CBSE Class 12 Sample Paper for 2022 Boards (MCQ Based - for Term 1)

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Question 29 - CBSE Class 12 Sample Paper for 2022 Boards (MCQ Based - for Term 1) - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

Last updated at May 29, 2023 by

The value of 𝑏 for which the function 𝑓(𝑥) = 𝑥 + 𝑐𝑜𝑠 𝑥 + 𝑏 is strictly decreasing over R is:

(a) 𝑏 < 1  (b) No value of b exists

(c) 𝑏 ≤ 1  (d) 𝑏 ≥ 1

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Question 29 The value of 𝑏 for which the function 𝑓(𝑥) = 𝑥 + 𝑐𝑜𝑠 𝑥 + 𝑏 is strictly decreasing over R is: (a) 𝑏 < 1 (b) No value of b exists (c) 𝑏 ≤ 1 (d) 𝑏 ≥ 1 Given 𝑓(𝑥) = 𝑥 + 𝑐𝑜𝑠 𝑥 + 𝑏 Now, 𝑓’(𝑥) = 1 − sin x Since 𝑓(𝑥) is strictly decreasing over R 𝑓’(𝑥) < 0 1 − sin x < 0 1 < sin x sin x > 1 Since −1 ≤ sin x ≤ 1 Thus, sin x > 1 is not possible Thus, for no value of b, 𝑓(𝑥) is strictly decreasing So, the correct answer is (B)

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