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.

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

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

Question 3.
x = sin t, y = cos 2t
Answer:
Given x = sin t and y = cos 2t
Differentiating both sides w.r.t t

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

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

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

Question 7.
x = \(\frac{\sin ^{3} t}{\sqrt{\cos 2 t}}\), y = \(\frac{\cos ^{3} t}{\sqrt{\cos 2 t}}\)
Answer:

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)

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

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

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: