Match the List-I with List-IIList-IList-IIFunctionRange of the princi…

The correct answer is Option (2) → (A) - (III), (B) - (IV), (C) - (I), (D) - (II)

(A) \( \cos^{-1}x \)

This matches (III) \( [0,\pi] \).

The domain is [−1, 1]; both end values 0 (at x = 1) and π (at x = −1) are attained.

(B) \( \mathrm{cosec}^{-1}x \)

This matches (IV) \( \left[-\frac{\pi}{2},\frac{\pi}{2}\right]-\{0\} \).

cosec y is undefined at y = 0, so 0 is removed from the range of sin⁻¹.

(C) \( \tan^{-1}x \)

This matches (I) \( \left(-\frac{\pi}{2},\frac{\pi}{2}\right) \).

tan y is undefined at \( \pm\frac{\pi}{2} \), so the end points are excluded.

(D) \( \cot^{-1}x \)

This matches (II) \( (0,\pi) \).

cot y is undefined at 0 and π, so the end points are excluded.

So the matching is (A)-(III), (B)-(IV), (C)-(I), (D)-(II).

Tip: The “co” functions cos⁻¹ and cot⁻¹ take values in [0, π] (open for cot⁻¹); sin⁻¹ and tan⁻¹ take values around 0 in [−π/2, π/2] (open for tan⁻¹).

NCERT (2026-27 edition):
Basic Concepts