If f (x) = and h(x) = n ∈ I, then which of the following …

Maths Differentiation and Applications of Derivatives General Single Correct MCQ

Published by: CGP EDU Academic Team

Published on: August 14, 2026

If f (x) = and

h(x) =

n ∈ I, then which of the following is (are) correct -

f(x) < M, then greatest value of M is less than 1

f(x) < M, then least value of M is 1

h(x) is decreasing only for a = b = n + 1 – n sin 1

h(x) is decreasing for b ≤ n + 1 – n sin 1 ≤ a

Text Solution

Verified by Experts

The correct answer is:

CHECK THE SOLUTION.

(b,d)

Clearly f(x) is periodic with period 1.

It is sufficient to consider f(x) in (0, 1)

f(x) = 1, f(x) = sin 1.

Also f(x) is decreasing

⇒ f(x) < 1 hence least value of M = 1.

 f(x) = 1 ; h(x) = a + (sin 1 – 1) n

f(x) = ;

h(x) = b + (sin 1 – 1) (n + 1)

So b ≤ (n + 1) – n sin 1 & a > (n + 1) – n sin 1

Previous Question Next Question

Get practice questions, solutions, and test series in one place.

Share your experience with this question and solution.

Send your comment, doubt, correction, or feedback to admin.

What students say about this solution

No reviews yet. Be the first to write a review.