CUET · MATHS · PYQ PAPER 2023
Match List I with List II
| LIST I | LIST II |
| A. \(\lim_{x \to 0} \frac{(1 - \cos 2x) \sin 5x}{x^2 \sin 3x}\) | I. 18 |
| B. \(\lim_{x \to \infty} \frac{(3x-5)(2x-7)}{(4x-9)(5x-3)}\) | II. \(\frac{10}{3}\) |
| C. \(\lim_{x \to 0} \frac{2 \sin^2 3x}{x^2}\) | III. \(\frac{3}{4}\) |
| D. \(\lim_{x \to \frac{\pi}{4}} \frac{1 - \cos^3 x}{2 \cot x - \cot^3 x}\) | IV. \(\frac{3}{10}\) |
Choose the correct answer from the options given below:
- A A-IV, B-I, C-III, D-II
- B A-III, B-II, C-IV, D-I
- C A-II, B-IV, C-I, D-III
- D A-I, B-III, C-II, D-IV
Answer & Solution
Correct Answer
(C) A-II, B-IV, C-I, D-III
Step-by-step Solution
Detailed explanation
A. \( \lim_{x \to 0} \frac{(1 - \cos 2x) \sin 5x}{x^2 \sin 3x} = \lim_{x \to 0} \frac{2 \sin^2 x \sin 5x}{x^2 \sin 3x} \) \(= \lim_{x \to 0} 2 \left(\frac{\sin x}{x}\right)^2 \left(\frac{\sin 5x}{5x}\right) \cdot 5 \cdot \left(\frac{3x}{\sin 3x}\right) \cdot \frac{1}{3} \)…
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