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CUET · MATHS · PYQ PAPER 2025

Match List-I with List-II (where \(c\) is an arbitrary constant)
List-I (Differential Equation)List-II (General solution)
(A) \(\frac{d y}{d x}=\frac{y}{x}, x \neq 0\)(I) \(y=c x, c\) is an arbitrary constant
(B) \(x d x-y d y=0 ; y \neq 0, x \neq 0\)(II) \(x^2-y^2=c, c\) is an arbitrary constant
(C) \(\frac{\left(x^2-1\right)}{y^2+1} \frac{d y}{d x}=1\)(III) \(2 x+3 y=c, c\) is an arbitrary constant
(D) \(2 d x+3 d y=0\)(IV) \(\left(x^3-y^3\right)=c+3(x+y), c\) is an arbitrary constant
Choose the correct answer from the options given below :

  1. A (A) - (IV), (B) - (I), (C) - (II), (D) – (III)
  2. B (A) - (II), (B) - (IV), (C) - (III), (D) - (I)
  3. C (A) - (III), (B) - (IV), (C) - (I), (D) - (II)
  4. D (A) (I), (B) – (II), (C) - (IV), (D) – (III)
Verified Solution

Answer & Solution

Correct Answer

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

Step-by-step Solution

Detailed explanation

(A) \(\frac{d y}{d x}=\frac{y}{x}\) \(\frac{d y}{y} = \frac{d x}{x}\) \(\int \frac{d y}{y} = \int \frac{d x}{x}\) \(\ln|y| = \ln|x| + \ln|c_1| \Rightarrow y = c x\) (A) matches (I) (B) \(x d x-y d y=0\) \(x d x = y d y\) \(\int x d x = \int y d y\)…