CUET Mathematics 2026 21st May Shift 1 PYQs

If $f(x) = |x| + |x - 5|$, then which of the following statements are TRUE?

(A) f is a continuous function every where

(B) f is a continuous function except $x = 5$ and $x = 0$

(C) f is a continuous function except $x = 0$ but not differentiable at $x = 5$

(D) f is a continuous function everywhere but not differentiable at $x = 0$ and $x = 5$

Choose the correct answer from the options given below:

If $x\sqrt{1+y}+y\sqrt{1+x}=0, x\neq y$, then $\frac{dy}{dx}$ is equal to

If $f(x) = x^3 e^{-x}$, then the value of $f''(1)$ is equal to