CUET Mathematics 2024 PYQs

If $f(x)=2\left(\tan ^{-1}\left(e^{x}\right)-\frac{\pi}{4}\right)$, then $f(x)$ is :

If a function $f(x)=x^{2}+b x+1$ is increasing in the interval $[1,2]$, then the least value of $b$ is :

$f(x)=\sin x+\frac{1}{2} \cos 2 x \text { in }\left[0, \frac{\pi}{2}\right]$

(A) $f^{\prime}(x)=\cos x-\sin 2 x$

(B) The critical points of the function are $x=\frac{\pi}{6}$ and $x=\frac{\pi}{2}$

(C) The minimum value of the function is $2$

(D) The maximum value of the function is $\frac{3}{4}$

Choose the correct answer from the options given below :