CUET Mathematics 2022 30 Aug Shift 1 PYQs

Which of the following statements are correct ?

(A) If $f : R \to R$ then $f(x) = |x|$ is continuous everywhere.

(B) If $f : R \to R$ then $f(x) = |x|$ is continuous everywhere but not differentiable at $x = 0$.

(C) Let $f : R - \{0\} \to R$ then $f(x) = \frac{1}{x}$ is continuous everywhere.

(D) Let $f : R \to R$ then $f(x) = |x - 1| + |x - 2|$ is continuous everywhere but not differentiable at exactly 2 points.

(E) If $f : R \to R$ then $f(x) = \cot x$ is continuous everywhere.

Choose the correct answer from the options given below :

If $y = \sqrt{2024x + 2025}$, then which of the following is correct?

If $y = \log_e\left(\frac{e^2}{x^2}\right)$ for $x \neq 0$, then $\frac{d^2y}{dx^2}$ equals