CUET Mathematics 2026 21st May Shift 2 PYQs

Match the LIST-I with LIST-II

LIST-I		LIST-II
A.	The degree of the differential equation $\left(\frac{d^3y}{dx^3}\right)^4+\left(\frac{d^2y}{dx^2}\right)^5+\left(\frac{dy}{dx}\right)+y=0$	I.	0
B.	The order of the differential equation $\left(\frac{d^3y}{dx^3}\right)^4+\left(\frac{d^2y}{dx^2}\right)^5+\left(\frac{dy}{dx}\right)+y^2=0$	II.	4
C.	The number of arbitrary constants in the general solution of a differential equation of second order is	III.	3
D.	The number of arbitrary constants in a particular solution of a differential equation of third order is	IV.	2

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Match List-I with List-II

List-I	List-II
Differential equation	Degree
(A) $\frac{d^2y}{dx^2} + \sqrt{\frac{dy}{dx}} - y = 0$	(I) 6
(B) $\sqrt{\frac{d^3y}{dx^3}} - \sqrt[12]{\frac{d^2y}{dx^2}} = 0$	(II) Not defined
(C) $\left(\frac{d^2y}{dx^2}\right)^2 + \frac{dy}{dx} + e^{\frac{dx}{dx}} = x^2$	(III) 3
(D) $\sqrt[3]{\frac{dy}{dx}} - \frac{d^2y}{dx^2} = e^x$	(IV) 2

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The general solution of the differential equation $\frac{dy}{dx}-\frac{y}{x}+\text{cosec}\left(\frac{y}{x}\right)=0$ is

(Consider $\log x=\log_e x$)