CUET Mathematics - If xy + x^2/y = x^3y + y, then dy/dx is equal to | PYQs + Solutions

CUET Mathematics 2025 30 May Shift 1

Calculus

Medium

applied

$\frac{y(3x^2y^2 + 2x + y^2)}{x^2y - x^2y^3 + x^2 - y^2}$

$\frac{y(3x^2y^2 - 2x - y^2)}{xy^2 - x^2y^2 - x^2 - y^2}$

$\frac{y(3x^2y^2 - 2x + y^2)}{x^2y - x^2y^3 + x^2 + y^2}$

$\frac{y(3y^2x^2 - y^2 + 2x)}{x^2y^3 - x^2y - x - y^2}$

✅ Correct Option: 2

Related questions:

21 May Shift 1

The greatest integer function $f(x) = [x]$ is differentiable for all values of

14 May Shift 2

Match List-I with List-II

List-I	List-II
Function	Derivative
(A) $y = \sin^{-1} x + \sin^{-1} \sqrt{1 - x^2}; \|x\| < 1$	(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:

30 May Shift 1

Match List-I with List-II

List-I	List-II
Function f(x)	Points of Non-Differentiability
(A) $f(x) = \|x\| + 1$	(I) Not differentiable at $x = 3$ only
(B) $f(x) = \|x - 3\|$	(II) Not differentiable at $x = -3$ only
(C) $f(x) = \|x + 3\|$	(III) Not differentiable at $x = 3, -3$ only
(D) $f(x) = \|x^2 - 9\|$	(IV) Not differentiable at $x = 0$ only

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CUET Mathematics 2025 30 May Shift 1 PYQs