CBSE Class 6 Hindi Grammar संधि Pdf free download is part of NCERT Solutions for Class 6 Hindi. Here we have given NCERT Class 6 Hindi Grammar संधि.

CBSE Class 6 Hindi Grammar संधि

संधि का अर्थ है-मेल। जब दो वर्षों के मेल से उनके मूल रूप में जो परिवर्तन या विकार आ जाता है, वह संधि कहलाता है; जैसे-

• नर + ईश = नरेश
• विद्या + अर्थी = विद्यार्थी

उपर्युक्त उदाहरणों में पहले शब्द के अंतिम वर्ण तथा दूसरे शब्द के पहले वर्ण के मेल में परिवर्तन आ गया है। यही परिवर्तन संधि है।

संधि विच्छेद – संधि का अर्थ है-मिलना, विच्छेद का अर्थ है-अलग होना। दो वर्षों के मेल से बने नए शब्द को वापस पहले की स्थिति में लाना संधि विच्छेद कहलाता है; जैसे–

• विद्यालय = विद्या + आलय
• सूर्योदय = सूर्य + उदय

संधि के भेद – संधि के तीन भेद होते हैं।
(क) स्वर संधि
(ख) व्यंजन संधि
(ग) विसर्ग संधि।

(क) स्वर संधि – स्वर संधि यानी स्वरों का मेल। दो स्वरों के मेल से होने वाले परिवर्तन को स्वर संधि कहते हैं; जैसे– महा + आत्मा = महात्मा, हिम + आलय = हिमालय।
स्वर संधि के पाँच भेद होते हैं

1. दीर्घ संधि
2. गुण संधि
3. वृधि संधि
4. यण संधि
5. अयादि संधि

1. दीर्घ संधि – जब ह्रस्व या दीर्घ स्वर के बाद ह्रस्व या दीर्घ स्वर आएँ, तो दोनों के मेल से दीर्घ स्वर हो जाता है। इसे दीर्घ संधि कहते हैं; जैसे
परम + अर्थ = परमार्थ
सार + अंश = सारांश
न्याय + अधीश = न्यायधीश
देह + अंत = देहांत
मत + अनुसार = मतानुसार
भाव + अर्थ = भावार्थ

अ + आ = आ

• हिम + आलय = हिमालय
• छात्र + आवास = छात्रावास

आ + आ = आ – विद्या + आलय = विद्यालय, शिव + आलय = शिवालय।
इ + इ = ई – अभि + इष्ट = अभीष्ट, हरी + इच्छा = हरीच्छा।
इ + ई = ई – हरि + ईश = हरीश, परि + ईक्षा = परीक्षा।
ई + इ = ई – शची + इंद्र = शचींद्र, मही + इंद्र = महेंद्र।
ई + ई = ई – रजनी + ईश = रजनीश, नारी + ईश्वर = नारीश्वर
उ + उ = ऊ – भानु + उदय = भानूदय, लघु + ऊर्मि = लघूर्मि
उ + ऊ = ऊ – लघु + ऊर्मि = लघूर्मि,
ऊ + ऊ = ऊ – भू+ उर्जा = भूर्जा, भू + ऊर्ध्व = भूर्ध्व

2. गुण संधि – अ/आ का मेल इ/ई से होने पर ए, उ + ऊ से होने पर ओ तथा ऋ से होने पर अर् हो जाता है। इसे गुण संधि कहते हैं; जैसे
अ/आ + इ + ई = ए – नर + इंद्र = नरेंद्र, नर + ईश = नरेश।
अ/आ + उ + ऊ = ओ – पर + उपकार = परोपकार, महा + उत्सव = महोत्सव।
अ/आ + ऋ + ऋ = अर – देव + ऋषि = देवर्षि, महा + ऋषि = महर्षि।

3. वृधि संधि – वृधि संधि में अ या आ के बाद यदि ए या ऐ हो तो दोनों का ‘ऐ’ होगा। यदि अ या आ के बाद ओ या आ
आए तो दोनों का ‘ओ’ होगा; जैसे
अ + आ + ए/ऐ = ऐ
एक + एक = एकैक, सदा + एव = सदैव
अ/आ + ओ + औ = औ = वन + औषधि = वनौषधि, जल + ओध = जलौध।

4. यण संधि – इ अथवा ई के बाद इ और ई को छोड़कर यदि कोई अन्य स्वर हो तो ‘इ’ अथवा ई के स्थान पर य् उ अथवा ऊ को छोड़कर कोई अन्य स्वर हो तो उनके स्थान पर ‘व’ और ‘ऋ’ को छोड़कर कोई अन्य स्वर हो तो उसके स्थान पर ‘र’ हो जाता है। इसे यणसंधि कहते हैं; जैसे
अति + अधिक = अत्यधिक, यदि + अपि = यद्यपि

5. अयादि संधि – यदि पहले शब्द के अंत में ए/ऐ, ओ/औ एक दूसरे के शब्द के आरंभ में भिन्न स्वर आए तो क्रमशः ए का अय, ऐ का आय, ओ का अव, तथा औ का आव हो जाता है। इसे अयादि संधि कहते हैं; जैसे
ने + अक = नायक, भो + अन = भवन
पौ + अक = पावक, भौ + अक = भावुक

(ख) व्यंजन संधि – व्यंजन का व्यंजन से अथवा किसी स्वर से मेल होने पर जो परिवर्तन होता है, वह व्यंजन संधि कहलाता . है; जैसे
सम + कल्प = संकल्प, जगत+ ईश = जगदीश।

व्यंजन संधि के प्रमुख नियम निम्नलिखित हैं-

(क) कवर्ग का तृतीय वर्ण-वर्गों के प्रथम वर्ण से परे वर्गों का तृतीय, चतुर्थ वर्ण कोई स्वर अथवा य, र, ल, वे, ह आदि वर्गों में से कोई वर्ण हो तो पहले वर्ण को अपने वर्ग का तृतीय वर्ण हो जाता है; जैसे।
दिक् + अंबर = दिगंबर, सत् + धर्म = सद्धर्म ।

(ख) खवर्ग का पंचम वर्ग-वर्ग के प्रथम या तृतीय वर्ण से परे पाँचवा वर्ण हो, तो उसके स्थान पर उसी वर्ग का पाँचवा वर्ण हो जाता है; जैसे

• वाक् + मय = वाङ्मय, सत् + मार्ग = सन्मार्ग
• जगत् + नाथ = जगन्नाथ, चित् + मय = चिन्मय।

(ग) त के बाद ज या झ हो तो ‘त’ के स्थान पर ‘न’ हो जाता है; जैसे
सत् + जन = सज्जान, विपत् + जाल = विपज्जाल, जगत् + जननी = जगज्जननी

(घ) त् के बाद ङ या ढ़ हो तो ‘त्’ के स्थान पर ‘ड’ हो जाता है; जैसे
उत् + डयन = उड्डयन, वृहत + टीका = वृहट्टीका।

(ङ) त् के बाद ल हो तो ‘त’ के स्थान पर ‘ल’ हो जाता है; जैसै
तत् + लीन = तल्लीन, उत् + लेख = उल्लेख

(च) त् के बाद श हो तो ‘त्’ के स्थान पर ‘च्’ और ‘श’ के स्थान पर ‘छ’ हो जाता है; जैसे
उत् + श्वास = उच्छवास, तत् + शिव = तच्छिव

(छ) यदि त्’ के बाद च्, छ हो तो ‘त्’ का ‘च’ हो जाता है; जैसे
उत् + चारण = उच्चारण, सत् + चरित्र = सच्चरित्र

(ज) त् के बाद ह हो तो ‘त्’ का ‘द्’ और ह का ‘ध’ हो जाता है; जैसे
उत् + हार = उद्धार, तत् + हित = तधित

(झ) ‘म’ के बाद कोई स्पर्श व्यंजन हो तो ‘म्’ का अनुस्वार या बाद वाले वर्ण के पंचम हो जाता है; जैसे
अहम् + कार = अहंकार, सम् + तोष = संतोष

(ज) “म्’ के बाद य, र, ल, व, स, श, ह हो, तो म् अनुस्वार हो जाता है; जैसे
सम् + योग = संयोग, सम् + वाद = संवाद, सम् + हार = संहार
अपवाद-यदि सम् के बाद ‘राट्’ हो तो म् का म् ही रहता है। जैसे
सम् + राट = सम्राट

(ट) “छ’ से पूर्व स्वर हो तो ‘छ’ से पूर्व ‘च’ आ जाता है।
परि + छेद = परिच्छेद, आ + छादन् = अच्छादन।

(ठ) ह्रस्व स्वर ‘इ’ उ के बाद यदि ‘र’ के बाद फिर ‘र’ हो तो ह्रस्व स्वर दीर्घ हो जाता है। ‘र’ का लोप हो जाता है; जैसे
निर + रस = नीरस, निर + रोग = नीरोग

(ड) न् का ‘ण’ होना–यदि ऋ र, ष के बाद ‘न’ व्यंजन आता है तो ‘न’ का ‘ण’ हो जाता है; जैसे
राम + अयन = रामायण, परि + नाम = परिणाम

(ढ) ह्रस्व के बाद ‘छ’ हो तो उसके पहले ‘च’ जुड़ जाता है। दीर्घ स्वर में विकल्प होता है।
परि + छेद = परिच्छेद, शाला + छादन = शालाच्छादन

कुछ अन्य उदाहरण

क् + ग् – वाक् + ईश = वागीश, दिक + अंत = दिगंत।
त् + ६ – तत् + भव = तद्भव, भगवत् + गीता = भगवदगीता ।
छ संबंधी नियम – स्व + छेद = स्वच्छेद, परि + छेद = परिच्छेद।
म संबंधी नियम – सम् + गति = संगति, सम् + तोष = संतोष।

(ग) विसर्ग संधि – विसर्ग का किसी स्वर या व्यंजन से मेल होने पर जो विकार (परिवर्तन) होता है वह विसर्ग संधि कहलाता है; जैसे

(क) विसर्ग के पहले ‘अ’ हो और बाद में कोई घोष व्यंजन, वर्ग का तीसरा, चौथा, पाँचवा वर्ण (य, र, ल, व, ह) हो तो ।
विसर्ग का ‘ओ’ हो जाता है। जैसे–
मनः + बल = मनोबल, मनः + रंजन = मनोरंजन, मनः + हर = मनोहर।

(ख) विसर्ग के बाद यदि च, छ हो, तो विसर्ग का ‘श’ हो जाता है; जैसे
निः + चिंत = निश्चित, निः + छल = निश्छल, दु: + चरित्र = दुश्चरित्र।

(ग) विसर्ग के बाद यदि ट, ठ हो तो विसर्ग का.ष हो जाता है; जैसे
धनुः + टंकार = धनुष्टंकार

(घ) विसर्ग के बाद यदि त, थ हो तो विसर्ग का ‘स’ हो जाता है; जैसे
दुः + तर = दुस्तर, नमः + ते = नमस्ते ।

(ङ) यदि विसर्ग के पहले ‘अ’ और ‘आ’ को छोड़कर कोई दूसरा स्वर आए और विसर्ग के बाद कोई स्वर हो या किसी वर्ग का तीसरा, चौथा या पाँचवा वर्ण हो या य, र, ल, व, ह हो तो विसर्ग के बाद कोई स्वर हो या किसी वर्ग का तीसरा, चौथा या पाँचवा वर्ण हो या य, र, ले,व, ह हो, तो विसर्ग के स्थान पर ‘र’ हो जाता है; जैसे
निः + बल = निर्बल, निः + लोभ = निर्लोभ, निः + विकार = निर्विकार।

(च) विसर्ग से परे श, ष, स हो तो विसर्ग के विकल्प से परे वाले वर्ण हो जाता है।
निः + संदेह = निस्संदेह, दु: + शासन = दुश्शासन

(छ) यदि विसर्ग के पहले इकार या उकार आए और विसर्ग के बाद का वर्ण क, ख, प, फ, हो तो विसर्ग का ष हो जाता है; जैसे
निः + कपट = निष्कपट, दुः + कर = दुष्कर।

(ज) यदि विसर्ग के बाद ‘अ’ न हो तो विसर्ग का लोप हो जाएगा; जैसे
अतः + एव = अतएव

बहुविकल्पी प्रश्न

1. ‘उपेंद्र’ शब्द का सही संधि विच्छेद है
(i) उपा + इंद्र
(ii) उप + इंद्र
(iii) उपे + इंद्र
(iv) उपी + इंद्र

2. ‘नयन’ में कौन सी संधि है
(i) यण संधि
(ii) गुण संधि
(ii) वृद्धि संधि
(iv) अयादि संधि

3. ‘एकैक’ में कौन सी संधि है
(i) यण संधि
(ii) दीर्घ संधि
(iii) गुण संधि
(iv) वृद्धि संधि

4. कौन-सा भेद संधि का नहीं है
(i) विसर्ग संधि
(ii) व्यंजन संधि
(iii) जल संधि
(iv) स्वर संधि

5. ‘हरिश्चंद्र’ में कौन-सी संधि है।
(i) स्वर संधि
(ii) विसर्ग संधि
(iii) व्यंजन संधि
(iv) उपर्युक्त में से कोई नहीं

6. स्वर संधि के कितने भेद होते हैं
(i) चार
(ii) पाँच
(iii) सात
(iv) छह

7. ‘प्रणाम’ का संधि विग्रह होगा–
(i) प्रण + आम
(ii) प्र + णाम
(iii) प्रण + नाम
(iv) प्र + णाम

8. जगदीश का विग्रह होगा
(i) जगदी + ईश
(ii) जगद + ईश
(iii) जगत् + ईश
(iv) जगती + ईश

उत्तर-
1. (ii)
2. (iv)
3. (iv)
4. (iii)
5. (ii)
6. (ii)
7. (ii)
8. (iii)

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Inside Our Earth Class 7 Extra Questions Social Science Geography Chapter 2

NCERT Extra Questions for Class 7 Social Science Geography Chapter 2 Inside Our Earth

Prelude

Question 1.
How is the earth a dynamic planet?
Answer:

• The earth is our homeland.
•  It is a dynamic planet.
  • It is constantly undergoing changes inside and outside.

Interior of the Earth

Question 1.
Have you ever wondered what lies in the interior of the earth? What is the earth made up of?
Ans.

•  Yes.
• The interior has three major layers of rocks of different densities.
• The earth is made up of rocks.

Question 2.
Describe the interior of the earth.
Answer:
Interior of the Earth

• The earth is made up of several concentric layers with one inside another, just like an onion.

Crust

• The uppermost layer on the earth’s surface is called the crust.
  •  It is the thinnest of all the layers.
  • It is about 35 km, thick on the continental masses and only 5 km thick on the ocean floors.
  • Main minerals constituent of the continental mass are silica and alumina.
  • It is thus called sial (si – silica and al – alumina).

• • The oceanic crust mainly consists of silica and magnesium.
  • It is therefore called sima (si – silica and ma – magnesium).

Mantle

• Just beneath the crust is the mantle.
  • It extends up to a depth of 2900 km below the crust.

Core

• The innermost layer is the core with a radius of about 3500 km.
  • It is mainly made up of nickel and iron.
  • Hence it is called nife (ni—nickel and fe—ferrous i.e., iron).
  • The central core has very high temperature and pressure.

Rocks and Minerals

Question 1.
What is earth’s crust made up of?
Answer:
Earth’s crust is made up of different type of rocks. Rock is a natural mass of mineral matter. It is of different sizes, colours and texture and shapes. Earth is made up of sedimentary, igneous or metamorphic rocks.

Question 2.
Describe igneous rocks.
Ans.

• Igneous Rocks
  • The molten rock material is called magma.
  • When it cools, it becomes solid.
  • Rocks formed in this way are called igneous rocks.
  • They are also called primary rocks because other rocks are formed out of these rocks.
• There are two types of igneous rocks.
  • Intrusive Rocks and
  • Extrusive Rocks

Formation of Extrusive and Intrusive Rocks

• Due to extreme heat in the interior of the earth, rocks are found in the form of molten material called magma.
• When magma comes out on the surface of the earth, it cools down and turns into solid rocks. Such rocks are termed as extrusive rocks.

Examples:

• Basalt.
• Deccan Trap is built of basalt.

When’the molten magma cools down within the interior of the earth, it becomes solid to form intrusive rocks.

Examples:

• Granite
• Garbo

Question 3.
What is lava?
Answer:
Lava is the hot red magma coming out from the interior of the earth to the surface. It cools down and become solid.

Question 4.
What are two types of Igneous rocks?
Answer:
Igneous rocks are formed by cooling of the lava. When the lava cools down on the crust it forms extrusive igneous rock for example basalt. They have grained structure.
Sometimes when it cools down deep inside the crust it forms intrusive igneous rocks. They have large grains for example Granite. Grinding stones are made of granite.

Question 5.
Define the term sediment.
Answer:
Rocks due to cracks and hitting, breakdown into smaller fragments called sediments.

Question 6.
Give an account of sedimentary rocks.
Answer:
Sedimentary Rocks
The small particles are called sediments.

• These sediments are transported and deposited by wind, water etc. in low areas.
• These loose sediments are compressed and hardened to form layers of rocks.
• These layered rocks are called sedimentary rocks.
• Examples:
  • Sandstone.
  • These rocks also contain fossils of plants, animals and other micro-organisms that once lived on them.

Question 7.
What are Fossils?
Answer:
Fossils:
The remains of dead plants and animals trapped in the layers of rocks are known as fossils.

Question 8.
How are metamorphic rocks formed?
Answer:
Igneous and Sedimentary rocks changes into metamorphic rocks under heat and pressure.

Metamorphic Rocks:
When under heat and pressure igneous rocks and sedimentary rocks change their form and more precious rocks are formed to be known as metamorphic rocks.
Examples:

• Granite into granite gneiss.
• Coal into slate.
• Slate into schist.
• Limestone into marble.

Limestone is changed into marble due to the following reasons:

• The overlying layers of rocks put pressure on the underlying rocks.
• From surface to interior of the earth, temperature and heat go on increasing.
• Due to pressure and heat, the original limestone changes into marble.g

Question 9.
What are the uses of rocks?
Answer:
Uses of Rocks:

• Hard rocks are used in making buildings and barrages.
• Houses and buildings are built of rocks (stones, slates, granite, marble).
• Stones are used in numerous games:
• Seven stones (phitthoo).
• Hop scotch (stapu, kit kit).
• Five stones (gitti).
• Rocks (stones and slates) are used in building bridges, embankments.

Question 10.
Briefly describe the ‘rock cycle’.
Answer:
One rock changes into another under certain conditions in a cyclic manner.
Molten magma cools down and solidify to form igneous rocks. These rocks are broken down due to pressure and climatic conditions into sediments.
These are transported and deposited to form sedimentary rocks. The igneous and sedimentary rocks under heat and pressure change into metamorphic rocks.
These metamorphic rocks under great heat and pressure melt down to form molten magma. This again cools down to form igneous rocks. This process of transformation of rocks is called ‘rock cycle’.

Question 11.
What are minerals? How are minerals important to us?
Answer:
Minerals:

• Rocks are made up of different minerals.
• Minerals are naturally occurring substances which have certain physical properties and definite chemical composition.
• Minerals are very important to us.
• Some are used as fuels.
• Examples:
  • Coal.
  • Natural gas.
  • Petroleum.
• They are also used in industries as energy and raw material.
• Examples:
  • Iron.
  • Aluminium.
  • Gold.
  • Uranium.
• They are used in medicine, in fertilisers etc.

Objective Type Questions

Question 1.
Fill in the blanks with appropriate words:
1. Lava is the molten magma from ……………………… of the earth’s surface.
2. Like a ………………………, the earth is made up of ……………………… layers.
3. Crust is about ……………………… km on the continental mass and ……………………… km on the
ocean floor.
4. Mantle forms about ……………………… of the earth’s volume.
5. Core has a radius of about ……………………… km and has very high temperature and ………………………
6. Limestone under excessive heat and pressure changes into ………………………
Answer:
1. interior
2. onion, concentric
3. 35 and 5
4. 16%
5. 3500, pressure
6. marble

Question 2.
State whether the given statements are true or false:
1. Crust is the thickest of all the layers.
2. Core is the innermost layer of the earth.
3. Mantle extends up to the depth of 2900 km.
4. The loose sediments are hardened to form metamorphic rocks.
5. Deccan plateau is made up of basalt.
6. Fossils are remains of dead plants and animals.
Answer:
1. False
2. True
3. True
4. False
5. True
6. True

Question 3.
Match the contents of Column A with that of Column B.

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

Multiple Choice Questions

Prelude

Question 1.
Where is the deepest mine in the world located?
(a) South America
(b) South Africa
(c) South India
(d) South Australia
Answer:
(b) South Africa

Question 2.
The depth of the deepest mine in South Africa is
(a) one km
(b) two km
(c) three km
(d) four km
Answer:
four km

Interior of the Earth

Question 1.
The upper most layer of the earth’s surface is called
(a) the crust
(b) the brust
(c) the roads
(d) the forest
Answer:
(c) the roads

Question 2.
What is the radius of the earth?
(a) 3671 km
(b) 7163 km
(c) 6371 km
(d) 1736 km
Answer:
(c) 6371 km

Rocks and Minerals

Question 1.
Any natural mass of mineral matter that makes up the earth’s crust is called a
(a) rock
(b) road
(c) sediment
(d) none of these
Answer:
(a) rock

Question 2.
The sediments are transported and deposited by
(a) wind
(b) water
(c) wind and water
(d) none of these
Answer:
(c) wind and water

Question 3.
The process of transformation of the rock from one form to another is known as
(a) road cycle
(b) food cycle
(c) rock cycle
(d) all of these
Answer:
rock cycle

Question 4.
Which rock is the molten magma made up of?
(a) Igneous
(b) Metamorphic
(c) Sedimentary
(d) None of these
Answer:
Igneous

Question 5.
What is the latin term of Igneous?
(a) Ignis
(b) Sedimentum
(c) Metamorphose
(d) None of these
Answer:
Ignis

Question 6.
Rocks which contain fossils are called
(a) metamorphic rocks
(b) igneous rocks
(c) core
(d) sedimentary rocks
Answer:
sedimentary rocks

Extra Questions for Class 7 Social Science

The post Inside Our Earth Class 7 Extra Questions Geography Chapter 2 appeared first on Learn CBSE.

Our Changing Earth Class 7 Extra Questions Social Science Geography Chapter 3

NCERT Extra Questions for Class 7 Social Science Geography Chapter 3 Our Changing Earth

Prelude

Question 1.
What are lithospheric plates?
Answer:

• The lithosphere is broken into numerous pieces.
• These big pieces are called lithospheric plates.
• The earth’s crust consists of several large and small, rigid, irregularly shaped plates/pieces.
• The movement of these plates causes changes on the surface of the earth.

Question 2.
Why do the lithospheric plates move slowly?
Answer:
The lithospheric plates move slowly because of the slow movement of molten magma inside the earth in a circular manner.

Question 3.
What are the two types of the earth’s forces?
Answer:
The earth’s movements are divided on the basis of the forces which cause them.

• The forces which act in the interior of the earth are called endogenic forces.
• The forces that work on the surface of the earth are called exogenic forces.
  • Endogenic forces sometimes produce sudden movements.,
  • At other times they produce slow movements.
  • Sudden movements are earthquakes and volcanoes.
  • They cause mass destruction over the surface of the earth.

Question 4.
Define a volcano.
Answer:
A volcano is a vent or a hole in the earth’s crust through which molten material erupts suddenly.

Question 5.
What are earthquakes? Define focus and epicentre.
Answer:
Earthquake

• When the lithosphere plates move, the surface of the earth vibrates.
• The vibrations travel all around the earth.
• These vibrations are called earthquake.

Focus:
• The place or point in the crust where the movement starts is called Focus.

Epicentre:
The place or the surface above the focus is called Epicentre.

• Vibrations travel outwards from the epicentre as waves.
• Greatest damage occurs closest to the epicentre.
• The strength of the earthquake decreases, going away from the centre.

Question 6.
What are three types of earthquake waves?
Answer:
There are three types of earthquake waves:

• P waves or longitudinal.
• S waves or transverse waves.
• L waves or surface waves.

Question 7.
How can we minimise the impact of an earthquake?
Answer:

• Earthquakes cannot be predicted.
• Their impact can certainly be minimised if we are prepared before hand.

Question 8.
Give an account of some common earthquake prediction methods adopted locally by people.
Answer:
Some of the common earthquake prediction methods adopted locally by people are:

• Wild animal behaviour.
• Agitated fish in the ponds.
• Snakes coming out to the surface from their holes.
• Animals trying to untie themselves and run away.
• Birds leaving their nests and beginning to chatter loudly.
• Aborigines beginning to run to higher grounds.

Question 9.
What is seismograph? How is the magnitude of earthquake measured?
Answer:

• An earthquake is measured with a machine.
• It is called a seismograph.
• The magnitude of the earthquake is measured on Richter scale.
  • An earthquake of 2.0 or less is felt only a little.
  • An earthquake over 5.0 causes damage from things falling.
  • A 6.0 or higher magnitude is considered very strong and 7.0 is classified as a major earthquake.

Question 10.
Explain Earthquake preparedness.
Answer:
Earthquake Preparedness:
When an earthquake strikes we should do the following:

• We should be in a safe spot like: under a kitchen counter, table or desk.
• We should stand against an inside comer or wall.
• We should stay away from fire places, areas around chimneys, windows that shatter including mirrors and picture frames.
• We should be prepared by arousing awareness amongst our friends and family members.
• We should face any disaster confidently.

NOTES: Case Study Bhuj Earthquake:

• An earthquake measuring 6.9 on richter scale hits Bhuj in Gujarat.
• Schools worst affected.
• Communication water power supply affected
• Hundreds of fire started
• Emergency declared and CM appeals for help.

Major Land Forms

Question 1.
What are the two processes which continuously wear away the landscape? Explain them.
Answer:
The Processes:

• • The landscape is continuously worn away by two processes.
• • They are:
  • Weathering and erosion.
  • Weathering is the breaking up of rocks on the earth’s surface.
  • Erosion is the wearing away of the landscape by different agents like water, wind and ice.
• The eroded material is carried away or transported by water, wind etc.
• They deposit material eventually.
• This process of erosion and deposition creates different landforms on the surface of the earth.

Work of a River

Question 1.
What is a waterfall? Explain with example.
Answer:
When the rivers tumble at steep angle over the hard rocks of a deep steep valley it forms a waterfall.
For example: Victoria waterfalls or Niagara waterfall.

Question 2.
Describe the work of a river.
Answer:
Work of a River:

• Running water in the river erodes the landscape.
• When the river tumbles at steep angle over very hard rocks or down a steep valley side, it forms a waterfall.
• When the river enters the plain it twists, turns and forms large bends. These bends are known as meanders.
• Due to continuous erosion and deposition along the sides of the meander, the ends of the meander loop come closer and closer.
  • In due course of time the meander loop cuts-off from the river and forms a cut-off lake.
  • It is called an ox-bow lake.
  • At times the river overflows its banks.
  • This leads to the flooding of the neighbouring areas.
  • The flood water deposits layers of fine soil and other material.
  • They’are called sediments, along its banks.
  • This leads to the formation of a flat fertile land called a flood plain.
• The raised banks are called levees.
• As the river approaches the sea, the speed of the running water decreases.
  • The river begins to break up into a number of streams. They are called distributaries.
  • Now the river becomes so slow that it begins to deposit its load.
  • Each distributary forms its own mouth.
  • The collection of sediments from all the mouths forms a delta, the triangular shaped land mass.

Work of Sea Waves

Question 1.
Write a note on the work of sea-waves.
Answer:
Work of Sea Waves

• Erosion and deposition of the sea waves form coastal land forms.
• Sea waves continuously strike at the rocks.
  • Cracks develop.
  • In course of time they become larger and wider.
  • Hollow like caves are formed on the rocks.
  • They are called sea caves.
• As caves become bigger and bigger only the roofs of the caves remain. This leads to formation of Sea arches.
• Continuous erosion breaks the roofs and only walls are left.
  • These wall-like features are called stacks.
• The steep rocky coast rising almost vertically above sea water is called sea cliff.
• The sea waves deposit sediments along the shores.
  • This leads to formation of sea beaches.

Work of Ice

Question 1.
Describe the work of ice.
Answer:
Work of Ice:

• Glaciers are “rivers” of ice.
• They too erode the landscape by bulldozing soil and stones to expose the solid rock below.
• Glaciers carve out deep hollows.
• As the ice melts they get filled up with water and become beautiful lakes in the mountains.
• The material carried by the glacier like big and small rocks, sand, silt gets deposited.
  • These deport from glacial moraines.

Work of Wind

Question 1.
Give an account of the work of wind.
Answer:
Work pi Wind

• An active agent of erosion and deposition in the deserts is wind.
• In deserts there are numerous rocks with a shape of a mushroom.
  • They are commonly called mushroom rocks.
  • Winds erode the lower section of the rock more than the upper part.
  • Such rocks have narrower base and wider top.
• When the wind blows, it lifts and transports sand from one place to another.
  • When it stops blowing, the sand falls and gets deposited in low hill like structures.
  • These are called sand dunes.
• When the grains of sand are very fine and light, the wind carries it over very long distances.
  • When such a sand is deposited in large areas, they are called loess. Large deposits of loess are found in China.

Objective Type Questions

Question 1.
Fill in the blanks with appropriate words:
1. Magma inside the earth moves in a ………………………. motion.
2. A ………………………… is a vent in the earth’s crust through which molten material comes
out.
3. The place in the crust where the earthquake starts is called ……………………..
4. The processes of …………………………….. and ………………………. create different landform on the surface of earth.
5. Deposition of layers of fine soil along the bank of rivers forms …………………………….
6. Sand deposits over larger areas are called………………………….
Answer:
1. circular
2. volcano
3. epicentre
4. erosion, deposition
5. flood plains
6. loess,

Question 2.
Write whether the given statements are true or false:
1. Sudden movements like earthquake do not cause mass destruction.
2. Deposition is breaking up of rocks on the earth’s surface.
3. Wearing away of the land by different agents like water, wind and ice is called erosion.
4. Sea caves become bigger and only the roof remains forming the sea arches.
5. Moraine is a depositional feature of glaciers,
6. River is an agent of erosion and deposition in the desert.
Answer:
1. False
2. False
3. True
4. True
5. True
6. False.

Question 3.
Match the contents of Column A with that of Column B

Answer:
1. (b)
2. (d)
3. (f)
4. (g)
5. (a)
6. (c).

Multiple Choice Questions

Prelude

Question 1.
The earth’s crust is broken into a number of huge parts. They are called
(a) lithospheric plates
(b) metamorphic plates
(c) sedimentary plates
(d) none of these
Answer:
lithospheric plates

Question 2.
Which one of the following forces originates in the interior of the earth?
(a) Exogenic forces
(b) Endogenic forces
(c) Both (a) and (b)
(d) None of these
Answer:
Endogenic forces

Question 3.
Sudden movements in the earth are called
(a) earthquakes
(b) building mountains
(c) focus
(d) none of these
Answer:
earthquakes

Question 4.
The place on the surface above the focus is known as
(a) epicentre
(b) focus
(c) forces
(d) lithosphere
Answer:
epicentre

Question 5.
What is the name of the instrument used for measuring earthquake?
(a) Thermometer
(b) Seismograph
(c) Weighing machine
(d) All of these
Answer:
(b) Seismograph

Question 6.
On which scale is the earthquake measured?
(a) Plane scale
(b) Richter scale
(c) Compass
(f) Divider
Answer:
Richter scale

Major Land Forms

Work of a River:

Question 1.
In which continent is the highest waterfall ‘Angel Falls of Venezuela’ located?
(a) South America
(b) South Africa
(c) South India
(d) North India
Answer:
South America

Question 2.
Where is ‘Niagara falls’ located?
(а) On the border between Canada and USA
(b) On the border between India and China
(c) On the border between India and Pakistan
(d) On the border between India and Nepal
Answer:
On the border between Canada and USA

Question 3.
The triangular collection of sediments at the mouth of a river forms
(a) beach
(b) delta
(c) arches
(d) glaciers
Answer:
delta

Work of Sea Waves

Question 1.
The steep rocky coast rising almost vertically above the sea water is called
(a) sea cliff
(b) beach
(c) sea cave
(d) erosion
Answer:
sea cliff

Work of Ice

Question 1.
Which of the following is an example of a glacier
(a) Gangotri
(b) Aravali
(c) both of these
(d) none of these
Answer:
Gangotri

Work of Wind

Question 1.
Deposition of sand in a low hill like structure is known as a: ‘
(a) Glacier
(b) Sand dimes
(c) Hill
(d) Desert
Answer:
Sand dimes

Extra Questions for Class 7 Social Science

The post Our Changing Earth Class 7 Extra Questions Geography Chapter 3 appeared first on Learn CBSE.

Air Class 7 Extra Questions Social Science Geography Chapter 4

NCERT Extra Questions for Class 7 Social Science Geography Chapter 4 Air

Prelude

Question 1.
Define the term atmosphere.
Answer:
Blanket of air surrounding the earth is known as the atmosphere.

Question 2.
How do all living beings depend on the atmosphere for their survival?
Answer:
All living beings depend on the atmosphere for their survival.

• Atmosphere provides them the air they breathe.
• It protects them from the harmful effects of the sun’s rays.
• Without its protection, they would be baked alive by the heat of the sun during day and get frozen during night.

Question 3.
What is green house effect?
Answer:
Carbon dioxide in the atmosphere traps the heat radiated from the earth creating a green house effect. This makes the temperatures livable. Without this earth would have been too cold to live. But the increased emissions from vehicles and factories increases the temperature leading to global warming.

Question 4.
What is global warming? What is its affect?
Answer:
When the heat retained through greenhouse gas increases the temperature of the earth, it causes global warming:

• The plants maintain the balance of gases. However this balance is upset by burning fuels such as coal, petroleum oil and large scale deforestation.
• This rise in temperature causes the snow in coldest parts to melt.
• As a result the sea level rises causing floods in the coastal areas.
• This may bring changes in weather and climate leading to extinction of certain plants and animal species.

Composition of the Atmosphere

Question 1.
Name the two gases which influence the atmosphere to a great extent.
Answer:

• Two gases such as carbon dioxide and ozone influence the atmosphere to a large extent.
• Their percentage in the atmosphere is as under:
• Carbon dioxide 0.03%
• Ozone 0.00006%

Question 2.
Describe the composition of the atmosphere.
Answer:
Composition of the Atmosphere:

• The air we inhale while breathing is actually a mixture of numerous gases.
  • Nitrogen and oxygen are two gases which make up the most of the atmosphere.
  • Carbon dioxide, helium, ozone, argon and hydrogen are found in lesser quantities.
  • Tiny dust particles are also present in the air.

Question 3.
How is nitrogen present in atmosphere used by plants?
Answer:
Nitrogen is the most plentiful gas in the air.

• Plants need nitrogen for their survival. They cannot take nitrogen directly from the air.
• Bacteria in the soil or the roots fix nitrogen by changing its form so that plants can use it.

Question 4.
Which is the second most plentiful gas in the atmosphere?
Answer:
Oxygen is the second most plentiful gas in the atmosphere. Humans and animals use it for breathing. Green plants produce oxygen through photosynthesis and thus oxygen balance is maintained in air. This gets disturbed if we cut trees.

Question 5.
Explain how the oxygen and carbon dioxide balance is maintained in air?
Answer:
Green plants use carbon dioxide to make their food and during this process release oxygen:

• Humans and animals release carbon dioxide and take oxygen from air.
• The amount of carbon dioxide released by them is equal to amount used by plants
  to make their food. Hence a balance is maintained.
• But now the excess of carbon dioxide is released by burning of fuels. The reduction in number of plants upset the balance of gases like carbon dioxide affecting earth’s weather and climate.

Question 6.
Explain the circulation of air in atmosphere.
Answer:
When air is heated it expands, becomes lighter and rises up:

• Cold air is dense, so, it sinks down.
• When hot air rises up, cold air from surrounding areas fills in the gap.
• This is the process of circulation of air.

NOTES: News reports around the world

• Due to burning of fuels and cutting of trees C02 level are increasing
• Globed sunscreen thinned
• Warning unstoppable
• It can bring back Jurassic era.

Structure of the Atmosphere

Question 1.
Discuss the structure of the atmosphere.
Answer:
Structure of the Atmosphere

• The atmosphere is divided into five layers according to height, starting from the earth’s surface.
• They are
  • Troposphere
  • Stratosphere
  • Mesosphere
  • Thermosphere
  • Exosphere

Question 2.
Which is most important layer of the atmosphere?
Answer:
Troposphere

• Troposphere is the important layer of the atmosphere.
• Its average height is 13 km.
  • It is 8 kilometres on the poles and 18 kilometres on the equator.
• The air (which living beings breathe) exists here.
• All the weather phenomena like winds, rainfall, fog, hailstorm etc. occur in this layer.

Question 3.
Which layer the most suitable conditions for flying aeroplanes?
Answer:
Stratosphere

• The stratosphere lies above the troposphere.
• It extends up to a height of 50 km.
• This layer is almost free from clouds.
• No weather phenomenon occurs in this layer making conditions most ideal for flying aeroplanes.
• Stratosphere contains a layer of ozone gas.
• It protects living beings from the harmful effects of the sun rays.

Question 4.
What is the third layer of atmosphere?
Answer:
Mesosphere

• Mesosphere is the third layer of the atmosphere.
• It lies above the stratosphere.
• It extends up to a height of 80 km.
• Meteorites bum up in this layer on entering from the space.

Question 5.
Briefly write about thermosphere?
Answer:
Thermosphere

• In thermosphere temperature rises very rapidly with increasing height.
• Ionosphere is a part of this layer.
• It extends between 80 and 400 km.
• This layer helps in radio transmission.
  • Radio waves transmitted from the earth are reflected back to the earth by this layer.

Question 6.
Which is the uppermost layer of the atmosphere?
Answer:
Exosphere

• The uppermost layer of the atmosphere is known as exosphere.
• This layer has very thin air.
• Light gases like helium and hydrogen float into the space from here.

Weather and Climate

NOTES: Many questions are asked about days conditions especially on an important day like cricket match or wedding etc. Questions like’ will it rain or will it be sunny; etc. basically are related to day’s weather. Such questions are not asked about climate

Question 1.
What is weather?
Answer:
Weather is the day to day condition of the atmosphere. For example a sunny day or rainy day. Weather is like a control knob of climate.

Question 2.
Define the term climate.
Answer:
The sum total of all weather conditions prevailing over large area for a longer period of time is called climate.

Question 3.
What is the difference between weather and climate?
Answer:
Weather is hour-hour conditions of atmosphere like hot humid weather may make us irritable but same day breezy or pleasant evening may make one cheerful. We have hot or cold climate over a period of few months.
Therefore we have daily forecast of weather and long term predictions of climatic conditions.

Question 4.
Name different types of weather measuring instruments.
Answer:
Thermometer – measures temperature
Barometer – measures atmospheric pressure
Rain gauge – measures amount of rainfall
Wind wane – shows direction of wind

Temperature

Question 1.
What is temperature?
Answer:

• The degree of hotness or coldness is called the temperature.
• Temperature changes not only between day and night but also from season to season.

Question 2.
What is insolation?
Answer:
Insolation is the incoming solar energy intercepted by the earth. It influences the distribution of temperature.

Question 3.
Why are poles covered with snow?
Answer:
The amount of insolation decreases from equator towards poles, therefore the temperature also reduces. But if the earth’s temperature rises too high, it would be too warm to raise crops.

Question 4.
Why cities are more hotter than villages?
Answer:
The temperature in cities is much higher than that of villages because the concrete and metals in the buildings and the tar and asphalt in the roads gets heated throughout the day and absorbs heat. This heat is released at night hence there is the difference in the temperature.
The crowded high rise buildings trap the warm air and thus raise the temperature of the cities.

Air Pressure

Question 1.
Why don’t we feel the air pressure?
Answer:
The air above us presses us from all sides with great force but we do not feel it. This happens because our body exerts a counter pressure.

Question 2.
Define the term air pressure.
Answer:
Air pressure is the pressure exerted by the weight of air on the earth’s surface. As we move in the upper layers of atmosphere, the pressure falls rapidly.

Question 3.
How does air pressure vary from equator to poles and from surface to heights?
Answer:
Variation in Distribution of Pressure

• As we go up the layers of atmosphere, the pressure falls rapidly.
  • The air pressure is highest at sea level
  • It decreases with increase in height.
• Horizontally the distribution of air pressure is influenced by temperature of air at a given place.

Question 4.
What is the relation between temperature and pressure?
Answer:
Distribution of air pressure is influenced by the temperature of the area:

• Where temperature is high the air gets heated and rises. This creates a low pressure area.
• Low pressure is associated with cloudy skies and wet weather.
• In areas with low temperature, the air is cold and heavy so, it sinks down. This creates a high pressure area.
• High pressure is associated with clear and sunny skies.
• Air always moves from high pressure to low pressure areas.

Question 5.
Why do Astronauts wear a protective gear on moon?
Answer:
Astronauts wear a protective suit filled with air when they go to moon because the counter pressure exerted by the body would make the blood vessels burst.

Wind

Question 1.
Define the term wind. Explain with examples.
Answer:
The movement of air from high pressure to low pressure areas is called wind. For example wind blows dry leaves or strong wind uproots trees. Blowing smoke or dust is the work of wind. Strong wind makes it difficult to walk or hold umbrella.

Question 2.
Which are the three components of cyclone?
Answer:
Three components of cyclone are wind velocity, rain and tidal surge.

Question 3.
What are the various categories of wind? Explain with a diagram.
Answer:
Winds can be broadly divided into three types:

• Permanent winds – which blow constantly throughout the year in a particular direction.
  Example, easterlies and westerlies.
• Seasonal winds – which change directions in different seasons. For example, monsoon winds.
• Local winds – blow only during a particular period of the day or the year in a small area. For example, land or sea breeze, or loo.

Question 4.
What is Cyclone?
Answer:
A powerful and destructive storm with very high speed winds that moving in circular motion around an area of low pressure.

Question 5.
Describe the fury of cyclone taking example of ‘Super cyclone’ of Odisha.
Answer:
Odisha on eastern sea coast of India is prone to cyclones originating in Bay of Bengal.

• Odisha was hit by cyclone on 17th-18th October 1999 and again on 29th October.
• Cyclone originated as a ‘depression’ in the Gulf of Thailand near Port Blair.
• It moved in northwest direction on 25th October and intensified into super cyclone and hit Odisha.
• Wind speed was upto 260 km/hr which lasted for 36 hours.
• Trees were uprooted kutcha houses, roof tops industrial sheds etc blown away.
• Power supply and communication lines damaged.
• Continues rains flooded the major rivers. Tidal waves swept 20 km of inland areas including cities of Bhubaneshwar and Cuttack and destructed 28 coastal towns.
• 7-10 m high tidal waves caused damage to paddy crops, vegetables fruits and agricultural land turned infertile due to salination.
• 13 million people were affected. Livestock was killed.
• Plantations of teak, sal, bamboo, mangrove forests of Paradeep and Konark disappeared.

Moisture

Question 1.
What is humidity?
Answer:
When water evaporates from different water bodies and land it turns into water vapours or moisture. Moisture in air at any time is known as humidity.

Question 2.
What is a humid day?
Answer:
A day when air is full of water vapour is called a humid day. With the air getting warmer its capacity to hold moisture increases so it becomes more humid. On such days clothes takes longer to dry and even body sweat does not evaporate easily.

Question 3.
How are clouds formed? How do clouds cause precipitation?
Answer:

• When water vapour rises, it starts cooling.
• Water vapour condenses which results in formation of droplets of water.
• These droplets hanging in the air above are called clouds.
• Clouds are masses of these water droplets.
• When these droplets of water become too heavy to float in the air, they come down as precipitation.

Question 4.
Why do jet planes leaves a white trail behind them?
Answer:
Jet planes flying in the sky leave a white trail behind them,

• The moisture from their engines condenses.
• We see trails of this condensed moisture for sometime when there is no air movement to disturb it.
• These trails of condensed moisture are actually clouds.

Question 5.
What are different forms of precipitations?
Answer:
Different forms of precipitations are: dew, rainfall, hail, snowfall, fog, sleet.

Question 6.
What is rain? What is its importance?
Answer:
Precipitation in liquid form is called rain. Most of the ground water comes from rainwater. It is important for survival of plants and animals. It brings fresh water to earth.
If rainfall is more or trees are cut on hills, rain water can cause flooding in low lying areas. If it is less than water scarcity or drought may occur.

Question 7.
What are the types of rainfall?
Answer:
Based on the mechanism rainfall can be of three types: Convectional, Orographic or Cyclonic.

Objective type Questions

Question 1.
Fill in the blanks with appropriate words:
1. Earth is surrounded by a blanket of air called ………………..
2. Green plants produce ……………………… during photosynthesis.
3. Increased volume of ……………………. is affecting the earth’s weather and climate.
4. Ionosphere is the part of ……………………….
5. Amount of rainfall is measured by ………………………
6. Insolation influences the distribution of ……………………
Answer:
1. atmosphere
2. oxygen
3. carbon dioxide
4. thermosphere
5. rain gauge
6. temperature

Question 2.
State whether the given statements are true or false.
1. Hot air is dense and heavy and cold air is lighter and expands.
2. Without Green house effect earth would have been too cold to live.
3. Ionosphere contains the ozone layer.
4. Helium and hydrogen float from exosphere into space.
5. Wind – vane shows the direction of wind.
6. Air moves from high pressure to low pressure.
Answer:
1. False
2. True
3 False
4. True
5. True
6. True.

Question 3.
Match the contents of Column A with that of Column B

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

Multiple Choice Question

Question 1.
Which gas released in the atmosphere creates a greenhouse effect trapping the heat?
(a) Carbon dioxide
(b) Oxygen
(c) Nitrogen
(d) All of these
Answer:
Carbon dioxide

Question 2.
Excess amount of C02 is responsible for
(a) global cooling
(b) global warming
(c) both (a) and (b)
(d) none of these
Answer:
global warming

Question 3.
What are the important objects for survival of plants and animals?
(a) Rainfall
(b) Sun light
(c) Oxygen
(d) All of these
Answer:
All of these

Composition of the Atmosphere

Question 1.
Which one of the following gases is present in the atmosphere in the highest amount?
(a) Oxygen
(b) Carbon dioxide
(c) Nitrogen
(d) Lithium
Answer:
Nitrogen

Question 2.
Which gas is used by the green plants to make their food?
(a) Oxygen
(b) Carbon dioxide
(c) Nitrogen
(d) None of these
Answer:
Carbon dioxide

Question 3.
Which is the important gas used by human beings for breathing?
(a) Nitrogen
(b) Carbon dioxide
(c) Oxygen
(d) Sodium chloride
Answer:
Oxygen

Question 4.
When the air is heated it becomes
(a) Lighter?
(b) Heavier?
(c) Colder?
(d) None of these
Answer:
Lighter?

Structure of the Atmosphere

Question 1.
What is the average height of the troposphere?
(a) 3 km
(b) 6 km
(c) 9 km
(d) 13 km
Answer:
13 km

Question 2.
As we go up in troposphere layer of the atmosphere the pressure
(a) increases
(b) decreases
(c) no change
(d) all of these
Answer:
decreases

Question 3.
Which one of the following gases protects us from harmful sun’s rays?
(a) Ozone
(6) Nitrogen
(c) Carbon dioxide
(d) Oxygen
Answer:
Ozone

Weather and Climate

Question 1.
Which of the following are part of weather forecast in the newspapers?
(a) Temperature
(b) Humidity
(c) Time of Sunset
(d) All of These
Answer:
All of These

Temperature

Question 1.
Which element of weather is measured in degree Celsius?
(a) Temperature
(b) Pressure
(c) Wind
(d) Gravity
Answer:
Temperature

Question 2.
The water boils at
(a) 10°C
(b) 50°C
(c) 75°C
(d) 100°C
Answer:
100°C

Air Pressure

Question 1.
Where is the air pressure highest?
(a) Moon
(b) Pressure
(c) Stratosphere
(d) Gravity
Answer:
Pressure

Wind

Question 1.
What is very hot wind called?
(a) Loo
(b) Sea Level
(c) Monsoon air
(d) Exosphere
Answer:
Loo

Question 2.
Which one of the following is a local wind?
(a) Sea breeze
(b) Trade wind
(c) Monsoon wind
(d) None of these
Answer:
Sea breeze

Moisture

1. Rain, snow sleet or hail are the different forms of:
(a) Condensation
(b) Evaporation
(c) Precipitation
(d) All of these
Answer:
Precipitation

Extra Questions for Class 7 Social Science

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NCERT Solutions for Class 11 Maths Chapter 1 Ex 1.2

Get Free NCERT Solutions for Class 11 Maths Chapter 1 Sets Ex 1.2 PDF in Hindi and English Medium. Sets Class 11 Maths NCERT Solutions are extremely helpful while doing your homework. Sets Exercise 1.2 Class 11 Maths NCERT Solutions were prepared by Experienced LearnCBSE.in Teachers. Detailed answers of all the questions in Chapter 1 Class 11 Sets Ex 1.2 provided in NCERT Textbook.

Free download NCERT Solutions for Class 11 Maths Chapter 1 Sets Ex 1.2 PDF in Hindi Medium as well as in English Medium for CBSE, Uttarakhand, Bihar, MP Board, Gujarat Board, BIE, Intermediate and UP Board students, who are using NCERT Books based on updated CBSE Syllabus for the session 2019-20.

Q.1: Which of the following given below is null set?
(i).  Set of odd natural numbers which is divisible by 2.
(ii).  Set of even numbers which are prime
(iii).  {x: x is a natural number, x<5 and x>7}
(iv).  {y: y is a point common to any two parallel lines}

Solution:

Q.2:  State whether the following sets are infinite or finite:
(i).  A set of months of a year.
(ii).  {1, 2, 3 ….}
(iii).  {1, 2, 3…99, 100}
(iv).  The set of positive integers which are greater than 100.
(v).  The set of prime numbers which are less than 99

Solution:

Q.3: State whether the following sets are infinite or finite:
(i).  The set of lines parallel to the x – axis.
(ii).  The set of letters in the vowels.
(iii).  The set of numbers multiple of 10.
(iv).  The set of humans living on Earth.
(v).  The set of circles passing through the origin (0, 0).

Solution:

Q.4: In the following set given below, state whether A = B or not:
(i).  A = {w, x, y, z}
B = {z, y, x, w}
(ii).  A = {5, 9, 13, 17}
B = {9, 5, 17, 19}
(iii).  A = {4, 2, 6, 10, 8}
B = {x: x is positive even integer and x≤10 }
(iv).   A = {x: x is a multiple of 10}
B = {10, 15, 20, 25, 30 …}

Solution:

Q.5 In the following set given below, is the pair of sets equal?
(i). A = {3, 4}
B = {y: y is solution of y²+5y+6=0}
(ii).  A = {a: a is a letter in the word FOLLOW}
B = {b: b is a letter in the word WOLF}

Solution:

Q.6: From the following sets, select equal sets:
A = {2, 4, 8, 12}
B = {1, 2, 3, 4}
C = {4, 8, 12, 14}
D = {3, 1, 4, 2}
E = {–1, 1}
F = {0, a}
G = {1, –1}
H = {0, 1}

Solution:

NCERT Solutions for Class 11 Maths Chapter 1 Sets Ex 1.2 in Hindi

(v) 99 से छोटे अभाज्य पूर्णांकों का समुच्चय {2, 3, 5, 7, …… 97} है जिसमें अवयवों की संख्या निश्चित है।
अत: यह एक परिमित समुच्चय है।

प्रश्न 3.
निम्नलिखित समुच्चयों में से प्रत्येक के लिए बताइए कि कौन परिमित है और कौन अपरिमित है?
(i) x-अक्ष के समांतर रेखाओं का समुच्चय।
(ii) अंग्रेजी वर्णमाला के अक्षरों का समुच्चय।
(iii) उन संख्याओं का समुच्चय जो 5 के गुणज हैं।
(iv) पृथ्वी पर रहने वाले जानवरों का समुच्चय
(v) मूल बिन्दु (0, 0) से होकर जाने वाले वृत्तों का समुच्चय।
हल:
(i) x-अक्ष के समांतर अनंत रेखाएँ खींची जा सकती हैं। अत: यह एक अपरिमित समुच्चय है।
(ii) अंग्रेजी वर्णमाला में कुल 26 अक्षर होते हैं। इन अक्षरों से बनने वाला समुच्चय परिमित होगा।
(iii) 5 से विभाजित होने वाली संख्याओं का समुच्चय {5, 10, 15, 20, ….} है, जिसमें अनंत अवयव हैं। अतः यह एक अपरिमित समुच्चय है।
(iv) पृथ्वी पर रहने वाले जानवरों का समुच्चय परिमित होगा।
(v) मूल बिन्दु को केन्द्र मानकर अनन्त वृत्त चे जा सकते हैं। अत: यह अपरिमित होगा।

प्रश्न 4.
निम्नलिखित में बताइए कि A = B है अथवा नहीं है।
(i) A = {a, b, c, a}, B = {a, c, b, a}
(ii) A = {4, 8, 12, 16}, B = {8, 4, 16, 18}
(iii) A = {2, 4, 6, 8, 10}, B = {x : x सम धन पूर्णाक है और x ≤ 10}
(iv) A = {x : x संख्या 10 का एक गुणज है}, B = {10, 15,20, 25, 30, …}
हल:
(i) A और B दोनों समुच्चयों के अवयव a, b, c, d हैं अतः A = B.
(ii) A में अवयव 12 है परन्तु B में नहीं है अतः A ≠ B.
(iii) A और B दोनों समुच्चयों में अवयव 2, 4, 6, 8 और 10 हैं। अतः A = B.
(iv) A = {10, 20, 30, 40, …..}, B = {10, 15, 25, 30, ….}
10 के गुणजों में 5, 15, 25 नहीं आता है। अतः A ≠ B.

प्रश्न 5.
क्या निम्नलिखित समुच्चय युग्म समान हैं ? कारण सहित बताइए।
(i) A = {2, 3}
B = {x : x समीकरण x² + 5x + 6 = 0 का एक हल है।}
(ii) A = {k : x शब्द ‘FOLLOW’ का एक अक्षर है।}
B = {y : y शब्द ‘WOLF का एक अक्षर है।}
हल:
(i) A = {2, 3}, B = x : x समीकरण x² + 5x + 6 = 0} = {-2, -3}
स्पष्ट है कि समुच्चय A और B के अवयव भिन्न हैं।
अत: A ≠ B.
(ii) A = {F, O, L, W}, B = {W, O, L, F}
समुच्च्य A और B के अवयव समान हैं। अत: A = B.

प्रश्न 6.
नीचे दिए गए समुच्चयों में से समान समुच्चयों का चयन कीजिए:
A = {2, 4, 8, 12}
B = {1, 2, 3, 4}
C = {4, 8, 12, 14}
D = {3, 1, 4, 2}
E = {- 1, 1}
F = {0, a}
G = {1, -1}
H = {0, 1}
हल:
यहाँ समुच्चय B और D के अवयव 1, 2, 3, 4, हैं।
B = D
तथा समुच्चय E और G में -1, 1 अवयव समान हैं।
E = G

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NCERT Solutions for Class 9 Maths Chapter 5 Introduction to Euclid Geometry Ex 5.2 are part of NCERT Solutions for Class 9 Maths. Here we have given NCERT Solutions for Class 9 Maths Chapter 5 Introduction to Euclid Geometry Ex 5.2.

NCERT Solutions for Class 9 Maths Chapter 5 Introduction to Euclid Geometry Ex 5.2

Question 1.
How would you rewrite Euclid’s fifth postulate so that it would be easier to understand?
Solution:
Two distinct intersecting lines cannot be parallel to the same line.

Question 2.
Does Euclid’s fifth postulate imply the existence of parallel lines? Explain.
Solution:
Yes.
According to Euclid’s fifth postulate when line x falls on line y and z such that ∠1+ ∠2< 180°. Then, line y and line z on producing further will meet in the side of ∠1 arid ∠2 which is less than 180°.

We find that the lines which are not according to Euclid’s fifth postulate. i.e., ∠1 + ∠2 = 180°, do not intersect.

We hope the NCERT Solutions for Class 9 Maths Chapter 5 Introduction to Euclid’s Geometry Ex 5.2 help you. If you have any query regarding NCERT Solutions for Class 9 Maths Chapter 5 Introduction to Euclid’s Geometry Ex 5.2, drop a comment below and we will get back to you at the earliest.

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NCERT Solutions for Class 11 Maths Chapter 1 Sets Ex 1.3

Get Free NCERT Solutions for Class 11 Maths Chapter 1 Sets Ex 1.3 PDF in Hindi and English Medium. Sets Class 11 Maths NCERT Solutions are extremely helpful while doing your homework. Sets Exercise 1.3 Class 11 Maths NCERT Solutions were prepared by Experienced LearnCBSE.in Teachers. Detailed answers of all the questions in Chapter 1 Class 11 Sets Ex 1.3 provided in NCERT Textbook.

Free download NCERT Solutions for Class 11 Maths Chapter 1 Sets Ex 1.3 PDF in Hindi Medium as well as in English Medium for CBSE, Uttarakhand, Bihar, MP Board, Gujarat Board, BIE, Intermediate and UP Board students, who are using NCERT Books based on updated CBSE Syllabus for the session 2019-20.

Q.1: Fill in the blanks properly using ⊂ and ⊄.
(i).  {3, 4, 5} ____ {2, 3, 4, 5, 6}
(ii).  {a, b, c} ____ {d, c, d}
(iii).  {y: y is a pupil of Class 11 of the school} ____ {y: y is students of the school}
(iv).  {y: y is a circle in the plane} ____ {y: y is a circle in the same plane with radius 2 unit}
(v).  {y: y is an equilateral triangle in a plane} ____ {y: y is a rectangle in the same plane}
(vi).  {y: y is an equilateral triangle in a plane} ____ {y: y is a triangle in the plane}
(vii).  {y: y is an odd natural number} ____ {x: x is an integers}

Solution:

Q.2: State whether the given statements are true or false:
(i).  {b, c} ⊄ {c, d, e}
(ii).  {a, e, i} ⊂ {x: x is a vowel in the English alphabets}
(iii).  {1, 2, 3} ⊂{1, 2, 4, 5}
(iv).  {c} ⊂ {b, c, d}
(v).  {b} ∈ {a, b, c, d}
(vi).  {y: y is an even natural no. less than 6} ⊂ {y: y is a natural no. which can divide 36}

Solution:

Q.3: Let X = {11, 12, {13, 14}, 15}. According to the given set which of the given statements are false? Explain why.
(i).  {13, 14} ⊂ X
(ii).  {13, 14} ∈ X
(iii).  {{13, 14}} ⊂ X
(iv).  11 ∈ X
(v).  11 ⊂ X
(vi).  {11, 12, 15} ⊂ X
(vii).  {11, 12, 15} ∈ X
(viii).  {11, 12, 13} ⊂ X
(ix).  Ø ∈ X
(x).  Ø ⊂ X
(xi).  {Ø} ⊂ X

S 

Q.4: Write all the subsets of the given sets:
(i).  {b}
(ii).  {b, c}
(iii).  {2, 3, 4}
(iv).  Ø

Solution:

Q.5: How many elements has P(X), if X = Ø ?

Solution:

Q.6: Write the given in the form of intervals:
(i).  {y: y ∈ R, –5 < y ≤ 7}
(ii).  {y: y ∈ R, –13 < y < –11}
(iii).  {y: y ∈ R, 1 ≤ y < 8}
(iv).  {y: y ∈ R, 4 ≤ y ≤ 5}

Solution:

Q.7:  Write the given intervals in the form of set – builder:
(i).  (–4, 1)
(ii).  [7, 13]
(iii).  (7, 13]
(iv).  [–24, 6)

Solution:

Q.8: What universal set/ sets would you propose for the given sets?

(i).  The set of right triangles
(ii).  The set of isosceles triangles

Solution:

Q.9: X = {1, 3, 5}, Y = {2, 4, 6} and Z = {0, 2, 4, 6, 8}

Which of the given sets can be considered as the universal set for the given sets X, Y and Z?
(i).  {0, 1, 2, 3, 4, 5, 6}
(ii).  Ø
(iii).  {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
(iv).  {1, 2, 3, 4, 5, 6, 7, 8}

Solution:

NCERT Solutions for Class 11 Maths Chapter 1 Sets Ex 1.3 in Hindi

प्रश्न 2.
जाँचिए कि निम्नलिखित कथन सत्य हैं अथवा असत्य हैं:
(i) {a, b} ⊄ {b, c, a}
(ii) {a, e} ⊂ {x : x अंग्रेजी वर्णमाला का एक स्वर है।
(iii) {1, 2, 3} ⊂ {1, 3, 5}
(iv) {a} ⊂ {a, b, c}
(v) {a} ⊂ {a, b, c}
(vi) {x : x संख्या 6 से कम एक सम प्राकृत संख्या है। ⊂ {x : x एक प्राकृत संख्या है, जो संख्या 36 को विभाजित करती है।
हल:
(i) समुच्चय {a, b} के अवयव a, b दासमुच्चय {b, c, a} में है।
{a, b} ⊄ {b, c, a}
अतः उपरोक्त कथन असत्य है।
(ii) a, e दोनों ही स्वर हैं।
{a, e} = {x : x, अंग्रेजी वर्णमाला का एक स्वर है।
अतः यह कथन सत्य है।
(iii) समुच्चय {1, 2, 3} और {1, 3, 5} में अवयव 2 समुच्चय {1, 3, 5} नहीं है।
{1, 2, 3} ⊂ {1, 3, 5} कथने असत्य है।
(iv) a ∈ {a, b, c}
{a} ⊂ {a, b, c} यह कथन सत्य है।
(v) {4} समुच्चय है, अवयव नही है।
{a} } ∈ {a, b, c} कथन असत्य है।
(vi) सम प्राकृत संख्या 2, 4 संख्या 6 से कम है तथा 36 को विभाजित करती है।
{x : x एक सम प्राकृत संख्या है जो 6 से कम है} ⊂ {x : x एक सम प्राकृत संख्या 36 को विभाजित करती है। अतः यह कथन सत्य है।}

प्रश्न 3.
मान लीजिए कि A = {1, 2, 3, 4, 5}, निम्नलिखित में से कौन सा कथन सही नहीं है और क्यों?
(i) {3, 4} ⊂ A
(i) {3, 4} ∈ A
(iii) {{3, 4}} ⊂ A
(iv) 1 ∈ A
(v) 1 ⊂ A
(vi) {1, 2, 5} ⊂ A
(vii) {1, 2, 5} ∈ A
(viii) {1, 2, 3} ⊂ A
(ix) Φ ∈ A
(x) Φ ⊂A
(xi) {Φ} ⊂ A
हल:
(i) सही नहीं है। समुच्चय {3, 4} एक अवयव है।
(ii) सही है। क्योंकि {3, 4} समुच्चय A का एक अवयव है।
(iii) सही है। A के अवयव {3, 4} का एक उपसमुच्चय है।
(iv) 1 ∈ A, सही है।
(v) 1 ⊂ A सही नहीं है क्योंकि 1 एक समुच्चय नहीं है।
(vi) {1, 2, 5} ⊂ A सही है। समुच्चय {1, 2,5} के अवयव 1, 2, 5 समुच्चय A में है।
(vii) {1, 2, 5} ∈ सही नहीं है। {12, 5} अवयव नहीं है। यह एक समुच्चय है।
(viii) {1, 2, 3} ⊂ A सही नहीं है। अवयव 3 समुच्चय में नही है।
(ix) Φ ∈ A, सही नहीं है। Φ एक समुच्चय है, अवयव नहीं है।
(x) {Φ} ⊂ A सही है। सभी समुच्चयों का उपसमुच्चय है।
(xi) {Φ} ⊂ A सही नहीं है। {Φ} समुच्चय का समुच्चय है।

प्रश्न 4.
निम्नलिखित समुच्चयों के सभी उपसमुच्चय लिखिए।
(i) {a}
(ii) {a, b}
(iii) {1, 2, 3}
(iv) Φ
हल:
(i) Φ, {a}
(ii) Φ, {a}, {b}, {a, b}
(iii) Φ, {1}, {2}, {3}, {1, 2}, {2, 3}, {1, 3}, {1, 2, 3}
(iv) Φ

प्रश्न 5.
P (A) के कितने अवयव हैं, यदि A = Φ
हल:
A = Φ, P(A) = Φ इस प्रकार P (A) को 2° = 1 अवयव है।

प्रश्न 6.
निम्नलिखित को अंतराल रूप में लिखिए:
(i) {x : x ∈R, -4 < x ≤ 6}
(ii) {x : x ∈R, -12 < x < -10}
(iii) {x : x ∈ R, 0 ≤ x < 7}
(iv) {x : x ∈ R, 3 ≤ x ≤ 4}
हल:
वांछित अंतराल इस प्रकार हैं।
(i) (-4, 6]
(ii) (-12, – 10)
(iii) [0, 7)
(iv) [3, 4]

प्रश्न 7.
निम्नलिखित अंतरालों को समुच्चय निर्माण रूप में लिखिए:
(i) (-3, 0)
(ii) [6, 12]
(iii) (6, 12]
(iv) [-23, 5]
हल:
(i) (-3, 0) = {x : x ∈ R, -3 < x < 0}
(ii) [6, 12] = {x : x ∈ R, 6 ≤ x ≤ 12}
(iii) (6,12] = {x : x ∈ R, 6 < x ≤ 12}।
(iv) [-23, 5] = {x : x ∈ R, -23 ≤ x ≤ 5}

प्रश्न 8.
निम्नलिखित में से प्रत्येक के लिए आप कौन सा सार्वत्रिक समुच्चय प्रस्तावित करेंगे?
(i) समकोण त्रिभुजों का समुच्चय
(ii) समद्विबाहु त्रिभुजों का समुच्चय
हल:
दोनों समुच्चयों के लिए सार्वत्रिक समुच्चय :
{x : x समतल में स्थित एक त्रिभुज}

प्रश्न 9.
समुच्चय A = {1, 3, 5}, B = {2, 4, 6} और C = {0, 2, 4, 6, 8} प्रदत्त हैं। इन तीनों समुच्चयों A, B और C के लिए निम्नलिखित में से कौन सा (से) सार्वत्रिक समुच्चय लिए जा सकते हैं?
(i) {0,1, 2, 3, 4, 5, 6}
(ii) Φ
(iii) {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
(iv) {1, 2, 3, 4, 5, 6, 7, 8}
हल:
समुच्चय (iii),
तीनों समुच्चय A, B, C के लिए {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10} सार्वत्रिक समुच्चय हैं।

The post NCERT Solutions for Class 11 Maths Chapter 1 Sets Ex 1.3 appeared first on Learn CBSE.

NCERT Solutions for Class 11 Maths Chapter 1 Sets Ex 1.4

Get Free NCERT Solutions for Class 11 Maths Chapter 1 Sets Ex 1.4 PDF in Hindi and English Medium. Sets Class 11 Maths NCERT Solutions are extremely helpful while doing your homework. Sets Exercise 1.4 Class 11 Maths NCERT Solutions were prepared by Experienced LearnCBSE.in Teachers. Detailed answers of all the questions in Chapter 1 Class 11 Sets Ex 1.4 provided in NCERT Textbook.

Free download NCERT Solutions for Class 11 Maths Chapter 1 Sets Ex 1.4 PDF in Hindi Medium as well as in English Medium for CBSE, Uttarakhand, Bihar, MP Board, Gujarat Board, BIE, Intermediate and UP Board students, who are using NCERT Books based on updated CBSE Syllabus for the session 2019-20.

Q.1: Find the union of each of the following pairs of sets:
(i). P = {1, 4, 6} and Q = {1, 3, 4}
(ii). X = {a, e, i, o, u} and Y = {x, y, z}
(iii). X = {x: x is a natural number and multiple of 3} and Y = {x: x is a natural number less than 6}
(iv). X = {x: x is a natural number and 1 < x ≤ 5} and Y = {x: x is a natural number and 5 < x < 10}
(v). X = {4, 5, 6} and Y = Φ

Solution:

Q.2:  Let A = {x, y} and B = {x, y, z}
Is A ⊂ B? What is A ∪ B?

Solution:

Q.3: If X and Y are two sets such that X ⊂ Y, then what is X ∪ Y?

Solution:

Q.4: If P = {1, 2, 3, 4}, Q = {3, 4, 5, 6}, R = {5, 6, 7, 8} and S = {7, 8, 9, 10}
Find the following:
(i).  P ∪ Q
(ii).  P ∪ R
(iii).  Q ∪ R
(iv).  Q ∪ S
(v).  P ∪ Q ∪ R
(vi).  P ∪ Q ∪ S
(vii).  Q ∪ R ∪ S

Solution:

Q.5:  Find the intersection of each of the following pairs of sets:
(i).  P = {1, 4, 6} and Q = {1, 3, 4}
(ii).  X = {a, e, i, o, u} and Y = {x, y, z}
(iii).  X = {x: x is a natural number and multiple of 3} and Y = {x: x is a natural number less than 6}
(iv).  X = {x: x is a natural number and 1 < x ≤ 5} and Y = {x: x is a natural number and 5 < x < 10}
(v).  X = {4, 5, 6} and Y = Φ

Solution 5:

Q.6: If A = {3, 5, 7, 9, 11}, B = {7, 9, 11, 13}, C = {11, 13, 15} and D = {15, 17}
Find the following:
(i).  A ∩ B
(ii).  B ∩  C
(iii).  A ∩  C ∩  D
(iv).  A ∩  C
(v).   B ∩  D
(vi).  A ∩  (B ∪ C)
(vii).  A ∩  D
(viii).  A ∩  (B ∪ D)
(ix).  (A ∩  B) ∩  (B ∪ C)
(x).  (A∪  D) ∩  (B ∪ C)

Solution:

Q.7: If A = {y: y is a natural number}, B ={y: y is an even natural number}, C = {y: y is an odd natural number} and D = {y: y is a prime number}
Find the following:
(i). A ∩ B
(ii). A ∩ C
(iii). A ∩ D
(iv). B ∩ C
(v). B ∩ D
(vi). C ∩ D

Solution 7:

Q.8: Which of the given pairs of sets are disjoint?
(i).  A = {1, 2, 3, 4} and B = {x: x is a natural number and 4 ≤ x ≤ 6}
(ii).  A = {a, e, i, o, u} and B = {c, d, e, f}
(iii).  A = {x: x is an even integer} and B = {x: x is an odd integer}

Solution:

Q.9: If A = {3, 6, 9, 12, 15, 18, 21}, B = {4, 8, 12, 16, 20}, C = {2, 4, 6, 8, 10, 12, 14, 16} and D = {5, 10, 15, 20}
Find the following:
(i).  A – B
(ii).  A – C
(iii).  A – D
(iv).  B – A
(v).  C – A
(vi).  D – A
(vii).  B – C
(viii).  B – D
(ix).  C – B
(x).  D – B
(xi).  C – D
(xii).  D – C

Solution 9:

Q.10: If X = {a, b, c, d} and Y = {f, b, d, g}
Find the following:
(i).  X – Y
(ii).  Y – X
(iii).  X ∩ Y

Solution:

Q.11: What is R – Q, if R is the set of real numbers and Q is the set of rational?

Solution:

Q.12: State whether the following statements are true or false. Give reason.
(i).  A = {2, 3, 4, 5} and B = {3, 6} are disjoint sets.
(ii).  A = {a, e, i, o, u } and B = {a, b, c, d} are disjoint sets.
(iii).  A = {2, 6, 10, 14} and B = {3, 7, 11, 15} are disjoint sets.
(iv).  A = {2, 6, 10} and B = {3, 7, 11} are disjoint sets.

Solution:

NCERT Solutions for Class 11 Maths Chapter 1 Sets Ex 1.4 in Hindi

प्रश्न 4.
यदि A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {5, 6, 7, 8} और D = {7, 8, 9, 10}, तो निम्नलिखित ज्ञात कीजिए:
(i) A ∪ B
(ii) A ∪ C
(ii) B ∪ C
(iv) B ∪ D
(v) A ∪ B ∪ C
(vi) A ∪ B ∪D
(vii) B ∪ C ∪ D
हल:
(i) A ∪ B = {1, 2, 3, 4} ∪ {3, 4, 5, 6} = {1, 2, 3, 4, 5, 6}
(ii) A ∪ C = {1, 2, 3, 4} ∪ {5, 6, 7, 8} = {1, 2, 3, 4, 5, 6, 7, 8}
(iii) B ∪ C = {3, 4, 5, 6} ∪ {5, 6, 7, 8} = {3, 4, 5, 6, 7, 8}
(iv) B ∪ D = {3, 4, 5, 6} ∪ {7, 8, 9, 10} = {3,4, 5, 6, 7, 8, 9, 10}
(v) A ∪ B ∪C = ({1, 2, 3, 4} {3, 4, 5, 6}) ∪ {5, 6, 7, 8} = {1, 2, 3, 4, 5, 6} ∪ {5, 6, 7, 8} = {1, 2, 3, 4, 5, 6, 7, 8}.
(vi) A ∪ B ∪ D = ({1, 2, 3, 4} ∪ {3, 4, 5, 6}) ∪ {7, 8, 9, 10} = {1, 2, 3, 4, 5, 6} ∪ {7, 8, 9, 10} = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
(vii) B ∪ C ∪ D = ({3, 4, 5, 6} ∪ {5, 6, 7, 8}) ∪ {7, 8, 9, 10} = {3, 4, 5, 6, 7, 8} ∪ {7, 8, 9, 10) = {3, 4, 5, 6, 7, 8, 9, 10}

प्रश्न 5.
प्रश्न 1 में दिए प्रत्येक समुच्चय युग्म का सर्वनिष्ठ समुच्चय ज्ञात कीजिए:
हल:
(i) X ∩ Y= {1, 3, 5} ∩ {1, 2, 3} = {1, 3}
(ii) A ∩ B = {a, e, i, o, u} ∩ {a,b,c} = {a}.
(iii) A ∩ B = {3, 6, 9 …..} ∩ {1, 2, 3, 4, 5} = {3}.
(iv) A ∩ B = {2, 3, 4, 5, 6} ∩{7, 8, 9} = Φ
(v) A ∩ B = {1, 2, 3} ∩ Φ = 0

प्रश्न 6.
यदि A = {3, 5, 7, 9, 11}, B = {7, 9, 11, 13}, C = {11, 13, 15} और D = {15, 17}; तो निम्नलिखित ज्ञात कीजिए:
(i) A ∩ B
(ii) B ∩C
(iii) A ∩ C ∩D
(iv) A ∩C
(v) B ∩ D
(vi) Á ∩ (B ∪ C)
(vii) A ∩ D
(viii) A ∩(B ∪D)
(ix) (A ∩ B) ∩ (B ∪ C)
(x) (A ∪ D) ∩ (B ∪ C)
हल:
(i) A ∩ B = {3, 5, 7, 9, 11} ∩ {7, 9, 11, 13} = {7, 9, 11}
(ii) B ∩ C = {7, 9, 11, 13} ∩ {11, 13, 15} = {11, 13}
(iii) Á ∩ C ∩ D = ({3, 5, 7, 9, 11} ∩ {11, 13, 15}) ∩ {15, 17} = {11} ∩{15, 17} = Φ
(iv) A ∩ C = {3, 5, 7, 9, 11} ∩ {11, 13, 15} = {11}.
(v) B ∩ D = {7, 9, 11, 13} ∩ {15, 17} = Φ
(vi) A ∩ (B ∪ C) = {3, 5, 7, 9, 11} ∩ ({7, 9, 11, 13} ∪ {11, 13, 15}) = {3, 5, 7, 9, 11} ∩ {7, 9, 11, 13, 15} = {7, 9, 11}.
(vii) A ∩ D = {3, 5, 7, 9, 11} ∩ {15, 17} = Φ
(viii) A ∩(B ∪D) = {3, 5, 7, 9, 11} ∩{7, 9, 11, 13} ∪{15, 17}) = {3, 5, 7, 9, 11} ∩ {7, 9, 11, 13, 15, 17} = {7, 9, 11).
(ix) A ∩ B = {3, 5, 7, 9, 11} ∩ {7, 9, 11, 13} = {7, 9, 11}
B ∪ C = {7, 9, 11, 13} ∪ {11, 13, 15) = {7, 9, 11, 13, 15).
(A ∩ B) ∩ (B ∪ C) = {7, 9, 11} ∩ {7, 9, 11, 13, 15} = {7, 9, 11}.
(x) A ∪ D = {3, 5, 7, 9, 11} ∪ {15, 17} = {3, 5, 7, 9, 11, 15, 17}
B ∪ C = {7, 9, 11, 13} ∪ {11, 13, 15} = {7, 9, 11, 13, 15}
(A ∪ D) ∩ (B ∪ C) = {3, 5, 7, 9, 11, 15, 17} ∩ {7, 9, 11, 13, 15} = {7, 9, 11, 15}

प्रश्न 7.
यदि A = {x : x एक प्राकृत संख्या है}, B = {x : x एक सम प्राकृत संख्या है} C = {x : x एक विषम प्राकृत संख्या है}, D = {x : एक अभाज्य संख्या है} तो निम्नलिखित को ज्ञात कीजिए:
(i) A ∩ B
(ii) A ∩C
(iii) A ∩ D
(iv) B ∩C
(v) B ∩D
(vi) C ∩ D
हल:
A = {x : x एक प्राकृत संख्या है} = {1, 2, 3, 4……} B = {x : x एक समं प्राकृत संख्या है} = {2, 4, 6, 8…} C = {x : x एक विषम प्राकृत संख्या है} = {1, 3, 5, 7…} D = {x : x एक अभाज्य संख्या है} = {2, 3, 5, 7, 11….}
(i) A ∩ B = {1, 2, 3, 4….} ∩{2, 4, 6, 8….} = {2, 4, 6, 8….} = B
(ii) A ∩C = {1, 2, 3, 4……} ∩ {1, 3, 5, 7….} = {1, 3, 5, 7….} = C
(iii) A ∩D = {1, 2, 3, 4…} ∩ {2, 3, 5, 7…..} = {2, 3, 5, 7……} = D
(iv) B ∩ C = {2, 4, 6, 8…} ∩ {1, 3, 5, 7……} = Φ
(v) B ∩D = {2, 4, 6, 8…..} ∩ {2, 3, 5, 7…..} = {2}
(vi) C ∩D = {1, 3, 5, 7…..} ∩{2, 3, 5, 7, 11…….} = {3, 5, 7, 11, 13……} = {x : x एक विषम अभाज्य संख्या}

प्रश्न 8.
निम्नलिखित समुच्चय युग्मों में से कौन से युग्म असंयुक्त हैं?
(i) {1, 2, 3, 4} तथा {x : x एक प्राकृत संख्या है और 4 ≤ x ≤ 6}
(ii) {a, e, i, 0, u} तथा {c, d, e, f}
(iii) {x : x एक सम पूर्णांक है। और {x : x एक विषम पूर्णाक है।
हल:
(i) मान लीजिए E = {1, 2, 3, 4} F = {x : x एक प्राकृत संख्या और 4 ≤ x ≤ 6} = {4, 5, 6} अवयव 4, E और F दोनों समुच्चयों में है। अत: दोनों युग्म असंयुक्त नहीं हैं।
(ii) दिये हुए समुच्चयों में अवयव उभयनिष्ठ है। अत: यह असंयुक्त समुच्चय नहीं है।
(iii) मान लीजिए A = {x : x एक सम पूर्णांक हैं। = {….-4, -2, 0, 2, 4…} B = {x : x एक विषम पूर्णांक है} = {….-5, -3, -1, 1, 3, 5…..} A और B समुच्चयों में कोई भी अवयव उभयनिष्ठ नहीं है। अत: यह समुच्चय असंयुक्त है।

प्रश्न 9.
यदि A = {3, 6, 9, 12, 15, 18, 21}, B = {4, 8, 12, 16, 20}, C = {2, 4, 6, 8, 10, 12, 14, 16}, D = {5, 10, 15, 20}, तो निम्नलिखित को ज्ञात कीजिए:
(i) A – B
(ii) A – C
(iii) A – D
(iv) B – A
(v) C – A
(vi) D – A
(vii) B – C
(viii) B – D
(ix) C – B
(x) D – B
(xi) C – D
(xii) D – C
हल:
(i) A – B = {3, 6, 9, 12, 15, 18, 21} – {4, 8, 12, 16, 20} = {3, 6, 9, 15, 18, 21}
(ii) A – C = {3, 6, 9, 12, 15, 18, 21} – {2, 4, 6, 8, 10, 12, 14, 16} = {3, 9, 15, 18, 21}
(iii) A – D = {3, 6, 9, 12, 15, 18, 21} – {5, 10, 15, 20} = {3, 6, 9, 12, 18, 21}
(iv) B – A = {4, 8, 12, 16, 20} – {3, 6, 9, 12, 15, 18, 21} = {4, 8, 16, 20}
(v) C – A = {2, 4, 6, 8, 10, 12, 14, 16} – {3, 6, 9, 12, 15, 18, 21} = {2, 4, 8, 10, 14, 16}
(vi) D – A = {5, 10, 15, 20} – {3, 6, 9, 12, 15, 18, 21} = {5, 10, 20}
(vii) B – C = {4, 8, 12, 16, 20} – {2, 4, 6, 8, 10, 12, 14, 16} = {20}
(viii) B – D = {4, 8, 12, 16, 20} – {5, 10, 15, 20} = {4, 8, 12, 16}
(ix) C – B = {2, 4, 6, 8, 10, 12, 14, 16} – {4, 8, 12, 16, 20} = {2, 6, 10, 14}
(x) D – B = {5, 10, 15, 20} – {4, 8, 12, 16, 20} = {5, 10, 15}
(xi) C – D = {2, 4, 6, 8, 10, 12, 14, 16} – {5, 10, 15, 20} = {2, 4, 6, 8, 12, 14, 16}
(xii) D – C = {5, 10, 15, 20} – {2, 4, 6, 8, 10, 12, 14, 16} = {5, 15, 20}

प्रश्न 10.
यदि X = {a, b, c, d} औरै Y = {f, b, d, g} तो निम्नलिखित को ज्ञात कीजिए:
(i) X – Y
(ii) Y – X
(iii) X ∩ Y
हल:
(i) X – Y= {a, b, c, d} – {f, b, d, g} = {a, c}
(ii) Y – X = {f, b, d, g} – {a, b, c, d} = {f, g}
(iii) X ∩Y= {a, b, c, d} ∩ {f, b, d, g} = {b, d}

प्रश्न 11.
यदि R वास्तविक संख्याओं और Q परिमेय संख्याओं के समुच्चय हैं, तो R – Q क्या होगा?
हल:
R = {x : x एक वास्तविक संख्या है।} p= {x : x एक परिमेय संख्या है।}
R – Q = {x : x एक अपरिमेय संख्या है।} अत: यह अपरिमेय संख्याओं का समुच्चय है।

प्रश्न 12.
बताइए कि निम्नलिखित कथनों में से प्रत्येक सत्य है या असत्य? अपने उत्तर का औचित्य भी बताइए।
(i) {2, 3, 4, 5} तथा {3, 6} असंयुक्त समुच्चय हैं।
(ii) {a, e, i, 0, u} तथा {a, b, c, 4} असंयुक्त समुच्चय हैं।
(iii) {2, 6, 10, 14} तथा {3, 7, 11, 15} असंयुक्त समुच्चय हैं।
(iv) {2, 6, 10} तथा {3, 7, 11} असंयुक्त समुच्चय हैं।
हल:
(i) यह कथन सत्य नहीं है क्योंकि समुच्चय {2, 3, 4, 5} और {3, 6} में अवयव 3 उभयनिष्ठ है।
(ii) यह कथन सत्य नहीं है क्योंकि समुच्चय {a, e, i, o, u} और {a, b, c, d} में अवयव a उभयनिष्ठ है।
(iii) यह कथन सत्य है क्योंकि समुच्चय {2, 6, 10, 14} और {3, 7, 11, 15} में कोई अवयव उभयनिष्ठ नहीं है। अत: यह समुच्चय असंयुक्त है।
(iv) यह कथन सत्य है क्योंकि समुच्चय {2, 6, 10} और {3, 7, 11} में कोई अवयव उभयनिष्ठ नहीं है। अतः यह समुच्चय असंयुक्त है।

The post NCERT Solutions for Class 11 Maths Chapter 1 Sets Ex 1.4 appeared first on Learn CBSE.

NCERT Solutions for Class 11 Maths Chapter 1 Sets Ex 1.5

Get Free NCERT Solutions for Class 11 Maths Chapter 1 Sets Ex 1.5 PDF in Hindi and English Medium. Sets Class 11 Maths NCERT Solutions are extremely helpful while doing your homework. Sets Exercise 1.5 Class 11 Maths NCERT Solutions were prepared by Experienced LearnCBSE.in Teachers. Detailed answers of all the questions in Chapter 1 Class 11 Sets Ex 1.5 provided in NCERT Textbook.

Free download NCERT Solutions for Class 11 Maths Chapter 1 Sets Ex 1.5 PDF in Hindi Medium as well as in English Medium for CBSE, Uttarakhand, Bihar, MP Board, Gujarat Board, BIE, Intermediate and UP Board students, who are using NCERT Books based on updated CBSE Syllabus for the session 2019-20.

Q.1: Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9}
X = {1, 2, 3, 4, 5}
Y = {2, 4, 6} and
Z = {2, 4, 5, 6}.
Find the following sets:
(i).   X’
(ii).  Y’
(iii).  (X∪Y)′
(iv).  (X∪Z)′
(v).  (X′)‘
(vi).  (Y–Z)′

Solution:

Q.2: If U = {a, b, c, d, e, f, g, h}, find the complements of the given sets:
(i).  W = {a, b, c}
(ii).  X = {d, e, f, g}
(iii).  Y = {a, c, e, g}
(iv).  Z = {f, g, h, a}

Solution:

Q.3: Take natural numbers as the universal set. Write the complements of the given sets:
(i).  A = {y: y is an even natural number}
(ii).  B = {y: y is an odd natural number}
(iii).  C = {y: y is a positive multiple of 3}
(iv).  D = {y: y is a prime number}
(v).  E = {y: y is a natural number divisible by 3 and 5}
(vi).  F = {y: y is a perfect square}
(vii).  G = {y: y is perfect cube}
(viii).  H = {y: y + 5 = 8}
(ix).  I = {y: 2y + 5 = 9}
(x).  J = {y: y ≥ 7}
(xi).  K = {y: y ∈ N and 2y + 1 > 10}

Solution:

Q.4: If U = {1, 2, 3, 4, 5,6,7,8, 9}
A = {2, 4, 6, 8} and, B = {2, 3, 5, 7}.
Verify that:
(i).  (A∪B)′ = A′∩B′
(ii).  (A∩B)′ = A′∪B′

Solution:

Q.5: Draw the Venn diagrams for the following:
(i).  (A∪B)′
(ii).  A′∩B′
(iii).  (A∩B)′
(iv).  A′∪B′

Solution:

Q.6: Let U be the universal set that is the set of all triangles in a plane. If X is the set of all triangles with at least one angle different from 60∘, what is X’ ?

Solution:

Q.7: Complete the given statements using proper symbols:
(i).  A∪A′
(ii).  Ø ∩A
(iii).  A∩A′
(iv).  U′∩A

Solution:

NCERT Solutions for Class 11 Maths Chapter 1 Sets Ex 1.5 in Hindi

प्रश्न 3.
प्राकृत संख्याओं के समुच्चय को सार्वत्रिक समुच्चय मानते हुए, निम्नलिखित समुच्चयों के पूरक लिखिए:
(i) {x : x एक प्राकृत सम संख्या है।}
(ii) {x : x एक प्राकृत विषम संख्या है।}
(iii) {x : x संख्या 3 को एक धन गुणज है।}
(iv) {x : x एक अभाज्य संख्या है।}
(v) {x : x, 3 और 5 से विभाजित होने वाली एक संख्या है।}
(vi) {x : x एक पूर्ण वर्ग संख्या है।}
(vii) {x : x एक पूर्ण घन संख्या है।}
(viii){x : x + 5 = 8}
(ix) {x : 2x + 5 = 9}
(x) {x : x ≥ 7}
(xi) {x : x ∈ N और 2x + 1 > 10}
हल:
(i) {x : x एक विषम प्राकृत संख्या है।}
(ii) {x : एक सम संख्या है।}
(iii) {x : x ∈ N और x संख्या 3 का धन गुणज नहीं है।}
(iv) {x : x = 1 और x एक धन भाज्य संख्या है।}
(v) {x : x ∈ N और x, संख्या 3 व 5 किसी से भी विभाजित नहीं होती।}
(vi) {x : x ∈ N तथा x एक पूण वर्ग संख्या नहीं है।}
(vii) {x : x ∈ N तथा x एक पूर्ण वर्ग घन संख्या नहीं है।}
(viii) {x : x ∈ N तथा x ≠ 3}
(ix) {x : x ∈ N तथा x ≠ 2}
(x) {x : x ∈ N तथा x < 7}
(xi) {x : x ∈ N तथा x < }

प्रश्न 4.
यदि U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {2, 4, 6, 8} और B = {2, 3, 5, 7}, तो सत्यापित कीजिए कि:
(i) (A ∪ B)’ = A’ ∩ B’
(ii) (A ∩ B)’ = A’ ∪ B’
हल:
(i) A ∪ B = {2, 4, 6, 8} ∪{2, 3, 5, 7} = {2, 3, 4, 5, 6, 7, 8}
बायाँ पक्ष = (A ∪B)’ = U – (A ∪ B) = {1, 2, 3, 4, 5, 6, 7, 8, 9} – {2, 3, 4, 5, 6, 7, 8} = {1, 9}
A’ = U – A = {1, 2, 3, 4, 5, 6, 7, 8, 9} – {2, 4, 6, 8} = {1, 3, 5, 7, 9}
B’ = U – B = {1, 2, 3, 4, 5, 6, 7, 8, 9} – {2, 3, 5, 7} = {1, 4, 6, 8, 9}
दायाँ पक्ष = A’ ∩ B’ = {1, 3, 5, 7, 9} ∩ {1, 4, 6, 8, 9} = {1, 9}
अतः (A ∪ B)’ = A’ ∩ B’.
(ii) बायाँ पक्ष = (A ∩B)’
(A ∩B) = {2, 4, 6, 8} ∩ {2, 3, 5, 7} = {2}
(A ∩ B)’ = {1, 2, 3, 4, 5, 6, 7, 8, 9} – {2} = {1, 3, 4, 5, 6, 7, 8, 9}
दायाँ पक्ष : A’ ∪ B’ = {1, 3, 5, 7, 9} ∪ {1, 4, 6, 8, 9} = {1, 3, 4, 5, 6, 7, 8, 9}
अत: (A ∩ B)’ = A’ ∪ B’.

प्रश्न 5.
निम्नलिखित में से प्रत्येक के लिए उपयुक्त वेन आरेख खींचिए।
(i) (A ∪ B)’
(ii) A’ ∩ B’
(iii) (A ∩B)’
(iv) (A’ ∪ B’)
हल:
छायांकित क्षेत्र को निम्नलिखित समुच्चयों द्वारा दर्शाते हैं:

प्रश्न 6.
मान लीजिए कि किसी समतल में स्थित सभी त्रिभुजों का समुच्चय सार्वत्रिक समुच्चय U है। यदि A उन सभी त्रिभुजों का समुच्चय हैं जिनमें कम से कम एक कोण 60° से भिन्न है, तो A’ क्या है?
हल:
U = {x : समतल में एक त्रिभुज है।}
A = {x : x एक त्रिभुज जिसका कम से कम एक कोण 60° का न हो।}
A’ = {सभी समबाहु त्रिभुजों का समुच्चय है।}

प्रश्न 7.
निम्नलिखित कथनों को सत्य बनाने के लिए रिक्त स्थान भरिए:
(i) A ∪ A’ = ………..
(ii) Φ’ ∩ A = ………..
(iii) A ∩A’ = ………….
(iv) U’ ∩ A = …………
हल:
(i) A ∪ A’ = U
(ii) Φ’ ∩ A = U ∩ A = A
(iii) A ∩A’ = Φ
(iv) U’ ∩ A = Φ ∩ A = Φ

The post NCERT Solutions for Class 11 Maths Chapter 1 Sets Ex 1.5 appeared first on Learn CBSE.

NCERT Solutions for Class 11 Maths Chapter 1 Sets Ex 1.6

Get Free NCERT Solutions for Class 11 Maths Chapter 1 Sets Ex 1.6 PDF in Hindi and English Medium. Sets Class 11 Maths NCERT Solutions are extremely helpful while doing your homework. Sets Exercise 1.6 Class 11 Maths NCERT Solutions were prepared by Experienced LearnCBSE.in Teachers. Detailed answers of all the questions in Chapter 1 Class 11 Sets Ex 1.6 provided in NCERT Textbook.

Free download NCERT Solutions for Class 11 Maths Chapter 1 Sets Ex 1.6 PDF in Hindi Medium as well as in English Medium for CBSE, Uttarakhand, Bihar, MP Board, Gujarat Board, BIE, Intermediate and UP Board students, who are using NCERT Books based on updated CBSE Syllabus for the session 2019-20.

Q.1: If A and B are two sets such that n(A) = 16, n(B) = 24 and n(A∪B) = 39. Find n(A∩B).

Solution:

Q.2: If A and B are two sets such that A∪B has 17 elements, A has 9 elements and B has 14 elements. How many elements does A∩B have?

Solution:

Q.3: In a group there are 450 people, 200 speaks Hindi and 270 can speak English. How many people can speak both English and Hindi?

Solution:

Q.4: If X and Y are two sets such that X has 22 elements, Y has 34 elements, and n(X∩Y) has 10 elements, how many elements does n(X∪Y) have?

Solution:

Q.5: If A and B are two sets such that A has 45 elements, n (A ∩ B) has 15 elements and n (A ∪ B) has 70 elements, how many elements does B have?

Solution:

Q.6:There are 70 people, out of which 35 like tea, 55 like coffee, and each person likes at least one of the two beverages. How many people like both tea and coffee?

Solution:

Q.7: There are 70 students in a group, 35 like cricket, 15 like both tennis and cricket. How many like tennis only and not cricket? How many like tennis?

Solution:

Q.8: In a committee, 60 people speak French, 30 speak Spanish and 20 speak both Spanish and French. How many speak at least one of these two languages?

Solution:

NCERT Solutions for Class 11 Maths Chapter 1 Sets Ex 1.6 in Hindi

प्रश्न 4.
यदि S और T दो ऐसे समुच्चय हैं कि S में 21, T में 32 और S ∩ T में 11 अवयव हों तो S ∪T में कितने अवयव होंगे?
हल:
यहाँ n(S) = 21, n (T) = 32, n(S ∩T) = 11
n(S∪T) = n(S) + n(T) – n(S ∩ T) = 21 + 32 – 11 = 53 – 11 = 42.

प्रश्न 5.
यदि X और दो ऐसे समुच्चय हैं कि X में 40, X ∪Y में 60, और X ∩ Y में 10 अवयव हों, तो ? में कितने अवयव होंगे?
हल:
n(X) = 40, n(X ∪Y) = 60, n(X ∩ Y) = 10, n(Y) = ?
n(X ∪ Y) = n(X) + n(Y) – n (X ∩Y)
60 = 40 + n (Y) – 10
n(Y) = 60 – 40 + 10 = 30.

प्रश्न 6.
70 व्यक्तियों के समूह में 37 कॉफी, 52 चाय पसंद करते हैं और प्रत्येक व्यक्ति दोनों में से कम से कम एक पेय पसंद करता है, तो कितने व्यक्ति कॉफी और चाय दोनों पसंद करते हैं?
हल:
मान लिया C, कॉफी पीने वाले लोगों के समुच्चय को और T, चाय पीने वाले लोगों के समुच्चय हों, तब
n(C ∪T) = 70, n(C) = 37, n(T) = 52
n(C ∪T) = n (C) +n(T) – n(C ∩ T)
70 = 37 + 52 – n(C ∩T)
n(C ∩ T) = 37 + 52 -70 = 89 – 70 = 19.

प्रश्न 7.
65 व्यक्तियों के समूह में, 40 व्यक्ति क्रिकेट और 10 व्यक्ति क्रिकेट तथा टेनिस दोनों को पंसद करते हैं, तो कितने व्यक्ति केवल टेनिस को पंसद करते हैं किंतु क्रिकेट को नहीं? कितने व्यक्ति टेनिस को पंसद करते हैं?
हल:
मान लीजिए C, क्रिकेट पंसद करने वाले लोगों का समुच्चय है और T टेनिस पंसद करने वालों का समुच्चय हो, तब
n(C ∪T) = 65, n(C) = 40, n(C ∩T) = 10
हम जानते हैं कि
n(C ∪ T) = n(C) + n(T) – n(C ∩ T)
65 = 40 + n(T) – 10 = 30 + n(T)
n(T) = 65 – 30 = 35
केवल टेनिस पंसद करने वालो की संख्या = n(T) – n(C ∩T) = 35 – 10 = 25.
इस प्रकार टेनिस पंसद करने वालों की संख्या जो क्रिकेट पंसद नहीं करते = 25
अत: टेनिस पंसद करने वाले लोगों की संख्या = 35.

प्रश्न 8.
एक कमेटी में, 50 व्यक्ति फ्रेंच 20 व्यक्ति स्पेनिश और 10 व्यक्ति स्पेनिश और फ्रेंच दोनों ही भाषाओं को बोल सकते हैं। कितने व्यक्ति इन दोनों ही भाषाओं में से कम से कम एक भाषा बोल सकते हैं?
हल:
मान लीजिए फ्रांसीसी बोलने वाले लोगों के समुच्चय को F से तथा स्पैनिश बोलने वाले लोगों के समुच्चय का S से निरुपित किया हो, तब
n(F) = 50, n(S) = 20, n(F ∩S) = 10
अब, n(F ∪S) = n(F) + n (S) – n (F ∩S) = 50 + 20 – 10 = 60
कम से कम एक भाषा बोलने वाले लोगों की संख्या = 60.

The post NCERT Solutions for Class 11 Maths Chapter 1 Sets Ex 1.6 appeared first on Learn CBSE.

NCERT Solutions for Class 11 Maths Chapter 1 Sets Miscellaneous Exercise

Get Free NCERT Solutions for Class 11 Maths Chapter 1 Sets Miscellaneous Exercise PDF in Hindi and English Medium. Sets Class 11 Maths NCERT Solutions are extremely helpful while doing your homework. Sets Miscellaneous Exercise Class 11 Maths NCERT Solutions were prepared by Experienced LearnCBSE.in Teachers. Detailed answers of all the questions in Chapter 1 Class 11 Sets Miscellaneous Exercise provided in NCERT Textbook.

Free download NCERT Solutions for Class 11 Maths Chapter 1 Sets Miscellaneous Exercise PDF in Hindi Medium as well as in English Medium for CBSE, Uttarakhand, Bihar, MP Board, Gujarat Board, BIE, Intermediate and UP Board students, who are using NCERT Books based on updated CBSE Syllabus for the session 2019-20.

Solution 1:

Solution 2:

Solution 3:

Solution 4:

Solution 5:

Solution 6:

Solution 7:

Solution 8:

Solution 9:

Solution 10:

Solution 11:

Solution 12:

Solution 13:

Solution 14:

Solution 15:
  

Solution 16:

NCERT Solutions for Class 11 Maths Chapter 1 Sets Miscellaneous Exercise in Hindi

प्रश्न 3.
मान लीजिए A, B और Cऐसे समुच्चय हैं कि A ∪ B = A ∪ C तथा A ∩ B = A ∩ C, तो दर्शाइए कि B = C
हल:
दिया है:
A ∪ B = A ∪ C
(A ∪ B) ∩ C = (A ∪ C) ∩ C = C [(A ∪ C) ∩ C = C ]
(A ∩ C) ∩ (B ∩ C) = C
(A ∩ B) ∪ (B ∩ C) = C ….(i) [A ∩ C = A ∩ B = दिया है।]
A ∪ B = A ∪ C
(A ∪ B) ∩ B = (A ∪ C) ∩ B
B = (A ∪C) ∩ B = (A ∩ B) ∪ (C ∩ B)
या (A ∩ ) ∪ (B ∩ C) = B ……(ii)
(i) और (ii) से B = C प्राप्त होता है।

प्रश्न 4.
दिखाइए कि निम्नलिखित चार प्रतिबन्ध तुल्य हैं:
(i) A ⊂ B
(ii) A – B = Φ
(iii) A ∪ B = B
हल:
(i) A ⊂ B अर्थात् समुच्चय A के सभी अवयव B में हैं।
A – B = Φ अर्थात (i) ⇔ (ii)
(ii) A – B = Φ ⇔ समुच्चय A के सभी अवयव B में हैं।
A ∪ B = B
अर्थात (ii) ⇔ (iii)
(iii) A ∪ B = B ⇔ समुच्चय A के सभी अवयव B में है।
समुच्चय A और B मे समुच्चय A के अवयव उभयनिष्ठ है।
A ∩B = A
इससे स्पष्ट है सभी कथन समान हैं।

प्रश्न 5.
दिखाइए कि यदि A ⊂ B तो C – B ⊂ C – A.
हल:
मान लीजिए x ∈ C – B ⇒ x ∈ C पंरतु x ∈ B
दिया है: A ⊂ B ⇒ यदि x ∉ B ⇒ x ∉ A
अर्थात, x ∈ C और x ∉ A ⇒ x ∈ C – A
यहाँ हम पाते हैं कि
यदि x ∈ C – B तब x ∈ C – A
⇒ C – B ⊂ C – A.

प्रश्न 6.
मान लीजिए कि P(A) = P(B), सिद्ध कीजिए कि A = B.
हल:
मान लीजिए x, समुच्चय A का कोई अवयव है।
तब एक उपसमुच्चय X (मान लो) ऐसा होगा जिसमे x ∈ A जिसके अनुसार
X ⊂ A ⇒ X ∈ P(A)
X ∈ P(B) [P(A) = P(B)]
X ⊂ B या x ∈ B
अर्थात यदि
x ∈ A तब x ∈ B ⇒ A ∈ B …..(i)
y समुच्चय B का कोई अवयव हो, तब
समुच्चय B का कोई उपसमुच्चय Y (मान लो) होगा जिससे y ∈ Y
Y ⊂ B ⇒ Y ∈P(B)
Y ∈P(A) [P(A) = P(B)]
Y ⊂ A यदि y ∈ B तब y ∈ A
B ⊂ A ………(ii)
समीकरण (i) और (ii) से, हम पाते हैं।
A = B.

प्रश्न 7.
किन्हीं भी समुच्चयों A तक B के लिए क्या यह सत्य है कि P(A) ∪ P(B) = P(A ∪ B) ? अपने उत्तर का औचित्य बताइए।
हल:
मान लीजिए।
A = {a}, B = {b}, और A ∪ B = {a, b}
P(A) = {Φ, {a}}, P(B) = {Φ, {b}}
P(A) ∪ P(B) = {Φ, {4}, {5}} …(i)
अब A ∪ B = {a, b}
P(A ∪ B) = {Φ, {a}, {b}, {a, b}}
समी. (i) और (ii) से हम देखते हैं कि
अतः P(A) ∪ P(B) ≠ P(A ∪ B)

प्रश्न 8.
किन्हीं दो समुच्चयों A तथा B के लिए सिद्ध कीजिए कि
A = (A ∩ B) ∪ (A – B) और A ∪ (B – A) = A ∪ B.
हल:
(i) दायाँ पक्ष = (A ∩ B) ∪ (A – B)
= (A ∩ B) ∪ (A – B) [A – B = A ∩ B’]
= (A ∩ (B ∪ B’) (वितरण गुण से)
= A ∩ U (यहाँ U सार्वत्रिक समुच्चय)
= A
अतः (A ∩ B) ∪ (A – B) = A.
(ii) बायाँ पक्ष = A ∪ (B – A)
= A ∪ (B ∩ A’) [B – A = B ∩ A’]
= (A ∪ B) ∩ (A ∪ A’) (वितरण गुण से)
= (A ∪ B) ∩ U [यहाँ U सार्वत्रिक समुच्चय]
= A ∪ B
अतः : A ∪ (B – A) = A ∪ B

प्रश्न 9.
समुच्चयों के गुणधर्मों का प्रयोग करके सिद्ध कीजिए कि
(i) A ∪ (A ∩ B) = A
(ii) A ∩ (A ∪ B) = A.
हल:
(i) बायाँ पक्ष = A ∪ (A ∩ B)
= (A ∪ A) ∩ (A ∪ B) (वितरण गुण से)
= A ∩ (A ∪ B) (A ∪ A = A)
= A [A ⊂ A ∪ B]
A ∪ (A ∩ B) = A.
(ii) बायाँ पक्षु = A ∩ (A ∪ B)
= (A ∩ A) ∪ (A ∩ B) [वितरण गुण से]
= A ∪ (A ∩ B) [A ∩ A = A]
= A [A ∩ B ⊂ A]
अतः A ∩(A ∪ B) = A.

प्रश्न 10.
दिखलाइए कि A ∩ B = A ∩ C का तात्पर्य B = C आवश्यक रूप से नहीं होता।
हल:
मान लीजिए A = {1, 2}, B = {1, 7} तथा C = {1, 4} हो, तब
A ∩ B = {1, 2} ∩ {1, 7} = {1}
A ∩ C = {1, 2} ∩ {1, 4} = {1}
A ∩ B = A ∩ C
B ≠ C
यदि A ∩ B = A ∩ C तो आवश्यक नूह है कि B = C.

प्रश्न 11.
मान लीजिए कि A और B समुच्चय हैं। यदि किसी समुच्चय X के लिए A∪ X = B ∪ X = Φ तथा A ∪ X = B ∪ X तो सिद्ध कीजिए कि A = B.
हल:
दिया है A ∪ X = B ∪ X, जब कि X कोई समुच्चय है।
A ∩ (A ∪ X) = A ∩ (B ∪ X) [A ⊂ A ∪X, A ∩ (A ∪ X) = A]
A = A ∩ (B ∪ X)
= (A ∩ B) ∪ (A ∩ X) [वितरण गुण से]
= (A ∩ B) ∪ Φ (दिया है, A ∩ X = Φ
= A ∩ B
A ⊂ B ……(i)
A ∪ X = B ∪ X
B ∩(A ∪ X) = B ∩ (B ∪ X)
B ∩(A ∪ X) = B [B ⊂ B ∪ X]
(B ∩ A) ∪ (B ∩ X) = B [वितरण गुण से]
(B ∩ A) ∪ Φ = B [दिया है: B ∩ X = Φ]
(B ∩ A) = B
B ⊂ A …..(ii)
समी. (i) और (ii) से, हम पाते हैं कि A = B.

प्रश्न 12.
ऐसे समुच्चय A, B और C ज्ञात कीजिए ताकि A ∩ B, B ∩ C तथा A ∩ C आरिक्त समुच्चय हों और A ∩ B ∩ C = Φ.
हल:
मान लीजिए। A = {1, 2}, B = {2, 3}, C = {1, 3}
A ∩ B = {1, 2} ∩ {2, 3} = {2},
B ∩ C = {2, 3} ∩ {1, 3} = {3}
C ∩ A = {1, 3} ∩ {1, 2} = {1}
अतः A ∩ B, B ∩ C, C ∩ A रिक्त समुच्चय नहीं हैं।
A ∩ B ∩ C = (A ∩ B) ∩ C = {2} ∩ {1, 3} = Φ
इति सिद्धम्

प्रश्न 13.
किसी विद्यालय के 600 विद्यार्थियों के सर्वेक्षण से ज्ञात हुआ कि 150 विद्यार्थी चाय, 225 विद्यार्थी कॉफी तथा 100 विद्यार्थी चाय और कॉफी दोनों पीते हैं। ज्ञात कीजिए कि कितने विद्यार्थी न तो चाय पीते हैं और न कॉफी पीते हैं।
हल:
मान लीजिए 7 और C चाय तथा कॉफी पीने वाले विद्यार्थियों के समुच्चय हों, तब
n(T) = 150, n(C) = 225, n(T ∩ C) = 100
n(T ∪ C) = n(T) + n(C) – n(T ∩ C) = 150 + 225 – 100 = 275
= उन विद्यार्थियों की संख्या जो चाय या कॉफी पीते हैं या चाय और कॉफी दोनों पीते हैं।
विद्यार्थियों की कुल संख्या = 600
उन विद्यार्थियों की संख्या जो चाय या कॉफी कुछ भी नहीं पीते = 600 – 275 = 325.

प्रश्न 14.
विद्यार्थियों के समूह में, 100 विद्यार्थी हिन्दी, 50 विद्यार्थी अंग्रेजी तथा 25 विद्यार्थी दोनों भाषाओं को जानते हैं। विद्यार्थियों में से प्रत्येक या तो हिन्दी या अंग्रेजी जानता है। समूह में कुल कितने विद्यार्थी हैं?
हल:
पाना तथा क्रमशः हिन्दी और अंग्रेजी जानने वालों के समुच्चय हों, तब
n(H) = 100, n(E) = 50, n(H ∩ E) = 25
n(H ∪ E) = n(H) + n(E) – n(H ∩E) = 100 + 50 – 25 = 125
उन विद्यार्थियों की संख्या जो हिन्दी या अंग्रेजी जानते हैं = 125.

प्रश्न 15.
60 लोगों के सर्वेक्षण में पाया गया कि 25 लोग समाचार पत्र H, 26 लोग समाचार पत्र T, 26 लोग समाचार पत्र I, 9 लोग H तथा I दोनों, 11 लोग H तथा T दोनों, 8 लोग T तथा I दोनों और 3 लोग तीनों ही समाचार पत्र पढ़ते हैं, तो निम्नलिखित ज्ञात कीजिए:
(i) कम से कम एक समाचार पत्र पढ़ने वालों की संख्या।
(ii) ठीक ठीक केवल एक समाचार पत्र पढ़ने वालों की संख्या।
हल:
कुल लोगों की संख्या जिनका सर्वेक्षण किया गया = 60
H समाचार पत्र पढ़ने वालों की संख्या, n (H) = 25
T समाचार पत्र पढ़ने वालों की संख्या, n (T) = 26
I समाचार पत्र पढ़ने वालों की संख्या, n (I) = 26

H और I समाचार पत्र पढ़ने वालों की संख्या, n (H ∩ I) = 9
H और I समाचार पत्र पढ़ने वालों की संख्या, n (H ∩ T) = 11
T और I समाचार पत्र पढ़ने वालों की संख्या, n (T ∩ I) = 8
तीनों समाचार पत्र पढ़ने वालों की संख्या, n (H ∩ T ∩ I) = 3
H और I समाचार पत्र पढ़ने वाले तथा T समाचार पत्र न पढ़ने वालों की संख्या = 9 – 3 = 6
H और T समाचार पत्र पढ़ने वाले तथा I समाचार पत्र न पढ़ने वालों की संख्या = 11 – 3 = 8
T और I समाचार पत्र पढ़ने वाले तथा H समाचार पत्र न पढ़ने वालों की संख्या = 8 – 3 = 5
केवल H समाचार पत्र पढ़ने वालों की संख्या = 25 – 8 – 6 – 3 = 8
केवल T समाचार पत्र पढ़ने वालों की संख्या = 26 – 8 – 3 – 5 = 10
केवल I समाचार पत्रं पढ़ने वालों की संख्या = 26 – 6 – 3 – 5 = 12
कम से कम एकं समाचार पत्र पढ़ने वालों की संख्या = केवेल एक समाचार पत्र पढ़ने वालों की संख्या + केवल दो समाचार पत्र पढ़ने वालों की संख्या + तीनों समाचार पत्र पढ़ने वालों की संख्या = (8 + 10 + 12) + (8 + 6 + 5) + 3 = 30 + 19 + 3 = 52
वैकल्पिक विधि :
n(H ∪ T ∪ I) = n(H) + n(T) + n(I) – n(H ∩ T) – n(T ∩ I) – n(H∩I) + n(H ∩ T ∩ I)
= 25 + 26 + 26 – 11 – 8 – 9 + 3 = 77 – 28 + 3 = 80 – 28 = 52

(ii) केवल H और T समाचार पत्र पढ़ने वालों की संख्या = 11 – 3 = 8
केवल T और 1 समाचार पत्र पढ़ने वालों की संख्या = 8 – 3 = 5
केवल 1 और H समाचार पत्र पढ़ने वालों की संख्या = 9 – 3 = 6
तीनों समाचार पत्र पढ़ने वालों की संख्या = 3
केवल एक समाचार पत्र पढ़ने वालों की संख्या = 52 – (8 + 5 + 6 + 3) = 52 – 22 = 30.

प्रश्न 16.
एक सर्वेक्षण में पाया गया कि 21 लोग उत्पाद A, 26 लोग उत्पाद B, 29 लोग उत्पाद C पसंद करते हैं। यदि 14 लोग उत्पाद A तथा B, 12 लोग उत्पाद C तथा A, 14 लोग उत्पाद B तथा C और 8 लोग तीनों ही उत्पादों को पसंद करते हैं। ज्ञात कीजिए कि कितने लोग केवल उत्पाद C को पसंद करते हैं?
हल:
दिया है:
n(A) = 21,
n(B) = 26,
n(C) = 29
n(A ∩ B) = 14,
n(A ∩ C) = 12
n(B ∩ C) = 14,
n(A ∩ B ∩ C) = 8
n(A ∩ C) = 12,
P(A ∩ B ∩ C) = 8

n(केवल A और C) = 12 – 8 = 4
n(केवल B और C) = 14 – 8 = 6
n(केवल C) = n(C) – n (केवल A और C) – n (केवल B और C) – n(A ∩ B ∩ C) = 29 – 4 – 6 – 8 = 29 – 18 = 11. .

The post NCERT Solutions for Class 11 Maths Chapter 1 Sets Miscellaneous Exercise appeared first on Learn CBSE.

Water Class 7 Extra Questions Social Science Geography Chapter 5

NCERT Extra Questions for Class 7 Social Science Geography Chapter 5 Water

Prelude

Question 1.
When you think of water, what images came to your mind?
Answer:
Three states of water: solid, liquid and gaseous.

• Water running in rivers, canals, streams etc.
• Frozen and moving like glaciers.
• In the form of steam (evaporation)
• In the form of droplets (condensation)
• Falling as rainfall (Rainfall)
• As ground water/Water in taps.
• In the wells, ponds, pools etc

Question 2.
Where do the puddles of water vanish?
Answer:
Most of the water percolates into the ground.

• The sun’s heat evaporates the water as vapours. On cooling these vapours condenses and forms clouds
• Then this water may fall on land or sea as rain, snow or sleet.

Question 3.
What is water cycle?
Answer:
The continuous circulation of water between oceans, atmosphere and land is called water cycle.

Question 4.
What is a terrarium?
Answer:

• A terrarium is an artificial enclosure used for keeping small house plants.
• Our earth is like a terrarium.

Question 5.
Why is our earth like a terrarium?
Answer:
Our earth is like a terrarium as the water which existed centuries ago still exists. The water used to irrigate fields in Haryana might have in Amazon River centuries ago.

Question 6.
Name the sources of fresh water.
Answer:

• Rainfall, snow, rivers, ponds, springs and glaciers etc.
• Water from underground.

Question 7.
Why is sea water salty?
Answer:
There is a large amount of water in seas and oceans but it is salty or saline. It is because it contains a large amount of dissolved salts like sodium chloride or common salt.

Distribution of Water Bodies

Question 1.
Define salinity.
Answer:
Salinity is the amount of salt in grams present in 1000 grams of water. The average salinity of oceans is 35 parts per thousand (= 0.035%)

Question 2.
Discuss the distribution of water bodies.
Answer:

• Nearly 75% of the earth’s surface is covered with water.
• There is more water than land on the earth, still so many countries face water scarcity due to the fact that most of this water is salty or it is polluted beyond use.
• Moreover all the water on the earth is not available to us.
• The following table gives the distribution of water in percentage.

Question 3.
Why is water important to us? Suggest few ways to conserve water.
Answer:
Water is very necessary for us. Water alone can quench the thirst thirsty.
Water is needed for survival of plant and animal life.
Water is very essential and we should conserve it:

• By not wasting it during brushing, bathing, washing etc.
• By trapping the rain water by water shed development or rain water harvesting.
• By recycling water.
• By making check dams and bunds on the fields etc.

Question 4.
Swimmers can float in dead sea. Give reasons.
Answer:
Dead Sea in Israel has salinity of 45 parts per thousand and there the water is dense making it easier for swimmers to float.

Ocean Circulation

Question 1.
What is so magical or fascinating about sea?
Answer:
The continuous movement of ocean water is fascinating. The wet sand on beach, sea birds, the salty cool breeze, rhythmic movement of waves attracts one and all. On the other hand the water of ponds, lakes etc is calm.

Question 2.
Which movements occur in oceans?
Answer:The movements of oceans are categorized as tides, currents and waves.

Waves

Question 1.
What are sea waves?
Ans,
Sea Waves:

• When the water on the surface of the ocean rises and falls alternately, they are called waves.
• When we are playing throw ball on the beach and the ball falls into the water, it begins to go up and down.
• It is fun that the ball gets washed back to the shore by the waves.

Question 2.
How are Tsunamis formed? How do they cause destruction?
Answer:
Tsunami is a Japanese word meaning harbour waves.

• Winds blowing at high speed during a storm form huge waves.
• An earthquake, volcanic eruption or underwater landslides can shift large amount of ocean water.
• These tidal waves called Tsunami may be as high as 15 m. It travels at a speed of more than 700 km/hr.
• The areas near the coasts get submerged and it leads to earthquakes also.

Question 1.
Briefly write about the sequence of events leading to Tsunami of 2004 in the Indian Ocean.
Answer:
Tsunami of 26 December 2004 was the result of the earthquake that had its epicentre close to western boundary of Sumatra. It caused havoc in the Indian Ocean.

• Due to the earthquake measuring 9.0 on Richter scale the Indian plate went under Burma plate.
• The ocean floor was displaced by about 10-20 m. Huge mass of ocean water flowed to fill the gap.
• After thrusting the Indian plate and Burma plate, this water rushed back towards the coastline.
• Tsunami at the speed of 800km /hr washed some of the islands in the Indian Ocean.
• As the wave moved away from the epicentre of earthquake the speed declined 700-900km/hr to 70-80km/hr.
• Waves travelled up to a depth of 3 km from the coast:

Question 4.
What were the effects of the Tsunami?
Ans.
Tsunami caused severe destruction.

• Some of the islands of Indian Ocean were completely washed away.
• Indira point in Andaman got completely submerged.
• More than 10,000 people were killed and more than a lakh of houses were affected.
• Coastal areas of Tamil Nadu. Kerala, Puducherry, Andhra Pradesh and the Andaman and Nicobar islands were worst affected.

Question 5.
Can such an event be predicted in advance?
Answer:
Earthquake cannot be predicted in advance but it is possible to give 3-4 hour notice of potential Tsunami. Such system are there in Pacific Ocean but not in Indian Ocean. Seismic activity and Tsunami threat is higher in the Pacific.

Question 6.
Why was the Tsunami of December 26, 2004 very devastating?
Answer:

• The Tsunami that ravaged the South and South-east Asian coasts in December 2004 was the most devastating Tsunami in the last several hundred years.
• The large damage caused to life and property was primarily a result of the following:
  • lack of monitoring,
  • the early warning systems, and
  • lack of knowledge among the coast dwellers of the Indian ocean.
• The first indication that Tsunami is approaching was the rapid withdrawal of water from the coastal region.
• It was followed by destructive wave.
• When this happened on the coast, instead of people going to high ground, they started assembling at the coast to view the miracle.
• It resulted in a large casualty of curious onlookers when the gigantic wave-tsunami struck.

Tides

Question 1.
What are tides?
Answer:
The rhythmic rise and fall of ocean water twice a day is called a tide. When water rises to its highest level and covers much of the ocean it is called high tide. During low tide the water falls to its lowest level and recedes from the shore.

Question 2.
Explain Spring and Neap Tides.
Answer:
During the full moon and new moon days, the sun, the moon and the earth are in the same liiie.

• On this day the tides are highest.
• These tides are called Spring Tides.
• But when the moon is in its first and last quarter, the ocean waters get drawn in diagonally opposite direction by the gravitational pull of the sun and the earth.
• It results in low tides.
• These tides are called Neap Tides.

Question 3.
Describe the importance of tides to man.
Answer:

• High tides help in navigation.
  • They raise the water level close to the shores.
  • This helps the ships to arrive at the harbour more easily.
• The high tides also help in fishing.
  • Many more fish come closer to the shore during the high tides.
  • This enables fishermen to get a plentiful catch.
• The rise and fall of water due to tides is used to generate electricity in some places like the gulf of Khambant.

Ocean Currents

Question 1.
What are Ocean currents?
Answer:
Ocean currents are streams of water flowing constantly on the ocean surface in definite directions. They may be warm or cold currents:

• Warm currents originate near equator and move towards poles. They bring about warm temperatures over land surfaces, for example Gulf stream.
• Cold currents originate near poles and move towards tropical or lower latitudes. They bring about coolness over land surfaces, for example Labrador current.

Question 2.
Explain the advantages and disadvantages of ocean currents to man.
Answer:
The ocean currents influence the temperature conditions of the coastal areas.

• Warm currents increase the temperature over land surface.
• The areas where warm and cold currents meet, provide the best fishing grounds of the world.
• Seas Around Japan and the eastern coast of North America are such examples.
• The areas where a warm and cold current meet, also experience foggy weather making it difficult for navigation.

Question 3.
Seas around Japan are good fishing ground but difficult for navigation. Give reasons.
Answer:
Cold and warm currents meet and create good fishing grounds around Japan and Eastern Coast of North America.

Objective Type Questions

Question 1.
Fill in the blanks with appropriate words:
1. The major sources of fresh water are rivers and ………………….
2. About …………………% of water is present in the oceans and ………………….% as ice-caps.
3. The movements that occur in oceans are waves, …………… and ………………
4. ……………………… Point in the Andaman and Nicobar islands got submerged after the
tsunami of 2004.
5. High tides help in …………………..and fishing.
6. ………………………sea is the largest lake.
Ans.
1. springs and glaciers (Any one)
2. 97.3 and 02.0
3. tides and currents
4. Indira
5. navigation
6. Caspian.

Question 2.
State whether the given statements are true or false.
1. We have about 0.68% of water as ground water.
2. Ocean water is calm and still.
3. Tsunami can be caused by underwater landslides.
4. Tides are highest on a full or new moon day.
5. Cold currents carry water from lower latitudes to poles.
6 Tides help in generating electricity.
Answer:
1. True
2 False
3. True
4. True
5. False
6. True.

Question 3.
Match the contents of Column A with that of Column B

Answer:
1. (d)
2. (e)
3. (6)
4. (c)
5. (a).

Multiple Choice Questions

Question 1.
Which is the process through which water continuously changes its form?
(a) Water cycle
(b) Food cycle
(c) Rain
(d) All of these
Answer:
Water cycle

Question 2.
Which water is salty?
(a) River water
(6) Pond water
(c) Rain water
(d) Sea water
Answer:
Sea water

Question 3.
Which one of the following is an artificial enclosure for keeping small house plants?
(a) Terrarium
(6) Thermosphere
(c) Climate
(d) Evaporation
Answer:
Terrarium

Distribution of Water Bodies

Question 1.
Sea water contains
(a) 97.3% of salt
(6) 2% of salt
(c) 0.68% of salt
(d) 0.973% of salt
Answer:
97.3% of salt

Ocean Circulation

Question 1.
Which day of the year is celebrated as Water Day?
(a) 26 January
(b) 15 January
(c) 15 August
(d) 22 March
Answer:
22 March

Question 2.
The movements that occur in oceans can be broadly called
(a) wave
(b) circulation
(c) water cycle
(d) all of these
Answer:
circulation

Waves

Question 1.
Which is the Japanese word which means ‘Harbour Waves’?
(a) Tsunami
(b) Sea wave
(c) Ocean wave
(d) None of these
Answer:
Tsunami

Question 2.
When did Tsunami strike the Indian ocean?
(a) 26 December, 2004
(6) 26 December, 2005
(c) 26 December, 2006
(d) 26 December, 2007
Answer:
26 December, 2004

Question 3.
The largest Tsunami wave travels at the speed of
(a) more than 700 km per hour
(b) more than 500 km per hour
(c) more than 250 km per hour
(d) more than 100 km per hour
Answer:
more than 700 km per hour

Tides

Question 1.
The rhythmic rise and fall of ocean water twice in a day is known as
(a) tide
(b) wave
(c) Ocean currents
(d) None of these
Answer:
tide

Ocean Currents

Question 1.
The Labrador and Gulf stream are the examples of:
(a) Tides
(b) Ocean currents
(c) Tsunami
(d) Waves
Answer:
Ocean currents

Extra Questions for Class 7 Social Science

The post Water Class 7 Extra Questions Geography Chapter 5 appeared first on Learn CBSE.

NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities

Topics and Sub Topics in Class 11 Maths Chapter 6 Linear Inequalities:

NCERT Solutions for Class 11 Maths Chapter 6 Exercise 6.1

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More Resources for CBSE Class 11

• NCERT Solutions
• NCERT Solutions Class 11 Maths
• NCERT Solutions Class 11 Physics
• NCERT Solutions Class 11 Chemistry
• NCERT Solutions Class 11 Biology
• NCERT Solutions Class 11 Hindi
• NCERT Solutions Class 11 English
• NCERT Solutions Class 11 Business Studies
• NCERT Solutions Class 11 Accountancy
• NCERT Solutions Class 11 Psychology
• NCERT Solutions Class 11 Entrepreneurship
• NCERT Solutions Class 11 Indian Economic Development
• NCERT Solutions Class 11 Computer Science

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NCERT Solutions for Class 11 Maths Chapter 6 Exercise 6.3

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NCERT Solutions for Class 11 Maths Chapter 6 Miscellaneous Solutions

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NCERT Solutions for Class 11 Maths Chapter 6 .1 Linear Inequalities Ex 6 in Hindi

प्रश्न 1.
हल कीजिए : 24x < 100, जब
(i) x एक प्राकृत संख्या है।
(ii) x एक पूर्णांक है। 24x < 100
हल:
24x < 100
24 से दोनों पक्षों में भाग करने पर
x < अर्थात x <
(i) यदि x एक प्राकृत संख्या है तो हल {1, 2, 3, 4} है।
(ii) यदि x एक पूर्णांक संख्या है तो हल {…. -3, -2, -1, 0, 1, 2, 3, 4}.

प्रश्न 2.
हल कीजिए: 12x > 30, जब
(i) x एक प्राकृत संख्या है।
(ii) x एक पूर्णाक है।
हल:
– 12x > 30
-12 से दोनों पक्षों में भाग करने पर,
x < अर्थात x <
(i) यदि x प्राकृत संख्या है तो कोई हल नहीं है।
(ii) यदि x पूर्णाक संख्या है तो हल {….. -5, -4, -3} है।

प्रश्न 3.
हल कीजिए : 5x – 3 < 7, जब
(i) x एक पूर्णाक है।
(ii) x एक वास्तविक संख्या है।
हल:
5x – 3 < 7
दोनों पक्षों में 3 जोड़ने पर,
5x < 10
5 से भाग देने पर
x <
अर्थात x < 2
(i) यदि x एक पूर्णांक संख्या है तो हल {…. -2, -1, 0, 1}.
(ii) यदि x एक वास्तविक संख्या है तो हल x ∈ (-∞, 2).

प्रश्न 4.
हल कीजिए : 3x + 8 > 2, जब
(i) x एक पूर्णाक है।
(ii) एक वास्तविक संख्या है।
हल:
3x + 8 > 2
3x > 2 – 8 या 3x > -6 .
3 से भाग करने पर
x > या x > -2
(i) यदि x एक पूर्णांक संख्या है तो हल {-1, 0, 1, 2,….}.
(ii) यदि x एक वास्तविक संख्या है तो हल x ∈ (-2, ∞).

प्रश्न 5.
हल कीजिए : 4x + 3 < 6x + 7.
हल:
4x + 3 < 6x + 7
6x को बाएँ पक्ष में तथा 3 को दाएँ पक्ष में रखने पर,
4x – 6x < 7 – 3,
-2x < 4 -2 से भाग देने पर, x > या x > -2
दी हुई असमिका का हल है: x = (-2, ∞).

प्रश्न 6.
हल कीजिए : 3x – 7 > 5x – 1
हल:
3x -7 > 5x – 1
5x को बाएँ पक्ष में और 7 को दाएँ पक्ष में रखने पर,
3x – 5x > -1 + 7
या
-2x > 6
-2x से भाग देने पर।
x < -3
दी हुई असमिका का हल है x ∈ (-∞, – 3).

प्रश्न 7.
हल कीजिए : 3(x – 1) ≤ 2 (x – 3).
हल:
असमिका
3(x – 1) ≤ 2 (x – 3)
3x – 3 ≤ 2x – 6
2x को बाएँ पक्ष में और 3 को दाएँ पक्ष में रखने पर,
3x – 2 ≤ 3 – 6
x < – 3
हल है : x ∈ (-∞, – 3].

प्रश्न 8.
हल कीजिए : 3 (2 – x) ≥ 2 (1 – x).
हल:
दी हुई असमिका 3(2 – x) ≥ 2 (1 – x)
6 – 3x ≥ 2 – 2x
2x को बायीं ओर तथा 6 को दायीं ओर रखने पर,
2x – 3x ≥ 2 – 6
या
-x ≥ -4 या x ≤ 4
हल है : x ∈ (-∞, 4]

प्रश्न 13.
हल कीजिए : 2 (2x + 3) – 10 < 6 (x – 2)
हल:
दी हुई असमिका 2 (2x + 3) – 10 < 6 (x – 2)
4x + 6 – 10 < 6x – 12
6x को बायीं ओर तथा -4 को दार्थी ओर रखने पर,
4 – 6x < -12 + 4
-2x < -8 (-1) से गुणा करने पर, x > 4
हल है :
x ∈ (4, ∞)

प्रश्न 14.
हल कीजिए : 37 – (3x + 5) ≥ 9x – 8(x – 3).
हल:
दी हुई असमिका 37 – (3x + 5) ≥ 9x – 8(x – 3)
37 – 3x – 5 ≥ 9x – 8x + 24
– 3x + 32 ≥ x + 24
x को बायीं ओर तथा 32 को दायीं ओर रखने पर
-3x – x ≥ 24 – 32
– 4x ≥ – 8
(-1) से गुणा करने पर तथा 4 से भाग देने पर।
x ≤ या x ≤ 2
हल है: x ∈ (-∞, 2].

प्रश्न 17 से 20 तक की असमिकाओं को हल ज्ञात कीजिए तथा उन्हें संख्या रेखा पर आलेञ्चित कीजिए।

प्रश्न 17.
3x – 2 < 2x + 1
हल:
दी हुई असमिका . 3x – 2 < 2x + 1
2x को बायीं ओर तथा 2 को दायीं ओर रखने पर,
3x – 2x < 1 + 2
x < 3
हल है : x ∈ (-∞, 3).

प्रश्न 18.
5x – 3 ≥ 3x – 5.
हल:
दी हुई असमिका
5x -3 ≥ 3x – 5
3x को बायीं ओर तथा 3 को दायीं ओर रखने पर,
5x – 3x ≥ -5 + 3
2x ≥ -2
2 से भाग देने पर
x ≥ -1
हल है x ∈ [-1, ∞).

प्रश्न 19.
3 (1 – x) < 2 (x + 4).
हल:
दी हुई असमिका
3(1 – x) < 2(x + 4)
3 – 3x < 2x + 8
2x को बायीं ओर तथा 3 को दार्थी ओर रखने पर,
-3x – 2x < 8 – 3
– 5x < 5 -5 से भाग देने पर x > -1
हल है: x ∈ (-1, ∞)

प्रश्न 21.
रवि ने पहली दो एकक परीक्षा में 70 और 75 अंक प्राप्त किए हैं। वह न्यूनतम अंक ज्ञात कीजिए, जिसे वह तीसरी एकक परीक्षा में पाकर 60 अंक का न्यूनतम औसत प्राप्त कर सके।
हल:
मान लीजिए तीसरे एकक परीक्षा में x अंक प्राप्त किए।

प्रश्न 22.
किसी पाठ्यक्रम में ग्रेड A पाने के लिए एक व्यक्ति को सभी पाँच परीक्षाओं (प्रत्येक 100 अंकों में से) में 90 अंक या अधिक अंक का औसत प्राप्त करना चाहिए यदि सुनीता के प्रथम चार परीक्षाओं के प्राप्तांक 87, 92, 94 और 95 हों तो वह न्यूनतम अंक ज्ञात कीजिए जिसे पांचवीं परीक्षा में प्राप्त करके सुनीता उस पाठ्यक्रम में ग्रेड A पाएगी।

प्रश्न 23.
10 से कम क्रमागत विषम संख्याओं के ऐसे युग्म ज्ञात कीजिए जिनके योगफल 11 से अधिक हों।
हल:
मान लीजिए x और x + 2 दो विषम परिमेय संख्याएँ हैं।
x तथा x + 2 दोनों ही 10 से कम हैं।
⇒ x < 10 और x + 2 < 10 या x < 8 दोनों का योगं 11 से अधिक है। x + (x + 2) > 11
2x + 2 > 11 या 2x > 11 – 2
2x > 9 या x > या x > 4
अर्थात् यदि x = 5 हो, तब दूसरी संख्या = x + 2 = 7
इसी प्रकार यदि x = 7, तो x + 2 = 9
दूसरा युग्म (7, 9)
x = 9 नहीं हो सकता क्योंकि x + 2 = 11 > 10
अत: वांछित युग्म है (5, 7), 7, 9).

प्रश्न 24.
क्रमागत सर्म संख्याओं के ऐसे युग्म ज्ञात कीजिए जिनमें से प्रत्येक 5 से बड़े हों, तथा उनका योगफल 23 से कम हो।
हल:
मान लीजिए x और x + 2 दो सम संख्याएँ हैं।
x और x + 2 दोनों ही 5 से बड़ी है।
⇒ x > 5
x + (x + 2) < 23
2x + 2 < 23
2x < 23 – 2 = 21
2x < 21 या x <
यदि x = 10, x + 2 = 12 ⇒ x + (x + 2) < 23
इसी प्रकार (6, 8), (8, 10) युग्म भी दी हुई शर्त पूरी करते हैं। वांछित युग्म (6, 8), (8, 10), (10, 12).

प्रश्न 25.
एक त्रिभुज की सबसे बड़ी भुजा सबसे छोटी भुजा की तीन गुनी है तथा त्रिभुज की तीसरी भुजा सबसे बड़ी भुजा से 2 सेमी कम है। तीसरी भुजा की न्यूनतम लंबाई ज्ञात कीजिए जबकि त्रिभुज का परिमाप न्यूनतम 61 सेमी है।
हल:
मान लीजिए त्रिभुज की सबसे छोटी भुजा = x सेमी
सबसे बड़ी भुजा = 3x सेमी
तीसरी भुजा = 3x – 2 सेमी
प्रश्नानुसार
x + 3x + (3x – 2) ≥ 61
7x – 2 ≥ 61
7x ≥ 61 + 2 = 63
x ≥ 9
सबसे छोटी भुजा 9 सेमी है।

प्रश्न 26.
एक व्यक्ति 91 सेमी लंबे बोर्ड में से तीन लंबाईयाँ काटना चाहता है। दूसरी लंबाई सबसे छोटी लंबाई से 3 सेमी अधिक और तीसरी लंबाई सबसे छोटी लंबाई की दूनी है। सबसे छोटे बोर्ड की संभावित लंबाई क्या है, यदि तीसरा टुकड़ा दूसरे टुकड़े से कम से कम 5 सेमी अधिक लंबा हो ?
हल:
मान लीजिए कटे हुए सबसे छोटे बोर्ड की लंबाई = x सेमी
दूसरे कटे हुए बोर्ड की लम्बाई = x + 3
तीसरे कटे हुए बोर्ड की लम्बाई = 2x सेमी
दिया है कि
x + (x + 3) + 2x ≤ 91
4x + 3 ≤ 91
4x ≤ 91 – 3 = 88
4x ≤ 88
x ≤ 22 ……(1)
यह भी दिया गया है कि 2x ≥ (x + 3) + 5
2x ≥ x + 8
x ≥ 8 ……(2)
सबसे छोटे बोर्ड की लम्बाई कम से कम 8 सेमी हो और अधिक से अधिक 22 सेमी हो।

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NCERT Solutions for Class 11 Maths Chapter 3 Exercise 3.1 Trigonometric Functions in English as well as in Hindi free to use and download.

NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions

NCERT Solutions for Class 11 Maths Chapter 3 Exercise 3.1

Ex 3.1 Class 11 Question 1:

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More Resources for CBSE Class 11

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NCERT Solutions for Class 11 Maths Chapter 3 Exercise 3.2

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NCERT Solutions for Class 11 Maths Chapter 3 Exercise 3.3

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11 Maths Chapter 3 Exercise 3.3 Question 24:

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Class 11 Maths NCERT Solutions Chapter 3 Exercise 3.4

Trigonometric Functions class 11 Ex 3.4 Question 1:

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NCERT Solutions for Class 11 Maths Chapter 3 Miscellaneous Exercise

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Exercise 3.1

Q.1: Calculate the radian measurement of the given degree measurement:

(i). 25∘

(ii). 240∘

(iii). −47∘30‘

(iv). 520∘

Q.2: Calculate the degree measurement of the given degree measurement: [Use π = ]

(i)

(ii) -4

(iii)

(iv)

Q.3: In a minute, wheel makes 360 revolutions. Through how many radians does it turn in 1 second?

Q.4: Calculate the degree measurement of the angle subtended at the centre of a circle of radius 100 m by an arc of length 22 m.

Q.5: In a circle of diameter 40 m, the length of the chord 20 m. Find the length of minor arc of chord.

Q.6: In two circles, arcs which has same length subtended at an angle of 60∘ and 75∘ at the center. Calculate the ratio of their radii.

Q.7: Calculate the angle in radian through which a pendulum swings if the length is 75 cm and the tip describes an arc of length

(i) 10 cm

(ii) 15 cm

(iii) 21 cm

Exercise 3.2

Q.1: Calculate the values of five trigonometric func. if cosy = and y lies in 3^rd quadrant.

(i) sec y

(ii) sin y

(iii) cosec y

(iv) tan y

(v) cot y

Q.2: Calculate the other five trigonometric function if we are given the values for sin y = , where y lies in second quadrant.

Q.3: Find the values of other five trigonometric functions if coty=, where y lies in the third quadrant.

Q.4: Find the values of other five trigonometric if secy=, where y lies in the fourth quadrant.

Q.5: Find the values of other five trigonometric function if tan y = and y lies in second quadrant.

Q.6: Calculate the value of trigonometric function sin 765°.

Q.7: Calculate the value of trigonometric function cosec [-1410°]

Q.8: Calculate the value of the trigonometric function tan .

Q.9: Calculate the value of the trigonometric function sin .

Q.10: Calculate the value of the trigonometric function cot

Exercise 3.3

Q.1: Prove:

sin²+cos²–tan²=

Q.2: Prove:

2sin²+cosec²6cos²=

Q.3: Prove:

cot²+cosec+3tan²latex s=2]\frac { \pi }{ 6 } [/latex]=6

Q.4: Prove:

2sin²+2cos²+2sec²=10

Q.5: Calculate the value of:

(i). sin75∘

(ii). tan15∘

Q.6:Prove:

cos(–x)cos(–y)–sin(–x)sin(–y)=sin(x+y)

Q.7: Prove:

Q.8: Prove:

Q.9: Prove:

Q.10: Prove:

sin(n+1)xsin(n+2)x+cos(n+1)xcos(n+2)x=cosx

Q.11 Prove:

=−√2sinx

Q.12: Prove:

sin²6x–sin²4x=sin2x sin10x

Q.13: Prove:

cos²2x–cos²6x=sin4x sin8x

Q.14:Prove:

sin2x+2sin4x+sin6x=4cos²x sin4x

Q.15: Prove:

cot4x(sin5x+sin3x)=cotx(sin5x–sin3x)

Q.16: Prove:

Q.17: Prove:

Q.18: Prove:

Q.19: Prove:

Q.20: Prove:

Q.21: Prove:

Q.22: Prove:

cotxcot2x–cot2xcot3x–cot3xcotx=1

Q.23: Prove:

Q.24: Prove:

cos4x=1–8sin²xcos²x

Q.25: Prove:

cos6x=32cos⁶x–48cos⁴x+18cos²x−1

Exercise 3.4

Q.1: Find general solutions and the principle solutions of the given equation: tan x = √3

Q.2: Find general solutions and the principle solutions of the given equation: sec x = 2

Q.3: Find general solutions and the principle solutions of the given equation: cot = −√3

Q.4: Find general solutions and the principle solutions of the given equation: cosec x = -2

Q.5: Find the general solution of the given equation: cos 4x = cos 2x

Q.6: Find the general solution of the given equation: cos 3x + cos x – cos 2x = 0

Q.7: Find the general solution of the given equation: sin 2x + cos x = 0

Q.8: Find the general solution of the given equation: sec²2x=1–tan2x

Q.9: Find the general solution of the given equation: sin x + sin 3x + sin 5x = 0

Miscellaneous Exercise

Q.1: Prove that:

Q.2: Prove that:

(sin3x+sinx)sinx+(cos3x–cosx)cosx=0

Q-3: Prove that:

(cosx+cosy)²+(sinx–siny)²=4cos²

Q-4: Prove that:

(cosx–cosy)²+(sinx–siny)²=4sin²

Q-5: Prove that:

sinx+sin3x+sin5x+sin7x=4cosxcos2xcos4x

Q-6: Prove that:

Q-7: Show that: sin3y+sin2y–siny=4sinycoscos

Q-8: The value of tany= where y in in 2^nd quadrant then find out the values of sin,cos and tan.

Q-9: The value of cosy= where y in in 3^rd quadrant then find out the values of sin,cos and tan.

Q-10: The value of siny= where y in in 2^nd quadrant then find out the values of sin,cos and tan.

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NCERT Solutions for Class 11 Maths Chapter 10 Ex 10.2

NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.2 are part of NCERT Solutions for Class 11 Maths. Here we have given Class 11 Maths NCERT Solutions Straight Lines Exercise 10.2.

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Maths NCERT Solutions Class 11 Maths Chapter 10 Exercise.10.2

 Q-1. Write all the possible equations for the two axis, which is x- axis and y- axis.

Q-3. Write the equation for the line which passes through the point (0, 0) with having slope S.

Q-4. Write the equation for the line which passes through ( 3, 3√3 ) which is inclined on x- axis at an angle 75∘.

Q-5. Write the equation for the line which intersects x – axis at a distance 4 units away from the left side of the origin having slope -3.

Q-6. Write the equation for the line which intersects the y – axis at a distance 3 units above the origin which makes an angle 60∘ along the positive direction of the corresponding axis, i.e., x- axis.

Q-7. Write the equation of the line passing through the two points (-2, 2) and (3, -5).

Q-8. Write the equation for the line which is at a perpendicular distance of 7 units from the point (0, 0) and the perpendicular makes an angle of 45∘ along the positive x- axis.

Q-9. Consider a triangle ABC whose vertices are A (3, 2), B (-3, 4) and C (5, 6). Write the equation for the median through one of the vertex of the triangle say, C.

Q-10. Get the equation for the line which is passing through (-4, 5) and which is perpendicular to the line passing through two points (3, 6) and (-4, 7).

Q-11. Consider a line which is perpendicular to the line segment joining the two points (2, 0) and (3, 4) dividing it in 1 : p ratio. Find the equation for such a line.

Q-12. What will be the equation for the line which cuts off intercepts equally on the co-ordinate axes and which passes through the point (3, 4).

Q-13. A line is passing through (3, 3) and making intercepts on the coordinate axes. The sum of the two intercepts is 12. Find the equation of the line.

Q-15. What will be the equation of the line perpendicular to the line from the origin meets at       (-3, 10)?

Q-16. Consider a copper rod having length L (in centimeters) which is a linear function of the Celsius temperature which is C. Express L in terms of C, for an experiment. Assume that, L = 127.952 when C = 24, and L = 128.987 when C = 114.

Q-17. A milk store owner observed that, he can sell at least 1000 liters of milk every week at a price of Rs. 15/liter and also, 1240 liters of milk every week at a price of Rs. 17/liter. Consider a linear relation between the demand and estimated selling price, find how many liters would he will sell every week at a cost of Rs.18/liters?

Q-19. The point R (m, n) divides the line segment PQ in the ratio of 2: 3 between both the axes. What will be the equation of the line?

Q-20. Show that the three points (4, 1), (-3, -3) and (11, 5) are collinear by using the concept of the equation of a line.

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NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines

NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Miscellaneous Questions are part of NCERT Solutions for Class 11 Maths. Here we have given Class 11 Maths NCERT Solutions Straight Lines Ch 10 Miscellaneous Questions with Solutions.

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