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CUET · MATHS · PYQ PAPER 2025

Match List-l with List-ll
List-l (Differential Equation)List-ll (Order and degree of differential equation)
(A) \(\frac{d^2 y}{d x^2}+2\left(\frac{d y}{d x}\right)^2=e^{\frac{d y}{d x}}+1\)(I) Order = 1, Degree = 2
(B) \(\left(\frac{d^2 y}{d x^2}\right)^2+4\left(\frac{d y}{d x}\right)^3=e^y-1\)(II) Order = 2, Degree = 1
(C) \(3\left(\frac{d y}{d x}\right)+4 y+e^y=\frac{d x}{d y}\)(III) Order = 2 , Degree = 2
(D) \(\frac{d^2 y}{d x^2}+3\left(\frac{d y}{d x}\right)=\left(e^y+\frac{d y}{d x}\right)^2\)(IV) Order = 2, Degree = Not defined
Choose the correct answer from the options given below :

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

Answer & Solution

Correct Answer

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

Step-by-step Solution

Detailed explanation

(A) \(\frac{d^2 y}{d x^2}+2\left(\frac{d y}{d x}\right)^2=e^{\frac{d y}{d x}}+1\) Highest order derivative: \(\frac{d^2 y}{d x^2}\) (Order = 2). Equation is not a polynomial in derivatives due to \(e^{\frac{d y}{d x}}\). Degree = Not defined. (A) matches (IV). (B)…