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