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CUET · MATHS · PYQ PAPER 2025

Match List-I with List-II
List-I (Integral)List-II (Solution: C is an arbitrary constant)
(A) \(\int \frac{d x}{x^2+25}\)(I) \(\frac{1}{10} \log \left|\frac{5+x}{5-x}\right|+C\)
(B) \(\int \frac{d x}{x^2-25}\)(II) \(\log \left|x+\sqrt{x^2-25}\right|+C\)
(C) \(\int \frac{d x}{25-x^2}\)(III) \(\frac{1}{5} \tan ^{-1}\left(\frac{x}{5}\right)+C\)
(D) \(\int \frac{d x}{\sqrt{x^2-25}}\)(IV) \(\frac{1}{10} \log \left|\frac{x-5}{x+5}\right|+C\)
Choose the correct answer from the options given below:

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

Answer & Solution

Correct Answer

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

Step-by-step Solution

Detailed explanation

(A) \(\int \frac{d x}{x^2+25} = \frac{1}{5} \tan ^{-1}\left(\frac{x}{5}\right)+C\) (A) matches with (III). (B) \(\int \frac{d x}{x^2-25} = \frac{1}{2 \cdot 5} \log \left|\frac{x-5}{x+5}\right|+C = \frac{1}{10} \log \left|\frac{x-5}{x+5}\right|+C\) (B) matches with (IV). (C)…