Class 9

MP Board Class 9th Maths Solutions Chapter 1 संख्या पद्धति Ex 1.1

प्रश्न 1.
क्या शून्य एक परिमेय संख्या है? क्या इसे आप \(\frac { p }{ q }\) के रूप में लिख सकते हैं, जहाँ p और q पूर्णांक हैं और q ≠ 0. (2018)
उत्तर:
हाँ, 0 = \(\frac { p }{ q }\); जहाँ p एवं q पूर्णांक हैं तथा p = 0 एवं q ≠ 0.

प्रश्न 2.
3 और 4 के बीच छः परिमेय संख्याएँ ज्ञात कीजिए। (2019)
हल:
3 और 4 को हर (6 + 1) अर्थात् 7 लेकर परिमेय संख्या के रूप में लिखने पर,

अतः अभीष्ट छः परिमेय संख्याएँ होंगी: \(\frac { 22 }{ 7 }\), \(\frac { 23 }{ 7 }\), \(\frac { 24 }{ 7 }\), \(\frac { 25 }{ 7 }\), \(\frac { 26 }{ 7 }\) एवं \(\frac { 27 }{ 7 }\).

प्रश्न 3.
\(\frac { 3 }{ 5 }\) एवं \(\frac { 4 }{ 5 }\) के बीच पाँच परिमेय संख्याएँ ज्ञात कीजिए। (2018)
हल:
\(\frac { 3 }{ 5 }\) एवं \(\frac { 4 }{ 5 }\) को उनके हर एवं अंश को (5 + 1) अर्थात् 6 से गुणा करके लिखने पर:
\(\frac { 3 }{ 5 }\) = \(\frac { 18 }{ 30 }\) एवं \(\frac { 4 }{ 5 }\) = \(\frac { 24 }{ 30 }\)
अतः अभीष्ट पाँच परिमेय संख्याएँ होंगी : \(\frac { 19 }{ 30 }\), \(\frac { 20 }{ 30 }\), \(\frac { 21 }{ 30 }\), \(\frac { 22 }{ 30 }\) एवं \(\frac { 23 }{ 30 }\).

प्रश्न 4.
नीचे दिए गए कथन सत्य हैं या असत्य ? कारण के साथ अपने उत्तर लिखिए :
(i) प्रत्येक प्राकृत संख्या एक पूर्ण संख्या होती है। (2018)
(ii) प्रत्येक पूर्णांक एक पूर्ण संख्या होती है।
(iii) प्रत्येक परिमेय संख्या एक पूर्ण संख्या होती है।
उत्तर:
(i) सत्य है, क्योंकि पूर्ण संख्या के संग्रह में सभी प्राकृत संख्याएँ समाहित हैं।
(ii) असत्य है, क्योंकि – 2 एक पूर्णांक है लेकिन पूर्ण संख्या नहीं।
(iii) असत्य है, क्योंकि \(\frac { 1 }{ 2 }\) एक परिमेय संख्या है लेकिन पूर्ण संख्या नहीं।

MP Board Class 9th Maths Solitions

MP Board Class 9th Maths Solutions Chapter 4 Linear Equations in Two Variables Ex 4.3

Question 1.
Draw the graph of each of the following linear equations in two variables:

1. x + y = 4
2. x – y = 2
3. y = 3x
4. 3 = 2x + y

solution:
1. x + y = 4
Take x = 1
1 + y = 4
∴ y = 3

Take x = 2,
2 + y = 4
∴ y = 2

Take x = 0,
0 + y = 4
∴ y = 4

The solutions are:

The graph is shown below.

2. x – y = 2
Take x = 1,
1 – y = 2
y = 2 – 1
∴ y = – 1

Take x = 2,
2 – y = 2
– y = 2 – 2
∴ y = 0

Take x = 0,
0 – y = 2
∴ y = – 2

3. y – 3x
Take x = 0,
y = 3 x 0 = 0

Take x = 1,
y = 3 x 1 = 3

Take x = 2,
y = 3 x 2 = 6

4. 3 = 2x + y
Take x = 1,
3 = 2 x 1 + y
3 = 2 + y
3 – 2 = y
∴ y = 1

Take x = 0
3 = 2 x 0 + y
∴ y = 3 – 0 = 3

Take x = -1,
3 = 2 x – 1 + y
3 = – 2 + y
∴ y = 3 + 2 = 5

Online nonlinear function calculator system of equations. Welcome to our step-by-step math Solve·

Question 2.
Give the equations of two lines passing through (2, 14). How many more such lines are there and why?
Solution:
Two lines passing through point (2, 14)

1. x + y = 16
2. 2x + y – 18

Infinitely many lines can be drawn through (2, 14).

Question 3.
If the point (3, 4) lies on the graph of the equation 3y = ax + 7, find the value of a.
Solution:
Putting the value of x = 3 and y = 4 in 3y = ax + 7, we get
3 x 4 = a x 3 + 7
12 = 3a + 7
3a = 12 – 7
a = \(\frac{5}{3}\)

Question 4.
The taxi fare in a city is as follows: For the first kilometer, the fare is ₹ 8 and for the subsequent distance it is ₹ 5 per km. Taking the distance covered as x km and total fare as ₹ y, write a linear equation for this information and draw its graph.
Solution:
Distance covered = x km
Total fare = ₹ y
Fare of 1st km = ₹ 8
Fare for subsequent kms = ₹ 5 per km

According to question, y = 8 + 5 (x – 1) = 8 + 5x – 5
y = 3 + 5x
Take x = 0,
y = 3 + 5 x 0
∴ y = 3

Take x = 1,
y = 3 + 5 x 1
y = 3 + 5
∴ y = 8

Take x = 2
y = 3 + 5 x 2
∴ y = 13

Question 5.
From the choices given below, choose the equation whose graphs are given in Fig. (a) and Fig. (b)
For Fig. (a)

1. y = x
2. x + y = 0
3. y = 2x
4. 2 + 3y = 7x

For Fig. (b)

1. y = x + 2
2. y = x – 2
3. y = – x + 2
4. x + 2y = 6

Solution:
1. Since (-1, 1), (0, 0) and (1, -1) satisfies the equation x + y = 0.
The equation of the graph is x + y = 0

2. Since (-1,3), (0, 2) and (2, 0) satisfies the equation y = x + 2.
The equation of the graph is y = – x + 2.

Question 6.
If the work done by a body on application of a constant force is directly proportional to the distance traveled by the body, express this in the form of an equation in two variables and draw the graph of the same by taking the constant force as 5 units. Also read from the graph the work done when the distance traveled by the body is:

1. 2 units
2. 0 units.

Solution:
Let y be the work done and x be the distance covered. y ∝ x where k is the constant force.
y = kx, (Given)
k = 5
∴ y = 5x

Take x = 0
y = 5 x 0 = 0

Take x = 1
y = 5 x 1 = 5

Take = 2
y= 5 x 2 = 10

When the distance travelled is –

1. x = 2 units y = 10 units
2. x = 0 units y = 0 units.

Question 7.
Yamini and Fatima, two students of class IX of a school, to gether contributed ₹ 100 towards the Prime Minister’s Relief Fund to help the earthquake victims. Write a linear equation which satisfies this data. (You may take their contributions as ₹ x and ₹ y). Draw the graph of the same.
Answer:
Let the contribution of Yamini be ₹ x and that of Fatima be ₹ y.
According to question
x + y = 100

Take x = 30,
30 + y = 100
y = 100 – 30
y = 70

Take = 40,
40 + y = 100
y = 100 – 40
y = 60

Take = 50,
50 + y = 100
y = 100 – 50
y = 50

Question 8.
In countries like USA and Canada, temperature is measured in Fahrenheit, whereas in countries like India, it is measured in Celsius. Here is a linear equation that converts Fahren-heit to Celsius.
F = (\(\frac{9}{5}\)) C + 32

1. Draw the graph of the linear equation above using Celsius for x – axis and Fahrenheit for y – axis.
2. If the temperature is 30°C, what is the temperature in Fahrenheit?
3. If the temperature is 95°F, what is the temperature in Celsius?
4. If the temperature is 0°C, what is the temperature in Fahrenheit and if the temperature is 0°F, what is the temperature in Celsius?
5. Is there a temperature which is numerically the same in both Fahrenheit and Celsius? If yes, find it.

1. F = \(\frac{9}{5}\) + 32
Take C = – 5,
F = \(\frac{9}{5}\) x (- 5) + 32
= – 9 + 32 = 23
C = – 10,
F = \(\frac{9}{5}\) x – 10 + 32 = 14
C = – 15,
F = \(\frac{9}{5}\) x – 15 + 32 = 5

2. From the graph, when temperature is 30°C, temperature in °F is 86°.

3. When F = 95°, C = 35°.
\(\frac{63×5}{9}\) = 35°

4. C = 0°, F = 32°
F = 0°, C = – 17.7°

5. F = – 40°, C = – 40°

MP Board Class 9th Maths Solutions

In this article, we will share MP Board Class 9th Maths Solutions Chapter 4 दो चरों वाले रैखिक समीकरण Additional Questions Pdf, These solutions are solved subject experts from the latest edition books.

MP Board Class 9th Maths Solutions Chapter 4 दो चरों वाले रैखिक समीकरण Additional Questions

MP Board Class 9th Maths Chapter 4 अतिरिक्त परीक्षोपयोगी प्रश्न

MP Board Class 9th Maths Chapter 4 दीर्घ उत्तरीय प्रश्न

प्रश्न 1.
दर्शाइए कि बिन्दु A(1, 2), B(-1,-16) और C(0, – 7) रैखिक समीकरण y = 9x – 7 के आलेख पर स्थित है। (2019)
हल:
बिन्दु A(1, 2) के निर्देशांकों का मान समीकरण में रखने पर,
∴ 9x – 7 = 9 x 1 – 7 = 9 – 7 = 2 = y.
⇒ दायाँ पक्ष = बायाँ पक्ष
बिन्दु B(-1, – 16) के निर्देशांकों का मान समीकरण में रखने पर,
∴ 9x – 7 = 9x (-1) – 7 = – 9 – 7 = – 16 = y
⇒ दायाँ पक्ष = बायाँ पक्ष
बिन्दु C(0, – 7) के निर्देशांकों का मान समीकरण में रखने पर,
∴ 9x – 7 = 9 (0) – 7 = 0 – 7 = – 7 =y
⇒ दायाँ पक्ष = बायाँ पक्ष अतः दिए हुए बिन्दु A, B एवं C समीकरण y = 9x – 7 के आलेख पर स्थित हैं।

प्रश्न 2.
रैखिक समीकरण 3x + 4y = 6 का आलेख खींचिए। यह आलेख X-अक्ष और Y-अक्ष को किन बिन्दुओं पर काटता हैं? (2019)
हल:
समीकरण 3x + 4y = 6 (दिया है)


अतः संलग्न चित्र 4.18 अभीष्ट आलेख है तथा यह आलेख -अक्ष को बिन्दु (2, 0) पर एवं Y-अक्ष को बिन्दु (0, 1\(\frac { 1 }{ 2 }\)) पर काटता है।

प्रश्न 3.
वह रैखिक समीकरण जो फॉरेनहाइट (F) को सेल्सियस (C) में बदलती है, सम्बन्ध c = \(\frac { 5F – 160 }{ 9 }\) से दी जाती है।
(i) यदि तापमान 86°F है, तो सेल्सियस में तापमान क्या है ?
(ii) यदि तापमान 35°C है, तो फॉरेनहाइट में तापमान क्या है ?
(iii) यदि तापमान 0°C है तो फॉरेनहाइट में तापमान क्या है तथा यदि तापमान 0°F है, तो सेल्सियस में तापमान क्या है ?
(iv) तापमान का वह कौन-सा संख्यात्मक मान है जो दोनों पैमानों (मात्रको) में एक ही है ?
हल:

MP Board Class 9th Maths Chapter 4 लघु उत्तरीय प्रश्न

प्रश्न 1.
उस सरल रेखा से निरूपित समीकरण का आलेख खींचिए जो X-अक्ष के समानान्तर है और उसके नीचे 3 मात्रक की दूरी पर है।
उत्तर:
अभीष्ट चित्र संलग्न है।

प्रश्न 2.
उस रैखिक समीकरण का आलेख खींचिए जिसके हल उन बिन्दुओं से निरूपित हैं जिनके निर्देशांकों का योग 10 इकाई है।
हल:
प्रश्नानुसार, अभीष्ट समीकरण होगा : x + y = 10
यदि x = 0 तो 0 + y = 10 ⇒ y = 10
यदि x = 5 तो 5 + y = 10 ⇒ y = 10 – 5 = 5
यदि x = 10 तो 10 + y = 10 ⇒ y = 10 – 10 = 0

अतः उपर्युक्त चित्र अभीष्ट आलेख है।

प्रश्न 3.
समीकरण y = 2x + 1 का आलेख खींचिए। (2019)
हल:
निर्देशः उपर्युक्त प्रश्न के समीकरण की तरह हल कीजिए।

प्रश्न 4.
रैखिक समीकरण x + 2y = 8 का वह हल ज्ञात कीजिए जो निम्नलिखित पर एक बिन्दु निरूपित करता है:
(i) X-अक्ष
(ii) Y-अक्ष।
हल:
(i) चूँकि X-अक्ष पर बिन्दु की कोटि y = 0. इसलिए x + 2 x 0 = 8 ⇒ x + 0 = 8
⇒ x = 8
अतः समीकरण का अभीष्ट हल : x = 8, y = 0.

(ii) चूँकि Y-अक्ष पर बिन्दु की भुंज x = 0. इसलिए
0 + 2y = 8 ⇒ 2y = 8 ⇒ y = 8/2 = 4
अतः समीकरण का अभीष्ट हल : x = 0, y = 4.

प्रश्न 5.
मान लीजिए.y, x के अनुक्रमानुपाती है। यदि x = 4 होने पर y = 12 हो, तो एक रैखिक समीकरण लिखिए। जब x = 6, तोy का क्या मान है ?
हल:
चूँकि y α x
⇒ y = Cx
जब x = 4 होने पर y = 12 हो, तो
12 = C x 4
⇒ C = 12/4 = 3 C का मान समीकरण y = Cx में रखने पर,
y = 3x अतः अभीष्ट समीकरण : y = 3x.
अब x = 6 का मान समीकरण y = 3x में रखने पर,
y = 3 x 6 = 18
अतः एका अभीष्ट मान = 18.

MP Board Class 9th Maths Chapter 4 अति लघु उत्तरीय प्रश्न

प्रश्न 1.
निम्नलिखित कथन सत्य हैं या असत्य लिखिए। अपने उत्तरों का औचित्य दीजिए।
(i) बिन्दु (0, 3) रैखिक समीकरण 3x + 4y = 12 के आलेख पर स्थित है।
(ii) रैखिक समीकरण x + 2y = 7 के आलेख बिन्दु (0, 7) से होकर जाता है।
(iii) सारणी :

से प्राप्त बिन्दुओं के निर्देशांक समीकरण x – y + 2 = 0 के कुछ हलों को निरूपित करते हैं।
(iv)दो चरों वाली रैखिक समीकरण के आलेख का प्रत्येक बिन्दु उस समीकरण का एक हल निरूपित नहीं करता है।
(v) दो चरों वाली रैखिक समीकरण के आलेख का एक सरल रेखा में होना आवश्यक नहीं है।
उत्तर:
(i) कथन सत्य है, क्योंकि बिन्दु के निर्देशांक समीकरण को सन्तुष्ट करते हैं।
(ii) कथन असत्य है, क्योंकि बिन्दु के निर्देशांक समीकरण को सन्तुष्ट नहीं करते हैं।
(iii) कथन सत्य है, क्योंकि बिन्दु (3, -5) के निर्देशांक समीकरण को सन्तुष्ट नहीं करते हैं।
(iv) कथन असत्य है, क्योंकि दो चरों वाली रैखिक समीकरण का प्रत्येक बिन्दु उस समीकरण का एक हल निरूपित करता है।
(v) कथन असत्य है, क्योंकि दो चरों वाली रैखिक समीकरण का आलेख सदैव एक सरल रेखा होती है।

प्रश्न 2.
वह रैखिक समीकरण लिखिए जिसकी कोटि उसके भुज से तीन गुनी है। (2019)
उत्तर:
y = 3x.

MP Board Class 9th Maths Chapter 4 वस्तुनिष्ठ प्रश्न

बहु-विकल्पीय प्रश्न

प्रश्न 1.
रैखिक समीकरण 2x – 5y = 7 :
(a) का एक अद्वितीय हल है
(b) के दो हल हैं
(c) के अपरिमित रूप से अनेक हल हैं
(d) का कोई हल नहीं है।
उत्तर:
(c) के अपरिमित रूप से अनेक हल हैं

प्रश्न 2.
यदि (2,0) रैखिक समीकरण 2x + 3y = k का हल है, तो k का मान है :
(a) 4
(b) 6
(c) 5
(d) 2.
उत्तर:
(a) 4

प्रश्न 3.
रैखिक समीकरण 2x + 3y = 6 का आलेख -अक्ष को निम्नलिखित में से किस बिन्दु पर काटता
(a) (2, 0)
(b) (0, 3)
(c) (3, 0)
(d) (0, 2).
उत्तर:
(d) (0, 2).

प्रश्न 4.
X-अक्ष पर स्थित किसी बिन्दु का रूप होता है :
(a) (x, y)
(b) (0, y)
(c) (x, 0)
d) (x, 4).
उत्तर:
(c) (x, 0)

प्रश्न 5.
रेखा y = x पर स्थित किसी बिन्दु का रूप होता है :
(a) (a, a)
(b) (0, a)
(c) (a, 0)
(d) (a, – a).
उत्तर:
(a) (a, a)

प्रश्न 6.
X-अक्ष की समीकरण का रूप है :
(a) x = 0
(b) y = 0
(c) x + y = 0
(d) x = y
उत्तर:
(b) y = 0

प्रश्न 7.
दो चरों वाला रैखिक समीकरण है : (2019)
(a) ax² + bx + c = 0
(b) ax + b = 0
(c) ax³ + bx² + c = 0
(d) ax + by + c = 0.
उत्तर:
(d) ax + by + c = 0.

प्रश्न 8.
x = 5, y = 2 निम्नलिखित रैखिक समीकरण का हल है:
(a) x + 2y = 7
(b) 5x + 2y = 7
(c) x + y = 7
(d) 5x + y = 7.
उत्तर:
(c) x + y = 7

प्रश्न 9.
रैखिक समीकरण 2x + 3y = 6 का आलेख एक रेखा है जो X-अक्ष को निम्नलिखित बिन्दु पर मिलती है:
(a) (0, 2)
(b) (2, 0)
(c) (3, 0)
(d) (0, 3).
उत्तर:
(c) (3, 0)

प्रश्न 10.
(a, a) रूप का बिन्दु सदैव स्थित होता है :
(a) X-अक्ष पर
(b) Y-अक्ष पर
(c) रेखा y = x पर
(d) रेखा x + y = 0 पर।
उत्तर:
(c) रेखा y = x पर

प्रश्न 11.
(a,-a) रूप का बिन्दु सदैव रेखा पर स्थित होता है :
(a) x = a
(b) y = -a.
(c)y = x
(d) x + y = 0.
उत्तर:
(d) x + y = 0.

प्रश्न 12.
दो संख्याओं का योग 25 व अन्तर 5 है, तो वे संख्याएँ होंगी : (2018)
(a) 15, 10
(b) 20, 5
(c) 13, 12
(d) 30, 5
उत्तर:
(a) 15, 10

रिक्त स्थानों की पूर्ति
1. एक ऐसा समीकरण जिसका आलेख एक सरल रेखा होता है, …… समीकरण कहलाता है।
2. रैखिक समीकरण ax + by + c = 0 का आलेख एक ……..रेखा है।
3. x और y का मान युग्म (x, y) जो दिए हुए समीकरण ax + by + c = 0 को सन्तुष्ट करता है, उक्त समीकरण का ………. कहलाता है।
4. जब किसी समीकरण निकाय का कोई भी हल नहीं होता, तब निकाय ……….. निकाय कहलाता है।
5. जब किसी समीकरण निकाय का कोई हल होता है, तब निकाय …………. निकाय कहलाता है।
6. दो चरों वाले एक घात समीकरण का ग्राफ ………… को प्रदर्शित करता है। (2018)
7. यदि एक समीकरण x + 2y = 5 में x = 1 है, तब y का मान ……….. है। (2019)
उत्तर:
1. रैखिक,
2. सरल,
3. हल,
4. असंगत,
5. संगत,
6. सरल रेखा,
7. 2 (दो)।

जोड़ी मिलान
स्तम्भ ‘A’                                      स्तम्भ ‘B’
1. रेखाएँ सम्पाती हों                  (a) y का मान शून्य
2. रेखाएँ प्रतिच्छेदी हों               (b) x का मान शून्य
3. रेखाएँ समानान्तर हों             (c) अनन्ततः अनेक हल
4. रेखा X-अक्ष को काटे            (d) अद्वितीय हल
5. रेखा Y-अक्ष को काटे             (e) कोई हल नहीं
उत्तर:
1. → (c),
2. → (d),
3. → e),
4. → (a),
5. → (b)

सत्य/असत्य कथन
1. समीकरण x + 2y = 5 में यदि x = 1 तो y = 2 होगा।
2. रैखिक समीकरण का आलेख एक वृत्त होता है।
3. दो चरों वाले एकघातीय समीकरण रैखिक समीकरण कहलाते हैं।
4. X-अक्ष का समीकरण x = 0 होता है। (2019)
5. Y-अक्ष, के समानान्तर रेखा का समीकरण x = + a होता है।
6. समीकरण x +2y = 3 का एक हल (1, 1) है। (2019)
7. बिन्दु (0, 5) समीकरण y = 5x + 5 का हल है। (2019)
8. मूल-बिन्दु से गुजरने वाली रेखा का आलेख y = kx रूप द्वारा प्रदर्शित होता है। (2019)
9. रैखिक समीकरण 2x -3y = 0 में चर 2 एवं – 3 है। (2019)
उत्तर:
1. सत्य,
2. असत्य,
3. सत्य,
4. असत्य,
5. सत्य,
6. सत्य,
7. सत्य,
8. सत्य,
9. असत्य।

एक शब्द/वाक्य में उत्तर

1. जब किसी समीकरण निकाय के अनन्ततः अनेक हल हों तो उसका आलेख कैसा होगा?
2. जब किसी समीकरण निकाय का अद्वितीय हल हो, तो उसका आलेख कैसा होगा?
3. जब किसी समीकरण निकाय का कोई हल न हो, तो उसका आलेख कैसा होगा?
4. यदि \(\frac { { a }_{ 1 } }{ { a }_{ 2 } } \neq \frac { { b }_{ 1 } }{ { b }_{ 2 } }\), तो निकाय का हल क्या होगा?
5. यदि \(\frac { { a }_{ 1 } }{ { a }_{ 2 } } =\frac { { b }_{ 1 } }{ { b }_{ 2 } }\neq \frac { { c }_{ 1 } }{ { c }_{ 2 } }\) तो निकाय का हल क्या होगा?
6. यदि \(\frac { { a }_{ 1 } }{ { a }_{ 2 } } =\frac { { b }_{ 1 } }{ { b }_{ 2 } }= \frac { { c }_{ 1 } }{ { c }_{ 2 } }\), तो निकाय का हल क्या होगा?
7. रैखिक समीकरण में चर राशि की उच्चतम घात होती है। (2018)
8. दो.चरों वाला एक रैखिक समीकरण लिखिए। (2019)
9. यदि x = 2, y = 1 समीकरण 2x + 3y =k का हल है, तब k का मान क्या होगा? (2019)
उत्तर:
1. सम्पाती रेखाएँ,
2. प्रतिच्छेदी रेखाएँ,
3. समानान्तर रेखाएँ,
4. अद्वितीय हल,
5. कोई हल नहीं,
6. अनन्ततः अनेक हल,
7. एक,
8. ax + by + c = 0,
9. 7 (सात)।

In this article, we will share MP Board Class 9th Sanskrit Solutions Chapter 2 अलसस्य स्वप्नः Pdf, These solutions are solved subject experts from the latest edition books.

MP Board Class 9th Sanskrit Solutions Durva Chapter 2 अलसस्य स्वप्नः (कथा)

MP Board Class 9th Sanskrit Chapter 2 पाठ्य पुस्तक के प्रश्न

प्रश्न 1.
एकपदेन उत्तरं लिखत (एक शब्द में उत्तर लिखो)।
(क) विप्रपुत्रस्य नाम किम् आसीत्? (विप्र पुत्र का नाम क्या था?)
उत्तर:
विप्रपुत्रस्य नाम सोम शर्मा आसीत्। (विप्र पुत्र का नाम सोम शर्मा था।)

(ख) सक्तुभिः कति रुप्यकाणि उत्पत्स्यन्ते? (सत्तू से कितने रुपये हुये?)
उत्तर:
सक्तुभिः शतम् रुप्यकाणि उत्पस्यन्ते (सत्तू से सौ रुपये हुए।)

(ग) विप्रः कं सततम् अवलोकयति? (विप्र किसे एकटक देख रहा था?)
उत्तर:
विप्रः सक्तुम सततम् अवलोकयति। (विप्र सत्तू को एकटक देख रहा था।)

(घ) अश्वानां विक्रयात् किं भविष्यति? (घोड़ों को बेचने से क्या होगा?)
उत्तर:
अश्वानां विक्रयात् सुवर्णम् भविष्यति। (घोड़ों को बेचने से स्वर्ण मुद्रा आयेगी।)

(ङ) विप्रस्य प्रहारेण कः भग्नः? (विप्र के प्रहार से क्या टूट गया?)
उत्तर:
विप्रस्य प्रहारेण घटः भग्नः। (विप्र के प्रहार से घड़ा टूट गया।)

प्रश्न 2.
एक वाक्येन उत्तर लिखत् (एक वाक्य में उत्तर लिखो)
(क) विप्रः स्वपत्नी किम् अभिधारयति? (ब्राह्मण अपनी पत्नी से क्या बोलेगा?)
उत्तर:
गृहाण तावद् बालकम्। (अपने बच्चे को पकड़ो।)

(ख) घट कैः सम्पूरितः? (घड़े में क्या भरा था?)
उत्तर:
सक्तुभिः। (सत्तू)।

(ग) सुवर्णेन किं सम्मत्स्यत्? (स्वर्ण मुद्रा से क्या बनेगा?)
उत्तर:
चतुः शालम् गृहम्। (चौकोर घर)।

(घ) सोम शर्मा कुतः विप्रसमीपम् आगच्छति? (सोम शर्मा ब्राह्मण के पास कहां आयेगा?)
उत्तर:
अश्वखुरासन्नवर्ती। (घुड़साल में मेरे समीप)।।

(ङ) विप्रः पुत्रम् कुतः अवधारयिष्यति? (ब्राह्मण पुत्र को कहां ग्रहण करेगा?)
उत्तर:
अश्वशालयः पृष्ठदेशे। (घुड़साल के पीछे)।

प्रश्न 3.
अधोलिखित प्रश्नानाम् उत्तराणि लिखत् (नीचे लिखे प्रश्नों के उत्तर लिखो)
(क) सोम शर्मा पितरं दृष्ट्वा किं करिष्यति? (सोम शर्मा पिता को देखकर क्या करेगा?)
उत्तर:
ितु समीपम् आगमिष्यति। (पिता को देखकर उसके पास जायेगा।)

(ख) विप्रः रात्रो सुप्तः किं चिन्तयामास? (ब्राह्मण रात में सोते हुए क्या विचार किया?)
उत्तर:
अयं घटः सक्तुभि परिपूर्णः वर्तते। (इस घेड़े में सत्तू भरा हुआ है।)

(ग) विप्रः कं कदा कुतश्च अवधारिष्यति? (ब्राह्मण किसको कहा और कब धारण करेगा?)
उत्तर:
पुत्रम् अश्वशालायाः पृष्ठ देशे। (पुत्र को अश्वशाला के पीछे के भाग में ब्राह्मण ग्रहण करेगा।)

(घ) यदा दुर्भिक्षं भविष्यति तदा सक्तुभिः किंकिंभविष्यति? (जब अकाल होगा तब सत्तू के द्वारा क्या-क्या होगा?)
उत्तर:
स्वकणाम् सतम्। (अकाल के समय सैकड़ों रुपये सत्तू से प्राप्त होंगे)

(ङ) अस्याः कथायाः आशयः कः? (इस कथा का सार क्या है?)
उत्तर:
अविचार्यं न कर्तव्यम्। (बिना विचारे कोई कार्य नहीं करना चाहिए।) यही इस कथा का सार है।)

प्रश्न 4.
उदाहरणानुसारं शब्दानां धातु प्रत्यय च पृथक कुरुत

प्रश्न 5.
अव्ययः वाक्यनिर्माणं कुरुत
यथा- सः अत्र अस्ति।
(क) च – रमेश सुरेशश्च आपणं गच्छति।
(ख) अपि – अहं अपि भोपालम् गमिष्यामि।
(ग) तावत् – तावत् वर्षा वभूव।
(घ) न – अहं न गमिष्यामि।
(ङ) ततः – ततः पुत्रः आगतः।

प्रश्न 6.
उदाहरणानुसारं शब्दानां विभक्तिं, वचनं च लिखत्

प्रश्न 7.
संधिविच्छेदं कृत्वा संधिः नाम लिखत्
(क) तद्यदि
उत्तर:
तत् + यदि = व्यंजन

(ख) कदाचिद्रात्रो
उत्तर:
कदाचित् + रात्रो = व्यंजन

(ग) तदनेन
उत्तर:
तत + अनेन = व्यंजन

(घ) कश्चित
उत्तर:
कः + चित = विसर्ग

(ङ) तथैव
उत्तर:
तथा + ऐव = वृद्धि स्वर

प्रश्न 8.
क्रियापदानां धातु लकारम्, पुरुषं च लिखत्क्रियापदम्

प्रश्न 9.
शुद्धवाक्यानां समक्षम् “आम्” अशुद्ध वाक्यानां समक्षं “न” इति लिखत्

उत्तर:
(क) न
(ख) आम्
(ग) आम्
(घ) आम्
(ङ) आम्

प्रश्न 10.
रिक्तस्थानानि पूरयत् (खाली स्थान भरो)
(क) स एव पाण्डुरः शेते सोम शर्मा पिता यथा।
(ख) सुवर्णेन चतुः शालम् गृहं सम्पत्स्ये।
(ग) अजाभिः प्रभूता गा गृहीष्यामि।
(घ) तस्य अहम सोम शर्मा इति नाम करिष्यामि।
(ङ) वऽवा प्रसवतः प्रभूता अस्वाः भविष्यति

प्रश्न 11.
यथायोग्यं योजयत् (सही जोड़ी बनाओ)

अलसस्य स्वप्नः पाठ-सन्दर्भ प्रतिपाद्य

यह कथा विष्णु शर्मा द्वारा रचित सुप्रसिद्ध कथा ग्रंथ ‘पंचतंत्र’ के ‘अपरीक्षित कारक’ नामक कृति से बालकों के ज्ञान-वृद्धि के उद्देश्य से ली गई है।

अलसस्य स्वप्नः पाठ का हिन्दी अर्थ

1. कस्मिंश्चिन्नगरे कश्चित् स्वभाव कृपणः विप्रः प्रतिवसति स्म। तेन भिक्षार्जितैः
भुक्तशेषैः सक्तुभिः कलशः सम्पूरितः। तं च घटं नागदन्ते अवलम्ब्य तस्याधस्तात् खट्वां निधाय सततम् एकदृष्ट्या तम् अवलोकयति।

शब्दार्थ :
कस्मिं-किसी-any; स्वभावकृपणा-स्वभाव से कँजूस-miser by nature; विप्रः-ब्राह्मण-Pandit, Wiseman; प्रतिवाति-रहता-Lives; भिक्षार्जितः-भिाक्षा के द्वारा अर्जित-Collection begging: भुक्तशेषैः-खाने से बचे हुए-Remaining food; सक्तुभिः-सत्तू-Power of Gram; तं-उसे-Complet, full, finish; च-और-him/ her/its; अवलम्ब्य-अवलंबित-Support; खटवां-खूटी-Nails; अवलोकयति-देखता था-Looks.

हिन्दी अर्थ :
किसी नगर में स्वभाव से कंजूस (कृपण) एक ब्राह्मण रहता था। वह भिक्षा से प्राप्त भोजन के बाद बचे हुए सत्तू को एक घड़े में भरता जाता। तब उस घड़े को एक खूटी से लटका कर उसके नीचे चारपाई पर बैठ घड़े को निरंतर देखता जाता।

2. अथ कदाचिद्रात्रौ सुप्तश्चिन्तयामास-यत् अयं घटः सक्तुभि परिपूर्णः वर्तते। तद्यदि दुर्भिक्षं भवति, तदनेन रुप्यकाणां शतमुत्पत्स्यते। ततस्तेन मया अजाद्वयं ग्रहीतव्यम्। ततः षाण्मासिकात् आप्रसववशात् ताभ्यां यूथंभविष्यति। ततोऽजाभिः प्रभूता गा गृहीष्यामि। गोभिर्महिषीः। महिषीभिर्वडवा। वडवाप्रसवतः प्रभूता अश्वा भविष्यन्ति। तेषां विक्रयात् प्रभूतां सुवर्णं भविष्यति। सुवर्णेन चतुः शालं गृहे सम्पत्स्यते।

शब्दार्थ :
अथ-इस प्रकार-This type; कदाचित-किसी-Anybody; सुप्त-सोते हुए-With sleeping; अयं-इस-This; सक्तुभि-सत्तू-Powder of gram; परिपूर्णः-परिपूर्ण-fulfill, over; शतमुत्पत्स्यते-सौहो जायेंगे-Hundred will be; तेन-उससे-Its; अजदूयं-दो बकरी-Two she goat; गृहीत्यम्-खरीदी जायेगी-Will have purchased; दुर्भिक्षम-अकाल-Starving; षाण्मासिकात्-छः महीने में होने वाली-Six monthly/Half yearly; ताभ्याम्-उससे-His; यूथम्-झुण्ड (समूह)-Group; गृहीष्यामि-ग्रहण करना-Will recieve; तेषां-उनके-Them; विक्रयात्-विक्रय से-From sell; प्रभूतं-बहुत अधिक-Very much; सुवर्ण-सोना-Gold; चतुःशालं-चौकोर-Square; गृहम्-घर-Home, House, Residence; सम्पत्स्यते-निर्मित करूँगा-Will build;

हिन्दी अर्थ :
तत्पश्चात् रात्रि में शयन करते समय मन में यह विचार करता कि सत्तू से यह कलश पूरी तरह भरा हुआ है। यदि अकाल पड़ जाता तो इसके द्वारा सैकड़ों रुपये प्राप्त हो जाएँगे। फिर उन रुपयों से वह दो बकरियाँ खरीदेगा। पुनः उन बकरियों से छः माह बाद पैदा होने वाले बच्चों का एक बहुत बड़ा समूह ही जाएगा। फिर वह इन बकरियों के बेचने से होने वाली आय से गायें, भैसें, भैसों से होने वाली आय से थोड़ी, उस घोड़ी से (अच्छे) किस्म के घोड़े होंगे। उन घोड़ों के बेचने से बहुत अधिक स्वर्ण प्राप्त होगा। उन स्वर्ण मुद्राओं से एक अच्छा घर निर्मित करूँगा।

3. ततः कश्चिद विप्रः मम गृहम् आगत्य रूपाढ्यां कन्यां मह्यं दास्यति। तत्सकाशात् पुत्रो मे भविष्यति। तस्य अहं “सोमशा” इति नाम करिष्यामि। ततः तस्मिञ्जानुचलन-योग्ये सजाते अहं पुस्तकंगृहीत्वा अश्वशालायाः पृष्ठदेशे उपविष्टस्तदवधारयिष्यामि। अत्रान्तरे सोमशर्मा मां दृष्ट्वा जनन्युत्सङ्गात् जानुचलनपरः अश्वखुरासन्नवर्ती मत्समीपमा गमिष्यति। ततोऽहं स्वपत्नी कोपाविष्टोऽभिधास्यामि ‘गृहाण तावद बालकम्। सा अपि गृहकर्म व्यग्रतयाऽस्मद्वचनं न श्रोष्यति। ततोऽहं समुत्थाय तं ताडयिष्यामि।

शब्दार्थ :
कश्चिद-कोई-Anybody; आगत्य-आकर-After coming; रूपाढ्यां रूपमति-Beautiful; दास्यति-देगा-Will give; तस्य-उससे-Her/Him; भविष्यति-होगा-Will/Shall; करिष्यामि-करूंगा-Will do/shall do; गृहीत्वा-ग्रहण करके-Except; जानुचलनयोग्ये-घुटने से चलने योग्य होने पर-Walking with knee, With fulfill of qualification; उत्सङ्गात्-गोद से-by lap; भग्नः-टूट गया-broke; षाण्डुरताम्-पीले रंग का-The colour of yellow; असम्भव्याम-असम्भव-Impossible; पृष्ठदेशे-पृष्ठ देश में-Behind of the stable; धारयिष्यामि-धारण करूँगा-Keep,except; तावद् बालकम-तुम्हारे बालक का-To your son; श्रोष्यति-सुना जाता है-Is listen; ताडयिस्यामि-पिटाई करूँगा-Will beating;

हिन्दी अर्थ :
तत्पश्चात् कोई ब्राह्मण मेरे घर आकर अपनी रूपवती कन्या मुझे देगा। उससे मेरा पुत्र होगा। उसका नाम मैं सोम शर्मा रलूँगा। तत्पश्चात् बालक के चलने योग्य हो जाने पर मैं पुस्तक लेकर घुड़साल के पीछे बैठकर अध्ययन करूँगा और बालक सोम शर्मा मुझे देखकर घुटने के बल घोड़े के खुरों के पास से होता हुआ घुड़साल में मेरे पास आ जाएगा। तब मैं अपनी पत्नी को गुस्से में डाँटते हुए पकड़ने को कहूँगा। वह भी गृहकार्य में व्यस्त होने के कारण मेरे वचन नहीं सुनेगी तो मैं उसकी पिटाई करूँगा।

4. एवं तेन ध्यानस्थितेन प्रहारो दत्तो यथा स घटो भग्नः स्वयं च पाण्डुरतां गतः अतोऽहं ब्रवीमि –
अनागतवती चिंताम असम्भाव्यां करोति यः।
स एव पाण्डुरः शेते सोमशर्मपिता यथा ॥

शब्दार्थ :
अनागतवतीम्-न आयी हुई को-Unreachable/miss call; ध्यानस्थितेन-ध्यान करते हुए-With meditate; ततैव-इसी प्रकार-This type; प्रहारो-प्रहार किया-Stroke.
हिन्दी अर्थ-इस प्रकार वह ब्राह्मण मन में ध्यान करते हुए उसी प्रकार प्रहार किया जिससे वह घड़ा फूट गया और ब्राह्मण (सत्तू के गिरने से) पीला पड़ गया। अतः मैं कहता हूँ –

“न आई हुई की चिंता करते हुए असंभावित कार्य की जो कल्पना करता है वह सोम शर्मा के पिता की तरह पीले रंग का हो जाता है।

MP Board Class 9th Social Science Solutions Chapter 18 Food Security in India

MP Board Class 9th Social Science Chapter 18 Text Book Questions

Choose the Correct Answer:

Question 1.
Kharif crop is –
(a) Wheat
(b) Gram
(c) Paddy
(d) Oat.
Answer:
(c) Paddy

Question 2.
The part of Public Distribution System is –
(a) Shoe shop
(b) Gold & Silver shop
(c) Ration shop
(d) Grocery shop.
Answer:
(c) Ration shop

Question 3.
Target-ted public distribution is related to –
(a) Women
(b) Gents
(c) People living below the poverty line
(d) None of these.
Answer:
(c) People living below the poverty line

Question 4.
How much cereal is given under Antyodaya Anna Yojna –
(a) 5 kg
(b) 10 kg
(c) 15 kg
(d) 25 kg.
Answer:
(d) 25 kg.

MP Board Class 9th Social Science Chapter 18 Very Short Answer Type Questions

Question 1.
Write the names of coarse cereal.
Answer:
Sorghum (Jowar), bajra (pearl millet) and maize.

Question 2.
In which years did India face famine?
Answer:
India had to face famine is the years 1835, 1877 and 1943.

Question 3.
What is Rojgar Ashwasan Yojna?
Answer:
Under Rojgar Ashwasan Yojna 100 days employment can be provided to 18 – 60 year old unskilled labor so that they are able to earn and purchase food grains through revamped public distribution system.

Question 4.
What is meant by minimum support price?
Answer:
Declaration of support price of agricultural crops means to give the guarantee of a minimum price to farmers for their crops.

Question 5.
Write the names of any two schemes launched for food security.
Answer:

• Target-ted public distribution system
• Kam Ke Badle Anaj Yojna.

MP Board Class 9th Social Science Chapter 18 Short Answer Type Questions

Question 1.
What are the main factors of food security? Write about them.
Answer:
The main factors of food security are –

• Availability of food to the whole population of the country.
• Availability of enough money (purchasing power) to purchase the available food.
• Food should be available to all at affordable prices.
• The quality of the available food should be good.

To calculate the pH of a buffer, go to the buffer pH calculator.

Question 2.
What is Buffer Stock? Explain.
Answer:
if the production of food grains is less then to face such crisis of shortage and to distribute them through Public Distribution System, the stock of food grains kept by the government is known as Buffer Stock. Buffer Stock is the stock of food grains namely wheat and rice procured by government through Food Corporation of India (FCI).

The FCI purchases wheat and rice from farmers in states where there is surplus production. These food grains are stored in large granaries. It helps in resolving the problem of shortage of food grains during emergencies.

Question 3.
Explain Target-ted Public Distribution System.
Answer:
In 1997 target-ted Public Distribution System was introduced to ensure the availability of minimum quantity of food grains to families living below the poverty line. In this system food grains are provided to the poor on special low prices by issuing specific ration cards.

This is the largest food security plan of the world. In this system 3.5 kg. of food grains per month per family is being provided from 1st April, 2006. In the same way under the “Antyodaya Anna Yojna” 25 kg. of wheat at. Rs. 2/- per kg. and rice at Rs. 3/- per kg. is being provided to very poor families through Public Distribution System.

Under this system a differential price system was adopted including people below the poverty line (BPL) and also for people above the poverty line (APL)- in which prices of wheat and rice are fixed.

Question 4.
What is Revamped Public Distribution System? Explain.
Answer:
Revamped Public Distribution System In January 1992, the Public Distribution System was amended and a revised Public Distribution System was introduced to supply essential goods to consumers of remote area, schedule tribes, backward classes, drought – affected and mountainous areas of the country. Its characteristics are as follows:

1. Preference has been given to the people of drought – affected areas, desert areas, mountainous area and slums in urban areas.

2. It is aimed at providing more quantity of food at comparatively low prices. Other than six chief essential commodities goods like tea, soap, pulse, iodized salt are included in it.

3. Rojgar Aswan Plan has been started in the development blocks included under this plan, in which 100 days employment can be provided tr 18 – 60 – year – old unskilled labor so that they are able to earn and purchase food-grains through Revamped Public Distribution System.

Question 5.
What is the role of cooperative in food security? Explain.
Answer:
In India the role of cooperative is very important in providing food security. This work is done by the consumer cooperative societies through the ration shops for the sale of food grains for the poor. In India there are different system of consumer cooperatives at national, state, district and village levels.

Out of these National Consumers. Cooperative (Federation) Ltd. is an organization at national level. State Cooperative Consumers’ Organization is affiliated to this forum (federation). There are 794 consumer cooperative stores at central level (wholesale) and 24,078 stores’at primary level.

In rural areas nearly 44,418 village level primary agricultural credit society are distributing essential goods along with their ordinary business. To fulfill the needs of consumers, consumer cooperative societies are running nearly 37,226 retail selling centers in urban and semi – urban areas.

Question 6.
Differentiate between Kharif and Rabi Crops.
Answer:
Kharif:

• Kharif crops are shown in June or early July and harvested at tire end of Monsoon. This means sowing is done at the onset of monsoon (June and July) while harvesting is done at the end of Monsoon (October and November).
• Kharif crops are rice, jowar, maize, millet, groundnut, jute and cotton pulses are also grown in this session.
• Kharif crops are of tropical climate. (Some changes in this pattern take place, see the note in bracketed column of rabi crop.)

Rabi:

• Rabi crop season starts in November-December and hares – ting .takes place in the months of April and May.
• the major rabi crops are – wheat, barley, gram,, linseed, rasped and mustard.
• in the southern half of the Indian peninsula where temperatures are sufficiently high and rain occurs in winters this classification become blurred. Crops like Jowar are grown in.

MP Board Class 9th Social Science Chapter 18 Long Answer Type Questions

Question 1.
What are the major cereals of India? Describe.
Answer:
India is an agricultural country and the chief occupations is farming. Cereals are grown is about 70 to 80% of the total agricultural land. rice, wheat millers and maize are the major cereals.

1. Rice:
Rice is the staple food crap of India. It thrives well in hot and humid climate. It requires temperature of 25°C, and rainfall of 100 cm and above and loamy fertile soil. The chief rice producing areas in India are the coastal strips, the Gainga Plains, the Brahmaputra valley, the deltas of Godavari, Krishna and Kaveri.

High yielding varieties, improved planting techniques, irrigation facilities and use of fertilizers have enabled Sadie to increase the production of rice in 1985-86 to 61 million tonnes and average yield per hectare rose to 15.7 Quintilian (2 \(\frac { 1}{2}\) tonnes, increase)

2. Wheat:
Wheat is the second important food crop of India. It requires a cool and moist climate during growing season and a dry climate at the time of ripening. Annual rainfall of 50 to 75 cm and fertile and sandy soil is very suitable – The chief wheat growing areas are Punjab, Haryana IIP, Bihar, MP., Rajashtan Maharashtra, etc.

because all the conditions far wheat production are found here. The use of high yielding varieties,, fertilizers and irrigation facilities helped to raise fire average yield per acre and increased the production of wheat 51 million mark in 1985 – 89. This breakthrough in the production of wheat is called the Green Resolution.

3. Millets:
Sorghum (Jo-war) and bajra are important millets in India. Sorghum (Jowar) In India Jowar has been grown from ancient period. It is used as fodder for cattle and as a food for human beings. In India it is food of the poor, ha foreign countries it is used to prepare starch and glucose.

In northern India it is a Kharif crop but in southern India it is a crop of Kharif and Rabi both. About 87 percent of the total production of Jowar (sorghum) in the country is produced in Madhya Pradesh, Maharashtra, Karnataka and Andhra Pradesh.

4. Bajra:
It is a Kharif crop in northern India. In southern India it is a crop of Rabi and Kharif both. It is used as fodder for cattle. India is the largest producer of Bajra in the world, hi India main Bajra producing states are Rajasthan, Gujarat, Maharashtra, Uttar Pradesh, Tamilnadu, Haryana, Karnataka, Andhra Pradesh and Punjab. Of the total production of Bajra in the country 96 per cent is grown here.

5. Maize:
Maize is the crop of plains and mountainous region. It is used as fodder for cattle and as food to eat. Man uses its different varieties for food products. In foreign countries starch and glucose are prepared from this. In India it is grown in about all states but mainly it is grown in Uttar Pradesh, Punjab, Bihar, Madhya Pradesh, Rajasthan, Gujarat and Karnataka.

Question 2.
What is food security and why is it necessary? Explain.
Answer:
Food security related to the food – related needs of man. In simple words food security means availability of nutritive food to all. Also people should have purchasing power (money) for the arrangement and availability of food at reasonable prices. According to the World Development Report, 1986 “Food security is the availability of adequate food at all time for active and healthy life for all”.

Necessity of Food Security:
In the present Indian situation food security has become very important. Our economy is developing but the population is also increasing rapidly. So to meet the increasing demand, food security has become necessary. The causes responsible for this can be divided into two parts internal causes and external causes.

I. Internal causes:
Internal causes include those which are related to the internal conditions of the country. Following factors are included in these.

1. Basis of life:
India is a country of large population and the birth rate is also very high. Therefore food security is necessary.

2. Dependence on Monsoon:
Majority of crops in India are dependent on monsoon for irrigation, but the monsoon is always uncertain and irregular. The distribution of rains is uneven too. Consequently droughts and famines are common features of our economy. Therefore food security is necessary.

3. Low Productivity:
In India the productivity of food grains regarding per hectare and per labor is low. From this point of view also food security is necessary.

4. Natural Calamities:
Other than the problem of monsoon, flood, insects and pets, cold waves, soil erosion etc. also destroy the food crops in some or the – other part of the country. So the problem of shortage of food crops arises. The famine in Orissa of 1835 in Punjab and Madhya Pradesh in 1877 and in West Bengal in 1943, lacks of people died of hunger. So food security is necessary to face these natural calamities.

5. Continuously Rising Prices:
The prices of food grains are increasing continuously which results in starvation. So food security is necessary to overcome this problem.

6. Progress of the Country:
No country can progress without self-sufficiency of food, and for this food security is necessary.

II. External causes:
External causes include those causes which are related to the relation of the other countries with our country. Following are the external causes:

1. Dependence on Foreign Countries:
Food is the basic need of human beings. So when this requirement is not fulfilled it becomes the primary duty of the Government to fulfill these needs of the people. If there is a shortage of food we have to depend on foreign countries. Whenever there is inadequate supply of food-grains in our country we have to import even if food graii are costly or cheap the quality is good or bad. Thus dependence on foreign countries increases.

2. Decrease in Foreign Exchange:
Whenever we import things like food grains we have to spend our foreign exchange unnecessarily. We can meet our demand for food ourselves but we cannot. This results in shortage of foreign exchange to purchase very important commodities.

3. Foreign Pressure:
Countries which supply food grains to other countries become influential and then they pursue them to follow their policies. These countries dominate those countries which import food grains from them, as a result they lose their freedom to decide their foreign policies.

In the year 1965 – 66 and 1966 – 67 due to the failure of monsoon India had to face a devastating drought and therefore wheat was imported from America. During these frequent emergencies of food grains India experienced that food security is very essential to save people from starvation, to protect self – respect that honor and sovereignty and for the development of the country.

Question 3.
How does the government provide food security to the poor? Explain.
Answer:
Government provides food security to the poor through the following measures:

1. Public Distribution System.
2. Alertness of Government
3. Measures taken in a Critical Situation.

1. Public Distribution System:
By Public Distribution System is meant that system in which different consumer goods are sold in sufficient quantity of fixed prices to the consumers specially to the poor section of society. In this system different goods such as wheat, rice, sugar, imported edible oil, coal and kerosene oil etc. are sold through ration shops or cooperative consumer stores.

The profit rate for these sellers ’are fixed and they have to sell the goods to the ration card holders on fixed price and in fixed quantities. There are three kinds of ration cards B.P.L. card, A.P.L card and Antyodaya cards. BPL cards are meant for those people who are below poverty line, APL cards are meant for those people who are above poverty line and Antyodaya cards are issued to those people who are the poorest of the poor.

The Public Distribution System is regulated by central and state government together. The central government allots food grains and other commodities to state and determines prices also. The state has the right to add transportation charges etc. to the prices fixed by Central Govt.

The transportation, collection, distribution and inspection of these goods processed under this system is done by state government. It is clear from the above table that Public Distribution System plays an important role in providing food-grains to people.

The state government can include those goods also in Public Distribution System which it can purchase if required. In India distribution of food-grains is increasing continuously through Public Distribution System as shown in the given table:

Public Distribution System and Distribution of Food Grains:

2. Alertness of Government:
Our government is very alert in providing food security to the poor. It has developed food security system to make food grains available at reasonable prices to the poor and other people.

3. Measures Taken in a Critical Situation:
The government takes several steps in order to make food grains available to the poor during the period of food crisis arising due to any other reasons or due to natural calamities. Some of these measures are given below:

I. Efforts to Increase Food Grains:
For food security it is important that the production of food grains should be enough in quantity. In this the contribution of green revolution is quite important under Green Revolution mechanization of agriculture, use of high yielding hybrid variety of seeds, fertilizers and insecticides and irrigation facilities were extended.

Also due to promotion of consolidation of land holdings, abolishing of mediators, today the country has become self-sufficient in the field of food grains. The progress of food grains in India can be explained on the basis of following table:

Food Grain Production in India (in crore tonnes):

II. Minimum Support Price:
The prices of agriculture products are very flexible, at the time of harvesting the supply increases, due to which there is enough decrease in price. As prices at this time go down below the fixed limit the producer finds it difficult to get the cost of their products.

1. Therefore government declares minimum support price for agricultural products, under which when market price of food-grains becomes less than its support price, the government starts purchasing food grains on self-declared support price. Due to which farmers get inspired to produce more and more and the government procures food grain for “Buffer Stocks”.

2. The support prices declared by the government during last years are shown here in following table:

Support of Different Food Grains (Rupees per quintal):

III. Buffer Stock:
If the production of food grains is less than to face such crisis of shortage and to distribute them through Public Distribution System, the stock of food grains kept by government is known as Buffer Stock. Buffer stock is the Stock of food grains, namely wheat and rice procured by government through Food Corporation of India (FCI).

The FCI purchases wheat and rice from farmers in states where there is surplus production. The farmers are paid a pronounced price for their crop. This price is called “Minimum Support Price”. The government declares these prices before the sowing season to provide incentives to farmers for raising production of these crops.

These food grains are stored in large granaries. It helps in resolving the problem of shortage of food grains during emergencies. The table of Buffer Stock explains that in the past years in India the stocks has been greater than fixed minimum quantity which is a sign of strong food security of India.

Status of Buffer Stock in India (in million tonnes):

Question 4.
What steps has the government taken to increase food grains?
Answer:

Government provides food security to the poor through the following measures:

1. Public Distribution System.
2. Alertness of Government
3. Measures taken in a Critical Situation.

1. Public Distribution System:
By Public Distribution System is meant that system in which different consumer goods are sold in sufficient quantity of fixed prices to the consumers specially to the poor section of society. In this system different goods such as wheat, rice, sugar, imported edible oil, coal and kerosene oil etc. are sold through ration shops or cooperative consumer stores.

The profit rate for these sellers ’are fixed and they have to sell the goods to the ration card holders on fixed price and in fixed quantities. There are three kinds of ration cards B.P.L. card, A.P.L card and Antyodaya cards. BPL cards are meant for those people who are below poverty line, APL cards are meant for those people who are above poverty line and Antyodaya cards are issued to those people who are the poorest of the poor.

The Public Distribution System is regulated by central and state government together. The central government allots food grains and other commodities to state and determines prices also. The state has the right to add transportation charges etc. to the prices fixed by Central Govt.

The transportation, collection, distribution and inspection of these goods processed under this system is done by state government. It is clear from the above table that Public Distribution System plays an important role in providing food-grains to people.

The state government can include those goods also in Public Distribution System which it can purchase if required. In India distribution of food-grains is increasing continuously through Public Distribution System as shown in the given table:

Public Distribution System and Distribution of Food Grains:

2. Alertness of Government:
Our government is very alert in providing food security to the poor. It has developed food security system to make food grains available at reasonable prices to the poor and other people.

3. Measures Taken in a Critical Situation:
The government takes several steps in order to make food grains available to the poor during the period of food crisis arising due to any other reasons or due to natural calamities. Some of these measures are given below:

I. Efforts to Increase Food Grains:
For food security it is important that the production of food grains should be enough in quantity. In this the contribution of green revolution is quite important under Green Revolution mechanization of agriculture, use of high yielding hybrid variety of seeds, fertilizers and insecticides and irrigation facilities were extended.

Also due to promotion of consolidation of land holdings, abolishing of mediators, today the country has become self-sufficient in the field of food grains. The progress of food grains in India can be explained on the basis of following table:

Food Grain Production in India (in crore tonnes):

II. Minimum Support Price:
The prices of agriculture products are very flexible, at the time of harvesting the supply increases, due to which there is enough decrease in price. As prices at this time go down below the fixed limit the producer finds it difficult to get the cost of their products.

1. Therefore government declares minimum support price for agricultural products, under which when market price of food-grains becomes less than its support price, the government starts purchasing food grains on self-declared support price. Due to which farmers get inspired to produce more and more and the government procures food grain for “Buffer Stocks”.

2. The support prices declared by the government during last years are shown here in following table:

Support of Different Food Grains (Rupees per quintal):

III. Buffer Stock:
If the production of food grains is less than to face such crisis of shortage and to distribute them through Public Distribution System, the stock of food grains kept by government is known as Buffer Stock. Buffer stock is the Stock of food grains, namely wheat and rice procured by government through Food Corporation of India (FCI).

The FCI purchases wheat and rice from farmers in states where there is surplus production. The farmers are paid a pronounced price for their crop. This price is called “Minimum Support Price”. The government declares these prices before the sowing season to provide incentives to farmers for raising production of these crops.

These food grains are stored in large granaries. It helps in resolving the problem of shortage of food grains during emergencies. The table of Buffer Stock explains that in the past years in India the stocks has been greater than fixed minimum quantity which is a sign of strong food security of India.

Status of Buffer Stock in India (in million tonnes):

Question 5.
What is Public Distribution System and what are its main constituents? Describe.
Answer:
By Public Distribution System is meant that system in which different consumer goods are sold in sufficient quantity at fixed prices to the consumers specially to the poor section of society. In this system different goods (wheat, rice, sugar, imported edible oil, coal and kerosene oil etc.) are sold through ration shops or cooperative consumer stores.

The profit rate for these sellers are fixed and they have to sell the goods to the ration card holders on fixed price and in fixed quantities. There are three kinds of ration cards BPL Card, APL Card and Antyodaya Card. BPL cards are for people below poverty line. APL cards are for people above poverty line.

Antyodaya Cards are meant for the poorest of the poor. The Public Distribution System is regulated by central and state government together. The central government allots food grains and other commodities to state and determines prices also. The state has the right to add transportation charge etc.

to the prices fixed by Central Government. The transportation, collection, distribution and inspection of these goods processed under this system is-done by state government. The state government can include those goods also in Public Distribution System which it can purchase if required.

The main constituents of Public Distribution System. Public Distribution System includes fair-price shops. Fair Price Shop for selling cloth, soft coke depot, Super market and Kerosene shops. In India distribution of food grains is increasing continuously through Public Distribution System. The following table will show that Public Distribution system plays an important role in providing food grains to people.

Public Distribution System and Distribution of Food Grains (in million tonnes):

Question 6.
How is the Public Distribution System conducted? Describe.
Answer:

By Public Distribution System is meant that system in which different consumer goods are sold in sufficient quantity at fixed prices to the consumers specially to the poor section of society. In this system different goods (wheat, rice, sugar, imported edible oil, coal and kerosene oil etc.) are sold through ration shops or cooperative consumer stores.

The profit rate for these sellers are fixed and they have to sell the goods to the ration card holders on fixed price and in fixed quantities. There are three kinds of ration cards BPL Card, APL Card and Antyodaya Card. BPL cards are for people below poverty line. APL cards are for people above poverty line.

Antyodaya Cards are meant for the poorest of the poor. The Public Distribution System is regulated by central and state government together. The central government allots food grains and other commodities to state and determines prices also. The state has the right to add transportation charge etc.

to the prices fixed by Central Government. The transportation, collection, distribution and inspection of these goods processed under this system is-done by state government. The state government can include those goods also in Public Distribution System which it can purchase if required.

The main constituents of Public Distribution System. Public Distribution System includes fair-price shops. Fair Price Shop for selling cloth, soft coke depot, Super market and Kerosene shops. In India distribution of food grains is increasing continuously through Public Distribution System. The following table will show that Public Distribution system plays an important role in providing food grains to people.

Public Distribution System and Distribution of Food Grains (in million tonnes):

MP Board Class 9th Social Science Chapter 18 Other Important Questions

Question 1.
Choose the right answer:
(i) Kharif crops are sown in the month of –
(a) October
(b) November
(c) December
(d) January
Answer:
(a) October

Question 2.
Rabi crops are harvested in the month of –
(a) February or March
(b) March or April
(c) April or May
(d) May or June.
Answer:
(b) March or April

Question 3.
In production of food grains India stands third after –
(a) America and Australia
(b) America and China
(c) America and Canada
(d) China and Canada.
Answer:
(b) America and China

Question 4.
Antyodaya ration cards are meant for those who are –
(a) Below poverty line
(b) Above poverty line
(c) Poorest of the poor
(d) None of the above.
Answer:
(c) Poorest of the poor

Question 5.
Target-ted Public Distribution System was introduced in the year –
(a) 1997
(b) 1998
(b) 1999
(d) 2000.
Answer:
(a) 1997

Fill in the blank:

1. Reserve stock of food grains to meet …………… situations.
2. ……………. cards for people below poverty line.
3. ……………. cards for the poorest of the poor.
4. In India two kinds of wheat are grown……………… and mikrani wheat.
5. India is second largest producer of ………………… in the world.

Answer:

1. Emergency
2. BPL
3. Antyodaya
4. Walgair wheat
5. Rice.

MP Board Class 9th Social Science Chapter 18 Very Short Answer Type Questions

Question 1.
Name the main requirements of life?
Answer:
Food, clothing and housing.

Question 2.
How does the World Development Report 1986? Define Food security.
Answer:
According to the World. Development Report 1986, “Food security is the availability of adequate food at all time for active and healthy life for all”.

Question 3.
On what three factors does food security depend?
Answer:
Food security depends on three factors Public Distribution System, alertness of government and the measures taken in a situation of crisis.

Question 4.
Name the major cereals?
Answer:
The major Cereals are rice, wheat, mullets and maize.

Question 5.
Name some rabi crops?
Answer:
Some rabi crops are wheat, oat, gram, etc.

Question 6.
Name rice producing states of India?
Answer:
Rice producing states of India are West Bengal, Uttar Pradesh, Andhra Pradesh, Chhattisgarh, Madhya Pradesh, Bihar, Tamil Nadu, Orissa, Punjab amd Assam.

Question 7.
When was Public Distribution System amended?
Answer:
Public Distribution System was amended in January 1992.

Question 8.
What are the parts of Public Distribution System?
Answer:
Public Distribution System includes fair price shops, soft coke depot, super market and kerosene shops.

Question 9.
Name two crops used as fodder for cattle?
Answer:
Jowar and Bajra.

Question 10.
What type of economy have we?
Answer:
We have developing economy.

MP Board Class 9th Social Science Chapter 18 Short Answer Type Questions

Question 1.
What does food security generally imply? Mention the stages of food security?
Answer:
The food security generally implies that the whole population at all time, should have access to minimum quantity of cereals, but due to continuous changes in a developing country there can be following stages of food security:

• Availability of adequate food grains.
• Availability of food grains and pulses in adequate quantity.
• Availability of milk and milk products along with food grains and pulses.
• Availability of food-grains, pulses, milk and milk products, vegetables, fruits etc.

Question 2.
Describe the chief crops of India and their cultivation regions.
Answer:
The chief crops of India paddy (rice), wheat, bajra, jowar, maize, gram and pulses. Their cultivation regions

1. Paddy (rice):
West Bengal, Uttar Pradesh, Andhra Pradesh, Chhattisgarh, Madhya Pradesh, Bihar, Tamilnadu, Orissa, Punjab, Assam.

2. Wheat:
Uttar Pradesh, Punjab, Haryana, Madhya Pradesh, Bihar, Rajasthan, Maharashtra, West Bengal, Uttarakhand, Gujarat.

3. Bajra:
Rajasthan, Maharashtra, Tamilnadu, Punjab, Uttar Pradesh, Gujarat.

4. Jowar:
Madhya Pradesh, Maharashtra, Karnataka, Andhra Pradesh.

5. Maize:
Uttar Pradesh, Karnataka, Andhra Pradesh, Madhya Pradesh, Punjab, Bihar, Rajasthan.

6. Gram & Pulses:
Madhya Pradesh, Uttar Pradesh, Maharashtra, Punjab, Karnataka.

Question 3.
What do you understand by ‘Fair Price Shop’? What are its benefits?
Answer:
Sugar, cereals, kerosene etc. are distributed to the ration card holders through ration shops which are also known as ‘Fair Price Shops’. Any family with a ration card can buy stipulated amount of these items, every month from nearby ration shop. At these shops all the items are sold at a price lower than the market price. Today there are about 4.6 lakh ration shops in the country.

Question 4.
Write a short note on Buffer Stock?
Answer:
If the production of food grains is less than to face such crises of shortage and to distribute them through Public Distribution System, the stock of food grains kept by government is known as Buffer Stock. Buffer Stock is the stock of food grains namely wheat and rice procured by government through Food Corporation of India (FCI).

The FCI purchases wheat and rice from farmers in states where there is surplus production. These food grains are stored in large granaries. It helps in resolving the problem of shortage of food grains during emergencies.

MP Board Class 9th Social Science Solutions Chapter 18 Food Security in India

Question 1.
Describe coarse crops.
Answer:
Sorghum (Jowar), bajra and maize are coarse crops.

1. Sorghum (Jowar):
Jowar is used as fodder for cattle and as food for human beings. In India it is food of the poor and in foreign countries it is used to prepare starch and glucose. About 87% of the total production of jowar in the country is produced in Madhya Pradesh, Maharashtra, Karnataka and Andhra Pradesh.

2. Bajra:
It is used as fodder for cattle. India is the largest producer of bajrai in the world. The main bajra producing states of India are Rajasthan, Gujarat, Maharashtra, Uttar Pradesh, Tamilnadu, Haryana etc. Of the total production of bajra in the country 96% is grown here.

3. Maize:
It is used as food and fodder. In India it is grown in about all states but mainly it is grown in Uttar Pradesh, Punjab, Bihar, Madhya Pradesh, Rajasthan, Gujarat and Karnataka.

Question 2.
Why has food security become necessary in India? What are the causes responsible for this?
Answer:

Food security related to the food – related needs of man. In simple words food security means availability of nutritive food to all. Also people should have purchasing power (money) for the arrangement and availability of food at reasonable prices. According to the World Development Report, 1986 “Food security is the availability of adequate food at all time for active and healthy life for all”.

Necessity of Food Security:
In the present Indian situation food security has become very important. Our economy is developing but the population is also increasing rapidly. So to meet the increasing demand, food security has become necessary. The causes responsible for this can be divided into two parts internal causes and external causes.

I. Internal causes:
Internal causes include those which are related to the internal conditions of the country. Following factors are included in these.

1. Basis of life:
India is a country of large population and the birth rate is also very high. Therefore food security is necessary.

2. Dependence on Monsoon:
Majority of crops in India are dependent on monsoon for irrigation, but the monsoon is always uncertain and irregular. The distribution of rains is uneven too. Consequently droughts and famines are common features of our economy. Therefore food security is necessary.

3. Low Productivity:
In India the productivity of food grains regarding per hectare and per labor is low. From this point of view also food security is necessary.

4. Natural Calamities:
Other than the problem of monsoon, flood, insects and pets, cold waves, soil erosion etc. also destroy the food crops in some or the – other part of the country. So the problem of shortage of food crops arises. The famine in Orissa of 1835 in Punjab and Madhya Pradesh in 1877 and in West Bengal in 1943, lacks of people died of hunger. So food security is necessary to face these natural calamities.

5. Continuously Rising Prices:
The prices of food grains are increasing continuously which results in starvation. So food security is necessary to overcome this problem.

6. Progress of the Country:
No country can progress without self-sufficiency of food, and for this food security is necessary.

II. External causes:
External causes include those causes which are related to the relation of the other countries with our country. Following are the external causes:

1. Dependence on Foreign Countries:
Food is the basic need of human beings. So when this requirement is not fulfilled it becomes the primary duty of the Government to fulfill these needs of the people. If there is a shortage of food we have to depend on foreign countries. Whenever there is inadequate supply of food-grains in our country we have to import even if food graii are costly or cheap the quality is good or bad. Thus dependence on foreign countries increases.

2. Decrease in Foreign Exchange:
Whenever we import things like food grains we have to spend our foreign exchange unnecessarily. We can meet our demand for food ourselves but we cannot. This results in shortage of foreign exchange to purchase very important commodities.

3. Foreign Pressure:
Countries which supply food grains to other countries become influential and then they pursue them to follow their policies. These countries dominate those countries which import food grains from them, as a result they lose their freedom to decide their foreign policies.

In the year 1965 – 66 and 1966 – 67 due to the failure of monsoon India had to face a devastating drought and therefore wheat was imported from America. During these frequent emergencies of food grains India experienced that food security is very essential to save people from starvation, to protect self – respect that honor and sovereignty and for the development of the country.

MP Board Class 9th Social Science Solutions

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Solution:

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

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

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

Some Observations:

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

MP Board Class 9th Maths Solutions

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

Question 1.
A traffic signal borard, indicating ‘SCHOOL AHEAD’, is an equilateral triangle with side ‘a’ Find the area of the signal board, using Heron’s formula. If its perimeter is 180 cm, what will be the area of the signal board?
Solution:

Question 2.
The triangular side walls of a flyover have been used for advertisements. The sides of the walls are 122 m, 22 m and 120 m (see Fig.) the advertisements yield an earning of ₹ 5000/m² per year. Acompany hired one of its walls for 3 months. How much rents did it pay?

Solution:

s = \(\frac{122+120+22}{2}\) = \(\frac{264}{2}\) = 132 m
s – a = 132 – 122 = 10 m
s – b = 132 – 22 = 12m
s – c = 132 – 22 = 110 m
area of triangular portion of wall = \(\sqrt{32x10x12x110}\)
= \(\sqrt{2x2x3x11x10x2x2x3x11x10}\)
= 10 x 2 x 2 x 3 x 11 = 1320 m²
Rate = ₹ 5000/m² per year
Rent for 3 months = 1320 x \(\frac{5000×3}{12}\)
= 330 x 5000
= ₹ 16,50,000

Question 3.
There is a slide in a park. One of its side walls has been painted in some colour with a message “Keep The Park Green And Clean” (see Fig.). If the sides of the wall are 15 m, 11 m and 6 m, find the area painted in colour.

Solution:
a = 15 m
b = 11 m
c = 6m
p = a + b + c
= 15 + 11 + 6
= 32 m P

s = \(\frac{P}{2}\) = \(\frac{32}{2}\) = 16m
s – a = 16 – 15 = 1 m
s – b = 16 – 11 = 5 m
s – c = 16 – 6 = 10m
Area of triangular park = \(\sqrt{16x1x5x10}\)
= \(\sqrt{2x2x2x2x1x5x2x5}\)
= 2 x 2 x 5√2 = 2o\(\sqrt{2m^{2}}\)

Question 4.
Find the area of a triangle two sides of which are 18 cm and 10 cm and the perimeter is 42 cm.
Solution:

a = 18 cm
b = 10 cm
Let the third side be c
p = 42 cm
18 + 10 + C = 42
C = 14
S = \(\frac{P}{2}\) = \(\frac{42}{2}\) = 21 cm
s – a = 21 – 18 = 3
s – b = 21 – 10 = 11
s – c = 21 – 14 = 7
Area of ∆ = \(\sqrt{21x3x11x7}\) = \(\sqrt{3x7x3x11x7}\)
= 3 x 7\(\sqrt{11}\) = 21\(\sqrt{11}\) cm²

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

Question 6.
An isosceles triangle has perimeter 30 cm and each of the equal sides is 12 cm. Find the area of the triangle.
Solution:

a = 12 cm
b = 12cm
Let the third side be c.
p = a + b + c
30 = 12 + 12 + c
c = 30 – 24 = 6 cm
s = \(\frac{P}{2}\) = \(\frac{30}{2}\) = 15
s – a = 15 – 12 = 3
s – b = 15 – 12 = 3
s – c = 15 – 6 = 9
Area of ∆ = \(\sqrt{5x3x3x9}\)
= \(\sqrt{5x3x3x3x3x3}\)
= 3 x 3\(\sqrt{15}\) = 9\(\sqrt{15}\) cm²

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

Class 10 Maths formulas are the cornerstone of numeracy skills.

Example 1:
A triangle and a parallelogram have the same base and the same area. If the sides of the triangle are 13 cm, 14 cm and 15 cm and the parallelogram stands on the base 14 cm, And the height of the parallelogram.
Solution:

Here, a = 13 cm,
b = 14 cm,
c = 15 cm
Base of parallelogram =14 cm.

= 7 x 3 x 2 x 2
= 84 cm²
Let h be the height of the parallelogram ADEC.
Area of parallelogram ADEC = Area of ∆ABC (given)
Base x height = 84
14 x height = 84
h = \(\frac{84}{14}\)
= 6 cm.

Example 2:
The sides of a quadrilateral, taken in order are 5, 12, 14 and 15 meters respectively, and the angle contained by the first two sides is a right angle. Find its area.
Solution:

Here, AB = 5m
BC = 12m
CD = 14m
DA = 15 m
Join AC. The ABCD is divided into two triangles ABC and ACD. The area of the quadrilateral is equal to sum of areas of ∆ABC and ∆ADC.
In ∆ABC

area of ABCD
= ar (∆ABC) + ar (∆ACD) –
= (84 + 30)m² = 114m²

Example 3:
In a parallelogram measure of adjacent sides are 34 cm and 20 cm. One of the diagonals is 42 cm. Find the area of the parallelogram.
Solution: In Fig.

AB = DC = 34 cm
AD = BC = 20 cm
AC =42 cm.
We know that the diagonal of a parallelogram divides it into two tri¬angles of equal area.
∴ Area of parallelogram ABCD = 2 x Area of (∆ABC)
Consider ∆ABC
a = 34cm
b = 20cm
c = 42cm
s = \(\frac{a+b+c}{2}\)
= \(\frac{34+20+42}{2}\)
= \(\frac{96}{2}\) = 48 cm
s – a = 48 – 34 = 14 cm
s – b = 48 – 20 = 28 cm
s – c = 48 – 42 = 6 cm
By Heron’s formula,

= 2 x 2 x 6 x 14
= 336 cm²
∴ Area of (∥^gm ABCD) = 2 x 336
= 672 cm²

Example 4:
A rhombus sheet, whose perimeter is 32 m and whose one diagonal is 10 m long, is painted on both sides at the rate of? 5 per m2. Find the cost of painting.
Solution:

Given P = 32m
BD = 10m
Rate of painting = ₹ 5/m²
Let the sides of rhombus be x m.
P = Ax
⇒ 32 = 4x
∴ x = 8m
So, AB = BC = CD = DA = 8 m
We know that the diagonal of a rhombus divides it into two triangles of equal area. .
∴ Area of rhombus ABCD = 2 x area of ∆ABD
Consider ∆ABD
a = 8m
b = 8m
c = 10m
S = \(\frac{a+b+c}{2}\) = \(\frac{8+8+10}{2}\)
= 13 m.
s – a = 13 – 8 = 5 m
s – b = 13 – 8 = 5m
s – c = 13 -10 = 3 m
By Heron’s formula,
Area of ∆ABD = \(\sqrt{s(s-a)(s-b)(s-c)}\)
= \(\sqrt{3x5x5x3}\)
= 5 x \(\sqrt{39}\)
= 5 x 6.24 = 31.2 m²
Area of rhombus ABCD = 2 x 31.2 = 62.4 m²
Area of rhombus to be painted = 2 x area of rhombus (∴ Painting is to be done on both sides)
= 2 x 62.4 = 124.80
Cost of painting = Rate x Area
= 5 x 124.80
= ₹ 624.

Example 5:
Two parallel sides of a trapezium are 60 cm and 77 cm other sides are 25 cm and 26 cm. Find the area of trapezium.
Solution:

Given AB = 60 cm
DC = 77 cm
AD = 25 cm
BC =26 cm
Draw a line BE ∥ AD from point B.
In ABED
AB ∥ DE
AD ∥ BE
ABED is a parallelogram.
AB = DE = 60
EC = 77 – 60 = 17 cm.
AD = BE = 25 cm
In ∆BEC
a = EC = 17 cm
b = BE = 25 cm
c = BC = 26cm
s = \(\frac{17+25+36}{2}\)
s – a = 34 – 17 = 17 cm
s – b = 34 – 25 = 9 cm
s – c = 34 – 26 = 8cm
By Heron’s formula,

MP Board Class 9th Maths Solutions

MCQ Questions for Class 9 English Moments Chapter 1 The Lost Child MCQ with Answers

MP Board Class 9th General English Unseen Passages

Factual Passages

Q. 1. Read the following paragraph and answer the questions.

The first computer was built in the early nineteenth century by Charles Babbage. He called it a ‘difference engine’: It could carry out long calculations and print the results. Later he invented a better machine called an ‘analytical engine’. The computer that you use has been developed by several scientists working independently or as a team. It is being improved everyday.

The computer can work out calculations and provide answers to complicated problems in a flash. A man would take days, or even months, to work the same thing out. But it cannot do things on its own. All the information it needs to do something is fed into it. This information is called data. Then it must be given clear and precise instructions about what to do with this data. These instructions have to be in a language that the computer understands. The information and the instructions make up a computer program. If a computer gives an incorrect answer, something must be wrong with the programme and not with the machine.

The computer also has a memory. It can store away information and use it later. It can, therefore, be compared to the human brain. But it can solve problems much faster and more accurately than the human brain. It can be made to play games like chess and can translate words from one language to another. (If you like, it can correct your spelling mistakes in what you write.) But it cannot take decisions or think up new deas. That is where it cannot compete with the human brain.

Questions
(1) What two things could the first computer developed by Charles Babbage do?
(2) What is a computer program?
(3) In what way is the computer better than a human brain?
(4) Give a word from the passage that means same as ‘correctly’.
(5) Find a word from the passage that means ‘without anybody’s help’.
Answers
(1) It could carry out long calculations and print the results.
(2) A computer program consists of information and instructions.
(3) A computer is better than a human brain because it solves problems much faster and more accurately than human brain.
(4) accurately.
(5) independently.

Q. 2. Read the given passage and answer the following questions.

Kalpana Chawla, the astronaut who died on aboard the space shuttle Columbia, had been sponsoring two students from her school (Tagore Bal Niketan in Kamal) each year since 1997 for the International Space School Camp in Houston.

Manpreet Kaur and Namita Alung visited NASA in August 2002. “We spent an excellent day with KC; she even cooked for us and made us feel totally at home,” said Namita. These two and other youngsters who benefited from this programme say KC, as she was popularly known might have been the first Indian-born woman in space but was entirely unaffected by her success.

Gaurav Goel of the 1999 batch and now an engineering student at Ambala said, “Not only was KC down to earth, she still retained the Indian in herself despite living in US for so many years.”

Even as a student, Kalpana had looked out for other students. She used to pay the fees for two of her college mates who could not afford it. “It is possible that to this day they are not aware that Kalpana used to pay their tuition fees,” says Sovina Sood, Kalpana’s junior in the Punjab Engineering College.

Sovina who now teaches Civil Engineering said that sometimes Kalpana would hand over the money to her “but-ask me not to disclose it to anybody.”

Questions
(1) What did Kalpana Chawla do since 1997?
(2) Who visited NASA in August 2002?
(3) What did Kalpana Chawla do for her college mates when she was a student?
(4) Give a word from the passage that means same as ‘getting advantage’.
(5) Sponsoring means—
(a) to provide support, (b) contributing, (c) participating.
Answers
(1) Kalpana Chawla had been sponsoring two students from her school since 1997.
(2) Sanpreet Kaur and Namita Along visited NASA in August 2002.
(3) Kalpana Chawla used to pay the fees for two of her college mates.
(4) benefited.
(5) (b) contributing.

Q. 3. Read the following passage and answer the questions below it.

Ramcharit Manas is the holy book of Hindus.

It was written by Tulsidas. It is the story of Ram, the son of Dashrath, the king of Ayodhya. Ram is described as an ideal character. He is an ideal son, ideal husband, ideal brother and ideal ruler. He left Ayodhya to obey his father and lived in forest. When Ravana took away Sita, he attacked Lanka. Ravana was killed in the war and Sita was released. They returned to Ayodhya after 14 years of exile. Then Ram became the king of Ayodhya.

Questions
(1) Who wrote Ramcharit Manas?
(2) What does Ramcharit Manas describe?
(3) How is Ram described in the book?
(4) Find a-word from the passage that means same as ‘to set free’.
(5) Exile means—
(a) banishment, (b) movement, (c) to expel.
Answers
(1) Ramcharit Manas was written by Tulsidas.
(2) Ramcharit Manas describes the life of Lord Ram.
(3) Ram is described as an ideal character in the book.
(4) released.
(5) (a) banishment.

Q. 4. Read the following paragraph and answer the questions givep below it.

India is facing many dangerous problems. The main problems among them are unemployment, pollution, population and illiteracy. Due to these harmful problems our country cannot progress well. All of us and specially our government should make effective efforts to solve them. The role of students, teachers and of the whole society has great importance in this field. We should change our tendency, policy of education and should end these problems. Our state governments are trying their best to solve such huge problems. Every change needs enough time. Questions

(1) What are the main problems of India?
(2) Who can play the main role in this field?
(3) Give a suitable heading to the above passage.
(4) Give a word from the passage that means same as ‘producing a desired result’.
(5) Tendency means—
(a) habit, (b) behavior, (c) incline.
Answers
(1) The main problems of India are unemployment, pollution, population and illiteracy.
(2) Students, teachers and whole society can play the main role in this field.
(3) ‘Problems of India’.
(4) effective.
(5) (a) habit.

Q. 5. Read the following passage and answer the questions given below it.

Smoking is the single largest preventable cause of death worldwide. It is killing about 2,200 people in India everyday that means one every forty seconds. It is alarming that in spite of this, smoking is increasing among the youth of India. According to World Bank Study, India, Indonesia and China are the only countries in the world where incidence of smoking is going up. It is increasing not only in cities but also in towns and villages. Higher educated groups are also taking to smoking more readily.

Questions
(1) How many people in India die in a day due to smoking?
(2) In which countries is smoking going up?
(3) Who are taking up smoking more readily?
(4) Give a word from the passage that means the same as ‘reason’.
(a) cause (b) work (c) begin (d) habit.
(5) Find a word from the passage that means frightening or worrisome.
(a) beating (b) ringing (c) alarming (d) singing.
Answers
(1) Smoking is killing about 2,200 people in India everyday.
(2) Smoking is going up in India, Indonesia and China.
(3) Higher educated groups are taking to smoking more readily.
(4) (a) cause.
(5) (c) alarming.

Literary Passages

Q. 1. Read the following stanzas and answer the questions given below.

Life has loveliness to sell,
All beautiful and splendid things.
Blue waves whitened on a cliff,
Soaring fire that sways and sings,
And children’s faces looking up,
Holding wonder like a cup.
Life has loveliness to sell,
Music like a curve of gold,
Scent of fine trees in the rain,
Eyes that love you, arms that hold,
And for your spirit’s still delight,
Holy thoughts that star the night.

Questions
(1) What does life have to sell?
(2) What do soaring fire do?
(3) With what music is compared?
(4) Find out a word from the poem that means same as ‘magnificent’.
(a) wonder (b) splendid (c) delight (d) spirit.
(5) Find a word from the passage that means ‘steep rock’.
(a) a small hill (b) island (c) cliff (d) curve.
Answers
(1) Life has. loveliness to sell.
(2) Soaring fire sways and sings.
(3) Music is compared with a curve of gold.
(4) (a) splendid
(5) (c) cliff.

Q. 2. Read the following paragraph and answer the questions given below.

A few days later, Premchand resigned his job of Inspector of Schools after having worked in the department for twenty years. He was a free man after all. Now he could write novels and stories about his country and its people. In his books he dealt with the lives of the peasants and workers. He revealed the greed and meanness of the money-lenders, landlords and priests. He attacked the social evils like dowry and early marriage. He held society responsible for the sins of women.

Questions
(1) Which job did Premchand resign?
(2) What kind of man was Premchand after his resignation?
(3) What did he reveal?
(4) Find out a word from the passage that means same as—‘Farmers’.
(5) Find out a word from the passage that means ‘one who lends money’.
Answers
(1) Premchand resigned the job of Inspector of Schools.
(2) Premchand was a free man.
(3) He revealed the greed and meanness of money lenders.
(4) Peasants.
(5) Money lenders.

Q. 3. Read the following poem and answer the questions given below it.

Unfolding Bud
One is amazed
By a water-lily bud
Unfolding
With each passing day
Taking on a richer colour
And new dimensions
One is not amazed
At a first glance,
By a poem,
Which is as tight closed
As a tiny bud.
Yet on is surprised
To see a poem
Gradually unfolding,
Revealing its rich feelings
As one reads it
Again
And over again.

Questions
(1) What two things amaze the poet?
(2) With what does a water-lily bud arrest one’s attention?
(3) What does a poem reveal?
(4) Find out a word from the passage that means same as : ‘leaf or a flower at the beginning of its growth’:
(a) bud (ii) colour (iii) thorn (iv) stem.
(5) ‘Gradually’ means :
(a) slowly, step by step (b) rapidly (c) surprisingly (d) frighteningly.
Answers
(1) An unfolding bud and an unfolding poem amaze the poet.
(2) A water-lily bud arrests one’s attention by taking on a richer colour.
(3) A poem reveals its rich feelings.
(4) (a) bud.
(5) (a) slowly, step by step.

Q. 4. Read the following passage and answer the questions given below it.

Long, long ago there lived an old woman who was very rich. She had a number of maids. They were made to work very hard to do their fixed duties at any given time.

Since there were np clocks to tell time, the old woman kept a cock. When it started crowing, everyone got up. The poor maids had to leave their beds as soon as the cock crew early in the morning every day. And the maids did not like it.’ But what could they possibly do?

The cock was their enemy, they thought. “The cock is a nuisance,” said one maid to another, “Why don’t we get rid of it ? ”

“How ?” asked her friends. “If we wring its neck and kill it, there will be no one to disturb us in our sleep. We could get up late every morning and then our mistress would not be able to say anything to us. ”

“A good idea”, cried the others. One of the maids, therefore, quietly caught hold of the bird and killed it. As a result, the next morning they were able to sleep late. The old woman slept late too, as there was no cock to wake her up. She woke up at last to discover how late it was, and that the cock was dead. She was, of course, angry, not only because she had lost her bird but also because her routine for the day had been upset.

She thought of a plan. From that day onwards she began to keep a watch herself at nights, making up for her loss of sleep by resting during the day. And as she kept watch, she went at odd hours of the night to wake up her maids so that they did not get their usual hours of sleep.

The maids found that they were worse off now.

“This is very bad”, said they. “Now the old woman wakes us up at all odd hours. We thought we had solved our problem by killing the cock. But we have not.”

You see, they were helpless now. They had to obey the old woman and work according to her set routine.

Questions
(1) Why did the maids kill the cock ?
(2) Why was the old woman angry ?
(3) Why were the maids worse off now ?
(4) Find a word from the passage that means ‘one that causes difficulty’.
(5) Wring means—
(a) to cut (b) to squeeze tightly (c) to kill.
Answers
(1) The maids killed the cock because it was their enemy, they thought.
(2) The old woman was angry not only because she had lost her bird but also because her routine for the day had been upset.
(3) The maids were worse off now because they did not get their usual hours of sleep.
(4) nuisance.
(5) (b) to squeeze tightly.

Discursive Passages

Q. 1. Read the following passage carefully and answer the questions given below it.

Home is the first and the most important school of character. It is a common saying that “Manners make the man”, and there is a second that “Mind makes the man”, but truer than either is a third that “Home makes the man”. For the home training includes not only manners and mind, but also character. It is mainly in the home that the heart is opened, the habits are formed, the intellect is awakened, and the character is moulded for good or for evil.

Questions
(1) Which is the first and most important school of character?
(2) What does home training include?
(3) Which is the common saying?
(4) Give a word from the passage that means same as ‘moral strength’.
(5) Find a word from the passage that means ‘reasoning power of the mind’.
Answers
(1) Home is the first and most important school of character.
(2) Home training includes not only manner and mind, but also character.
(3) The common saying is that “Manners make the man”.
(4) Character.
(5) Intellect.

Q. 2. Read the following passage carefully and answer the questions given below it.

There is no doubt that a common language used throughout the world does much to bring countries closer to each other. Though it is becoming increasingly easy to move from place to place, our inability to communicate with one another, gives rise to numerous misunderstandings and makes real contact between people of different “nationalities impossible. Many attempts have been made to overcome the problem and they have all failed. The fear of foreign influence and domination rules out the universal acceptance of any one of the existing major languages.

Questions
(1) What will help bring the countries of the world close to each other?
(2) What gives rise to numerous problems?
(3) What is the major problem in accepting one of the existing major languages as a common language?
(4) Find out a word from the passage that means the same as ‘surely’:
(a) no doubt (b) of course (c) easily (d) really.
(5) ‘So many’ means (a) contact (c) fear
Answers
(1) A common language will help the countries of the world to communicate with one another and create goodwill. Thus, the countries will come closer to one another.
(2) Our inability to communicate with each other gives rise to many problems.
(3) The fear of foreign influence and domination rules out the universal acceptance of any one of the existing major languages.
(4) (a) no doubt.
(5) (b) numerous.

Q. 3. Read the following passage carefully and answer the questions given below it.

Proper food is the basic requirement of health. Health does not mean absence of disease; it rather means the presence of energy and vitality. Most of the food we eat daily does not contain essential nutrients needed for preservation of health and prevention of disease. There are various kinds of food. Protective foods are essential for prevention of disease and are needed both by the healthy and sick. They are rich in proteins, vitamins and minerals. Energy giving food are rich in carbohydrates.

Questions
(1) What is the real meaning of health?
(2) Name two essential elements of protective food?
(3) What do energy giving foods contain?
(4) Find out a word from the passage that means same as ‘need’.
(a) requirement (b) prevention (c) disease (d) energy.
(5) ‘Power to live or grow’ means :
(a) variety (b) vitality (c) health (d) protein.
Answers
(1) Real meaning of health means the presence of energy and vitality.
(2) Vitamins and proteins.
(3) Energy giving foods are rich in carbohy-drates.
(4) (a) requirement.
(5) (b) vitality.

Q. 4. Read the following passage carefully and answer the questions given below it.

Discipline must be enforced early in life. Discipline at home makes for the future greatness of a child. It forms his character and makes him a fit citizen. The child who is allowed to have his own way becomes wayward. The child who is allowed all sorts of exercises like running in sun, exposing himself to cold, eating unwholesome things will fall ill very frequently. A child whose habits have been disciplined and who has been taught to rise early, attend to his lessons properly, take physical exercise at the proper time and avoid things that are injurious will grow up to be a useful member of the society. The spoilt child who has been allowed to run his own course will show vices contained in younger days. His parents would wish that he had not been at all.

Questions
(1) When should discipline be enforced?
(2) What does discipline do for a child?
(3) If a child is allowed to do what he likes, what will happen to him?
(4) Pick out from the passage a word which means the same as ‘often’.
(5) Wayward means—
(a) spoilt, (b) self willed, (c) destructive.
Answers
(1) Discipline should be enforced in early life.
(2) Discipline forms a child’s character and makes him a fit citizen.
(3) If a child is allowed to do what he likes he would become wayward and spoilt. He would show vices contained in younger days.
(4) frequently.
(5) (b) self willed.

MP Board Class 9th English Solutions

MP Board Class 9th Science Solutions Chapter 11 Work and Energy

Work and Energy Intext Questions

Work and Energy Intext Questions Page No. 148

Question 1.
A force of 7 N acts on an object. The displacement is, say 8 m, in the direction of the force (Fig. below). Let us take it that the force acts on the object through the displacement. What is the work done in this case?

Answer:
The work done W on the body by the force is given by:
Work done = Force × Displacement
W = F × s
Given:
F = 7 N
s = 8 m
Hence, work done, W = 7 × 8
= 56 Nm
= 56 J.

Work and Energy Intext Questions Page No. 149

Question 1.
When do we say that work is done?
Answer:
We can say a work is done whenever the conditions given below are satisfied:

1. A force is applied over the body.
2. A displacement of the body is caused by the applied force, along the direction of the applied force.

Question 2.
Write an expression for the work done when a force is acting on an object in the direction of its displacement.
Answer:
When a force ‘F’ displaces a body by a distance ‘d’ in the direction of the applied force, then the work done ‘W’ on the body is given by:
Work done = Force × Displacement
W = F × d.

Question 3.
Define 1 J of work.
Answer:
1 J is the amount of work done when an object is provided with a force of 1 N that displaces it through a distance of 1 m in the direction of the applied force.

Question 4.
A pair of bullocks exerts a force of 140 N on a plough. The field being ploughed is 15 m long. How much work is done in ploughing the length of the field?
Answer:
Here,
Applied force, F = 140 N
Displacement, d = 15 m
We know,
Work done is given by the expression:
Work done = Force × Displacement
W = F × d
So,
W= 140 × 15 = 2100 J
Hence, 2100 J of work is done in ploughing the length of the field.

Work and Energy Intext Questions Page No. 152

Question 1.
What is the kinetic energy of an object?
Answer:
The energy attained by or generated in a body due to its action or motion is called kinetic energy. Every object which possesses motion contain a kinetic energy. A body uses kinetic energy to do work. Kinetic energy can be used for any work to be performed. Kinetic energy is useful to generate other forms of energy too. It is expressed by KE and can be calculated by the following formula:
E_k = \(\frac { 1 }{ 2 }\) mv²
Here, m represents mass of object.
And ‘V’ gives the velocity by which object is shifting or working.

Question 2.
Write an expression for the kinetic energy of an object.
Answer:
Energy E_k is proportional to:

• Object’s mass and
• Square of its velocity.

Energy E_k due to a moving object with a body mass ‘m’ which is moving with a velocity v, can be given by the expression,
E_k = \(\frac { 1 }{ 2 }\) mv²
Its S.I. unit is joule (J).

Question 3.
The kinetic energy of an object of mass, m moving with a velocity of 5 ms^-1 is 25 J. What will be its kinetic energy when its velocity is doubled? What will be its kinetic energy when its velocity is increased three times?
Answer:
Given:
K.E. of the object = 25 J
Velocity of the object, v = 5 m/s
Putting value to formula:
∵ K.E = \(\frac { 1 }{ 2 }\) mv²

• m = 2 × K.E / v²
• m = 2 × \(\frac { 25 }{ 25 }\) = 2 kg

Condition 1:
If velocity is double, v = 2 × 5 = 10 m/s
∴ K.E. (for v = 10 m/s) = \(\frac { 1 }{ 2 }\) mv² = \(\frac { 1 }{ 2 }\) × 2 × 100 = 100 J

Condition 2:
If velocity is tripled, v = 3 × 5 = 15 m/s
∴ K.E. (for v = 10 m/s) = \(\frac { 1 }{ 2 }\) mv² = \(\frac { 1 }{ 2 }\) × 2 × 225 = 225 J.

Work and Energy Intext Questions Page No. 156

Question 1.
What is Power?
Answer:
Work done is calculated by the amount of power consumption. Power can be understood by the term efficiency of an object to consume or generate energy. So, power is the rate of doing work or the rate of transfer of energy. If W is the amount of work done in time t, then power is given by the expression,
Power = \(\frac { Work }{ Time }\) = \(\frac { Energy }{ Time }\)
or
P = \(\frac { W }{ T }\)
It is calculated in watt (W).

Question 2.
Define 1 watt of power.
Answer:
As we know that:
Power = \(\frac { Work }{ Time }\)
Hence,
A body is said to have power of 1 watt if its work is equal to 1 joule in 1 s, i.e.,
1 W = \(\frac { 1J }{ 1s }\)

Question 3.
A lamp consumes 1000 J of electrical energy in 10 s. What is its power?
Answer:
Power = \(\frac { Work }{ Time }\)
Given,
Work done = Energy consumed by the lamp = 1000 J
Time = 10 s
Putting values,
Power = \(\frac { 1000 }{ 10 }\) = 100 Js^-1
= 100 W.

Question 4.
Define average power.
Answer:
When efficiency of an operator is changed with time, average power is calculated.
The average power of an object is defined as the total work done by it in the total time taken.
Total time taken

Work and Energy NCERT Textbook Exercises

Question 1.
Look at the activities listed below. Reason out whether or not work is done in the light of your understanding of the term ‘work’.

• Suma is swimming in a pond.
• A donkey is carrying a load on its back.
• A wind – mill is lifting water from a well.
• A green plant is carrying out photosynthesis.
• An engine is pulling a train.
• Food grains are getting dried in the sun.
• A sailboat is moving due to wind energy.

Answer:
Work is done whenever the two given conditions are satisfied:

• A force is applied over the body.
• A displacement of the body is caused by the applied force, along the direction of the applied force.

Hence, work is done in case:

• Suma is swimming in a pond.
• A wind – mill is lifting water from a well.
• An engine is pulling a train.
• A sailboat is moving due to wind energy.

Work is not being done in case:

• A donkey is carrying a load on its back.
• A green plant is carrying out photosynthesis.
• Food grains are getting dried in the sun.

Explanation:

1. Suma applies a force to push the water backwards which causes a displacement. Hence, work is done by Suma while swimming.
2. While carrying a load, the donkey has to apply a force in the upward direction. But, displacement is exchanged with shifting, so the work done is zero.
3. A wind – mill works against the gravitational force to lift water. Hence, work is done.
4. In this case, chemical change occurs not a physical. Therefore, the work done is zero.
5. An engine applies force to pull the train. Therefore, there is a displacement in the train in the same direction. Hence, work is done by the engine on the train.
6. This is an example of evaporation. Hence, the work done is zero.
7. Wind energy applies a force on the sailboat to push it in the forward direction. Therefore, there is a displacement in the boat in the direction of force. Hence, work is done by wind on the boat.

Question 2.
An object thrown at a certain angle to the ground moves in a curved path and falls back to the ground. The initial and the final points of the path of the object lie on the same horizontal line. What is the work done by the force of gravity on the object?
Answer:
Gravitational forces are proportional to ‘h’ which is vertical displacement and work done by the force of gravity is considered only if vertical displacement occurs. Vertical displacement is given by the difference in the initial and final positions / heights of the object which is zero. In this case work done by gravity is given by thy expression,
W = mgh
Where,
h = Vertical displacement = 0
W = mg × 0 = 0 J
Therefore, the work done by gravity on the given object is zero joule.

Question 3.
A battery lights a bulb. Describe the energy changes involved in the process.
Answer:
When a battery lights a bulb, then the chemical energy of the battery is converted into electrical energy. When the bulb receives this electrical energy, then it converts it into light and heat energy. Hence, the transformation of energy is as follows:
Chemical Energy → Electrical Energy → Light Energy + Heat Energy

Question 4.
Certain force acting on a 20 kg mass changes its velocity from 5 ms^-1 to 2 ms^-1. Calculate the work done by the force.
Answer:
Kinetic energy is given by the expression, (E_k) = \(\frac { 1 }{ 2 }\) mv².
Where,
E_k = Kinetic energy of the object moving with a velocity,
v Kinetic energy when the object was moving with a velocity 5 ms^-1.
(E_k)₅ = \(\frac { 1 }{ 2 }\) × 20 × (5)² = 250 J
Kinetic energy when the object was moving with a velocity 2 ms^-1.
(E_k)₂ = \(\frac { 1 }{ 2 }\) × 20 × (2)² = 40 J

Question 5.
A mass of 10 kg is at a point A on a table. It is moved to a point B. If the line joining A and B is horizontal, what is the work done on the object by the gravitational force? Explain your answer.
Answer:
Work done by gravity depends only on the vertical displacement of the body. It does not depend upon the path of the body.
Therefore, by the expression,
W = mgh
Here,
Vertical displacement, h = 0
W = mg × 0 = 0
Hence, the work done by gravity on the body is zero.

Potential energy calculator will help you instantly determine the ultimate joule associated with a particular object.

Question 6.
The potential energy of a freely falling object decreases progressively. Does this violate the law of conservation of energy? Why?
Answer:
No. In freely falling object only potential energy decreases progressively, but at same time kinetic energy increases and total of both remains equal to initial energy.
Total energy = Potential energy + Kinetic energy
So, this process does not violate the law of conservation of energy. During the process, total mechanical energy of the body remains equal.

Question 7.
What are the various energy transformations that occur when you are riding a bicycle?
Answer:
When we ride a bicycle, the chemical energy of muscles of rider’s body gets transferred into heat energy and kinetic energy of the bicycle. Heat energy is changed to physical energy. Kinetic energy provides a velocity to the bicycle. The transformation can be shown as:
Muscular energy → Kinetic energy + Heat energy
During the transformation, the total energy remains conserved.

Question 8.
Does the transfer of energy take place when you push a huge rock with all your might and fail to move it? Where is the energy you spend going?
Answer:
When we push a huge rock, there is no transfer of muscular energy to the stationary rock. Here, the energy is completely spent doing work (pushing) against friction between the ground and the rock.

Question 9.
A certain, household has consumed 250 units of energy during a month. How much energy is this in joules?
Answer:
1 unit of energy is equal to 1 kilowatt hour (kWh).
1 unit = 1 kWh
1 k Wh = 3.6 × 10⁶ J
Therefore, 250 units of energy
= 250 × 3.6 × 10⁶ = 9 × 10⁸ J.

Question 10.
An object of mass 40 kg is raised to a height of 5 m above the ground. What is its potential energy? If the object is allowed to fell, find its kinetic energy when it is half – way down.
Answer:
Gravitational potential energy is given by the expression,
W = mgh
Where,
h = Vertical displacement = 5 m
m = Mass of the object = 40 kg
g = Acceleration due to gravity = 9.8 ms^-2
∴ W = 40 × 5 × 9.8 = 1960 J.
At half – way down, the potential energy of the object will be \(\frac { 1960 }{ 2 }\) = 980 J.
At this point, the object has an equal amount of potential and kinetic energy.
This is due to the law of conservation of energy.
Hence, half – way down, the kinetic energy of the object will be 980 J.

Question 11.
What is the work done by the force of gravity on a satellite moving round the earth? Justify your answer.
Answer:
Work is done whenever the two given conditions are satisfied:

1. A force acts on the body.
2. There is a displacement of the body by the application of force in or opposite to the direction of force.

If the direction of force is perpendicular to displacement, then the work done is zero. When a satellite moves around the Earth, then the direction of force of gravity on the satellite is perpendicular to its displacement. Hence, the work done on the satellite by the Earth is zero.

Question 12.
Can there be displacement of an object in the absence of any force acting on it? Think. Discuss this question with your friends and teacher.
Answer:
Yes. For a uniformly moving object, suppose an object is moving with constant velocity. The net force acting on it is zero. But, there is a displacement along the motion of the object. Hence, there can be a displacement without a force.

Question 13.
A person holds a bundle of hay over his head for 30 minutes and gets tired. Has he done some work or not? Justify your answer.
Answer:
When a person holds a bundle of hay over his head, then there is no displacement in the bundle of hay. And since
displacement of the body by the application of force is required to prove that work is done, no work is done here.
Here, force of gravity is acting on the bundle, but the person 1 is not applying any force on it. Hence, in the absence of force, work done by the person on the bundle is zero.

Question 14.
An electric heater is rated 1500 W. How much energy does it use in 10 hours?
Answer:
Energy consumed by an electric heater can be obtained with the help of the expression,
P = \(\frac { W }{ t }\)
Where,
Power rating of the heater, P = 1500, W = 1.5 kW
Time for which the heater has operated, t = 10 h
Work done = Energy consumed by the heater
Therefore,
Energy consumed = Power × Time = 1.5 × 10 = 15 kWh
Hence, the energy consumed by the heater in 10 h is 15 kWh.

Question 15.
Illustrate the law of conservation of energy by discussing the energy changes which occur when we draw a pendulum bob to one side and allow it to oscillate. Why does the bob eventually come to rest? What happens to its energy eventually? Is it a violation of the law of conservation of energy?
Answer:
According to law of conservation of energy, energy can be neither created nor destroyed. It can only be converted from one form to another. Considering the case of an oscillating pendulum.

When a pendulum moves from its actual position P to either of its extreme point A or B, it rises through a height h above the mean level P. Here at this point, the kinetic energy of the bob changes into potential energy and the kinetic energy becomes zero, and the bob possesses only potential energy.

When it moves towards point P, its potential energy decreases progressively. And the kinetic energy increases. As the bob reaches point P, its potential energy becomes zero and the bob possesses only kinetic energy. This process is repeated as long as the pendulum oscillates.

The pendulum loses its kinetic energy to overcome atmospheric friction and stops after some time. Hence law of conservation of energy is not violated and the total energy of the pendulum and the surrounding system remain conserved.

Question 16.
An object of mass, m is moving with a constant velocity, v. How much work should be done on the object in order to bring the object to rest?
Answer:
We know that Kinetic energy of an object of mass m, moving with a velocity, v is given by:
E_k = \(\frac { 1 }{ 2 }\) mv²
To bring the object to rest, total energy must be consumed.
So, \(\frac { 1 }{ 2 }\) mv² amount of work is required to be done on the object.

Question 17.
Calculate the work required to be done to stop a car of 1500 kg moving at a velocity of 60 km/h?
Answer:
Kinetic energy, E_k = \(\frac { 1 }{ 2 }\) mv²
Where,
Mass of car, m = 1500 kg
Velocity of car, v = 60 km/h
= 60 × \(\frac { 5 }{ 18 }\) ms^-1
E_k = \(\frac { 1 }{ 2 }\) × 1500 × [60 × \(\frac { 5 }{ 18 }\)]²
= 20.8 × 10⁴ J.
Hence, 20.8 × 10⁴ J of work is required to stop the car.

Question 18.
In each of the following a force, F is acting on an object of mass, m. The direction of displacement is from west to east shown by the longer arrow. Observe the diagrams carefully and state whether the work done by the force is negative, positive or zero.

Answer:
Case I: Here, the direction of force acting on the block is perpendicular to the displacement. Therefore, work done will be zero.

Case II: Here, the direction of force acting on the block is in the direction of displacement. Therefore, work done will be positive.

Case III: Here, the direction of force acting on the block is opposite to the direction of displacement. Therefore, work done will be negative.

Question 19.
Soni says that the acceleration in an object could be zero even when several forces are acting on it. Do you agree with her? Why?
Answer:
When all the forces cancel out each other, acceleration in an object will be zero even when several forces are acting on it. And as for a uniformly moving object, the net force acting on the object is zero. Hence, the acceleration of the object is zero. Hence, Soni is right.

Question 20.
Find the energy in kWh consumed in 10 hours by four devices of power 500 W each.
Answer:
We know,
P = \(\frac { W }{ t }\)
Given,
Power of the device (P) = 500 W = 0.50 kW
Total Time (t) = 10 h
Since,
Work done = Energy consumed by the device
Therefore, energy consumed
= Power × Time = 0.50 × 10 = 5 kWh
Hence, the energy consumed by four equal rating devices in 10 h will be:
4 × 5 kWh = 20 kWh
= 20 Units.

Question 21.
A freely falling object eventually stops on reaching the ground. What happens to its kinetic energy?
Answer:
As the object hits the ground, its kinetic energy gets converted into heat energy and sound energy. Sometimes, it also deform the ground and itself depending upon the nature of the ground and the amount of kinetic energy of the object. Freely falling object towards the ground feels following changes:

• Its potential energy decreases and kinetic energy increases.
• When the object touches the ground, all its potential energy gets converted into kinetic energy.

Work and Energy Additional Questions

Work and Energy Multiple Choice Questions

Question 1.
S.I. unit of work is ____________ .
(a) Newton
(b) Joule
(c) Watt
(d) All.
Answer:
(b) Joule

Question 2.
Work done is applied and displacement occurred is acute ____________ .
(a) Negative
(b) Zero
(c) Positive
(d) None.
Answer:
(c) Positive

Question 3.
Work done is negative, if angle formed between force applied and displacement occurred is ____________ .
(a) Obtuse
(b) Right angle
(c) Acute
(d) Zero.
Answer:
(a) Obtuse

Question 4.
Work is done if displacement of object occurs in ____________ .
(a) Opposite the direction of force
(b) The direction of force
(c) Zero
(d) Infinite.
Answer:
(b) The direction of force

Question 5.
Force is to work done ____________ .
(a) Inverse
(b) Zero
(c) Proportional
(d) Infinite.
Answer:
(c) Proportional

Question 6.
If direction of applied force and displacement are perpendicular then resultant work will be ____________ .
(a) Zero
(b) Positive
(c) Negative
(d) Infinite.
Answer:
(a) Zero

Question 7.
Writing for two hours is equal to work ____________ .
(a) 1 joule
(b) 2 joule
(c) Zero
(d) None.
Answer:
(c) Zero

Question 8.
Falling ball will have ____________ .
(a) Kinetic energy
(b) Potential energy
(c) Both
(d) None.
Answer:
(c) Both

Question 9.
If mass of an object is doubled over a pully, force required to displacement upto previous destination will be ____________ .
(a) Double
(b) Half
(c) Four times
(d) Equal.
Answer:
(a) Double

Question 10.
Change in kinetic energy, if velocity of an object is doubled will be ____________ .
(a) Double
(b) Half
(c) Equal
(d) 4 times.
Answer:
(d) 4 times.

Question 11.
Rate at which work is done is called ____________ .
(a) Work
(b) Power
(c) K.E.
(d) P.E.
Answer:
(b) Power

Question 12.
Running wings of a fan shows an example of ____________ .
(a) K.E.
(b) P.E.
(c) Work
(d) Power.
Answer:
(a) K.E.

Work and Energy Very Short Answer Type Questions

Question 1.
Give a formula / expression to give total energy.
Answer:
Total energy = Potential energy + Kinetic energy.

Question 2.
How displacement is related to work?
Answer:
Displacement is proportionally related to work.

Question 3.
What is a positive work?
Answer:
When displacement occurs in direction of force applied and object shifted forms an acute angle with force, work is termed as positive.

Question 4.
What kind of force is applied in a lift?
Answer:
Upward and gravitational force is applied in a lift.

Question 5.
What kind of quantity is power?
Answer:
It is scalar.

Question 6.
What will be the potential energy of an object at ground?
Answer:
PE = mgh
Here, h = 0
So, PE = mg.

Question 7.
What will be the work done if no force is being applied?
Answer:
Since, W = F × S
If F = 0;
W = 0 × S
Hence, W = 0
∴ No work will be done.

Question 8.
Name three forms of energy.
Answer:
Potential energy, Kinetic energy and Gravitational energy.

Question 9.
Write expression to calculate kinetic energy if mass of an object is m and its velocity is v.
Answer:
K.E. = \(\frac { 1 }{ 2 }\) mv².

Question 10.
Write expression for potential energy for an object being shifted to ‘d’ height and ‘a’ mass.
Answer:
PE = agd.

Question 11.
If a machine consumes 1000 J of energy in a second and runs for 5 hours, then calculate total energy consumed.
Answer:
P = \(\frac { W }{ t }\)
= 1000 × (5 × 3600)
= 18000000 joule
or
= 1.8 × 10⁷ joule.

Question 12.
What happen to potential and kinetic energy of a falling object?
Answer:
P.E. = decrease to zero
K.E. = increase from zero
Total P.E. converts to K.E.

Work and Energy Short Answer Type Questions

Question 1.
If a pulley is pulling a box towards itself with a force equal to 10 N and have drawn the box upto 2 m. Calculate the work done by it.
Answer:
Given, F = 10 N and s = 2 m
We know W = F × s
Putting values = 10 × 2
W = 20 Nm
or
20 J.

Question 2.
If a hammer operates over a pully machine with 21 J and pulls the balls to 7 m, Calculate the force applied by the hammer.
Answer:
Given:
W = 21 J and s = 7 m
Using formula W = \(\frac { F }{ s }\)
or
F = \(\frac { W }{ s }\)
Putting values F = \(\frac { 21 }{ 7 }\) = 3 N
Hence, F = 3 N was applied by the hammer.

Question 3.
Calculate the work done by a pair of bullocks if an object is pulled by them for 10 m which has mass equal to 20 kg and an acceleration of 20 ms^-1.
Answer:
Given, m = 20 kg, a = 20 ms^-1, s = 10 m
Using formula W = F × s
or
W = m × a × s
Putting values = 20 × 20 × 10
= 4000 kg ms^-2 m = 4000 J.

Question 4.
Give two examples of energy produced due to work or action.
Answer:
Examples showing production of kinetic energy:

1. Heat energy in body after exercise.
2. Generation of kinetic energy in a ball after falling through a point.

Question 5.
Read the following examples and tell in which case work is being done?

1. Manish is riding bicycle in a circular path.
2. John throws a pebble which comes back to initial height of ground.
3. Reading books for 2 hours.
4. Cooking pizza.

Answer:
Work is being done in none case because:

1. Case 1: In a circular path displacement is zero, hence work done is zero.
2. Case 2: Again no displacement occurs.
3. Case 3: Any kind of force is not being used, hence zero work.
4. Case 4: No force is applied here, so zero work.

Question 6.
(a) Under what conditions work is said to be done?
(b) A porter lifts a luggage of 1.5 kg from the ground and puts it on his head 1.5 m above the ground. Calculate the work done by him on the luggage.
Answer:
(a) Conditions for work to be done:

1. Force should be applied.
2. Body should move in the line of action of force.
3. Angle between force and displacement should not be 90°.

(b) Given,
Mass of luggage, m = 15 kg
Displacement, s = 1.5 m
Using formula:
Work done i.e., W = F × s = mg × s
= 15 × 10 × 1.5 = 225 J.

Question 7.
Four persons jointly lift a 250 kg box to a height of 1 m and hold it.

1. Calculate the work done by the persons in lifting the box.
2. How much work is done for just holding the box?
3. Why do they get tired while holding it? (g = 10 ms²)

Answer:

1. Given, F = 250 × 10 = 2500 N
   s = 1 m
   W = F × s = 2500 × 1 = 2500 J.
2. Zero work, as there is no displacement.
3. Men are applying a force which is opposite and equal to the gravitational force acting on the box. Muscular effort is involved and therefore persons feel tried.

Question 8.
(i) Justify that “a body at a greater height has larger energy”.
(ii) A body of mass 2 kg is thrown up at a velocity of 10 m/s. Find the potential energy at the highest point.
Answer:
(i) When an object is placed at a greater height, the height increases from the reference level (Velocity remains constant i.e., zero). Hence by comparing the potential energy at two points, we can see that the P.E. at greater height will be larger.

(ii) Given,
Using formula m = 2 kg, v = 10 m/s
Initial KE = \(\frac { 1 }{ 2 }\) mv²
= \(\frac { 1 }{ 2 }\) × 2 × (10)² = 100 J
Height will be
h = \(\frac { { v }^{ 2 }-{ u }^{ 2 } }{ 2g } \) = \(\frac { { 0 }^{ 2 }-{ 10 }^{ 2 } }{ 2×10 } \)
= \(\frac { -100 }{ 20 }\) = -5 m
So, magnitude of height = 5 m and
P.E. at highest point = mgh
= 2 × 10 × 5
= 100 J.

Question 9.
A light and a heavy object have the same momentum. What is the ratio of their kinetic energies? Which one has a larger kinetic energy?
Answer:
p₁ = m₁v₁, p₂ = m₂v₂
But p₁= p₂  or  m₁v₁ = m₂v₂
and If m₁ < m₂ then v₁ > v₂
(K.E.)₁ = \(\frac { 1 }{ 2 }\) m₁v₁²
(K.E.)₂ = \(\frac { 1 }{ 2 }\) m₂v₂²
(K.E.)₁ = \(\frac { 1 }{ 2 }\) (m₁v₁)v₁ = \(\frac { 1 }{ 2 }\) p₁v₁
(K.E.)₂ = \(\frac { 1 }{ 2 }\) (m₂v₂)v₂ = \(\frac { 1 }{ 2 }\) p₂v₂.

Question 10.
(i) Define 1 kWh. Relate it to joules.
(ii) Find the energy in kWh in the month of September by four devices of power 100 W each, if each one of them is used for 10 hours daily.
Answer:
(i) 1 kWh is the energy used in 1 hour at the rate of 1000 J/s (or 1 kW)
1 kWh = 3.6 × 10⁶ J

(ii) Energy consumed by four devices in the month of September
= 4 × \(\frac { 100 }{ 1000 }\) × 10 × 30
= 120 kWh.

Work and Energy Long Answer Type Questions

Question 1.
(i) Give SI unit and commercial unit of electrical energy.
(ii) Calculate the power of an electric motor that can lift 800 kg of water to store in a tank at a height of 1500 cm in 20 s. (g = 10 m/s²)
(iii) A lamp consumes 500 J of electrical energy in 20 seconds. What is the power of the lamp?
Answer:
(i) SI unit of electrical energy is Joules (J).
Commercial unit of electrical energy is kilowatt hour (kWh)

(ii) Given,
m = 800 kg,
h = 1500 cm = 15 m,
t = 20 sec, g = 10 m/s²
Using formula,
P = \(\frac { W }{ t }\) = \(\frac { mgh }{ t }\)
= \(\frac { 800×10×15 }{ 20 }\) = 600 W.

(iii) Given,
E = 500 J, t = 20 sec
Using formula,
power P = \(\frac { W }{ E }\) = \(\frac { 500 }{ 20 }\) = 25W.
& r E 20

Question 2.
(i) Name the commercial unit of electrical energy.
(ii) Establish the relationship between the SI unit and the commercial unit of electric energy.
(iii) If 4 bulbs of 50 W for 6 hours, 3 tube lights of 40 W for 8 hours, a T.V of 100 W for 6 hours, a refrigerator of 300 W for 24 hours are used. Calculate the electricity bill amount for a month of 30 days. The cost per unit is ? ₹2.50.
Answer:
(i) The commercial unit of energy is kilowatt hour (kWh)
(ii) The SI unit of energy is joule.
Now, 1 kWh = 1 kW × 1 h
= 1000 W × 1 h
= 1000 W × 3600 s
= 3600000 J
= 3.6 × 10⁶ J
1 kWh = 3.6 × 10⁶ J

(iii)

Total energy consumed = 9960 Wh = 9.960 kWh
Electricity bill amount = 9.960 units × ₹2.50 = ₹24.90
For 30 days = 30 × 24.90 = ₹747.

Question 3.
(i) Name the physical quantity defined by rate of doing work. Define its SI unit.
(ii) Why is concept of average power useful? How is it determined?
(iii) A boy of mass 45 kg runs up a staircase of 45 steps in 9 s. If the height of each step is 15 cm, find his power.
(g = 10 m/s²)
Answer:
(i) Power: Watt or J/s. 1 watt is the power of an object which does work at the rate of 1 J per second.

(ii) Power of an object may vary. Hence, average power is important in the case when the average power of the entire process within a given time is calculated.

(iii) P = \(\frac { mgh }{ t }\) = \(\frac { (50×10×45×0.15) }{ 9 }\) = 375 W.

Question 4.
(i) A body of mass 15 kg possesses kinetic energy of 18.75 kJ. Find the velocity.
(ii) An electric bulb of 100 W is used for 4 hours a day. Calculate the energy consumed by it in a day in joules and kilowatt hour unit.
Answer:
(i) K.E. = \(\frac { 1 }{ 2 }\) mv²
= 18.75 kJ = 18750
v² = \(\frac { 18750×2 }{ 15 }\)
v = √2500 m/s = 50 m/s

(ii) E = \(\frac { P }{ t }\) = 100 W × 4 h = 0.4 kWh
Energy consumed by it in a day = 0.4 × 3.6 × 10⁶ J
= 1.44 × 10⁶ J

Question 5.
(a) A stone is thrown upwards from a point A, as shown in the figure. After reaching the highest point B, it comes down. Explain the transformation of energy from A to B and B to A and also mention the type of energy possessed by the stone at point A, B and C of its journey.
(b) A body of mass 20 kg is dropped from a height of 100 m. Find its K.E. and P.E. after,
(i) First second
(ii) Second second
(iii) Third second
Answer:
(a) While moving upward (A to B) K.E → P.E. and while moving downward (B to A)
P.E.→ K.E.
At,
A → K.E.
B → P.E.
C → K.E. + P.E.

(b) Total Energy = mgh
= 20 × 10 × 100 = 2 × 10⁴ J

(i) After first, second: v = u + gt ms^-1
= 10 × 1 = 10 m/s
K.E. = \(\frac { 1 }{ 2 }\) mv².
= \(\frac { 1 }{ 2 }\) × 20 × 10 × 10
= 1000 J
P.E.= T.E. – K.E.
= 20,000 – 1000 = 19,000 J

(ii) After second, second: v = 20 ms^-1
K.E. = mgh + \(\frac { 1 }{ 2 }\) mv².
= 4,000 J
P.E. = T.E – K.E.
= 20,000 – 4,000 = 16,000 J

(iii) After third, second: v = 30 ms^-1
K.E. = mgh + \(\frac { 1 }{ 2 }\) mv².
= 9,000 J
P.E. = T.E.- K.E.
= 20,000 – 9,000 = 11,000 J

Work and Energy Higher Order Thinking Skills (HOTS)

Question 1.
Earth and other planets moves continuously around the sun. Do they work?
Answer:
No, Earth and other planets do not work while moving around the earth because they move in a circular path and reach the initial point after sometimes, so shows no displacement, hence no work is done by earth and other planets.

Question 2.
Generally heavy objects exert more power over other objects. Give reason.
Answer:
As expression, P = wit
On expanding, P = \(\frac { m.a.s }{ t } \)
Here, P is proportional to mass in p × m
Hence, heavy object exert more pressure or power.

VI. Value-Based Question

Question 1.
Ravi saw a lady labour who carried stones on her head from one point of the construction site to the other end which was some 500 m far. He prepares a trolley for the labour to carry the stones, to make her work easier:

1. Is any work done by the labour while carrying the stones from point A to point B on head by lady labour in the construction site?
2. Is any work done by pulling the trolley of stones from point A to point B?
3. What value of Ravi is seen in the above act?

Answer:

1. No work is said to be done in carrying the stones from point A to B on head by the lady.
2. Work is said to be done by pulling the trolley of stones.
3. Ravi showed kindness, general awareness and sympathy.

MP Board Class 9th Science Solutions

In this article, we will share MP Board Class 9th Sanskrit Solutions Chapter 5 सर्वदमनः भरतः Pdf, These solutions are solved subject experts from the latest edition books.

MP Board Class 9th Sanskrit Solutions Durva Chapter 5 सर्वदमनः भरतः (नाट्यांशः)

MP Board Class 9th Sanskrit Chapter 5 पाठ्य पुस्तक के प्रश्न

प्रश्न 1.
एकपदेन उत्तरं लिख-(एक शब्द में उत्तर दीजिए)
(क) ऋषि जनेन बालस्य नाम किं कृतम्? (ऋषिगणों के द्वारा बालक का नाम क्या रखा गया?)
उत्तर:
सर्वदमनः। (सर्वदमन)

(ख) उटजे कस्य मृत्तिकामयूरः तिष्ठति? (कुटिया में किसका मिट्टी का मयूर था?)
उत्तर:
मार्कण्डेयस्य ऋषिकुमारस्य वर्णचित्रितो। (कुटिया में मार्कण्डेय का मिट्टी का मयूर था।)

(ग) राजा बालस्य हस्ते के लक्षणम् अपश्यत्? (राजा बालक के हाथ में क्या लक्षण देखता है?)
उत्तर:
चक्रवर्ती। (चक्रवर्ती)।

(घ) रक्षा करण्डकं केन दत्तम्? (रक्षा ताबीज किसके द्वारा दिया गया?)
उत्तर:
भगवता मरीचेन् (ऋषि मरीच के द्वारा ताबीज दिया गया।)

(ङ) एकां वेणी का धृतवती? (एक चोटी किसने धारण की थी?)
उत्तर:
शकुन्तला। (शकुन्तला)

प्रश्न 2.
एक वाक्येन उत्तर लिखत (एक वाक्य में उत्तर लिखो)
(क) बालः सिंहशावकं किम् उक्तवान? (बालक ने सिंह के बच्चे से क्याकहा?)
उत्तर:
जिम्भस्व दंताम् ते गणिष्यामि। (बालक सिंह के बच्चे से बोला रे सिंह जभाई ले, मैं तेरे दांत गिनूंगा।)

(ख) द्वितीया तापसी सवर्दमनं किमर्थ क्रीडनकं दातुमिच्छति? (दूसरी तापसी सर्वदमन को किसलिए खिलौना देने की इच्छा करती है?)
उत्तर:
सिंहशावकम् त्यक्तुम्। (सिंह के बच्चे को छोड़ने के लिए दूसरा खिलौना देना चाहती है)

(ग) तापसी किमर्थम् आश्चर्ये निमग्नाना? (तापसी किसलिए आश्चर्यचकित हो गई?)
उत्तर:
रक्षाकरण्डकम्। (ताबीज के कारण तापसी आश्चर्य-चकित हो गई।)

(घ) राजा स्मृतिः कथम् उपलब्धा? (राजा की मृति किस प्रकार वापस आई।)
उत्तर:
अभिज्ञान दर्शनन (राजा की स्मृति विशेष चिह्न को देखकर आई)।

प्रश्न 3.
अधोलिखत प्रश्नानाम् उत्तराणि लिखत(क) औषधेः विषये तापसी राजानं किं कथयति? (औषधि के संबंध में तापसी को क्या कहती है?)
उत्तर:
पितरौ परित्यज्य सर्पिणी भूत्वा दशति (माता-पिता को छोड़कर यह औषधि सांप बनकर डंसती है।)

(ख) राजा बालस्य स्पर्श कृत्वा कीदृशमऽनुभवति? (राजा पुत्र का स्पर्श करके किस तरह का अनुभव किया?)
उत्तर:
स्वपुत्र मेवा। (राजा बालक का स्पर्श करके अपने पुत्र के समान खुशी का अनुभव किया।)

(ग) शकुन्तला वीक्ष्य राजा किम् अवोचत्? (शकुन्तला को देखकर राजा ने क्या कहा?)
उत्तर:
मम्-स्मृतिरूपलब्धा शकुन्तलां वीक्ष्य राजा अवोचत्। (शकुन्तला को देखकर राजा ने बस स्मृति की रूपवती मुझे सब कुछ याद आ गया ऐसा कहा।)

प्रश्न 4.
उचितेः शब्दैः रिक्तस्थान पूर्तिं कुरुत
(क) रे सिंहशावक जृम्भस्व दन्तान् ते गणयिष्याभि। (नखान्/दन्ताम्)
(ख) वत्स! मुञ्च बालमृगेन्द्रकम्। (बालमृगेन्द्रकम/क्रीडनकम्)
(ग) रक्षाकरण्डकमस्य मणिबंधे न दृश्यते। (अनुबन्धे/मणिबन्धे)
(घ) कोऽपि पुरुषः मां पुत्रइति आलिङ्गति। (भ्राताइति/पुत्रइति)
(ङ) आर्यपुत्र इदं ते अङ्गलीयकम्। (अङ्गुलीयकम्/वस्त्रम्)

प्रश्न 5.
युग्ममेलनं कुरुत?

प्रश्न 6.
शुद्धवाक्यानां समक्षम “आम” अशुद्धवाक्यानां समक्ष ‘न’ इति लिखत
यथा :
तेजसः बीजं बालः प्रतिभाति। – (आम्)
बाले चक्रवर्ति लक्षणं नास्ति। – (न)
(क) बालः सिंहशावकेन सह क्रीडति।
(ख) राजा बालं न लालयति।।
(ग) राज्ञः बालस्य च आकृतिः समाना वर्तते।
(घ) अपराजिता औषधिः भगवता कण्वेन दत्ता।
उत्तर:
(क) (आम्)
(ख) (न)
(ग) (न)
(घ) (आम्)

प्रश्न 7.
निम्नलिखित शब्दानां मूलशब्दं विभक्तिं वचनं च लिखत
उदाहरण, यथा

प्रश्न 8.
निम्नलिखित शिगपदानां धातु पुरुषं वचनं लकारं च लिखत
उदाहरणः यथा

प्रश्न 9.
निम्नलिखितानां प्रकृति प्रत्ययं च पृथक कुरुत
उदाहरण, यथा

सर्वदमनः भरतः पाठ-सन्दर्भ/प्रतिपाद्य

कालिदास सर्वश्रेष्ठ कवि कहे जाते हैं। इनकी उपमा सर्वोत्तम कही जाती है। इनके रघुवंशम् और कुमारसंभवम् दो महाकाव्य, ऋतुसंहार एवं मेघदूत दो खंडकाव्य, विक्रमोर्वशीय, मालविकाग्नि मित्रम् और अभिज्ञानशाकुन्तलम् नामक इनकी तीन नाटक कृतियाँ हैं। उसमें अभिज्ञानशाकुन्तलम् नाटक सबसे अच्छा है। उसी नाटक से प्रस्तुत पाठ उद्धृत है।

सर्वदमनः भरतः पाठ का हिन्दी अर्थ

1. (ततः प्रविशति तापसीभ्यः सह बालः)
बालः :
जृम्भस्व रे सिंहशावकः! जृम्भस्व, दन्तान् ते गणयिष्यामि।

प्रथमाः :
अविनीत! किं नु अपत्यनिर्विशेषाणि सत्त्वानि विप्रकरोषि। हन्त! वर्धत इव ते संरम्भः। स्थाने खलु ऋषिजनेन ‘सर्वदमन’ इति कृतनामधेयोऽसि ।

राजाः :
किं नु खलु बालेऽस्मिन्नौरस इव पुत्रे स्निह्यति मे हृदयम्। (विचिन्त्य) नूनमनपत्यता मां वत्सलयति।

द्वितीयाः :
एषा त्वां केशरिणी लङ्घयिष्यति, यद्यस्याः पुत्रकं न मोक्ष्यसि।

बालः :
(सस्मितम्) अहो! बलीयः खलु भीतोऽस्मि। (इत्यधरं दर्शयति)

राजाः :
(सविस्मयम्)
महतस्तेजसो बीजं बालोऽयं प्रतिभाति मे।
स्फुलिङ्गावस्थया वह्निरेधापेक्ष इव स्थितः॥

प्रथमा-वत्स! मुञ्च बालमृगेन्द्रकम्, अपरं ते क्रीडनकं दास्यामि।

शब्दार्थ :
जृम्भस्व-जंभाई ले-yawn; गणयिष्यामि-गिनूंगा-will count;जम्भव-जॅम्हाई लो-take yawn; अविनीत-उद्दण्ड-undiciple; संभव-उद्वेग, वेग प्रयास-forcely; उटजे-कुटिया में-in hut; स्निहयति-स्नेह करता है-loves; वत्सलयति-स्नेह पैदा करती है-growing the love; केशरिणी-सिंहनी-lioness; लपयिष्यति-आक्रमण कर देगी-will attack; यद्यस्याः -यदि तु इसके-ifyouit; न मोक्ष्यसि-नहीं छोड़ेगा-not left; भीतोऽस्मि-मैं डर गया हूँ-I am affraid of; महतस्तेजसो-महान व्यक्ति का तेज-Great persons ardour; प्रतिभाति-दिखाई देता है-looks; अपरं-दूसरा-other.

हिन्दी अर्थ :
(फिर दो तपस्विनियों के साथ बालक प्रवेश करता है।)

बालक :
जम्भाई ले, अरे सिंहशावक जम्माई ले। मैं तेरे दाँत गिनूँगा।

पहली तपस्विनी :
हे धृष्ट! हमारे द्वारा पुत्रों सदृश पालित इन जीवों को इस तरह क्यों परेशान करता है? हाय! तुम्हारी उद्दण्डता तो दिन-प्रतिदिन बढ़ती-सी जा रही है। ऋषि लोगों ने तुम्हारा नाम ‘सर्वदमन’ ठीक ही रखा है। तू तो किसी से भी भयभीत नहीं होता।

राजा :
(स्वगत) न जाने क्यों मेरे हृदय में इस बालक के प्रति पुत्रवत स्नेह हो रहा है। ठीक ही है, मेरा निःसन्तान होना ही मुझे दूसरे बच्चों में स्नेह उत्पन्न कर रहा है।

दूसरी तपस्विनी :
(बालक से) देख, यदि तू इस सिंह शावक को नहीं छोड़ेगा तो सिंहिनी तुम्हारे ऊपर आक्रमण कर देगी।

बालक :
(मुस्कुराता हुआ) (व्यंग्य रूप से) अहो! तुम्हारे कहने से तो मैं बहुत डर गया हूँ। मुँह बनाता हुआ हँसता है।

राजा :
(विस्मयपूर्वक) यह बालक तो मुझे किसी महान तेजस्वी पुरुष का अंश प्रतीत होता है। यह तो उसी प्रकार है जैसे चिनगारी के रूप में अग्नि। (जिस प्रकार एक चिनगारी काष्ठ के सान्निध्य में आते ही प्रचण्ड रूप धर लेती है, उसी प्रकार यह बालक भी समय पाकर प्रतापी, तेजस्वी एवं महान वीर होगा-ऐसा प्रतीत होता है।)

पहली तापसी :
हे बेटा! तुम सिंह शावक को छोड़ दो। मैं तुम्हें दूसरा खिलौना दूंगा।

2. बालः :
कुत्र! देहिंतत्। (इति हस्तं प्रसारयति)

राजा :
(बालस्य हस्तं दृष्ट्वा) कथं चक्रवर्तिलक्षणमप्यनेन धार्यते?

द्वितीया :
सुव्रते! मुञ्चैननैष शक्यो वाङ्मात्रेण शमयितुम्। तद् गच्छ मदीये उटजे सङ्कोचनस्य ऋषिकुमारस्य वर्णचित्रितो मृत्तिकामयूरतिष्ठति, तमस्योपहर।

प्रथमा :
तथा। (इति निष्क्रान्ता)

बाल :
तावदनेवैव क्रीडिष्यामि। (इति तापसी लोक्य हसति)

राजा :
स्पृह्यामि खलु दुर्ललितायास्मै। (निःश्वस्य)-
आलक्ष्यदन्तमुकुलाननिमित्तहासै
रव्यक्तवर्णरमणीयवचः प्रवृत्तीन।
अङ्काश्रयप्रणयिनस्तनयान् वहन्तो
धन्यास्तदङ्गरजसा कलुषी भवन्ति।।

तापसी-(साङ्गलितर्जनम्) भोः! न मां गणयसिः (पार्श्वमवलोक्य) कोऽत्र ऋषिकुमाराणाम (राजानं दृष्ट्वा) भद्रमुख! एहि तावन्मोचय अनेन दुर्मोक्षहस्तग्रहेण डिम्भकेन बाध्यमानं बालमृगेन्द्रम्।।

राजा :
तथा (इत्युपगम्य सस्मितम्)
अनेन कस्यापि कलाङ्करेण स्पृष्टस्य गात्रे सुखिता ममैवम्।
कां निवृतिं चेतसि तस्य कुर्याद् यस्यायमङ्गात् कृतिनः प्रसूतः॥
तापसी-(उभौं निर्वय) आश्चर्यमाश्चर्यम्।

शब्दार्थ :
कुत्र-कहां-where; हस्तं-हाथ को-to hand; दृष्ट्वा -देखकर-to look; धार्यते-धारण करता है-put on; सुव्रते-सुव्रत-Subrath namely; मुञ्चै नैष-इसे छोड़ दो-left it; वाङ्मात्रेण-वाणि मात्र से-only by tongue/voice; तमस्योपहर-इसे लेकर दे दो-come with that thing; निष्क्रान्ता-निकल जाते हैं-go out; विलोक्य-देखकर-to look;खलु-निश्चित ही-certainly; दुर्ललितायास्मै-प्यार करने के लिए ललक-for loving; कीडिष्यामि-खेलूंगा-will play; स्पृह्यामि-छूता हूँ-to tuch; प्रवृत्तीन्-प्रवृत्ति-Habit; आलक्ष्य-बिना कारण-without reason; गणयसि-गिनते हो-do count; कोऽत्र-यहां कौन है-who is here?

हिन्दी अर्थ :
बालक :
कहाँ है, मुझे दो-(ऐसा कहकर हाथ फैलाता है)।

राजा :
(बालक के हाथ को देखकर) क्या यह चक्रवर्ती के लक्षणों से युक्त है?

दूसरी तापसी :
सुव्रते! इसे छोड़ दो। यह देखने मात्र से मानने वाला नहीं है। इसलिए मेरी कुटी में रखा हुआ ऋषि कुमार मार्कण्डेय द्वारा बनाया गया मिट्टी का जो मोर है वही लाकर इसे दे दो।
प्रथम तापसी-अच्छा! लाती हूँ। (यह कहकर वह चली जाती है) बालक-तब तक मैं इसी से खेलूँगा। (तापसी की ओर देखकर हँसता है)

राजा :
इस हठीले बालक को देख इससे प्यार करने को मन ललचा रहा है। (निःश्वास लेकर) अकारण ही हँसने से जिसकी दंत पंक्तियाँ दिखाई पड़ रही हैं, तोतली बातें मन को मोह ले रही हैं, जिसे अपने अंक में ले लेने के लिए मन लालायित हो रहा है ऐसे प्राणी भाग्यवान व पुण्यात्मा ही होते हैं जिनके गाद में धूल-धूसरित एवं मलिन ऐसा बालक आकर उनकी गोद को धूत धूसरित करते हैं। (अर्थात् मिट्टी-धूल में खेलते हुए बालक भाग्यवानों की ही गोद में जाकर बैठते हैं और उन्हें भी धूल धूसरित करते हैं।)

तापसी :
(अपनी अंगुलियों से धमकाते हुए) अच्छा! यह मुझे कुछ भी नहीं समझ रहा है। (पीछे की ओर देखकर) यहाँ कौन ऋषि कुमार है? (राजा को देखकर) हे महानुभाव! अपनी बाल-क्रीड़ा द्वारा परेशान किए जाते हुए इस सिंह शावक को इस बालक से छुड़ा दीजिए। मेरे द्वारा यह नहीं छुड़ाया जा सकता क्यों कि इसने शावक को जोर से पकड़ रखा है।

राजा :
अच्छा (ऐसा कहकर हँसते हुए जाते हैं) अन्य किसी के भी कुल का यह अंकुर (दीपक) स्पर्श करने मात्र से जब मेरे हृदय में सुख का संचार करता है तब यह अपने माता-पिता को (जिसने इसे पाला-पोसा है) कितना सुख प्रदान करता होगा? तापसी-(दोनों अवाक् होकर) आश्चर्य है, आश्चर्य है।

3. राजा-आर्ये किमिव।
राजा-आर्ये किमिव।

तापसी :
अस्य बालकस्य असम्बद्धेऽपि भद्रमुखे संवादिनी आकृतिरिति विस्मितास्मि। अपि च धामशीलोऽपि भूत्वा अपरिचितस्यापि ते वचनेन प्रकृतिस्थः संवृत्त।

राजा :
(बालकमुपलालयन्) आर्य! न चेन्मुनिकुमारोऽयम् तत् कोऽस्य व्यपदेशः?

तापसी :
पौरव इति।

राजा :
(स्वगतम्) कथमेकान्वयोऽयमस्माकम्।

तापसी :
(प्रविश्य मयूरहस्ता) सर्वदमन शकुन्तलावण्यं प्रेक्षस्व।

बालः :
(सदृष्टिक्षेपम्) कुत्र वा मम माता?

उभे :
नामसादृश्येन वञ्चितो मातृवत्सलः।

द्वितीया :
वत्स अस्य मृत्तिकामयूरस्य रम्यत्वम् पश्येति भणितोऽसि।

राजा :
(आत्मगतम्) किंवा शकुन्तलेत्यस्य मातुराख्या। सन्ति पुनर्नामधेयसादृश्यानि।

बालः :
मातः रोचते में एष भद्रमयूरः। (इति क्रीडनकमादत्ते)

प्रथमा :
(विलोक्य सोद्वेगम) अहो रक्षाकरण्डकमस्य मणिबन्धे न दृश्यते।

शब्दार्थ :
आर्ये-आदरणीया-respected; भद्रमुखे-अच्छे मुख वाली-beautiful; आकृतिरिति-ऐसी आकृति-this type of shape; भूत्वा-होकर-done; संवृत्तः-होये-happened; अस्य-इसका-its; कोस्य-यह कौन है-who is this? मयूर हस्ता-हाथ में मोर-peacock in hand;शकुन्तलावण्यं-पक्षी का सुदूर-bird’s beautiful; कुत्र-कहाँ-where; रोचते-अच्छा लगता है-to seems good.

हिन्दी अर्थ :
राजा :
आर्ये! कैसा आश्चर्य!

तापसी :
इस बालक का आप से संबंध न होने पर भी इसका चेहरा आप से बहुत मिलता-जुलता है इसलिए मैं आश्चर्यचकित हो रही हूँ। और भी, यह हठी बालक आप से अपरिचित होने पर भी आपको देख शान्त हो गया।

राजा :
(उस बालक को प्यार करते हैं) यदि यह मुनिकुमार नहीं है तो यह किस कुल-गोत्र का है?

तापसी :
पौरव वंश। राजा-(अपने मन ही मन) क्या यह मेरे वंश का है?

तापसी :
(हाथ में मिट्टी के बने मोर के साथ प्रवेश) सर्वदमन! इस शकुन्त के लावण्य को देख।

बालक :
(इधर-उधर देखकर) मेरी माता कहाँ है?

दोनों :
नाम एक समान होने के कारण बेचारा ठगा गया।

दूसरी तापसी :
पुत्र! इस मिट्टी से बने शकुन्त (मोर) पक्षी की सुंदरता देखो।

राजा :
(मन-ही-मन) क्या इसकी माँ का नाम शकुन्तला है? किन्तु नाम की समानता तो बहुत मिलती है।

बालक :
माँ! यह मोर मुझे अच्छा लग रहा है (ऐसा कह खिलौने को हाथ में ले लेता है।)

पहली तापसी :
(देखते ही उद्वेगपूर्वक) इसके मणिबन्ध में रक्षा-सूत्र नहीं दिखाई दे रहा है? (आर्ये!)

4. राजाः :
अलमलमावेगने। नन्विदमस्य सिंहशावविमर्दात्परिभ्रष्टम्। (इत्यादातुमिच्छति)

प्रथमाः :
शृणोतु महाराजः एषाऽपराजिता नामौषधिरस्य जातकर्मसमये भगवता मारीचेन दत्ता। एतां किल मातापितरावात्मानं च वर्जयित्वापरो भूमिपतितां न गृह्णाति।

राजाः :
अथ गृह्णाति।

प्रथमाः :
ततस्तं सर्पो भूत्वा दशति।

राजाः :
(सहर्षम् आत्मगतम्) कथमिव सम्पूर्णमपि मे मनोरथंनाभिनन्दामि। (इति। बालं परिष्वजते)

(ततः प्रविशत्येकवेणीधरा शकुन्तला)
राजाः-(शकुन्तलां विलोक्य) अये सेयमत्रभवती शकुन्तला।

बालः :
(मातरमुपेत्य) मातः एष कोऽपि पुरुषो मां पुत्र इत्यालिङ्गति।

राजाः :
प्रिये क्रौर्यमपि मे त्वयि प्रयुक्तमनुकूलपरिणामं संवृत्तम् यदहमिदानीं त्वया प्रत्यभिज्ञातमात्मानं पश्यामि।

शकुन्तलाः :
(नाममुद्रां दृष्ट्वा) आर्यपुत्रं इदं तेऽङ्गलीयकम्।।

राजाः :
अस्मादङ्गलीयोपलम्भात्खलु स्मृतिरूपलब्धा।
(इति निष्क्रान्तः)

शब्दार्थ :
दातुमिच्छति-देने की इच्छा करता है-wish to give;जातकर्मसमये-जात कर्म के समय-ceremonyperformed at the birthofachild; दाता-दिया गया है-given; वर्जयितापरो-छोड़कर दूसरा-expect other; भूमिपतिता-भूमि पर गिरे हुए को-to fallen on the ground; न ग्रहणाति-ग्रहण नहीं करता-does not take; ततस्तं-तब उसे-then it; भूत्वा-होकर -across; सहर्षम्-हर्ष के साथ-with cheer; आत्मगतम्-मन में-in mind; विलोक्य-देखकर-looking; इत्यालिङ्गति-ऐसा आलिंगन करता है-armes; पश्यामि-देखता हूँ-look; त्वया-तुझसे-your.

हिन्दी अर्थ :
राजा :
घबराएं नहीं, सिंह शावक के साथ खेलते समय रगड़ से हाथ में बंधा रक्षा-सूत्र नीचे गिर गया (यह कह राजा उसे उठाना चाहता है।)

पहली तपस्विनी :
महाराज! सुनिए। यह अपराजिता नामक दिव्य औषधि (ताबीज) इस बालक के जात कर्म के समय पूज्य कश्यप ऋषि ने इसके हाथ में बाँध दी थी। इसके भूमि पर गिर जाने पर इस बालक के माता-पिता के अलावा किसी दूसरे द्वारा उठाया जाना वर्जित है (अर्थात् इसके माता-पिता के सिवा कोई दूसरा नहीं उठा सकता)।

राजा :
यदि कोई दूसरा उठा ले तो?

पहली तपस्विनी :
तो साँप बनकर यह डस लेता है।

राजा :
(मन में प्रसन्न होते हुए) तब तो मेरा मनोरथ पूर्ण हुआ (बालक को छाती से लगाता है) (तब एक वेणी धारण किए शकुन्तला प्रवेश करती है)।

राजा :
(शकुन्तला को देखकर) अरे, यह तो शकुन्तला ही है।

बालक :
(अपनी माँ के पास जाकर) माँ! ये कौन है जो मुझे बड़े स्नेह से पुत्र कहते हुए गले लगा रहे हैं।

राजा :
प्रिये! मैंने तुम्हारे साथ जो भी प्रतिकूल व्यवहार किया था, उसका परिणाम है कि अब तुम भी मुझे नहीं पहचान रही हो।

शकुन्तला :
आर्य पुत्र! क्या यह वही अंगूठी है?

राजा:
यह वही अँगूठी है जिससे हम स्मृति को उपलब्ध हुए हैं। (ऐसा कह निकल जाते हैं)।