CUET Mathematics - Consider the curve which is represented by the differential equation dy/dx = 1 + x + y + xy. If it passes through the point (0,0), then which of the following is/are true? (A) It is a straight line. (B) It is a parabola. (C) It also passes through the point (-1, 1/e - 1) (D) Its equation is xy(x + 1) = 0 Choose the correct answer from the options given below: | PYQs + Solutions

CUET Mathematics 2025 15 May Shift 2

Calculus

Medium

core

(A) only

(B) only

✅ Correct Option: 4

Related questions:

21 May Shift 2

Match List-I with List-II

List-I	List-II
(A) Integrating factor of $xdy - (y + x^2)dx = 0$	(I) $x^2$
(B) Integrating factor of $xdy + (2y + x^2)dx = 0$	(II) $x^3$
(C) Integrating factor of $(3y - x^2)dx + xdy = 0$	(III) $x$
(D) Integrating factor of $(y + 3x^2)dx + xdy = 0$	(IV) $\frac{1}{x}$

Choose the correct answer from the options given below:

22 May Shift 2

Match List-I with List-II

List-I	List-II
Differential Equation	Order and Degree
(A) $\left(\frac{d^2y}{dx^2}\right)^2 = e^x\left(\frac{dy}{dx}\right)^4 + 1 = 0$	(I) order = 1 and degree = 2
(B) $\left(\frac{dy}{dx}\right)^2 + xy = 0$	(II) order = 2 and degree = 1
(C) $\left(1 + \frac{dy}{dx}\right)^{3/2} = 4\left(\frac{d^2y}{dx^2}\right)^3$	(III) order = 2 and degree = 2
(D) $\frac{d^2y}{dx^2} + 1 = \frac{dy}{dx}$	(IV) order = 2 and degree = 4

Choose the correct answer from the options given below:

15 May Shift 1

Let $y(x) = a(x + 1) \log(x + 1) + bx + 5$ be the solution of the differential equation $x\frac{dy}{dx} = x + 1_{x}y(0) = 5$ , then the value of $(a + b)$ is:

CUET Mathematics 2025 15 May Shift 2 PYQs

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