CUET Mathematics 2025 19 May Shift 1 PYQs

If $xy = e^{(x-y)}$, then $\frac{dy}{dx}$ is equal to:

If the function

$f(x) = \begin{cases} k\cos x & , x \neq \frac{\pi}{2} \\ \pi - 2x & , x = \frac{\pi}{2} \\ 3 & , x = \frac{\pi}{2} \end{cases}$

is continuous at $x = \frac{\pi}{2}$, then $k$ is equal to

Match List-I with List-II

$\begin{array}{|l|l|} \hline \rule{0pt}{2.8ex}\text{List-I} & \text{List-II} \\[1.2ex] \hline \rule{0pt}{2.8ex}\text{(A) } f(x) = |x| & \text{(I) Not differentiable at } x=-2 \text{ only} \\[1.2ex] \hline \rule{0pt}{2.8ex}\text{(B) } f(x) = |x+2| & \text{(II) Not differentiable at } x=0 \text{ only} \\[1.2ex] \hline \rule{0pt}{2.8ex}\text{(C) } f(x) = |x^2-4| & \text{(III) Not differentiable at } x=2 \text{ only} \\[1.2ex] \hline \rule{0pt}{2.8ex}\text{(D) } f(x) = |x-2| & \text{(IV) Not differentiable at } x=2,-2 \text{ only} \\[1.2ex] \hline \end{array}$

Choose the correct answer from the options given below: