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Jee Main 2025 — Medium JEE math MCQ

\(\lim_{x \to 0} \csc x \left(\sqrt{2 \cos^2 x + 3 \cos x} - \sqrt{\cos^2 x + \sin x + 4}\right)\) is
  1. A. 0
  2. B. \( \frac{1}{\sqrt{15}} \)
  3. C. \( \frac{1}{2\sqrt{5}} \)
  4. D. \( -\frac{1}{2\sqrt{5}} \)

Solution

The correct option is **D**. (D. \( -\frac{1}{2\sqrt{5}} \))

MATH

medium • PYQ Reworded
Question
Read carefully, then pick the best option.
lim⁡x→0csc⁡x(2cos⁡2x+3cos⁡x−cos⁡2x+sin⁡x+4)\lim_{x \to 0} \csc x \left(\sqrt{2 \cos^2 x + 3 \cos x} - \sqrt{\cos^2 x + \sin x + 4}\right) is
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Jee Main 2025 — Medium JEE Mathematics MCQ | MyGoalPrep