JEE Main 2026 · 8 Apr · Shift 2 · Mathematics Q13

MathematicsSingle correct+4 / -1Question 13 of 75

For the function $f(x)=e^{\sin|x|}-|x|$ , $x\in\mathbf R$ , consider the following statements :

Statement I : $f$ is differentiable for all $x\in\mathbf R$ .

Statement II : $f$ is increasing in $\left(-\pi,-\dfrac\pi2\right)$ .

In the light of the above statements, choose the correct answer from the options given below :

Both Statement I and Statement II are true

Both Statement I and Statement II are false

Statement I is true but Statement II is false

Statement I is false but Statement II is true

Answer and worked solution

Official answer: A

At x = 0.

Both one-sided derivatives are 0, and f is smooth elsewhere: I is true.

On $(-\pi,-\tfrac\pi2)$ . $\cos x<0$ , so $f'=1-\cos x\,e^{-\sin x}>0$ : increasing. II is true.

(A)

Topics:Differentiability Monotonicity

JEE Main 2026 · 8 Apr · Shift 2, Mathematics question 13