CUET · MATHS · PYQ PAPER 2025

For the principal value branch, the value of \(\sin \left(\frac{\pi}{2}-\sin ^{-1}\left(-\frac{\sqrt{3}}{2}\right)\right)\) is

A \(\frac{1}{\sqrt{2}}\)
B \(\frac{\sqrt{3}}{2}\)
C \(\frac{1}{2}\)
D \(-\frac{\sqrt{3}}{2}\)

Verified Solution

Answer & Solution

Correct Answer

(C) \(\frac{1}{2}\)

Step-by-step Solution

Detailed explanation

\(\sin ^{-1}\left(-\frac{\sqrt{3}}{2}\right) = -\frac{\pi}{3}\) \(\sin \left(\frac{\pi}{2}-\left(-\frac{\pi}{3}\right)\right) = \sin \left(\frac{3\pi+2\pi}{6}\right)\) \(\sin \left(\frac{5\pi}{6}\right) = \frac{1}{2}\)

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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Match List-I with List-II

List-I (EM Waves)	List-II (Production)
(A) Infra-red rays	(I) Electrons in atoms emit light when they move from one energy level to a lower level
(B) Visible light rays	(II) Radioactive decay of the nucleus
(C) Ultraviolet rays	(III) Vibration of molecules
(D) Gamma rays	(IV) Inner shell electrons in atoms moving from one energy level to a lower level

Choose the correct answer from the options given below:

CUET 2025 Hard

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