Match List-I with List-II List-

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Target Exam

CUET

Subject

-- Mathematics - Section A

Chapter

Differential Equations

Question:

Match List-I with List-II

List-I Differential Equation	List-II Degree
(A) $xy\frac{d^2y}{dx^2}+x(\frac{dy}{dx})^2-y\frac{dy}{dx}=0$	(I) 3
(B) $\frac{d^2y}{dx^2} +\log (\frac{dy}{dx}=0$	(II) 1
(C) $(\frac{d^2y}{dx^2})^2+(\frac{dy}{dx})^3+\frac{dy}{dx}+1=0$	(III) not defined
(D) $2x^2(\frac{d^2y}{dx^2})^3-5(\frac{dy}{dx})^2+y=0$	(IV) 2

Choose the correct answer from the options given below.

Options:

(A)-(I), (B)-(II), (C)-(III), (D)-(IV)

(A)-(II), (B)-(III), (C)-(IV), (D)-(I)

(A)-(IV), (B)-(III), (C)-(I), (D)-(II)

(A)-(IV), (B)-(III), (C)-(II), (D)-(I)

Correct Answer:

(A)-(II), (B)-(III), (C)-(IV), (D)-(I)

Explanation:

The correct answer is Option (2) → (A)-(II), (B)-(III), (C)-(IV), (D)-(I)

List-I Differential Equation	List-II Degree
(A) $xy\frac{d^2y}{dx^2}+x(\frac{dy}{dx})^2-y\frac{dy}{dx}=0$	(II) 1
(B) $\frac{d^2y}{dx^2} +\log (\frac{dy}{dx}=0$	(III) not defined
(C) $(\frac{d^2y}{dx^2})^2+(\frac{dy}{dx})^3+\frac{dy}{dx}+1=0$	(IV) 2
(D) $2x^2(\frac{d^2y}{dx^2})^3-5(\frac{dy}{dx})^2+y=0$	(I) 3

(A) $x y \frac{d^2y}{dx^2}+x\Big(\frac{dy}{dx}\Big)^2-y\frac{dy}{dx}=0$.

Highest order derivative $\frac{d^2y}{dx^2}$ appears to power $1$. Degree $=1\Rightarrow$(II).

(B) $\frac{d^2y}{dx^2}+\log\!\Big(\frac{dy}{dx}\Big)=0$.

Contains $\log$ of a derivative, not a polynomial in derivatives. Degree not defined $\Rightarrow$(III).

Highest order derivative $\frac{d^2y}{dx^2}$ occurs with power $2$. Degree $=2\Rightarrow$(IV).

(D) $2x^2\Big(\frac{d^2y}{dx^2}\Big)^3-5\Big(\frac{dy}{dx}\Big)^2+y=0$.

Highest order derivative $\frac{d^2y}{dx^2}$ occurs with power $3$. Degree $=3\Rightarrow$(I).