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CUET · MATHS · PYQ PAPER 2025

Match List-I with List-II
List-I (Differential Equations)List-II (Order and degree)
(A) \(\frac{d y}{d x}+e^y=0\)(I) order 2, degree not defined
(B) \(\frac{d^2 y}{d x^2}=\left[1+\left(\frac{d y}{d x}\right)^2\right]^{3 / 2]}\)(II) order 2, degree 1
(C) \(\left(\frac{d^2 y}{d x^2}\right)^2+e^{\left(\frac{\text { 临 })}{}\right.}=0\)(III) order 1, degree 1
(D) \(\frac{d^2 y}{d x^2}+x \frac{d y}{d x}-2 y=\log x ; x>0\)(IV) order 2, degree 2
Choose the correct answer from the options given below:

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

Answer & Solution

Correct Answer

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

Step-by-step Solution

Detailed explanation

(A) \(\frac{d y}{d x}+e^y=0\): Order = 1, Degree = 1. Matches (III). (B) \(\frac{d^2 y}{d x^2}=\left[1+\left(\frac{d y}{d x}\right)^2\right]^{3 / 2]}\) \(\Rightarrow\) \(\left(\frac{d^2 y}{d x^2}\right)^2=\left[1+\left(\frac{d y}{d x}\right)^2\right]^3\): Order = 2, Degree = 2.…