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Home Questions BRHU38R62M
Target Exam

CUET

Subject

-- Mathematics - Section A

Chapter

Differential Equations

Question:

Match List-I with List-II

List-I

List-II

(A) The degree of differential equation $\frac{d^3y}{dx^3}= e^{\frac{dy}{dx}}$

(I) 2

(B) The order of differential equation $(\frac{dy}{dx})^2\frac{d^3y}{dx^3}=0$

(II) 4

(C) The sum of order and degree of differential equation $\frac{d}{dx}(\frac{d^2y}{dx^2})+(\frac{dy}{dx})^5= x$

(III) not defined

(D) The number of arbitrary constants in the general solution of a differential equation of order 2

(IV) 3

Choose the correct answer from the options given below:

Options:

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

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

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

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

Correct Answer:

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

Explanation:

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

List-I

List-II

(A) The degree of differential equation $\frac{d^3y}{dx^3}= e^{\frac{dy}{dx}}$

(III) not defined

(B) The order of differential equation $(\frac{dy}{dx})^2\frac{d^3y}{dx^3}=0$

(IV) 3

(C) The sum of order and degree of differential equation $\frac{d}{dx}(\frac{d^2y}{dx^2})+(\frac{dy}{dx})^5= x$

(II) 4

(D) The number of arbitrary constants in the general solution of a differential equation of order 2

(I) 2

(A) $\frac{d^{3}y}{dx^{3}} = e^{\frac{dy}{dx}}$ Degree is not defined because the highest derivative occurs inside a non-polynomial function (exponential). → (A) → (III)

(B) $\left(\frac{dy}{dx}\right)^{2}\frac{d^{3}y}{dx^{3}}=0$ Highest order derivative = 3 ⇒ order = 3 → (B) → (IV)

(C) $\frac{d}{dx}\left(\frac{d^{2}y}{dx^{2}}\right)+\left(\frac{dy}{dx}\right)^{5}=x$ Order = 3, degree = 1 ⇒ sum = 4 → (C) → (II)

(D) Differential equation of order 2 has 2 arbitrary constants → (D) → (I)

Correct matching:

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

CUET Questions