RBSE Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability Ex 5.6

Rajasthan Board RBSE Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability Ex 5.6 Textbook Exercise Questions and Answers.

Rajasthan Board RBSE Solutions for Class 12 Maths in Hindi Medium & English Medium are part of RBSE Solutions for Class 12. Students can also read RBSE Class 12 Maths Important Questions for exam preparation. Students can also go through RBSE Class 12 Maths Notes to understand and remember the concepts easily.

RBSE Class 12 Maths Solutions Chapter 5 Continuity and Differentiability Ex 5.6

Question 1.
x = 2at2, y = at4
Answer:
Given x = 2at2, y = at4
Differentiating both sides w.r.t t
RBSE Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability Ex 5.6 1

RBSE Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability Ex 5.6

Question 2.
x = a cos θ, y = b cos θ
Answer:
Given, x = a cos θ, y = b cos θ
Differentiating both sides w.r.t θ
RBSE Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability Ex 5.6 2

Question 3.
x = sin t, y = cos 2t
Answer:
Given x = sin t and y = cos 2t
Differentiating both sides w.r.t t
RBSE Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability Ex 5.6 3

RBSE Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability Ex 5.6

Question 4.
x = 4t and y = \(\frac{4}{t}\)
Answer:
Given, x = 4t and y = \(\frac{4}{t}\)
Differentiating both sides w.r.t t
RBSE Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability Ex 5.6 4

Question 5.
x = cos θ - cos 2θ, y = sin θ - sin 2θ
Answer:
Given, x = cos θ - cos 2θ
and y = sin θ - sin 2θ
Differentiating both sides w.r.t. θ
RBSE Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability Ex 5.6 5

RBSE Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability Ex 5.6

Question 6.
x = a(θ - sin θ), y = a(1 + cos θ)
Answer:
Given x = a(θ - sin θ)
and y = y = a(1 + cos θ)
Differentiating both sides w.r.t. θ
RBSE Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability Ex 5.6 6

Question 7.
x = \(\frac{\sin ^{3} t}{\sqrt{\cos 2 t}}\), y = \(\frac{\cos ^{3} t}{\sqrt{\cos 2 t}}\)
Answer:
RBSE Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability Ex 5.6 7
RBSE Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability Ex 5.6 8
RBSE Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability Ex 5.6 9

RBSE Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability Ex 5.6

Question 8.
x = a(cos t + log tan t/2), y = a sin t
Answer:
x = a(cos t + log tan t/2), y = a sin t
Differentiating both sides of t
x = a(cos t + log tan t/2)
RBSE Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability Ex 5.6 10

Question 9.
x = a sec θ, y = b tan θ
Answer:
Given, x = a sec θ, y = b tan θ
Differentiating both sides w.r.t. θ
RBSE Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability Ex 5.6 11

Question 10.
x = a(cos θ + θ sin θ)
y = a(sin θ - θ cos θ)
Answer:
Given, x = a(cos θ + θ sin θ)
and y a(sin θ - θ cos θ)
Differentiating both functions w.r.t. θ
RBSE Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability Ex 5.6 12

RBSE Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability Ex 5.6

Question 11.
If x = \(\sqrt{a^{\sin }-1} t\) and y = \(\sqrt{a^{\cos ^{-1} t}}\), then show that \(\frac{d y}{d x}=-\frac{y}{x}\).
Answer:
RBSE Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability Ex 5.6 13
RBSE Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability Ex 5.6 14

Bhagya
Last Updated on Nov. 2, 2023, 9:26 a.m.
Published Nov. 1, 2023