MP Board Class 6th Maths Solutions Chapter 3 संख्याओं के साथ खेलना Ex 3.5

MP Board Class 6th Maths Solutions Chapter 3 संख्याओं के साथ खेलना Ex 3.5

पाठ्य-पुस्तक पृष्ठ संख्या # 66-67

प्रश्न 1.
निम्नलिखित में कौन-से कथन सत्य हैं ?
(a) यदि कोई संख्या 3 से विभाज्य है, तो वह 9 से भी विभाज्य होती है।
(b) यदि कोई संख्या 9 से विभाज्य है, तो वह 3 से भी अवश्य विभाज्य होगी।
(c) एक संख्या 18 से भी विभाज्य होती है, यदि वह 3 और 6 दोनों से विभाज्य हो।
(d) यदि एक संख्या 9 और 10 दोनों से विभाज्य हो, तो वह 90 से भी विभाज्य होगी।
(e) यदि दो संख्याएँ सह-अभाज्य हों, तो इनमें से कम-से-कम एक अवश्य ही अभाज्य संख्या होगी।
(f) 4 से विभाज्य सभी संख्याएँ 8 से भी अवश्य विभाज्य होनी चाहिए।
(g) 8 से विभाज्य सभी संख्याएँ 4 से विभाज्य होनी चाहिए।
(h) यदि कोई संख्या दो संख्याओं को अलग-अलग पूरा-पूरा विभाजित करती है, तो वह उनके योग को भी पूरा-पूरा विभाजित करेगी।
(i) यदि कोई संख्या दो संख्याओं के योग को पूरी तरह विभाजित करती है, तो वह उन दोनों संख्याओं को अलग-अलग भी विभाजित करेगी।
उत्तर-
(a) असत्य,
(b) सत्य,
(c) असत्य,
(d) सत्य,
(e) असत्य,
(f) असत्य,
(g) सत्य,
(h) सत्य,
(i) असत्य

प्रश्न 2.
यहाँ 60 के लिए दो भिन्न-भिन्न गुणनखण्ड वृक्ष दिए हैं। इनमें अज्ञात संख्याएँ लिखिए।
हल :
MP Board Class 6th Maths Solutions Chapter 3 संख्याओं के साथ खेलना Ex 3.5 image 1

प्रश्न 3.
एक भाज्य संख्या के अभाज्य गुणनखण्डन में किन गुणनखण्डों को सम्मिलित नहीं किया जाता है?
उत्तर-
1 और स्वयं संख्या को भाज्य संख्या के अभाज्य गुणनखण्डन में सम्मिलित नहीं किया जाता है।

MP Board Solutions

प्रश्न 4.
चार अंकों की सबसे बड़ी संख्या लिखिए और उसे अभाज्य गुणनखण्डन के रूप में व्यक्त कीजिए।
हल :
चार अंकों की सबसे बड़ी संख्या = 9999
MP Board Class 6th Maths Solutions Chapter 3 संख्याओं के साथ खेलना Ex 3.5 image 2
∴ 9999 = 3 x 3 x 11 x 101

प्रश्न 5.
पाँच अंकों की सबसे छोटी संख्या लिखिए और उसे अभाज्य गुणनखण्डन के रूप में व्यक्त कीजिए।
हल :
पाँच अंकों की सबसे छोटी संख्या = 10000
MP Board Class 6th Maths Solutions Chapter 3 संख्याओं के साथ खेलना Ex 3.5 image 3
∴ 10000 = 2 x 2 x 2 x 2 x 5 x 5 x 5 x 5

प्रश्न 6.
1729 के सभी अभाज्य गुणनखण्ड ज्ञात कीजिए और उन्हें आरोही क्रम में व्यवस्थित कीजिए। अब दो क्रमागत अभाज्य गुणनखण्डों में यदि कोई सम्बन्ध है तो लिखिए।
हल :
MP Board Class 6th Maths Solutions Chapter 3 संख्याओं के साथ खेलना Ex 3.5 image 4
∴1729 = 7 x 13 x 19
स्पष्ट है कि दो क्रमागत गुणनखण्डों में 6 का अन्तर है।

प्रश्न 7.
तीन क्रमागत संख्याओं का गुणनफल सदैव 6 से विभाज्य होता है। इस कथन को कुछ उदाहरणों की सहायता से स्पष्ट कीजिए।
हल :
तीन क्रमागत संख्याओं के गुणनफल
(i) 11 x 12 x 13 = 1716
गुणनफल के अंकों का योग = 1 + 7 + 1 + 6 = 15

(ii) 15 x 16 x 17 = 4080
गुणनफल के अंकों का योग = 4 + 0 + 8 + 0 = 12

(iii) 25 x 26 x 27 = 17550
गुणनफल के अंकों का योग = 1 + 7 + 5 + 5 + 0 = 18
(a) प्रत्येक गुणनफल में इकाई का अंक 6, 4 और 0 है अतः गुणनफल 2 से विभाज्य है।
(b) प्रत्येक गुणनफल के अंकों का योग 3 से विभाज्य है
∴2 और 3 सह-अभाज्य संख्याएँ हैं इसलिए 2 x 3 = 6
प्रत्येक गुणनफल को विभाजित करेगा।
∴अतः तीन क्रमागत संख्याओं का गुणनफल सदैव 6 से विभाज्य होता है।

प्रश्न 8.
दो क्रमागत विषम संख्याओं का योग 4 से विभाज्य होता है। कुछ उदाहरण लेकर इस कथन का सत्यापन कीजिए।
हल :
माना कि विषम संख्याओं का योग निम्न है
(i) 211 + 213 = 424
(ii) 405 + 407 = 812
(iii) 541 + 543 = 1084
(iv) 101 + 103 = 204
योगों के दायें से इकाई और दहाई के दो अंक क्रमश: 24, 12, 48 और 04 हैं जो कि 4 से विभाज्य हैं।
अत: दो क्रमागत विषम संख्याओं का योग 4 से विभाज्य होता है।

MP Board Solutions

प्रश्न 9.
निम्न में से किन व्यंजकों में अभाज्य गुणनखण्डन किए गए हैं :
(a) 24 = 2 x 3 x 4
(b) 56 = 1 x 7 x 2 x 2 x 2
(c) 70 = 2 x 5 x 7
(d) 54 = 2 x 3 x 9
हल :
(a) और (d) में क्रमशः 4 और 9 के अभाज्य गुणनखण्डन नहीं हैं।
∴(b) और (c) व्यंजकों में अभाज्य गुणनखण्डन किये गये हैं।

प्रश्न 10.
बिना भाग किए ज्ञात कीजिए कि क्या 25110 संख्या 45 से विभाज्य है।
[संकेत : 5 और 9 सह-अभाज्य संख्याएँ हैं। दी हुई संख्या की 5 और 9 से विभाज्यता की जाँच कीजिए।]
हल :
∵संख्या 25110 में इकाई के स्थान पर 0 है। अतः संख्या 25110, 5 से विभाज्य है।
पुनः संख्या के अंकों का योग = 2 + 5 + 1 + 1 + 0 = 9, जो कि 9 से विभाज्य है।
इसलिए संख्या 25110, 9 से विभाज्य है।
अतः संख्या 25110, 45 से विभाज्य है।

प्रश्न 11.
संख्या 18, 2 और 3 से विभाज्य है। यह 2 x 3 = 6 से भी विभाज्य है। इसी प्रकार एक संख्या 4 और 6 दोनों से विभाज्य है। क्या हम कह सकते हैं कि वह संख्या 4 x 6 = 24 से भी विभाज्य होगी। यदि नहीं, तो अपने उत्तर की पुष्टि के लिए एक उदाहरण दीजिए।
हल :
यह आवश्यक नहीं है कि जो संख्या 4 और 6 से विभाज्य होगी वह उनके गुणनफल 4 x 6 = 24 से भी विभाज्य होगी।
क्योंकि 4 और 6 सह-अभाज्य संख्याएँ नहीं हैं।
संख्या 36, 4 और 6 दोनों से विभाज्य है, परन्तु संख्या 36 संख्या 24 से विभाज्य नहीं है।

प्रश्न 12.
मैं चार भिन्न-भिन्न अभाज्य गुणनखण्डों वाली सबसे छोटी संख्या हूँ। क्या आप मुझे ज्ञात कर सकते
हल :
चार भिन्न-भिन्न अभाज्य संख्याएँ 2, 3, 5 और 7 हैं।
∴अभीष्ट संख्या = 2 x 3 x 5 x 7 = 210

MP Board Solutions

पाठ्य-पुस्तक पृष्ठ संख्या # 68

प्रयास कीजिए

प्रश्न 1.
निम्न का म. स. ज्ञात कीजिए :
(i) 24 और 36
(ii) 15, 25 और 30
(iii) 8 और 12
(iv) 12, 16 और 28
हल :
(i)
MP Board Class 6th Maths Solutions Chapter 3 संख्याओं के साथ खेलना Ex 3.5 image 5
इस प्रकार 24 = 2 x 2 x 2 x 3.
36 = 2 x 2 x 3 x 3
24 और 36 के सार्व गुणनखण्ड 2, 2 और 3 हैं।
अतः 24 और 36 का म. स. = 2 x 2 x 3 = 12

(ii) ∵15 = 3 x 5
25 = 5 x 5
30 = 2 x 3 x 5
∴ म. स. = 5

(iii) ∵8 = 2 x 2 x 2
12 = 2 x 2 x 3
∴म. स. = 2 x 2 =4

(iv) ∵12 = 2 x 2 x 3
16 = 2 x 2 x 2 x 2
28 = 2 x 2 x 7
∴म. स. = 2 x 2 = 4

MP Board Class 6th Maths Solutions

MP Board Class 6th Maths Solutions Chapter 3 संख्याओं के साथ खेलना Ex 3.4

MP Board Class 6th Maths Solutions Chapter 3 संख्याओं के साथ खेलना Ex 3.4

पाठ्य-पुस्तक पृष्ठ संख्या # 63

प्रश्नावली 3.4

प्रश्न 1.
निम्न के सार्व गुणनखण्ड ज्ञात कीजिए :
(a) 20 और 28
(b) 15 और 25
(c) 35 और 50
(d) 56 और 120
हल :
(a) 20 के सभी गुणनखण्ड
= 1, 2, 4, 5, 10, और 20 …(1)
28 के सभी गुणनखण्ड = 1, 2, 4, 7, 14 और 28 …(2)
∴20 और 28 के सार्व गुणनखण्ड = 1, 2 और 4

(b) 15 के सभी गुणनखण्ड = 1, 3, 5 और 15 …(1)
∴25 के सभी गुणनखण्ड = 1, 5 और 25 …(2)
∴15 और 25 के सार्व गुणनखण्ड = 1 और 5

(c) 35 के सभी गुणनखण्ड = 1, 5, 7 और 35 …(1)
50 के सभी गुणनखण्ड = 1, 2, 5, 10, 25 और 50 …(2)
∴35 और 50 के सार्व गुणनखण्ड = 1 और 5

(d) 56 सभी गुणनखण्ड = 1, 2, 4, 7, 8, 14, 28 और 56 ….(1)
120 के सभी गुणनखण्ड = 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60 और 120 …(2)
∴56 और 120 के सार्व गुणनखण्ड = 1, 2, 4, और 8

प्रश्न 2.
निम्न के सार्व गुणनखण्ड ज्ञात कीजिए :
(a) 4, 8 और 12
(b) 5, 15 और 25
हल :
(a) 4 के सभी गुणनखण्ड = 1, 2 और 4
8 के सभी गुणनखण्ड = 1, 2, 4 और 8
12 के सभी गुणनखण्ड = 1, 2, 3, 4, 6 और 12
∴4,8 और 12 के सार्व गुणनखण्ड = 1,2 और 4

(b) 5 के सभी गुणनखण्ड =1 और 5
15 के सभी गुणनखण्ड = 1, 3, 5 और 15
25 के सभी गुणनखण्ड = 1, 5 और 25
∴5, 15 और 25 के सार्व गुणनखण्ड = 1 और 5

प्रश्न 3.
निम्न के प्रथम तीन सार्व गुणज ज्ञात कीजिए :
(a) 6 और 8
(b) 12 और 18
हल :
(a) 6 के गुणज = 6, 12, 18, [24], 30, 36, 42, [48], 54, 60, 66, [72] ,…..
8 के गुणज = 8, 16, [24], 32, 40, 48, 56, 64, [72],….
∴6 और 8 के प्रथम तीन सार्व गुणज =24, 48 और 72

(b) 12 के गुणज = 12, 24, [36], 48, 60, [72], 84, 96, [108], 120,…..
18 के गुणज = 18, [36], 54, [72], 90, [108], 126,……
∴12 और 18 के प्रथम तीन सार्व गुणज
= 36, 72 और 108

MP Board Solutions

प्रश्न 4.
100 से छोटी ऐसी सभी संख्याएँ लिखिए जो 3 और 4 के सार्व गुणज हैं।
हल :
3 के गुणज = 3, 6, 9, [12], 15, 18, 21, 24, 27, 30, 33, [36], 39, 42, 45, [48], 51, 54, 57, [60], 63, 66, 69, [72], 75, 78, 81, [84], 87, 90, 93, [96], 99……
4 के गुणज = 4, 8, [12], 16, 20, [24], 28, 32, [36], 40, 44, [48], 52, 56, [60], 64, 68, [72], 76, 80, [84], 88, 92, [96] ,…..
∴3 और 4 के सार्व गुणज = 12, 24, 36,48, 60, 72, 84, 96,….

प्रश्न 5.
निम्नलिखित में से कौन-सी संख्याएँ सहअभाज्य हैं ?
(a) 18 और 35
(b) 15 और 37
(c) 30 और 415
(d) 17 और 68
(e) 216 और 215
(f) 81 और 16
हल :
(a) ∵18 के गुणनखण्ड = 1, 2, 3, 6, 9 और 18
35 के गुणनखण्ड = 1, 5, 7, और 35
चूँकि इनका सार्व गुणनखण्ड 1 है।
∴18 और 35 का 1 के अतिरिक्त सार्व गुणनखण्ड नहीं है।
अतः 18 और 35 सह-अभाज्य संख्याएँ हैं।

(b) ∵15 के गुणनखण्ड = 1, 3, 5 और 15
37 के गुणनखण्ड = 1 और 37
∴इनका सार्व गुणनखण्ड 1 है।
∴15 और 37 का 1 के अतिरिक्त सार्व गुणनखण्ड नहीं है।
अतः 15 और 37 सह-अभाज्य संख्याएँ हैं।

(c) ∵30 के गुणनखण्ड = 1, 2, 3, 5, 6, 10, 15 और 30
415 के गुणनखण्ड = 1, 5, 83 और 415
∴इनके सार्व गुणनखण्ड 1 और 5 हैं।
अत: 30 और 415 सह-अभाज्य संख्याएँ नहीं हैं।

(d) ∵17 के गुणनखण्ड = 1 और 17
68 के गुणनखण्ड = 1, 2, 4, 17, 34 और 68
∴17 और 68 के सार्व गुणनखण्ड = 1 और 17
अतः 17 और 68 सह-अभाज्य संख्याएँ नहीं हैं।

(e) ∵216 के गुणनखण्ड = 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108 और 216
215 के गुणनखण्ड = 1, 5, 43 और 215
∴216 और 215 के सार्व गुणनखण्ड = 1
अत: 216 और 215 सह-अभाज्य संख्याएँ हैं।

(f) ∵81 के गुणनखण्ड = 1, 3, 9, 27 और 81
16 के गुणनखण्ड = 1, 2, 4, 8 और 16
∴81 और 16 के सार्व गुणनखण्ड = 1
अत : 81 और 16 सह-अभाज्य संख्याएँ हैं।

प्रश्न 6.
एक संख्या 5 और 12 दोनों से विभाज्य है। किस अन्य संख्या से यह संख्या सदैव विभाजित होगी?
हल :
दी हुई संख्या 5 और 12 के गुणनफल से विभाजित होगी।
अभीष्ट संख्या = 5 x 12 = 60
अतः संख्या 60 से सदैव विभाज्य होगी।

MP Board Solutions

प्रश्न 7.
एक संख्या 12 से विभाज्य है। और कौन-सी संख्याएँ हैं जिनसे यह संख्या विभाज्य होगी?
हल :
12 के गुणनखण्ड = 1, 2, 3, 4, 6 और 12
∴संख्या 12 से विभाज्य है। इसलिए यह 12 के गुणनखण्डों से भी विभाज्य होगी।
अतः संख्या 2, 3, 4 और 6 से भी विभाज्य होगी।

पाठ्य-पुस्तक पृष्ठ संख्या # 65

प्रयास कीजिए

प्रश्न 1.
16, 28 और 38 के अभाज्य गुणनखण्डन लिखिए।
हल :
(i)
MP Board Class 6th Maths Solutions Chapter 3 संख्याओं के साथ खेलना Ex 3.4 image 1
∴16 के अभाज्य गुणनखण्ड = 2 x 2 x 2 x 2

(ii)
MP Board Class 6th Maths Solutions Chapter 3 संख्याओं के साथ खेलना Ex 3.4 image 2
∴28 के अभाज्य गुणनखण्डन = 2 x 2 x 7.

(iii)
MP Board Class 6th Maths Solutions Chapter 3 संख्याओं के साथ खेलना Ex 3.4 image 3
∴38 के अभाज्य गुणनखण्ड = 2 x 19

पाठ्य-पुस्तक पृष्ठ संख्या # 66

प्रश्न 1.
ऐसा ही निम्न संख्याएँ लेकर कीजिए :
(a) 8
(b) 12
हल :
MP Board Class 6th Maths Solutions Chapter 3 संख्याओं के साथ खेलना Ex 3.4 image 4

MP Board Class 6th Maths Solutions

MP Board Class 6th Social Science Solutions Chapter 8 The Realms of the Earth

MP Board Class 6th Social Science Solutions Chapter 8 The Realms of the Earth

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

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

Question 1.
Question (a)
How many realms of earth are there?
Answer:
There are three realms of earth.

Question (b)
What is meant by Lithosphere?
Answer:
The realm of the earth consisting of rocks, stones and soil is called lithosphere.

MP Board Solutions

Question (c)
What are mountains?
Answer:
Mountains are highly elevated lands with steep slopes. They are higher than the surrounding areas. They have high peaks and deep valleys.

Question (d)
Define Biosphere?
Answer:
The zone of island, water and air which contains all forms of life is called plain and a plateau.

Plain:

  1. Plains are mostly made of the slit, mud and sand carried by the rivers.
  2. The plains offer most favourable living condition to the human being.
  3. The plains are suitable for agriculture.

Plateau:

  1. Plateaus are moderately elevated lands with flat tops.
  2. The life in plateaus are not very comfortable.
  3. The plateaus are not suitable for agriculture.

MP Board Solutions

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

Question 2.
Question (a)
What is lithosphere? Describe its different forms?
Answer:
1. The realm of the earth consisting of rocks, stones and soil is called lithosphere.

2. The small part of land surrounded by water are called islands and large masses of land are called continents. The surface of the land is not even.

3. Some parts are plain, others are rigid and some are very much elevated or too low. According to the shape of these parts, they are called mountains, plateaus and plains. These shapes are found in all the continents.

Question (b)
What is biosphere? How organisms depend on each other in the eco system?
Answer:
1. There is a very narrow zone on Earth where land, water and air come in contact with each other. This is called biosphere. All the living things such as plants, animals, and human being exist only in this zone (the biosphere). So biosphere is of great significance for all of us.

2. There are ten lakh species of animals in the animal kingdom. It includes microscopic organisms to large animals like the elephant and the whale fish.

3.The organisms in the animal kingdom move from one place to the other. Three lakh species of plants are found in the plant kingdom. It includes microscopic algae to large trees.

MP Board Solutions

Question 3.
Give one term for the following:

  1. The mixture of gases that envelopes the earth.
  2. The large quantity of water collected in earth.
  3. The part of land which rise high above the surrounding area.
  4. The part of land which rise abruptly from the low land and stretch far.
  5. Low – lying and relatively flat stretchs of land.
  6. The zone made by the Lithosphere, Hydrosphere and Atmosphere.

Answer:

  1. Air
  2. Oceans
  3. Mountain
  4. Plateau
  5. Plains
  6. Biosphere.

Question 4.
Match the Column
MP Board Class 6th Social Science Solutions Chapter 8 The Realms of the Earth
Answer:
MP Board Class 6th Social Science Solutions Chapter 8 The Realms of the Earth

Question 5.
Fill in the blanks:

  1. The land part of the earth is called ………………
  2. Lithosphere, hydrosphere and atmosphere collectively form ………………..
  3. Antarctica is spread on the …………… part of the earth.
  4. The gas which is found in least quantity in the atmosphere is ……………..
  5. The things given to us by nature should be used for …………….

Answer:

  1. lithosphere
  2. environment
  3. southern
  4. carbon – dioxide
  5. human welfare.

MP Board Solutions

Project Work

Question 1.
Make clay models of mountain, plateau and plain?
Answer:
Please do with the help of your teacher.

Question 2.
Look at the oceans in a map of the world and write their names as per their size?
Answer:
Please do with the help of your teacher.

Question 3.
Show the following in the given map?

  1. Arctic Ocean
  2. Indian Ocean
  3. Australia
  4. North America
  5. Africa

Answer:
MP Board Class 6th Social Science Solutions Chapter 8 The Realms of the Earth

MP Board Class 6th Social Science Solutions

MP Board Class 6th Maths Solutions Chapter 4 आधारभूत ज्यामितीय अवधारणाएँ Ex 4.5

MP Board Class 6th Maths Solutions Chapter 4 आधारभूत ज्यामितीय अवधारणाएँ Ex 4.5

पाठ्य-पुस्तक पृष्ठ संख्या # 89

प्रश्न 1.
चतुर्भुज PQRS का एक रफ चित्र खींचिए। इसके विकर्ण खींचिए। क्या विकर्णों का प्रतिच्छेद बिन्दु चतुर्भुज के अभ्यन्तर में स्थित है या बहिर्भाग में स्थित है ?
हल :
(a) PQRS एक चतुर्भुज है।
MP Board Class 6th Maths Solutions Chapter 4 आधारभूत ज्यामितीय अवधारणाएँ Ex 4.5 image 1
(b) इसके विकर्ण \(\overline{P R}\) और \(\overline{Q S}\) हैं। इनका प्रतिच्छेद बिन्दु O चतुर्भज PQRS के अभ्यन्तर में स्थित है।

MP Board Solutions

प्रश्न 2.
चतुर्भुज KLMN का एक रफ चित्र खींचिए। बताइए:
(a) सम्मुख भुजाओं के दो युग्म
(b) सम्मुख कोणों के दो युग्म
(c) आसन्न भुजाओं के दो युग्म
(d) आसन्न कोणों के दो युग्म
हल:
MP Board Class 6th Maths Solutions Chapter 4 आधारभूत ज्यामितीय अवधारणाएँ Ex 4.5 image 2
(a) सम्मुख भुजाओं के दो युग्म- \(\overline{K L}, \overline{N M}\) और \(\overline{K N}, \overline{M L}\)
(b) सम्मुख कोणों के दो युग्म- ∠K, ∠M और ∠N, ∠L
(c) आसन्न भुजाओं के दो युग्म- \(\overline{K L}, \overline{K N}\) और \(\overline{N M}, \overline{M L}\) अथवा \(\overline{K L}, \overline{L M}\) और \(\overline{N M}, \overline{N K}\)
(d) आसन्न कोणों के दो युग्म- ∠K, ∠L और ∠M, ∠N अथवा ∠K, ∠N और ∠L, ∠M आदि।

MP Board Solutions

प्रश्न 3.
खोज कीजिए :
पट्टियाँ और इन्हें बाँधने की वस्तुएँ लेकर एक त्रिभुज बनाइए और एक चतुर्भुज बनाइए। त्रिभुज के किसी एक शीर्ष पर पट्टियों को अन्दर की ओर दबाने का प्रयत्न कीजिए। यही कार्य चतुर्भुज के लिए भी कीजिए। क्या त्रिभुज में कोई परिवर्तन आया ? क्या चतुर्भुज में कोई परिवर्तन हुआ? क्या त्रिभुज एक दृढ़ (rigid) आकृति है ? क्या कारण है कि विद्युत् टॉवरों (Electric Towers) जैसी संरचनाओं में त्रिभुजीय आकारों का प्रयोग किया जाता है; चतुर्भुजीय आकारों का नहीं ?
हल :

  1. त्रिभुज के किसी एक शीर्ष पर पट्टियों को अन्दर की ओर दबाने से त्रिभुज में कोई परिवर्तन नहीं हुआ जबकि चतुर्भुज के साथ ऐसा करने से उसमें परिवर्तन हुआ है।
  2. त्रिभुज एक दृढ़ आकृति है।
  3. विद्युत् टॉवरों जैसी संरचनाओं में त्रिभुजीय आकारों का प्रयोग इसलिए करते हैं, क्योंकि त्रिभुज का आकार अधिक दृढ़ होता है।

MP Board Class 6th Maths Solutions

MP Board Class 9th Social Science Solutions Chapter 4 India: Drainage System

MP Board Class 9th Social Science Solutions Chapter 4 India: Drainage System

MP Board Class 9th Social Science Chapter 4 Text Book Questions

Choose the Correct Answer:

Question 1.
River in its last stage form –
(a) Waterfall
(b) Flood plains
(c) Delta or Estuary
(d) Ox-Bow lake
Answer:
(d) Ox-Bow lake

Question 2.
Which of the following is not the characteristics of the rivers of Northern India?
(a) Less number of Waterfalls
(b) Used for transportation
(c) Meanders are not formed
(d) Receives water from snow and rainfall.
Answer:
(c) Meanders are not formed

Question 3.
Which of the following separates India and Sri Lanka?
(a) Gulf of Cambay
(b) Rann of Kutch
(c) Bay of Bengal
(d) Gulf of Mannar
Answer:
(a) Gulf of Cambay

Question 4.
Which of the following river is known as Dakshin Ganga?
(a) The Narmada
(b) The Krishna
(c) The Kaveri
(d) The Godavari
Answer:
(d) The Godavari

Question 5.
Which states are drained by river Krishna?
(a) Maharashtra, Karnataka, Andhra Pradesh
(b) Maharashtra, Orissa, Andhra Pradesh
(c) Maharashtra, Kerala, Tamil Nadu
(d) Madhya Pradesh, Chhattisagarh, Orissa
Answer:
(a) Maharashtra, Karnataka, Andhra Pradesh

Fill in the blank:

  1. The state of five rives is known as ……………..
  2. The river Ganga rises from ………………. glacier.
  3. The Narmada rises from the …………….. pleatue in Madhya Pradesh.
  4. Hirakund Dam is built on the river ………………
  5. Nagarjun Sagar Dam is built on the river ……………….

Answer:

  1. Punjab
  2. Gangotri
  3. Amarkantak
  4. The Mahanadi
  5. The Krishna

MP Board Solutions

MP Board Class 9th Social Science Chapter 4 Very Short Answer Type Questions

Question 1.
What do you mean by Drainage System?
Answer:
Drainage System means the river system of a particular area.

Question 2.
What do you mean by river capturing?
Answer:
When one river captures the water of the other river it is called river capturing.

Question 3.
Name four tributaries of river Ganga.
Answer:
Yamuna, Ghaghra, Gandak and Kosi.

Question 4.
Name five tributaries of river Indus.
Answer:
Jhelum, Chinab, Ravi, Beas and Satluj.

Question 5.
What are the different names of river Brahmaputra in Bangladesh?
Answer:
Padma and Meghana are the different names of river Brahmaputra in Bangladesh.

Question 6.
Name five major lakes of India.
Answer:
Wular lake, Chilka lake, Koleru lake, Pullicat lake, Lonar lake.

MP Board Solutions

Question 7.
Name two rivers which drain in Arabian sea.
Answer:
The Narmada and the Tapi.

Question 8.
Which place is known as the region of five rivers?
Answer:
Punjab is known as the region of five rivers.

MP Board Class 9th Social Science Chapter 4 Short Answer Type Questions

Question 1.
Explain the Indus river system.
Answer:
Indus river system comprises the Indus and its tributaries. The length of the Indus river is about 2900 km. It rises in Tibet near Mansarovar and flows towards west forming a beautiful 500 meters deep gorge in the Laddakh district of Jammu and Kashmir. From here it flows towards Southwest, enters Pakistan and finally joins the Arabian Sea. The five tributaries of Indus are Jhelum, Chmab, Ravi, Beas and Satluj. This region of five rivers is known as Punjab.

Question 2.
Describe the characteristics of the rivers of Northern India.
Answer:
The characteristics of the rivers of Northern India are:

  • The rivers of Northern India have their origin in Himalayas and the Northern slopes of Peninsular India.
  • Waterfalls are less.
  • They are navigable.
  • These rivers form deep, valleys.
  • These rivers form meanders River courses often shift.
  • Receive water from ice and snow.

Question 3.
How do rivers affect the economy? Explain.
Answer:
Rivers play an important role in the economy of our country. Alluvial plains formed by rivers are used for agriculture. Rivers provide fresh drinking water. In the ancient times villages and cities were located on the bank of the rivers. Religious and cultural Centers are located on the banks. Dams are built for hydro – electricity and irrigation.

Question 4.
Explain the location of adjoining seas of India?
Answer:
Indian Peninsula is surrounded by seas from three sides. In its south lies the Indian Ocean, Arabian sea in the west and Bay of Bengal in the east. Andaman Sea is in the east of Andaman Nicobar Islands. Gulf of Mannar separates India and Sri Lanka. Gulf of Cam-bay and Rann of Kutch are located in the coastal part of Gujarat.

MP Board Solutions

Question 5.
What is river pollution? How could river pollution be prevented?
Answer:
Effluents from industries and sewage from houses are discharged in the rivers. Dead animals are thrown in the rivers. All this pollute the rivers. Spread of Water Hyacinth also pollute the rivers. To overcome the river pollution, it is essential to stop discharging industrial effluents in the rivers. Water of sewage line should be purified. Rivers should be cleaned time – to – time. Public awareness regarding this problem is much more important.

MP Board Class 9th Social Science Chapter 4 Long Answer Type Questions

Question 1.
Describe the drainage system of Northern India.
Answer:
The rivers of Northern India receive water from rainfall as well as melting of snow from ice-capped mountains. As these rivers flow through high mountains they form deep valleys, gorges and waterfalls. In their nature stage deposition in the plains take place. They form meanders, ox-bow lake and flood plains in their middle and lower course. Three large rivers originate from Himalayas:

1. The Indus River System:
This system comprises the Indus and its tributaires. The length of the Indus river is about 2900 km. It rises in Tribet near Mansarovar and flows towards west forming a beautiful 500 meters deep gorge in the Laddakh district of Jammu and Kashmir. From here it flows towards southwest, enters Pakistan and finally joins the Arabian sea. The five tributaries of Indus are Jhelum, Chin’ab, Ravi, Beas and Satluj. This region of five rivers is known as Punjab.

2. The Gangas River System:
The length of river Ganga is more than 2500 km. Its source is near Gangotri. The Ganga enters the plains near Haridwar. Its main tributaries are Yamuna, Ghaghra, Gandak and Kosi. These rivers form a fertile flood plain. They form meanders and ox-bow lakes. Near Ambala a water divide separates the Ganga and the Indus drainage system.

The Ganga receives some of its tributaries like Chambal, Ken, Betwa, Son and Damodar from the peninsular pleteau. Big dams have been built on these rivers which are used for hydro – electricity and irrigation. Flowing southward it forms a delta and finally joins Bay of Bengal. The main stream of the Ganges enters Bangladesh and when it joins Brahmaputra river it is called Meghana.

3. The Brahmaputra River System:
It rises near the Mansarovar iake and the Kailash mountains. It flows parallel to Himalayas and enters Arunachal Pradesh. In India it flows for 1400 km. Its tributaries include Dibang, Luhit, Dhansiri, Kalang etc. River courses often shift during floods. River islands are also formed. It is known as Tsangpo in Tibet, Brahmaputra in India and Padma and Meghana in Bangladesh. It forms a large delta and finally drains into Bay of Bengal.

Question 2.
Compare the rivers of Northern and Southern India.
Answer:
Rivers of Northern India:

  • The rivers of Northern India have their origin in Himalayas and the Northern slopes of Peninsular India.
  • Waterfalls are less.
  • They are navigable.
  • These rivers form deep valleys.
  • These rivers form meanders.
  • Receive water from melting ice and snow.

Rivers of Southern India:

  • The rivers of Southern India have their origin in Western Ghats, Satpura and Peninsular Plateau.
  • Waterfalls are more.
  • They are not navigable.
  • They flow in broad valleys.
  • These rivers do not form meanders.
  • Flow of water depends only on monsoon rainfall.

MP Board Class 9th Social Science Solutions Chapter 4 India Drainage System - 1

Question 3.
What is the importance of rivers in the economy? Explain.
Answer:
Rivers play an important role in the economy of our country. They are the lifeline of a country’s existence. Right from the beginning of the human civilization we have seen that people began to live on the bank of rivers. All the civilizations flourished there. The primary cause for this was that it had been the most convenient and cheapest means of transport. So, the trade and commerce flourished on the bailk of rivers. Most of the industrial towns have been settled along the river banks.

Dams and canals built on the rivers help us in our agriculture, which is the backbone of a country. We produce hydro -electricity from river water. Thus we see that rivers play a significant role in the economy of a country. Hence they must be protected from being polluted at all cost.

MP Board Solutions

Questions related to Skill Development

Show the following in the outline map of India

  1. Nilgiri Mountains
  2. Narmada River
  3. Sardar Sarovar Dam
  4. Krishna River
  5. Hirakud Dam

Or

  1. Himalayan Mountain
  2. Satpura Ranges
  3. The Ganga Drainage System
  4. Chambal River
  5. Gandhi Sagar Dam

Project Work:
1. Students will prepare a model of river originating from Himalayas.
2. Prepare a model or chart of dams / canals or different projects made by man on the rivers and give a classroom presentation.
Answer:
Attempt yourself.

MP Board Class 9th Social Science Chapter 4 other important questions

Choose the correct answer:

Question 1.
The Ganga enters the plains near –
(a) Prayag
(b) Haridwar
(c) Rameshwaram
(d) Kurushetra
Answer:
(b) Haridwar

Question 2.
The two large westward flowing rivers are –
(a) Narmada and Ganga
(b) Tapi and Brahmaputra
(c) Narmada and Tapi
(d) Krishna and Indu.
Answer:
(c) Narmada and Tapi

Question 3.
Hirakund dam has been built on the river –
(a) Mahanadi
(b) Ganga
(c) Brahamputra
(d) Narmada.
Answer:
(a) Mahanadi

Question 4.
Sambhar Lake is in –
(a) Rajasthan
(b) Gujarat
(c) Maharashtra
(d) Utter Pradesh.
Answer:
(a) Rajasthan

Question 5.
Indian Peninsula is surrounded by seas from –
(a) Four sides
(b) Three sides
(c) Two sides
(d) None of the above.
Answer:
(b) Three sides

MP Board Solutions

Fill in the blank:

  1.  ……………… Lake is situated in Orissa a state.
  2. Four tributaries of river Ganga are Yamuna, Ghagra …………… and ……………..
  3. Narmada river originates from ………………… state.
  4. River of Northern India are less …………………….
  5. Sambhar Lake is in ………………..

Answer:

  1. Chilka
  2. Gandak, Kosi
  3. Madhya Pradesh
  4. Waterfalls
  5. Rajasthan.

MP Board Class 9th Social Science Chapter 4 Very Short Answer Type Questions

Question 1.
Which two factors form the drainage system?
Answer:
Amount of rainfall and topography form the drainage system.

Question 2.
What do you know about water divide?
Answer:
When we observe the river map of India we find that any highland like mountains separates two neighboring drainage basins. This highland is known as water divide.

Question 3.
In which two categories are the Indian rivers divided?
Answer:
The Indian rivers are divided in the following two categories:

  • Rivers of Himalayas
  • Rivers of Peninsula India

Question 4.
What is the main feature of the Himalayan rivers.
Answer:
The Himalayan rivers receive water throughout the year.

Question 5.
What is the length of the Indus river?
Answer:
The length of the Indus river is about 2900 km.

MP Board Solutions

Question 6.
Where does the Brahmaputra river system rise?
Answer:
The Brahmaputra river system rises near the Mansarovar Lake and the Kailash mountains.

Question 7.
Name the rivers of Peninsular India?
Answer:
Mahanadi, Godawari, Krishna and Kaveri.

Question 8.
Where does the Narmada river drain?
Answer:
The Narmada river drains in Madhya Pradesh and Gujarat.

Question 9.
Which is the largest river systems of the Peninsular India?
Answer:
The Godavari is the largest river system of the Peninsular India.

Question 10.
Name four tributaries of the Godavari?
Answer:
Wardha, Manjra, Venganga and Penganga.

MP Board Solutions

Question 11.
Why are lakes important?
Answer:
Lakes are important for tourism, fish farming / formation of salt etc.

MP Board Class 9th Social Science Chapter 4 Short Answer Type Questions

Question 1.
Describe the Ganga Drainage System.
Answer:
The length of river Ganga in more than 2500 km. Its source is near Gangotri. The Ganga enters the plains near Haridwar. Its main tributaries are Yamuna, Ghaghara, Gandak and Kosi. These rivers form a fertile flood plain. They form meanders and ox-bow lakes. A water divide separates the Ganga and the Indus drainage system near Ambala.

The Ganga receives some of its tributatries like Chambal, Ken, Betwa, Son and Damodar from the Peninsular Plateau. Big dams have been built on these rivers which are used for hydro – electricity and irrigation. Flowing southward it forms a delta and finally join Bay of Bengal.

Question 2.
What are the main features of the rivers of Peninsular India?
Answer:
The main features of the rivers of Peninsular India are:

  • They are seasonal.
  • They flow frown a dry area.
  • They do not form the plains.
  • Rivers of Peninsular India like Mahanadi, Godawari, Krishna and Kavari flow eastward and drain into Bay of Bengal. They form Delta.
  • The rivers flowing into the west of Western Ghats are small.
  • Narmada and Tapi, the two large westward flowing rivers, flow in a rift valley and forming a tidal mouth it joins Arabian Sea.

Question 3.
What are the main features of the rivers of Southern India?
Answer:
The main features of the rivers of Southern India are:

  • The rivers of Southern India have their origin in Western Ghats, Satpura and Peninsular Plateau.
  • Waterfalls are, more.
  • Not navigable.
  • They flow in broad valleys
  • Meanders are not formed.
  • Flow of water depends only on Monsoon rainfall.

Question 4.
Describe the important lakes of India.
Answer:
Wular lake is the glacial lake of Kashmir. There are few lakes in South India. They are the Lonar in Buldhana district of Maharashtra, the Ghilka in Orissa, the Koleru in Andhra Pradesh ahd the Pullicat in Tamil Nadu. Lakes formed due to glacial erosion in Uttrakhand are Nainital, Bhimtal and Rakshastal etc. Sambhar lake of Rajasthan is famous as salt-water lake.

MP Board Solutions

MP Board Class 9th Social Science Chapter 4 Long Answer Type Question

Question 1.
Describe the rivers of Peninsular India.
Answer:
The rivers of Peninsular India are:

  • The Narmada,
  • The Tapi
  • The Godavari,
  • The Mahanadi
  • The Krishna
  • The Kaveri.

1. The Narmada:
It rises from Amarkantak Plateau in Madhya Pradesh flowing 1312 km. through a rift valley and finally drains in the Arabian Sea. It drains Madhya Pradesh and Gujarat. It forms Dhuandhar fall in the marble rocks of Bheraghat near Jabalpur. Its tributaries are very small.

2. The Tapi:
It rises near Multai in Betul district in Satpura range of Madhya Pradesh. It is 724 km. long. It flows in Madhya Pradesh, Maharashtra and Gujarat and finally reaches Gulf of Cambay.

3. The Godavari:
It rises from Western Ghat near Nasik and flows for 1500 km in Orissa and Andhra Pradesh and drains in Bay of Bengal. Wardha, Manjra, Venganga and Penganga are its tributaries. It is the largest river system in the Peninusular India.

4. The Mahanadi:
It rises in Sihawa, a highland of Chhattisgarh. It is 858 km. long. Its drainage basin lies in Maharashtra, Chhattisgarh, Jharkhand and Orissa, Hirakud Dam is build on this river.

5. The Krishna:
It rises in Maharashtra near Mahabaleshwar. It is 1400 km. long. It flows in Maharashtra, Karnataka and Andhra Pradesh. Its Major tributaries are Koyna, Panchganga, Malprabha, Ghatphrabha, Bhima, Musi and Tungbhadra. Almati and Nagarjun Sagar Dam are built on this river.

6. The Kaveri:
It rises in the Brahmagiri hills in Co-org district. It is 60 km. long. Its tributaries are Hemavati, Amaravati and Bhavani.

MP Board Class 9th Social Science Solutions

MP Board Class 9th Social Science Solutions Chapter 3 India: Location and Physical Divisions

MP Board Class 9th Social Science Solutions Chapter 3 India: Location and Physical Divisions

MP Board Class 9th Social Science Chapter 3 Text Book Questions

Choose the Correct – Answer:

Question 1.
Standard time of India is calculated from –
(a) 72° E. longitude
(b) 80°30′ W. longitude
(c) 82°30′ E. longitude
(d) 8.5° E. longitude.
Answer:
(c) 82°30′ E. longitude

Question 2.
Tropic of cancer does not pass through which state of India?
(a) Gujarat
(b) Maharashtra
(c) Chhattisgarh
(d) Orissa.
Answer:
(b) Maharashtra

Question 3.
Largest Union Territory of India is –
(a) Andaman Nicobar Islands
(b) Dadra and Nagar Haveli
(c) Lakshadweep
(d) Pondicherry.
Answer:
(a) Andaman Nicobar Islands

Question 4.
Indian Peninsular Plateau is made of which type of rocks?
(a) Metamorphic
(b) Sedimentary
(c) Oldest rock
(d) Granite.
Answer:
(c) Oldest rock

MP Board Class 9th Social Science Chapter 3 Very Short Answer Type Questions

Question 1.
What are the different names of India?
Answer:
The different names of India are Aryavarta, Hindustan and Bharat.,

Question 2.
What is the area of India?
Answer:
The area of India is 3’2,87,263 km2.

Question 3.
How many States and Union territories are there in India?
Answer:
India is a union of 28 states and 7 union territories.

Question 4.
Name two neighboring island countries of India.
Answer:
Srilanka and Maldives.

MP Board Solutions

Question 5.
Name any two lakes situated on the East Coast of India.
Answer:
Chilka and Pullical Lakes.

Question 6.
Which islands of India are formed by Corals?
Answer:
Laksha dweep islands of India are formed by corals.

Question 7.
Name two important peaks of the Himalayan range.
Answer:
Mt. Everest and Kanchanjunga.

Question 8.
What is the West-East extent of India? .
Answer:
West – East extent of India is from 68°7′ West to 97°25′ East.

MP Board Class 9th Social Science Chapter 3 Short Answer Type Questions

Question 1.
Explain the importance of the geographical location of India?
Answer:
The geographical location of India gives it a marked advantage for international trade.

Question 2.
Describe the northern Plain of India.
Answer:
The Great Northern Plain extends from the Punjab Plain in the west to the Brahmaputra Valley in the east. This plain lies to the south of the Himalayas. This plain possesses the alluvial deposits of the Ganga, the Indus and the Satluj etc. These rivers are perennial ones and flow down from the Himalayas. The average elevation of this plain is less than 300 meters above sea-level. The Ganga forms the largest part of it.

This region has rich alluvial soil and abundant water-supply so the means of livelihood are easily available here, and the density of population is the highest. The Punjab Plain forms the other part of the Great Northern Plain. The Brahmaputra Valley in Assam forms’ the eastern part of the Great Northern Plain. It is narrower than the Ganga Plain. It is frequently flooded area.

Question 3.
Describe briefly the Southern Plateau.
Answer:
The Southern Plateau lies to the south of the Indogangetic plain. It is triangular in shape. It is bounded in the north by the Vindhyas and Satpura hills while its eastern and western boundaries are formed by the Eastern and Western Ghats. Its surface is uneven and rocky.

The soil is not as fertile as in the northern plain. Since the Southern Plateau is formed of hard igneous and metamorphic rocks, the soil is black and literate. It is not as fertile as the alluvial soil of north plains. The average height of Southern plateau is about 600 feet. This area comparatively receives less rainfall as it is surrounded by mountains from all around.

MP Board Solutions

Question 4.
What is the importance of Himalayas for India? Explain.
Answer:
Himalayas are of great importance to India. They not only provide natural frontiers for the country but protect us from the cold winds blowing from the Siberia. They cause rainfall in India and are the source of timber, herbs and many other useful products. Himalayan peaks are snow covered throughout the year.

As such they are the source of important rivers like Ganga, the Indus, the Brahmaputra. These rivers bring along them the rich fertile alluvial soil and deposit the same in the great Northern Plain. These rivers have been used for irrigation and Hyde power and are thus important renewable natural resources.

Question 5.
Differentiate between Bangar and Khadar land.

Bangar Land:

  • It is the upland of the Northern Plains made by older deposition. Pebbles are also found here.
  • Flood water does not reach here.
  • Water level is deep.
  • It extends mainly in Punjab and the plains of Uttar Pradesh

Khadar Land:

  • It is the lowland of the Northern Plains made by the newer alluvium.
  • This land is submerged in flood water.
  • Underground water level is high.
  • It extends in eastern Uttar Pradesh, Bihar and Bengal.

Question 6.
Describe briefly the east coastal plain.
Answer:
The eastern coastal plain extends in the delta region of rivers Mahanadi, Godavari, Krishna and Kaveri flowing in the Bay of Bengal. Fertile alluvial soil is found here. Chilka, Kolerio and Pullicat lakes are situated on this coast. The northern part of the east coast is known as the Northern Cir-cars and its southern part is called the Coromandel coast.

MP Board Class 9th Social Science Chapter 3 Long Answer Type Questions

Question 1.
Describe the geographical division of India.
Answer:
India can be divided into the following geographical divisions:

  1. The Northern Mountains
  2. The Great Northern Plains
  3. The Peninsular Plateau
  4. The Coastal Region
  5. Islands

1. The Northern Mountains:
The Himalayas in the north are the new fold mountains which extend from Kashmir to Arunachal Pradesh in the north of India. Their length is about 2400 km and width varies from 150 to 400 km. The Himalayas have three main ranges:

  1. The Greater Himalayas,
  2. The Middle Himalayas or the Himachal
  3. Shivalik Ranges.

1.The Creator Himalayas or the Inner Himalayas or Himadri:
The Greater Himalayas are series of ranges which are always snow-capped. These ranges contain several high peaks which exceed, 8,000 meters above sea level. Mount Everest is the highest peak (8848 km) among them. In addition to that the Nanga Parbat, Kanchanjunga, Nanda Devi, etc. are some other high peaks. As these ranges remain always covered with snow so they are also called ’Himadri.

2. The Middle Himalayas or the Himachal:
Parallel to the south of the Greater Himalayas lies the rangers known as Middle Himalaya or Himachal. The height of these mountains varies between 3700 meters to 4500 meters and average width is 50 km. The Kashmir Valley and the Kangra and Kullu Valleys of Himachal are situated in these ranges. Pirpanjal and Dhauladhar are important ranges of this area. Hill stations like Shimla, Mussoorie, Nainital and Darjeeling belong to Middle Himalayas.

3. Shivalik Ranges:
These are the foot-hill ranges of Himalayas. They have an average height of 600 meters above the sea level. These ranges are often discontinuous. They have gentle slopes towards the north and steep slopes towards the . south. They represent the latest phase of folding and uplifting of the Himalayas.

In addition to these ranges, tine Zaskar and Ladakh ranges in Kashmir and the Kailash range in Tibet lie beyond the Himalayas. To the North-Eastern side of India lie the Naga, the Mizo and the Lushai hills. These hills are eastern extension of the Himalayas.

2. The Great Northern Plains:
The Great Northern Plains extend from the Punjab Plains m the west to the Brahmaputra valley in the east. This plain lies to the south of the Himalayas. This plain possesses the alluvial deposits of the Ganga, the Indus and the Satluj, etc. These rivers are perennial ones and flow down from the Himalayas. The average elevation of this plain is less than 300 meters above sea-level. The Ganga forms the largest part of it.

This region has rich alluvial soil and abundant water supply. So the means of livelihood are easily available here and the density of population is the highest. The Punjab plains forms the other part of the Great Norhtem Plain. The Brahmaputra valley in Assam forms the eastern part of the Great Northern Plain. It is narrower than the Ganga Plain. It is frequently flood area.

MP Board Class 9th Social Science Solutions Chapter 3 India Location and Physical Divisions - 1

3. The Peninsular Plateau:
The Plateau has the central high lands in the north and the Deccan Plateau in the south. The Narmada Valley divides it into two major sub – divisions. Tire central high lands comprises the Malwa Plateau, the small plateau of Bundelkhand and the Chhotanagpur plateau. The hills of tire Eastern Ghats extend to the west of the Deccan Plateau.

The north western part of the Deccan Plateau in Maharashtra consists of an extensive ‘lava’ belt called the Deccan trap region. The rest of the Deccan Plateau consists of crystalline me tarn opine rocks The coastal plains lie both on the eastern and the western sides of the Deccan Plateau.

The Eastern Coastal Plain is broad. The alluvial delta plains of the Mahanadi, the Godavari, the Krishna and the Kavery are part of the Eastern Coastal Plains. The Western Coastal plain is, however, not so broad. In fact, the Peninsular Plateau is an old stable block or shield which consists of ancient crystalline rocks.

4. The Coastal Plains:
The Deccan Plateau is flanked by the narrow coastal plains along the Arabian Sea and the Bay of Bengal. The coastal plain on the western coast is narrow and uneven. The fast flowing rivers and streams dissect this strip at many places. It covers the plains of Gujarat in the north.

The eastern coastal plain is relatively wide and more level. It consists of some of the most fertile and well watered deltas of Krishna, Godavari, Mahanadi and Kaveri. The western coast has estuaries in the north and lagoons, the salt water lakes in the south particularly in Kerala.

5. Islands:
The coral islands off the coast of Kerala are Lakshdweep Island each having area of a few kilometers. This is a horse shoe form of island made by the continuous work of coral polyps. In the eastern parts lie Andaman and Nicobar islands in the Bay of Bengal. Some of these Islands are of volcanic origin and are fairly large in shape.

MP Board Class 9th Social Science Solutions Chapter 3 India Location and Physical Divisions - 2

Question 2.
Describe the location and extent of India.
Answer:
India is situated in Northern Hemisphere in the southern part of the continent Asia. Towards its south lies the Indian Ocean. Bay of Bengal is in the east and Arabian sea is in the west. The latitudinal extent of the main land of India is 8°4′ North to 37°6’ North and the longitudinal extent is from 68°7′ East to 97°25′ East. The Tropic of Cancer (23°30’N) divides the country into almost two equal parts.

82°30′ is the standard meridian for Indian Standard Time. Standard time for the country is calculated from the stairdard meridian. Apart from the main land Andaman Nicobar Islands in the Bay of Bengal and Lakshadweep in the Arabian sea are also part of India. Tropic of Cancer divides the country into almost two equal parts.

Less area of India is situated on the eastern part of the standard meridian. The western c-f the country is Gujarat and the eastern state is Arunachal Pradesh. The northern most state of India is Jammu and Kashmir and the southern most state is Tamilnadu. The extreme southern point of India is located in Andman and Nicobar Islands.

MP Board Class 9th Social Science Solutions Chapter 3 India Location and Physical Divisions - 3

India is bounded by Pakistan, Afghanistan in the north-west, China, Nepai and Bhutan in the north, Bangladesh and Myanmar in the east and Sri Lanka in the South. Palk Straight is between India and Sri Lanka. Coastal Boundaries of India , India is the seventh largest country in the world in regard to area. 2.42% area of the world is in India. India covers an area of 32,87,263 km2.

Question 3.
Describe the Himalayan Mountain Range.
Answer:
India can be divided into the following geographical divisions:

  1. The Northern Mountains
  2. The Great Northern Plains.
  3. The Peninsular Plateau
  4. The Coastal Region
  5. Islands.

1. The Northern Mountains:
The Himalyas in the north are the new fold mountains which extend from Kashmir to Arunachal Pradesh in the north of India. Their length is about 2400 km and width varies from 150 to 400 km. The Himalayas have three main ranges:

  1. The Greater Himalayas,
  2. The Middle Himalayas or the Himachal
  3. Shivalik Ranges.

1. The Greater Himalayas or the Inner Himalayas or Himadri:
The Greater Himalayas are series of ranges which are always snow-capped. These ranges contain several high peaks which exceed, 8,000 meters above sea level. Mount Everest is the highest peak (8848 km) among them. In addition to that the Nanga Parbat, Kanchanjunga, Nanda Devi, etc. are some other high peaks. As these ranges remain always covered with snow so they are also called ’Himadri.

2. The Middle Himalayas or the Himachal:
Parallel to the south of the Greater Himalayas lies the rangers known as Middle Himalaya or Himachal. The height of these mountains varies between 3700 meters to 4500 meters and average width is 50 km. The Kashmir Valley and the Kangra and Kullu Valleys of Himachal are situated in these ranges. Pirpanjal and Dhauladhar are important ranges of this area. Hill stations like Shimla, Mussoorie, Nainital and Darjeeling belong to Middle Himalayas.

3. Shivalik Ranges:
These are the foot-hill ranges of Himalayas. They have an average height of 600 meters above the sea level. These ranges are often discontinuous. They have gentle slopes towards the north and steep slopes towards the . south. They represent the latest phase of folding and uplifting of the Himalayas.

In addition to these ranges, tine Zaskar and Ladakh ranges in Kashmir and the Kailash range in Tibet lie beyond the Himalayas. To the North-Eastern side of India lie the Naga, the Mizo and the Lushai hills. These hills are eastern extension of the Himalayas.

2. The Great Northern Plains:
The Great Northern Plains extend from the Punjab Plains m the west to the Brahmaputra valley in the east. This plain lies to the south of the Himalayas. This plain possesses the alluvial deposits of the Ganga, the Indus and the Satluj, etc. These rivers are perennial ones and flow down from the Himalayas. The average elevation of this plain is less than 300 meters above sea-level. The Ganga forms the largest part of it.

This region has rich alluvial soil and abundant water supply. So the means of livelihood are easily available here and the density of population is the highest. The Punjab plains forms the other part of the Great Norhtem Plain. The Brahmaputra valley in Assam forms the eastern part of the Great Northern Plain. It is narrower than the Ganga Plain. It is frequently flood area.

3. The Peninsular Plateau:
The Peninsular Plateau has the central high lands in the north and the Deccan Plateau in the south. The Narmada Valley divides it into two major sub – divisions. Tire central high lands comprises the Malwa Plateau, the small plateau of Bundelkhand and the Chhotanagpur plateau. The hills of tire Eastern Ghats extend to the west of the Deccan Plateau.

The north western part of the Deccan Plateau in Maharashtra consists of an extensive ‘lava’ belt called the Deccan trap region. The rest of the Deccan Plateau consists of crystalline me tarn opine rocks The coastal plains lie both on the eastern and the western sides of the Deccan Plateau.

The Eastern Coastal Plain is broad. The alluvial delta plains of the Mahanadi, the Godavari, the Krishna and the Kavery are part of the Eastern Coastal Plains. The Western Coastal plain is, however, not so broad. In fact, the Peninsular Plateau is an old stable block or shield which consists of ancient crystalline rocks.

4. The Coastal Plains:
The Deccan Plateau is flanked by the narrow coastal plains along the Arabian Sea and the Bay of Bengal. The coastal plain on the western coast is narrow and uneven. The fast flowing rivers and streams dissect this strip at many places. It covers the plains of Gujarat in the north. The eastern coastal plain is relatively wide and more level.

It consists of some of the most fertile and well watered deltas of Krishna, Godavari, Mahanadi and Kaveri. The western coast has estuaries in the north and lagoons, the salt water lakes in the south particulary in Kerala.

5. Islands:
The coral islands off the coast of Kerala are Laksh dweep Island each having area of a few kilometers. This is a horse shoe form of island made by the continuous work of coral polyps. In the eastern parts lie Andaman and Nicobar islands in the Bay of Bengal. Some of these Islands are of volcanic origin and are fairly large in shape.

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Question 4.
Describe the Peninsular Plateau.
Answer:
The Peninsular Plateau is a part of the oldest landmass the Gondwanaland. Its average height from the sea level is 600 to 900 meters. It is surrounded by seas from three sides and by landmass from one side so it is also known as Peninsular Plateau.

It is a triangular plateau with its base in the north, from Delhi, and Rajmahal Hills to northern plain. It is bordered by the Eastern Ghats in the east and by the Western Ghats in the west and Kanya Kumari is at the southern tip. Regarding area, the peninsular plateau is the largest physiographic division of the country.

The peninsular plateau is divided into two parts –

  1. The Central Highlands.
  2. The Deccan Plateau.

1. The Central Highlands:
The Northern part of the peninsular plateau comprises of plateaus, uncovered mountain ranges and low mountains. It is made up of hard igneous rocks. In the north-west it is flanked by the Aravallis, which are old folded mountains. On the southern boundary of the Central Highlands lies the Vindhyachal Mountains and it continues to the Kaimur range eastward. The Malwa Plateau lies in between Amrawati and Vindhyachal mountains.

This Plateau is drained by the Betwa, Parvati, Kali Sindh, Chambal and Mahi. The eastern part of the Central Highlands is known as Bundelkhand. The Baghelkhand Plateau is situated in the east of Kaimur Bhander hills. In the central part of Highlands Vindhyachal and Kaimur hills form an escarpment between the valleys of Narmada and Son rivers. The Chhotanagpur Pleteau of Jharkhand is also a part of this region. It is rich in minerals.

MP Board Class 9th Social Science Solutions Chapter 3 India Location and Physical Divisions - 4

2. The Deccan Plateau:
It extends from Satpura, Mahadev and Maikal hills in the north to the southern tip of peninsula. The north-western part of the plateau is mainly made up of volcanic deposit. The Western Ghats, from the western edge of the Deccan plateau, which run discontinuously from north to south almost parallel to the Arabian Sea. In Maharashtra and Karnataka they are called Shayadri.

The Ghats are crossed by three gaps:
Thalghat, Bhorghat and Palghat. They are called the Nilgiri’s in Tamilnadu and along Kerala and Tamilnadu borders, they are known as Anamalai and Cardamon Hills. Palghat gap separates Nilgiri and Anamalai Hills. The highest peak of Southern India, The Anai Mudi is in Palni Hills. The Eastern Ghat is 800 km. long. Its highest peak is Mahendragir.

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Question 5.
Write Short notes on Indian Coastal Region, Indian Islands.
Answer:
Indian Coastal Region:
The Peninsular Plateau of India from Kutch to Orisa is flanked by a narrow strip of coastal lowlands ‘or plains. Due to difference in their formation, this coastal plain is divided into two parts:

  1. The West Coastal Plain.
  2. The East Coastal Plains.

1. The West Coastal Plains:
extends from Gujarat to Kerala along with the Arabian Sea. These.plains are narrow and are known as Konkan in the north and Malabar in the south of Goa. The maximum width here is 40 km. Here the rivers are small and fast flowing. This region has very few major river like Narmada and Tapi. The rivers of the west coast form tire tidal mouth. The coastal plains of Kutch and Gujarat are arid.

2. The East Coastal Plain:
extends in the delta region of rivers Mahanadi, Godavari, Krishna and Kaveri flowing in the Bay of Bengal. Fertile alluvial soil is found here. Chilka, Koleru and Pullicat lakes are situated on this coast, the northern part of the East Coast is known as the Northern Circars and its southern part is called the Coromandel Coast.

Indian Islands:
The coral islands off the coast of Kerala are Lakshadweep Islands each having area of a few kilometers. This is a horse shoe form of island made by the continuous work of coral polyps. In the eastern parts lie the Andaman Nicobar Islands in the Bay of Bengal.

These islands are scattered in a large area and are far away from the main land. These islands are the peaks of sub merged hilly ranges. Some of them are of volcanic origin. There are nearly 300 known and unknown islands in Andaman and Nicobar covering an area of about 8249 km2.

Answer the following questions referring to the Map of India.

Question 1.
Latitude of Northern boundary of India.
Answer:
8°4′ North.

Question 2.
Name the states adjoining China.
Answer:
Arunachal Pradesh, Jammu & Kashmir, Himachal Pradesh, Uttarakhand and Sikkim.

Question 3.
Name the States through which Tropic of cancer pass through.
Answer:
Gujarat, Madhya Pradesh, Chhattishgarh, Jharkhand, West Bengal, Tripura and Mizoram.

Question 4.
Name the rivers which join Bay of Bengal.
Answer:
Ganga, Mahanadi, Krishna, Kaveri, Godavari etc.

Question 5.
Name any three gaps located in Himalayas.
Answer:
Shopkila, Nathula and Bomdila.

True or False:

  1. Indian ocean is situated in the south of India.
  2. The seven states of north-west are called “The Seven Sisters”
  3. The Andman and Nicobar Islands are situated in the Arabian Sea.
  4. Largest union territory of Indian is Andaman Nicobar Islands.
  5. The geographical location of India gives it a marked advantage for international trade.

Answer:

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

MP Board Class 9th Social Science Solutions Chapter 3 India Location and Physical Divisions - 5

Show the following in the outline map of India.

  1. Tropic of cancer and 82°30′ E. longitude.
  2. Union Territory – Chandigarh and Pondicherry.
  3. Bomdila and Nat-hula passes.
  4. Raipur and Bhopal
  5. Narmada River and Mahanadi.
  6. Himalayas and Vindhyans.

Answer:
Do yourself.

Project Work:
Divide the class in five groups and ask them to prepare a model and give presentation in the class on different physiographic features of India.

MP Board Solutions

MP Board Class 9th Social Science Chapter 3 Other Important Questions

Choose the correct answer:

Question 1.
The western state of India is
(a) Arunachal Pradesh
(b) Gujarat
(c) Madhya Pradesh.
(d) Kerala
Answer:
(b) Gujarat

Question 2.
The extreme southern point of India is located in –
(a) And man and Nicobar Islands
(b) Lakshadweep
(c) Kerala
(d) None of the above.
Answer:
(a) And man and Nicobar Islands

Question 3.
The width of the Himalayas varies from –
(a) 400 km in Kashmir.to 150 km in Arunachal Pradesh
(b) 200 km in Kashmir to 100 km in Arunachal Pradesh
(c) 500 km in Kashmir to 150 km in Arunachal Pradesh
(d) None of the above
Answer:
(a) 400 km in Kashmir.to 150 km in Arunachal: Pradesh.

Question 4.
Mt. Everest the highest peak in the world is located in –
(a) Sri Lanka
(b) Maldives
(c) Nepal
(d) Himachal
Answer:
(c) Nepal

Question 5.
The Chhotanagpur Plateau is in –
(a) Jharkhand
(b) Bihar
(c) Orissa
(d) Uttarakhand
Answer:
(a) Jharkhand

True or False.

  1. Tropic of cancer divides India into two equal parts.
  2. The highest mountain peak in India is Nanda Devi.
  3. The western state of Indian is Kerala.
  4. Largest union territory of Indian is Andaman Nicobar Islands.
  5. The geographical location of India gives it a marked advantage for international trade.

Answers:

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

MP Board Solutions

MP Board Class 9th Social Science Chapter 3 Very Short Answer Type Questions

Question 1.
In which hemisphere does India lie?
Answer:
India is located in the Northern Hemisphere.

Question 2.
Give Geographical location of India.
Answer:
India is situated in the north of Equator. In its south lies a great ocean called Indian Ocean. It is flanked by Pakistan in the West, Myanmar in the East, Bangladesh in East towards Bay of Bengal, China in the North and Sri Lanka in the South.

Question 3.
Name the countries that constitute Indian sub-continent.
Answer:
Pakistan in the north-west, India at the core, Nepal in the north, Bhutan in the north-east.

Question 4.
Name the standard meridian of India.
Answer:
82°5′ east longitude is the standard meridian of India.

Question 5.
Name the largest delta in the Indian sub-continent.
Answer:
The Sundar Ban Delta.

Question 6.
Which is the highest peak in India?
Answer:
The Kanchanjunga in Sikkim was regarded the highest peak in India till Sikkim was not merged with Indian territory,

Question 7.
What are known as the Great Himalayas or Inner- Himalayas or Himadri?
Answer:
The Northern most ranges are known as the Great Himalayas or Inner Himalayas or Himadri.

Question 8.
Name same important passes in Himalayas.
Answer:
Karakoram (Jammu and Kashmir),’Shopkila (Himachal Pradesh), Nathula (Sikkim), Bpmuila (Arunachal Pradesh).

MP Board Solutions

Question 9.
Define ‘Khadar’ and ‘Bangar’.
Answer:
The region where the flood water reaches every year is known as. ‘Khadar’ and where it does not reach is known as ‘Bangar’.

Question 10.
Where does the Malwa Plateau lie?
Answer:
The Malwa Plateau lies in between Amarawati and Vindhyachal mountains.

Question 11.
What is Maharashtra famous for?
Answer:
Maharashtra is famous for growing cotton.

Question 12.
Name some hill resorts located in plateau region.
Answer:
Ootakmand, Pachmarhi and Mahabaleshwar.

MP Board Class 9th Social Science Chapter 3 Short Answer Type Questions

Question 1.
What is a pass? Name some important passes of Indian Sub-continent?
Answer:
Gaps or openings in a mountain range which provide natural routes to pass through them are called Passes. Though Himalayas provide great barrier for the people to cross through from north but these passes made it possible to cross over. The Indian continent has the following important passes: The Karakoram Pass, The Shipkila Pass, The Nathula Pass, The Bomdila Pass.

MP Board Solutions

Question 2.
Why is Central plain called the ‘gift of Himalaya’?
Answer:
Central plain covers approximately one-fourth area of India which supports 45% population of the country. This plain is made up of the alluvial soil of Indus, Satluj, Ganga and Brahmputra rivers and have irrigation facilities. Therefore, it is called the ‘gift of Himalaya.

Question 3.
Describe briefly formation of the Northern Plains.
Answer:
Following the formation of the Himalayas, there started the work of mighty rivers and other agents of denudation. This Work or erosion continued for millions of years and ultimately resulting in deposition of silt. Thus, slowly and steadily were formed the Northern Plains. The work of erosion and deposition’ is still going on.

Question 4.
Distinguish between West Coastal Plain and East Coastal Plain.
Answer:
West Coastal Plain:

  1. They extend along the Arabian Coast.
  2. This plain is narrow.
  3. It is formed due to small but fast flowing rivers.
  4. Deltas are not found on this coast.

East Coastal Plain:

  1. They extend along the Bay of Bengal.
  2. This plain is wider.
  3. It is formed due to the deposition by the rivers Mahanadi, Godavari, Krishna and Kaveri.
  4. Deltas are found here.

MP Board Solutions

MP Board Class 9th Social Science Chapter 3 Long Answer Type Questions

Question 1.
Give an account of Deccan Plateau.
Answer:
The Deccan Plateau lies to the south of the Indogangetic plain. It is triangular in shape. It is bounded in the north by the Vindhyas and Satpura hills while its eastern and western boundaries are formed by the Eastern and Western Ghats. Its surface is uneven and rocky.

The soil is not as fertility as in the northern plain. Since the Deccan Plateau is formed of hard igneous and metamorphic rocks, the soil is black and literate. It is not as fertile as the alluvial soil of north plains. The average height of Deccan Plateau is about 600 feet.

This area comparatively receives less rainfall as it is surrounded by mountains from all around. The Krishna, the Godavari, the Mahanadi and Kaveri are the chief rivers. In this region, these rivers are swift and make waterfalls so they are not navigable. These rivers form big deltas at their mouth. The Deccan plateau has a coastal strip in the east and the west. The west coastal plain extends from Gujarat to Kerala.

The coastal strip along the Arabian Sea in the west is known as Konkan in the north and Malabar in the south. In the south, there are south salt water lakes called Lagoons. The coastal strip along the Bay of Bengal is broad and more leveled. The mountain ranges running from north to south along the Arabian sea coast has many names.

In Maharashtra and Karnataka they are called Sahyadri. Further in south, they are called the Nilgiries, in Tamil Nadu along the Kerala and Tamil Nadu border, they are known as Annamalai and Cardamon Hills. The Deccan Plateau is highest along its western edge and slopes towards the Bay of Bengal.

MP Board Class 9th Social Science Solutions

MP Board Class 6th Maths Solutions Chapter 4 आधारभूत ज्यामितीय अवधारणाएँ Ex 4.4

 MP Board Class 6th Maths Solutions Chapter 4 आधारभूत ज्यामितीय अवधारणाएँ Ex 4.4

पाठ्य-पुस्तक पृष्ठ संख्या # 88

प्रश्न 1.
त्रिभुज ABC का एक रफ चित्र खींचिए। इस त्रिभुज के अभ्यन्तर में एक बिन्दु P अंकित कीजिए और उसके बहिर्भाग में एक बिन्दु Q अंकित कीजिए। बिन्दु A इसके अभ्यन्तर में स्थित है या बहिर्भाग में स्थित है ?
हल :
संलग्न चित्र में ABC एक त्रिभुज है।
(i) बिन्दु P, ∆ABC के अभ्यन्तर में है।
(ii) बिन्दु Q त्रिभुज के बहिर्भाग में है।
(iii) नहीं, बिन्दु A न तो इसके अभ्यन्तर में स्थित है और न ही इसके बहिर्भाग में।

MP Board Class 6th Maths Solutions Chapter 4 आधारभूत ज्यामितीय अवधारणाएँ Ex 4.4 image 1

MP Board Solutions

प्रश्न 2.
(a) संलग्न आकृति में तीन त्रिभुजों की पहचान कीजिए।
(b) ज्ञात कोणों के नाम लिखिए।
(c) इसी आकृति में छः रेखाखण्डों के नाम लिखिए।
(d) किन दो त्रिभुजों में ∠B उभयनिष्ठ है ?

MP Board Class 6th Maths Solutions Chapter 4 आधारभूत ज्यामितीय अवधारणाएँ Ex 4.4 image 2

हल :
(a) तीन त्रिभुज- ∆ABC, ∆ABD, ∆ADC
(b) सात कोण- ∠B, ∠C, ∠BAC, ∠BAD, ∠CAD, ∠ADB, ∠ADC
(c) छः रेखाखण्ड- \(\overline{A B}, \overline{A C}, \overline{B C}, \overline{A D}, \overline{B D}, \overline{D C}\)
(d) ∆ABC और ∆ABD में ∠B उभयनिष्ठ है।

MP Board Class 6th Maths Solutions

MP Board Class 6th Maths Solutions Chapter 4 आधारभूत ज्यामितीय अवधारणाएँ Ex 4.3

MP Board Class 6th Maths Solutions Chapter 4 आधारभूत ज्यामितीय अवधारणाएँ Ex 4.3

पाठ्य-पुस्तक पृष्ठ संख्या # 87

प्रश्न 1.
नीचे दी आकृति में, कोणों के नाम लिखिए :
MP Board Class 6th Maths Solutions Chapter 4 आधारभूत ज्यामितीय अवधारणाएँ Ex 4.3 image 1
हल :
∠A अथवा ∠DAB ; ∠B अथवा ∠ABC ; ∠C अथवा ∠BCD; ∠D अथवा ∠CDA

प्रश्न 2.
संलग्न आकृति में, वे बिन्दु लिखिए जो
(a) ∠DOE के अभ्यन्तर में स्थित हैं।
(b) ∠EOF के बहिर्भाग में स्थित हैं।
(c) ∠EOF पर स्थित हैं।
MP Board Class 6th Maths Solutions Chapter 4 आधारभूत ज्यामितीय अवधारणाएँ Ex 4.3 image 2
हल :
(a) ∠DOE के अभ्यंतर में बिन्दु A है।
(b) ∠EOF के बहिर्भाग में बिन्दु A,C और D हैं।
(c) ∠EOF पर स्थित बिन्दु हैं, E,B,O और F।

MP Board Solutions

प्रश्न 3.
दो कोणों की रफ आकृतियाँ खींचिए जिससे
(a) उनमें एक बिन्दु उभयनिष्ठ हो।
(b) उनमें दो बिन्दु उभयनिष्ठ हों।
(c) उनमें तीन बिन्दु उभयनिष्ठ हों।
(d) उनमें चार बिन्दु उभयनिष्ठ हों।
(e) उनमें एक किरण उभयनिष्ठ हो।
हल :
(a) ∠PQS और ∠RQS में एक बिन्दु Q उभयनिष्ठ है।
MP Board Class 6th Maths Solutions Chapter 4 आधारभूत ज्यामितीय अवधारणाएँ Ex 4.3 image 3

(b) ∠AOB और ∠ODC में दो बिन्दु O तथा D उभयनिष्ठ है।
MP Board Class 6th Maths Solutions Chapter 4 आधारभूत ज्यामितीय अवधारणाएँ Ex 4.3 image 4

(c) ∠ABC और ∠QPR में तीन बिन्दु D, E तथा F उभयनिष्ठ हैं। .
MP Board Class 6th Maths Solutions Chapter 4 आधारभूत ज्यामितीय अवधारणाएँ Ex 4.3 image 5

(d) ∠BAC और ∠PQR में चार बिन्दु E, F G तथा H उभयनिष्ठ हैं।
MP Board Class 6th Maths Solutions Chapter 4 आधारभूत ज्यामितीय अवधारणाएँ Ex 4.3 image 6

(e) ∠RQS और ∠PQS में किरण QS उभयनिष्ठ है।
MP Board Class 6th Maths Solutions Chapter 4 आधारभूत ज्यामितीय अवधारणाएँ Ex 4.3 image 7

MP Board Class 6th Maths Solutions

MP Board Class 6th Maths Solutions Chapter 4 आधारभूत ज्यामितीय अवधारणाएँ Ex 4.1

MP Board Class 6th Maths Solutions Chapter 4 आधारभूत ज्यामितीय अवधारणाएँ Ex 4.1

पाठ्य-पुस्तक पृष्ठ संख्या # 80-81

प्रश्न 1.
संलग्न आकृति का प्रयोग करके, निम्न के नाम लिखिए :
(a) पाँच बिन्दु
(b) एक रेखा
(c) चार किरणें
(d) पाँच रेखाखण्ड
MP Board Class 6th Maths Solutions Chapter 4 आधारभूत ज्यामितीय अवधारणाएँ Ex 4.1 image 1
हल :
(a) पाँच बिन्दु-O, B, C, D, E
(b) एक रेखा-इसमें कई रेखाएँ हो सकती हैं \(\stackrel{\leftrightarrow}{D E}, \stackrel{\leftrightarrow}{D O}, \stackrel{\leftrightarrow}{D B}, \overrightarrow{E O}\) आदि।
(c) चार किरणें- \(\overrightarrow{D B}, \overrightarrow{D E}, \overrightarrow{E B}, \overrightarrow{O E}\) आदि (अनेक किरणें हो सकती हैं)।
(d) पाँच रेखाखण्ड- \(\overline{D E}, \overline{D O}, \overline{E O}, \overline{O B}, \overline{E B}\) आदि (अनेक रेखाखण्ड हो सकते हैं)।

प्रश्न 2.
संलग्न आकृति में दी हुई रेखा के सभी सम्भव प्रकारों के नाम लिखिए। आप इन चार बिन्दुओं में से किसी भी बिन्दु का प्रयोग कर सकते हैं।
MP Board Class 6th Maths Solutions Chapter 4 आधारभूत ज्यामितीय अवधारणाएँ Ex 4.1 image 2
हल :
रेखाओं को निम्न नामों से व्यक्त कर सकते हैं
\(\stackrel{\leftrightarrow}{AB}, \stackrel{\leftrightarrow}{AC}, \stackrel{\leftrightarrow}{AD}, \stackrel{\leftrightarrow}{BA}, \stackrel{\leftrightarrow}{BC}, \stackrel{\leftrightarrow}{BD}, \stackrel{\leftrightarrow}{CA}, \stackrel{\leftrightarrow}{CB}, \stackrel{\leftrightarrow}{CD}, \stackrel{\leftrightarrow}{DA}, \stackrel{\leftrightarrow}{DB}, \stackrel{\leftrightarrow}{DC}\)

प्रश्न 3.
संलग्न आकृति को देखकर नाम लिखिए :
(a) रेखाएँ जिसमें बिन्दु E सम्मिलित हैं
(b) A से होकर जाने वाली रेखा
(c) वह रेखा जिस पर O स्थित है
(d) प्रतिच्छेदी रेखाओं के दो युग्म
MP Board Class 6th Maths Solutions Chapter 4 आधारभूत ज्यामितीय अवधारणाएँ Ex 4.1 image 3
हल :
(a) ऐसी बहुत सी रेखाएँ है, जिनमें से एक है, \(\stackrel{\leftrightarrow}{EF}\) (या \(\stackrel{\leftrightarrow}{AE}\) )
(b) ऐसी बहुत सी रेखाएँ है, जिनमें से एक है, \(\stackrel{\leftrightarrow}{AE}\)
(c) \(\stackrel{\leftrightarrow}{CO}\) या \(\stackrel{\leftrightarrow}{CO}\)
(d) \(\stackrel{\leftrightarrow}{AE}\) और \(\stackrel{\leftrightarrow}{CO}\); \(\stackrel{\leftrightarrow}{AE}\) और \(\stackrel{\leftrightarrow}{EF}\)

MP Board Solutions

प्रश्न 4.
निम्नलिखित से होकर कितनी रेखाएँ खींची जा सकती हैं ?
(a) एक बिन्दु
(b) दो बिन्दु
हल :
(a) एक बिन्दु से अनगिनत रेखाएँ खींची जा सकती हैं।
(b) दो बिन्दुओं से केवल एक रेखा खींची जा सकती है।

प्रश्न 5.
निम्नलिखित स्थितियों में से प्रत्येक के लिए एक रफ (Rough) आकृति बनाइए और चित रूप से उसे नामांकित कीजिए :
(a) बिन्दु P रेखाखण्ड \(\overline{A B}\) पर स्थित है।
(b) रेखाएँ XY और PQ बिन्दु M पर प्रतिच्छेद करती हैं।
(c) रेखा l पर E और F स्थित हैं, परन्तु D स्थित नहीं है।
(d) \(\stackrel{\leftrightarrow}{OP}\) और \(\stackrel{\leftrightarrow}{OQ}\) बिन्दु O पर मिलती हैं।
हल:
MP Board Class 6th Maths Solutions Chapter 4 आधारभूत ज्यामितीय अवधारणाएँ Ex 4.1 image 4

प्रश्न 6.
रेखा \(\stackrel{\leftrightarrow}{MN}\) की संलग्न आकृति को देखिए। इस आकृति के सन्दर्भ में बताइए कि निम्नलिखित कथन सत्य हैं या असत्य :
MP Board Class 6th Maths Solutions Chapter 4 आधारभूत ज्यामितीय अवधारणाएँ Ex 4.1 image 5
(a) Q, M, O और P रेखा \(\stackrel{\leftrightarrow}{MN}\) पर स्थित बिन्दु हैं।
(b) M, O और N रेखाखण्ड \(\overline{MN}\) पर स्थित बिन्दु हैं।
(c) M और N रेखाखण्ड \(\overline{MN}\) के अन्त बिन्दु हैं।
(d) O और N रेखाखण्ड \(\overline{OP}\) के अन्त बिन्दु हैं।
(e) M रेखाखण्ड \(\overline{QO}\) को दोनों अन्त बिन्दुओं में से एक बिन्दु है।
(f) M किरण \(\overrightarrow{OP}\) पर एक बिन्दु है।
(g) किरण \(\overrightarrow{OP}\) किरण \(\overrightarrow{QP}\) से भिन्न है।
(h) किरण \(\overrightarrow{O P}\) वही है जो किरण \(\overrightarrow{O M}\) है।
(i) किरण \(\overrightarrow{O M}\) किरण \(\overrightarrow{O P}\) के विपरीत (opposite) नहीं है।
(j) O किरण \(\overrightarrow{O P}\) का प्रारम्भिक बिन्दु नहीं है।
(k) N किरण \(\overrightarrow{N P}\) और \(\overrightarrow{N M}\) का प्रारम्भिक बिन्दु है।
उत्तर-
(a) सत्य,
(b) सत्य,
(c) सत्य
(d) असत्य,
(e) असत्य,
(f) भसत्य,
(g) सत्य,
(h) असत्य,
(i) असत्य,
(j) असत्य,
(k) सत्य।

MP Board Solutions

पाठ्य-पुस्तक पृष्ठ संख्या # 83

इन्हें कीजिए

प्रश्न 1.
निम्न की सहायता से बहुभुज बनाने का प्रयत्न कीजिए :
1. माचिस की पाँच तीलियाँ
2. माचिस की चार तीलियाँ
3. माचिस की तीन तीलियाँ
4. माचिस की दो तीलियाँ
उपर्युक्त में से किस स्थिति में यह सम्भव नहीं हुआ ? क्यों?
हल :
MP Board Class 6th Maths Solutions Chapter 4 आधारभूत ज्यामितीय अवधारणाएँ Ex 4.1 image 6
4. माचिस की दो तीलियाँ-कोई बहुभुज सम्भव नहीं। चूँकि बहुभुज रेखाखण्डों से घिरी बन्द आकृति है। यह सम्भव नहीं कि दो रेखाखण्डों से एक बन्द घिरी हुई आकृति बनाई जाए। इसलिए दो माचिस की तीलियों से बहुभुज बनाना सम्भव नहीं है।

पाठ्य-पुस्तक पृष्ठ संख्या # 84

प्रश्न 1.
B और C इसके अन्य दो शीर्ष हैं। क्या आप इन बिन्दुओं पर मिलने वाली भुजाओं के नाम लिख सकते हैं?
हल :
इन भुजाओं के नाम हैं जिनके शीर्ष B और C हैं :
AB और BC, BC और CD

प्रश्न 2.
क्या AB और BC आसन्न भुजाएँ हैं? AE और DC के बारे में आप क्या कह सकते हैं?
हल :
चूँकि AB और BC में एक उभयनिष्ठ अंत बिन्दु है, इसलिए ये बहुभुज की आसन्न भुजाएँ हैं। AE और DC आसन्न भुजाएँ नहीं हैं। क्योंकि इनका उभयनिष्ठ अन्त बिन्दु नहीं है।

प्रश्न 3.
क्या रेखाखण्ड \(\overline{B C}\) एक विकर्ण है? क्यों या क्यों नहीं?
हल :
नहीं, रेखाखण्ड \(\overline{B C}\) विकर्ण नहीं है क्योंकि BC आसन्न शीर्षों को मिलाने वाला रेखाखण्ड है।

प्रश्न 4.
क्या आप आसन्न शीर्षों को जोड़कर विकर्ण प्राप्त कर सकते हैं?
हल :
नहीं, हम आसन्न शीर्षों को जोड़कर विकर्ण प्राप्त नहीं कर सकते हैं।

MP Board Class 6th Maths Solutions

MP Board Class 6th Maths Solutions Chapter 4 आधारभूत ज्यामितीय अवधारणाएँ Intext Questions

MP Board Class 6th Maths Solutions Chapter 4 आधारभूत ज्यामितीय अवधारणाएँ Intext Questions

पाठ्य-पुस्तक पृष्ठ संख्या # 75

प्रयास कीजिए

प्रश्न 1.
अपनी पेंसिल के नुकीले सिरे से एक कागज पर चार बिन्दु अंकित कीजिए तथा उन्हें नाम A, C, P और H दीजिए। इन बिन्दुओं को विभिन्न प्रकार से नाम दीजिए। नाम देने का एक प्रकार संलग्न आकृति के अनुसार हो सकता है।
MP Board Class 6th Maths Solutions Chapter 4 आधारभूत ज्यामितीय अवधारणाएँ Intext Questions image 1
हल :
हम इन बिन्दुओं को निम्न प्रकार से नाम दे सकते हैं :
MP Board Class 6th Maths Solutions Chapter 4 आधारभूत ज्यामितीय अवधारणाएँ Intext Questions image 2

प्रश्न 2.
आसमान में एक तारा हमें एक बिन्दु के अवधारण का आभास कराता है। अपने दैनिक जीवन से इसी प्रकार की पाँच स्थितियाँ चुनकर दीजिए।
हल :
पेंसिल की नोंक, सुई की नोंक, कागज का कोना, डेस्क का कोना, वर्ग का कोना।

पाठ्य-पुस्तक पृष्ठ संख्या # 76-77

रेखाखण्ड के कुछ उदाहरण – मेज का किनारा, किसी आयत/वर्ग की भुजा, घन/ घनाभ का किनारा, दोनों सिरों पर कसा हुआ धागा, A, B को जोड़ने वाला सबसे छोटा रास्ता।

प्रयास कीजिए

प्रश्न 1.
संलग्न आकृति में दिए रेखाखण्डों को नाम दीजिए। क्या A प्रत्येक रेखाखण्ड का एक अन्त बिन्दु है ?
MP Board Class 6th Maths Solutions Chapter 4 आधारभूत ज्यामितीय अवधारणाएँ Intext Questions image 3
हल :
दी हुई आकृति में \(\overline{A B}\) (या \(\overline{B A}\) ) तथा \(\overline{A C}\) (या \(\overline{C A}\) ) रेखाखण्ड हैं।
हाँ, A प्रत्येक रेखाखण्ड का अन्त बिन्दु है।

प्रतिच्छेदी रेखा युग्मों के उदाहरण – घन के आसन्न किनारे, श्यामपट की आसन्न भुजाएँ, अंग्रेजी वर्णमाला के अक्षर V तथा L

MP Board Solutions

पाठ्य-पुस्तक पृष्ठ संख्या # 78

इन्हें कीजिए

प्रश्न 1.
एक कागज लीजिए। इसे दो बार मोडिए (और मोड़ के निशान बनाइए) ताकि दो प्रतिच्छेदी रेखाएँ प्राप्त हो जाएँ और चर्चा कीजिए :
(a) क्या दो रेखाएँ एक से अधिक बिन्दुओं पर प्रतिच्छेद कर सकती हैं?
(b) क्या दो से अधिक रेखाएँ एक ही बिन्दु पर प्रतिच्छेद कर सकती हैं?
हल :
(a) नहीं, दो रेखाएँ एक से अधिक बिन्दुओं पर प्रतिच्छेद नहीं कर सकती हैं।
(b) हाँ, दो से अधिक रेखाएँ एक ही बिन्दु पर प्रतिच्छेद कर सकती हैं।

सोचिए, चर्चा कीजिए एवं लिखिए

आप समान्तर रेखाओं को और कहाँ देखते हैं ? इनके 10 उदाहरण ज्ञात करने का प्रयत्न कीजिए।
हल :
हम समान्तर रेखाओं को निम्नांकित में देख सकते हैं
पैमाने के सम्मुख किनारे, आयत के सम्मुख किनारे, श्यामपट के सम्मुख किनारे, खिड़की की सलाखें, रेल की पटरी, मेज के किनारे, घनाभ के किनारे, घन के किनारे, पेज के किनारे, अभ्यास-पुस्तिका/किताब के सम्मुख किनारे आदि।

पाठ्य-पुस्तक पृष्ठ संख्या # 79

सोचिए, चर्चा कीजिए एवं लिखिए

प्रश्न 1.
यदि \(\overrightarrow{P Q}\) एक किरण है, तो
(a) इसका प्रारम्भिक बिन्दु क्या है ?
(b) बिन्दु ए किरण पर कहाँ स्थित है ?
(c) क्या हम कह सकते हैं कि ए इस किरण का Q प्रारम्भिक बिन्दु है ?
MP Board Class 6th Maths Solutions Chapter 4 आधारभूत ज्यामितीय अवधारणाएँ Intext Questions image 4
हल :
\(\overrightarrow{P Q}\) एक किरण है :
(a) इसका प्रारम्भिक बिन्दु P है।
(b) बिन्दु Q, किरण \(\overrightarrow{P Q}\) पर स्थित है।
(c) नहीं, Q इस किरण का प्रारम्भिक बिन्दु नहीं है।
(Q, \(\overrightarrow{Q P}\) का प्रारम्भिक बिन्दु हो सकता है।)

MP Board Solutions

पाठ्य-पुस्तक पृष्ठ संख्या # 80

प्रयास कीजिए

प्रश्न 1.
संलग्न दी आकृति में दर्शाई गई किरणों के नाम लिखिए।
MP Board Class 6th Maths Solutions Chapter 4 आधारभूत ज्यामितीय अवधारणाएँ Intext Questions image 5
हल :
संलग्न चित्र में \(\overrightarrow{T A}, \overrightarrow{T N}, \overrightarrow{T B}\) और \(\overrightarrow{N B}\) किरणें हैं।

प्रश्न 2.
क्या T इन सभी किरणों का प्रारम्भिक बिन्दु है ?
हल :
नहीं, T किरण \(\overrightarrow{N B}\) का प्रारम्भिक बिन्दु नहीं है।

संलग्न आकृति में एक किरण OA दी है। यह O से प्रारम्भ होती है और A से होकर जाती है। यह किरण बिन्दु B से होकर भी जाती है।
MP Board Class 6th Maths Solutions Chapter 4 आधारभूत ज्यामितीय अवधारणाएँ Intext Questions image 6

MP Board Solutions

प्रश्न a.
(i) क्या आप इसे \(\overrightarrow{O B}\) भी कह सकते हैं ? क्यों? यहाँ \(\overrightarrow{O A}\) और \(\overrightarrow{O B}\) एक ही किरण को दर्शाते हैं।
(ii) क्या हम किरण \(\overrightarrow{O A}\) को किरण \(\overrightarrow{A O}\) लिख सकते हैं ? क्यों ? या क्यों नहीं ?
(iii) पाँच किरणें खींचिए और उनके उचित नाम लिखिए।
इन किरणों के सिरे पर लगे तीर क्या दर्शाते हैं ?
हल :
(i) हाँ, हम इसे \(\overrightarrow{O B}\) भी कह सकते हैं। क्योंकि एक किरण की कोई निश्चित लम्बाई नहीं होती है। किरण को अनिश्चित रूप से बढ़ाया जा सकता है। इसलिए \(\overrightarrow{O A}\) और \(\overrightarrow{O B}\) समान किरणें हैं।
MP Board Class 6th Maths Solutions Chapter 4 आधारभूत ज्यामितीय अवधारणाएँ Intext Questions image 7

(ii) यहाँ, \(\overrightarrow{O A}\) एक किरण है, जिसका प्रारम्भिक बिन्दु O हैं। इसे O से A की दिशा में अनिश्चित रूप से बढ़ाया गया है। दूसरी किरण \(\overrightarrow{A O}\) है, जिसका प्रारम्भिक बिन्दु A है। इसे A से O की दिशा में अनिश्चित रूप से बढ़ाया गया है।
अतः \(\overrightarrow{A O}\) और \(\overrightarrow{O A}\) अलग-अलग किरणें हैं। इस प्रकार \(\overrightarrow{O A}\) को \(\overrightarrow{A O}\) नहीं लिखा जा सकता है।

(iii) पाँच किरणें निम्नलिखित हैं
MP Board Class 6th Maths Solutions Chapter 4 आधारभूत ज्यामितीय अवधारणाएँ Intext Questions image 8
किरणों के सिरों पर लगे तीर दर्शाते हैं कि इन किरणों को तीर की दिशा में अनिश्चित रूप से बढ़ाया जा सकता है।

MP Board Class 6th Maths Solutions