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) \(\frac{1}{10} \log \left|\frac{x-5}{x+5}\right|+C\) |
- A (A) - (I), (B) - (IV), (C) - (II), (D) - (III)
- B (A) - (III), (B) -(IV), (C) - (I), (D) – (II)
- C (A) - (III), (B) -(IV), (C) - (II), (D) - (I)
- D (A) - (II), (B) - (IV), (C) - (III), (D) - (I)
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)…
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