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RBSE Solutions for Class 12 Maths Chapter 7 अवकलन Ex 7.4

May 10, 2019 by Fazal Leave a Comment

RBSE Solutions for Class 12 Maths Chapter 7 अवकलन Ex 7.4 is part of RBSE Solutions for Class 12 Maths. Here we have given Rajasthan Board RBSE Class 12 Maths 7 अवकलन Exercise 7.4.

Rajasthan Board RBSE Class 12 Maths Chapter 7 अवकलन Ex 7.4

प्रश्न 1.
(i) x = a sec t, y = b tan t
(ii) x = log t + sin t, y = et + cost
हल :
(i) x = a sec t, y = b tan t
x = a sec t
दोनों पक्षों का t के सापेक्ष अवकलन करने पर
\(\frac { dx }{ dt }\) = (a sec t) = a sec t tan t
तथा y = b tan t
दोनों पक्षों का t के सापेक्ष अवकलन करने पर
RBSE Solutions for Class 12 Maths Chapter 7 Ex 7.4 1

(ii) x = log t + sin t, y = et + cos t
x = log t + sin t
दोनों पक्षों का t के सापेक्ष अवकलन करने पर
RBSE Solutions for Class 12 Maths Chapter 7 Ex 7.4 2
दोनों पक्षों का t के सापेक्ष अवकलन करने पर
RBSE Solutions for Class 12 Maths Chapter 7 Ex 7.4 3
RBSE Solutions for Class 12 Maths Chapter 7 Ex 7.4 4

प्रश्न 2.
(i) x = log t, y = et + cost
(ii) x = a cos θ, y = b sin θ
हल :
(i) = log t, y = et + cost
∵ x = log t
दोनों पक्षों का t के सापेक्ष अवकलन करने पर
RBSE Solutions for Class 12 Maths Chapter 7 Ex 7.4 5
दोनों पक्षों का t के सापेक्ष अवकलन करने पर
RBSE Solutions for Class 12 Maths Chapter 7 Ex 7.4 6

(ii) x = a cos θ, y = b sin θ
∵ x = a cos θ
दोनों पक्षों का θ के सापेक्ष अवकलन करने पर
RBSE Solutions for Class 12 Maths Chapter 7 Ex 7.4 7
दोनों पक्षों का θ के सापेक्ष अवकलन करने पर
RBSE Solutions for Class 12 Maths Chapter 7 Ex 7.4 8
RBSE Solutions for Class 12 Maths Chapter 7 Ex 7.4 9

प्रश्न 3.
(i) x = cos θ – cos 2θ, y = sin θ – sin 2θ
(ii) x = a(θ – sin θ), y = a(1 + cos θ)
हल :
(i) = cos θ – cos 2θ
y= sin θ – sin 2θ
∵ x = cos θ – cos 2θ
दोनों पक्षों का θ के सापेक्ष अवकलन करने पर।
RBSE Solutions for Class 12 Maths Chapter 7 Ex 7.4 10
दोनों पक्षों का θ के सापेक्ष अवकलन करने पर।
RBSE Solutions for Class 12 Maths Chapter 7 Ex 7.4 11

(ii) x = a(θ – sin θ), y = a(1 + cos θ)
∵ x = a(θ – sin θ)
दोनों पक्षों का θ के सापेक्ष अवकलन करने पर।
RBSE Solutions for Class 12 Maths Chapter 7 Ex 7.4 12
दोनों पक्षों का θ के सापेक्ष अवकलन करने पर।
RBSE Solutions for Class 12 Maths Chapter 7 Ex 7.4 13
RBSE Solutions for Class 12 Maths Chapter 7 Ex 7.4 14

प्रश्न 4.
RBSE Solutions for Class 12 Maths Chapter 7 Ex 7.4 15
हल :
दिया है
RBSE Solutions for Class 12 Maths Chapter 7 Ex 7.4 16
RBSE Solutions for Class 12 Maths Chapter 7 Ex 7.4 17
RBSE Solutions for Class 12 Maths Chapter 7 Ex 7.4 18
दोनों पक्षों को t के सापेक्ष अवकलन करने पर
RBSE Solutions for Class 12 Maths Chapter 7 Ex 7.4 19
दोनों पक्षों को t के सापेक्ष अवकलन करने पर
RBSE Solutions for Class 12 Maths Chapter 7 Ex 7.4 20

प्रश्न 5.
RBSE Solutions for Class 12 Maths Chapter 7 Ex 7.4 21
(ii) x = a cos3 t, y = a3 sin t
हल :
RBSE Solutions for Class 12 Maths Chapter 7 Ex 7.4 22
θ के सापेक्ष अवकलन करने पर
RBSE Solutions for Class 12 Maths Chapter 7 Ex 7.4 23
θ के सापेक्ष अवकलन से करने पर
RBSE Solutions for Class 12 Maths Chapter 7 Ex 7.4 24

(ii) x = a cos3 t, y = a sin3 t
∵ x = a cos3 t
दोनों पक्षों का t के सापेक्ष अवकलन करने पर
RBSE Solutions for Class 12 Maths Chapter 7 Ex 7.4 25
दोनों पक्षों का t के सापेक्ष अवकलन करने पर
RBSE Solutions for Class 12 Maths Chapter 7 Ex 7.4 26
RBSE Solutions for Class 12 Maths Chapter 7 Ex 7.4 27

प्रश्न 6.
यदि
RBSE Solutions for Class 12 Maths Chapter 7 Ex 7.4 28
तथा
RBSE Solutions for Class 12 Maths Chapter 7 Ex 7.4 29
तब सिद्ध कीजिए कि
RBSE Solutions for Class 12 Maths Chapter 7 Ex 7.4 30
हल :
दिया है,
RBSE Solutions for Class 12 Maths Chapter 7 Ex 7.4 31
दोनों पक्षों का x के सापेक्ष अवकलन करने पर
RBSE Solutions for Class 12 Maths Chapter 7 Ex 7.4 32

We hope the given RBSE Solutions for Class 12 Maths Chapter 7 अवकलन Ex 7.4 will help you. If you have any query regarding RBSE Solutions for Class 12 Maths Chapter 7 अवकलन Ex 7.4, drop a comment below and we will get back to you at the earliest.

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