traffic signal borard, indicating ‘SCHOOL AHEAD’, is an equilateral triangle with side ‘a’ Find the area of the signal board, using Heron’s formula. If its perimeter is 180 cm, what will be the area of the signal board?
Solution:
MP Board Class 9th Maths Solutions Chapter 12 Heron’s Formula Ex 12.1 img-1

Question 2.
The triangular side walls of a flyover have been used for advertisements. The sides of the walls are 122 m, 22 m and 120 m (see Fig.) the advertisements yield an earning of ₹ 5000/m2 per year. Acompany hired one of its walls for 3 months. How much rents did it pay?
MP Board Class 9th Maths Solutions Chapter 12 Heron’s Formula Ex 12.1 img-2
Solution:
MP Board Class 9th Maths Solutions Chapter 12 Heron’s Formula Ex 12.1 img-3
s = \(\frac{122+120+22}{2}\) = \(\frac{264}{2}\) = 132 m
s – a = 132 – 122 = 10 m
s – b = 132 – 22 = 12m
s – c = 132 – 22 = 110 m
area of triangular portion of wall = \(\sqrt{32x10x12x110}\)
= \(\sqrt{2x2x3x11x10x2x2x3x11x10}\)
= 10 x 2 x 2 x 3 x 11 = 1320 m2
Rate = ₹ 5000/m2 per year
Rent for 3 months = 1320 x \(\frac{5000×3}{12}\)
= 330 x 5000
= ₹ 16,50,000

MP Board Solutions

Question 3.
There is a slide in a park. One of its side walls has been painted in some colour with a message “Keep The Park Green And Clean” (see Fig.). If the sides of the wall are 15 m, 11 m and 6 m, find the area painted in colour.
MP Board Class 9th Maths Solutions Chapter 12 Heron’s Formula Ex 12.1 img-4
Solution:
a = 15 m
b = 11 m
c = 6m
p = a + b + c
= 15 + 11 + 6
= 32 m P
MP Board Class 9th Maths Solutions Chapter 12 Heron’s Formula Ex 12.1 img-5
s = \(\frac{P}{2}\) = \(\frac{32}{2}\) = 16m
s – a = 16 – 15 = 1 m
s – b = 16 – 11 = 5 m
s – c = 16 – 6 = 10m
Area of triangular park = \(\sqrt{16x1x5x10}\)
= \(\sqrt{2x2x2x2x1x5x2x5}\)
= 2 x 2 x 5√2 = 2o\(\sqrt{2m^{2}}\)

Question 4.
Find the area of a triangle two sides of which are 18 cm and 10 cm and the perimeter is 42 cm.
Solution:
MP Board Class 9th Maths Solutions Chapter 12 Heron’s Formula Ex 12.1 img-6
a = 18 cm
b = 10 cm
Let the third side be c
p = 42 cm
18 + 10 + C = 42
C = 14
S = \(\frac{P}{2}\) = \(\frac{42}{2}\) = 21 cm
s – a = 21 – 18 = 3
s – b = 21 – 10 = 11
s – c = 21 – 14 = 7
Area of ∆ = \(\sqrt{21x3x11x7}\) = \(\sqrt{3x7x3x11x7}\)
= 3 x 7\(\sqrt{11}\) = 21\(\sqrt{11}\) cm2

MP Board Solutions

Question 5.
Sides of triangle are in the ratio of 12 : 17 : 25 and its perimeter is 540 cm. Find its area
Solution:
a = 12x
b = 17x
c = 25x
p = 12x + 11x + 25x = 540
54x = 540
x = \(\frac{540}{54}\) = 10
a = 12 x 10 = 120 cm
b = 17 x 10 = 170 cm
c = 25 x 10 = 250 cm
s = \(\frac{P}{2}\) = \(\frac{540}{2}\) = 270 cm
s – a = 270 – 120 = 150 cm
s – b = 270 – 170 = 100 cm
s – c = 270 – 250 = 20 cm
Area of ∆ = \(\sqrt{270x150x100x20}\)
= \(\sqrt{3x3x3x10x3x5x10x10x10x2x10}\)
= 3 x 3 x 10 x 10 x 10
= 9000 cm2

Question 6.
An isosceles triangle has perimeter 30 cm and each of the equal sides is 12 cm. Find the area of the triangle.
Solution:
MP Board Class 9th Maths Solutions Chapter 12 Heron’s Formula Ex 12.1 img-7
a = 12 cm
b = 12cm
Let the third side be c.
p = a + b + c
30 = 12 + 12 + c
c = 30 – 24 = 6 cm
s = \(\frac{P}{2}\) = \(\frac{30}{2}\) = 15
s – a = 15 – 12 = 3
s – b = 15 – 12 = 3
s – c = 15 – 6 = 9
Area of ∆ = \(\sqrt{5x3x3x9}\)
= \(\sqrt{5x3x3x3x3x3}\)
= 3 x 3\(\sqrt{15}\) = 9\(\sqrt{15}\) cm2

Area of Quadrilaterals:
To find the area of quadrilaterals divide the quadrilateral into two triangles using a diagonal and then use heron’s formula.

Class 10 Maths formulas are the cornerstone of numeracy skills.

Example 1:
A triangle and a parallelogram have the same base and the same area. If the sides of the triangle are 13 cm, 14 cm and 15 cm and the parallelogram stands on the base 14 cm, And the height of the parallelogram.
Solution:
MP Board Class 9th Maths Solutions Chapter 12 Heron’s Formula Ex 12.1 img-8
Here, a = 13 cm,
b = 14 cm,
c = 15 cm
Base of parallelogram =14 cm.
MP Board Class 9th Maths Solutions Chapter 12 Heron’s Formula Ex 12.1 img-9
= 7 x 3 x 2 x 2
= 84 cm2
Let h be the height of the parallelogram ADEC.
Area of parallelogram ADEC = Area of ∆ABC (given)
Base x height = 84
14 x height = 84
h = \(\frac{84}{14}\)
= 6 cm.

MP Board Solutions

Example 2:
The sides of a quadrilateral, taken in order are 5, 12, 14 and 15 meters respectively, and the angle contained by the first two sides is a right angle. Find its area.
Solution:
MP Board Class 9th Maths Solutions Chapter 12 Heron’s Formula Ex 12.1 img-10
Here, AB = 5m
BC = 12m
CD = 14m
DA = 15 m
Join AC. The ABCD is divided into two triangles ABC and ACD. The area of the quadrilateral is equal to sum of areas of ∆ABC and ∆ADC.
In ∆ABC
MP Board Class 9th Maths Solutions Chapter 12 Heron’s Formula Ex 12.1 img-11
area of ABCD
= ar (∆ABC) + ar (∆ACD) –
= (84 + 30)m2 = 114m2

Example 3:
In a parallelogram measure of adjacent sides are 34 cm and 20 cm. One of the diagonals is 42 cm. Find the area of the parallelogram.
Solution: In Fig.
MP Board Class 9th Maths Solutions Chapter 12 Heron’s Formula Ex 12.1 img-12
AB = DC = 34 cm
AD = BC = 20 cm
AC =42 cm.
We know that the diagonal of a parallelogram divides it into two tri¬angles of equal area.
∴ Area of parallelogram ABCD = 2 x Area of (∆ABC)
Consider ∆ABC
a = 34cm
b = 20cm
c = 42cm
s = \(\frac{a+b+c}{2}\)
= \(\frac{34+20+42}{2}\)
= \(\frac{96}{2}\) = 48 cm
s – a = 48 – 34 = 14 cm
s – b = 48 – 20 = 28 cm
s – c = 48 – 42 = 6 cm
By Heron’s formula,
MP Board Class 9th Maths Solutions Chapter 12 Heron’s Formula Ex 12.1 img-13
= 2 x 2 x 6 x 14
= 336 cm2
∴ Area of (∥gm ABCD) = 2 x 336
= 672 cm2

Example 4:
A rhombus sheet, whose perimeter is 32 m and whose one diagonal is 10 m long, is painted on both sides at the rate of? 5 per m2. Find the cost of painting.
Solution:
MP Board Class 9th Maths Solutions Chapter 12 Heron’s Formula Ex 12.1 img-14
Given P = 32m
BD = 10m
Rate of painting = ₹ 5/m2
Let the sides of rhombus be x m.
P = Ax
⇒ 32 = 4x
∴ x = 8m
So, AB = BC = CD = DA = 8 m
We know that the diagonal of a rhombus divides it into two triangles of equal area. .
∴ Area of rhombus ABCD = 2 x area of ∆ABD
Consider ∆ABD
a = 8m
b = 8m
c = 10m
S = \(\frac{a+b+c}{2}\) = \(\frac{8+8+10}{2}\)
= 13 m.
s – a = 13 – 8 = 5 m
s – b = 13 – 8 = 5m
s – c = 13 -10 = 3 m
By Heron’s formula,
Area of ∆ABD = \(\sqrt{s(s-a)(s-b)(s-c)}\)
= \(\sqrt{3x5x5x3}\)
= 5 x \(\sqrt{39}\)
= 5 x 6.24 = 31.2 m2
Area of rhombus ABCD = 2 x 31.2 = 62.4 m2
Area of rhombus to be painted = 2 x area of rhombus (∴ Painting is to be done on both sides)
= 2 x 62.4 = 124.80
Cost of painting = Rate x Area
= 5 x 124.80
= ₹ 624.

MP Board Solutions

Example 5:
Two parallel sides of a trapezium are 60 cm and 77 cm other sides are 25 cm and 26 cm. Find the area of trapezium.
Solution:
MP Board Class 9th Maths Solutions Chapter 12 Heron’s Formula Ex 12.1 img-15
Given AB = 60 cm
DC = 77 cm
AD = 25 cm
BC =26 cm
Draw a line BE ∥ AD from point B.
In ABED
AB ∥ DE
AD ∥ BE
ABED is a parallelogram.
AB = DE = 60
EC = 77 – 60 = 17 cm.
AD = BE = 25 cm
In ∆BEC
a = EC = 17 cm
b = BE = 25 cm
c = BC = 26cm
s = \(\frac{17+25+36}{2}\)
s – a = 34 – 17 = 17 cm
s – b = 34 – 25 = 9 cm
s – c = 34 – 26 = 8cm
By Heron’s formula,
MP Board Class 9th Maths Solutions Chapter 12 Heron’s Formula Ex 12.1 img-16

MP Board Class 9th Maths Solutions