CUET Mathematics 2025 29 May Shift 2 PYQs

Match List-I with List-II

List-I	List-II
Function	Derivative
---	---
(A) $y = \sin^{-1} x + \sin^{-1} \sqrt{1 - x^2}; \vert x\vert < 1$	(I) $\frac{dy}{dx} = \frac{1}{2y-1}$
(B) $y = \sqrt{x + y}, x+y > 0 \text{ and } y \neq \frac{1}{2}$	(II) $\frac{dy}{dx} = 10^x \log_e 10$
(C) $y = \log_{10} x, x > 0$	(III) $\frac{dy}{dx} = 0$
(D) $y = 10^x$	(IV) $\frac{dy}{dx} = \frac{1}{x \log_e 10}$

Choose the correct answer from the options given below:

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 $x^2 - y^2 = 1$, then which of the following is correct?

(A) $(x^2 - 1)\left(\frac{dy}{dx}\right)^2 = x^2$

(B) $(x^2 - 1)\left(\frac{d^2y}{dx^2}\right)^2 = x^2$

(C) $(x^2 - 1)^3\left(\frac{d^2y}{dx^2}\right)^2 = x^2$

(D) $(x^2 - 1)^3\left(\frac{d^2y}{dx^2}\right)^2 = 1$

Choose the correct answer from the options given below: