CUET Mathematics - Let y(x) be the solution curve of the differential equation x(1+y^2)dx - y(1+x^2)dy = 0 and it passes through the point (0, 1), then | PYQs + Solutions

CUET Mathematics 2026 22nd May Shift 2

Calculus

Medium

applied

$y^2=2x^2+1$

$y=(2x+1)^2$

$y=2x^2+3x+1$

$y^2=\log\lvert 1+x \rvert+x^2+1$

✅ Correct Option: 1

Related questions:

19 May Shift 1

Match List-I with List-II

List-I	List-II
Differential Equation	Order and degree of differential equation
(A) $\frac{d^2y}{dx^2} + 2\left(\frac{dy}{dx}\right)^2 = e^{\frac{dy}{dx}} + 1$	(I) Order = 1, Degree = 2
(B) $\left(\frac{d^2y}{dx^2}\right)^2 + 4\left(\frac{dy}{dx}\right)^3 = e^y - 1$	(II) Order = 2, Degree = 1
(C) $3\left(\frac{dy}{dx}\right) + 4y + e^y = \frac{dx}{dy}$	(III) Order = 2, Degree = 2
(D) $\frac{d^2y}{dx^2} + 3\left(\frac{dy}{dx}\right) = \left(e^y + \frac{dy}{dx}\right)^2$	(IV) Order = 2, Degree = Not defined

Choose the correct answer from the options given below:

19th May Shift 1

Match List-I with List-II

List-I	List-II
(A) $y + \frac{dy}{dx} = \frac{1}{4}\int y\,dx$	(I) Order 1, Degree 1
(B) $y = \frac{dy}{dx} + \frac{C}{dy/dx}$	(II) Order 2, Degree 2
(C) $(xy^2+x)dx + (y-x^2)dy = 0$	(III) Order 2, Degree 1
(D) $\left[\left\{1+\left(\frac{dy}{dx}\right)^2\right\}^{3/2}/\frac{d^2y}{dx^2}\right] = K$	(IV) Order 1, Degree 2

Choose the correct answer from the options given below:

21st May Shift 2

Let $y = f(x)$ be the solution curve of the differential equation $\dfrac{dy}{dx} + 2y^2 = 0$ if $f(1) = 1$ , then $f(2)$ is equal to

CUET Mathematics 2026 22nd May Shift 2 PYQs