JEE Main 2026 (8 Apr, Shift 2) Maths Q13: For the function…

Question

For the function $f(x) = \mathrm{e}^{\sin|x|} - |x|$, $x \in \mathbf{R}$, consider the following statements :
Statement I : $f$ is differentiable for all $x \in \mathbf{R}$.
Statement II : $f$ is increasing in $\left(-\pi, -\frac{\pi}{2}\right)$.
In the light of the above statements, choose the correct answer from the options given below :

Accepted Answer

Option 1: Both Statement I and Statement II are true

Answer

Both Statement I and Statement II are true

Answer

Both Statement I and Statement II are false

Answer

Statement I is true but Statement II is false

Answer

Statement I is false but Statement II is true

JEE Main 8 April 2026, Shift 2, Maths Q13

Same idea in other shifts