CBSE Class 12 Sample Paper for 2022 Boards (MCQ Based - for Term 1)
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CBSE Class 12 Sample Paper for 2022 Boards (MCQ Based - for Term 1)
Last updated at Dec. 16, 2024 by Teachoo
Transcript
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)
