Let and be the greatest integer . Then, the number of points, where the function , is not differentiable, is ____.

25 Explanation: in Total point of not differentiable = 25

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JEE 2023 — Mathematics PYQ

JEE | Mathematics | 2023

Let $a \in Z$ and $⌊ b ⌋$ be the greatest integer $\leq t$ . Then, the number of points, where the function $f (x) = [a + 13 sin x]$ , $x \in (0, π)$ is not differentiable, is ____.

Choose the correct answer:

A.
24
B.
25
(Correct Answer)
C.
26
D.
27

Correct Answer:

Explanation

$f (x) = [a + 13 sin x]$

$f (x) = a + [13 sin x]$ in $(0, π)$

$x \in (0, π)$

$\Rightarrow 0 < 13 \sin x \leq 13$

$\Rightarrow [13 sin x] = {0, 1, 2, 3, ..., 12, 13}$

Total point of not differentiable = 25

Explanation

$f (x) = [a + 13 sin x]$

$f (x) = a + [13 sin x]$ in $(0, π)$

$x \in (0, π)$

$\Rightarrow 0 < 13 \sin x \leq 13$

$\Rightarrow [13 sin x] = {0, 1, 2, 3, ..., 12, 13}$

Total point of not differentiable = 25

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