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 Equations	List-II Order and degree
(A) $\frac{dy}{dx}+e^y = 0$	(I) order 2, degree not defined
(B) $\frac{d^2y}{dx^2} =\left[1+(\frac{dy}{dx})^2\right]^{3/2}$	(II) order 2, degree 1
(C) $\left(\frac{d^2y}{dx^2}\right)^2+e^{(\frac{dy}{dx})}=0$	(III) order 1, degree 1
(D) $\frac{d^2y}{dx^2}+x\frac{dy}{dx}-2y= \log x;x>0$	(IV) order 2, degree 2

Choose the correct answer from the options given below:

Options:

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

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

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

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

Correct Answer:

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

Explanation:

The correct answer is Option (3) → (A)-(III), (B)-(IV), (C)-(I), (D)-(II)

List-I Differential Equations	List-II Order and degree
(A) $\frac{dy}{dx}+e^y = 0$	(III) order 1, degree 1
(B) $\frac{d^2y}{dx^2} =\left[1+(\frac{dy}{dx})^2\right]^{3/2}$	(IV) order 2, degree 2
(C) $\left(\frac{d^2y}{dx^2}\right)^2+e^{(\frac{dy}{dx})}=0$	(I) order 2, degree not defined
(D) $\frac{d^2y}{dx^2}+x\frac{dy}{dx}-2y= \log x;x>0$	(II) order 2, degree 1

$\text{(A)}\;\frac{dy}{dx}+e^{y}=0$

$\text{Order}=1,\;\text{Degree}=1$

$\text{(B)}\;\frac{d^{2}y}{dx^{2}}=\left[1+\left(\frac{dy}{dx}\right)^{2}\right]^{\frac{3}{2}}$

$\text{Order}=2,\;\text{Degree}=2$

$\text{(C)}\;\left(\frac{d^{2}y}{dx^{2}}\right)^{2}+e^{\frac{dy}{dx}}=0$

$\text{Order}=2,\;\text{Degree not defined}$

$\text{(D)}\;\frac{d^{2}y}{dx^{2}}+x\frac{dy}{dx}-2y=\log x,\;x>0$

$\text{Order}=2,\;\text{Degree}=1$

$\text{Correct match: (A–III), (B–IV), (C–I), (D–II)}$