Match List-I with List-II, List-I (Function), List-II (Principal value of y), (A) y=^(-1)(-1/2), (I) (3)/4, (B) y=^(-1)(-1/(3)), (II) -()/4, (C) y=cosec^(-1)(-2), (III) -()/6, (D) y=^(-1)(-1/(2)), (IV) (2)/3, Choose the correct answer from the options given below: Option 1: (A) - (III), (B) - (IV), (C) - (I), (D) - (II) Option 2: (A) - (IV), (B) - (III), (C) - (II), (D) - (I) Option 3: (A) - (IV), (B) - (III), (C) - (I), (D) - (II) Option 4: (A) - (III), (B) - (IV), (C) - (II), (D) - (I)

Answer: (A) - (III), (B) - (IV), (C) - (II), (D) - (I). Solution: ^(-1)(-1/2)=-()/6, so (A)-(III). Since the range of ^(-1) is (0,), ^(-1)(-1/(3))=(2)/3, so (B)-(IV). cosec^(-1)(-2)=-()/4 gives (C)-(II), and ^(-1)(-1/(2))=(3)/4 gives (D)-(I).

Geometry

Trigonometry

Easy

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Match List-I with List-II

List-I (Function) List-II (Principal value of y)
(A) $y=\sin^{-1}\left(-\frac{1}{2}\right)$ (I) $\frac{3\pi}{4}$
(B) $y=\cot^{-1}\left(-\frac{1}{\sqrt3}\right)$ (II) $-\frac{\pi}{4}$
(C) $y=cosec^{-1}(-\sqrt2)$ (III) $-\frac{\pi}{6}$
(D) $y=\cos^{-1}\left(-\frac{1}{\sqrt2}\right)$ (IV) $\frac{2\pi}{3}$

Choose the correct answer from the options given below:

List-I (Function)	List-II (Principal value of y)
(A) $y=\sin^{-1}\left(-\frac{1}{2}\right)$	(I) $\frac{3\pi}{4}$
(B) $y=\cot^{-1}\left(-\frac{1}{\sqrt3}\right)$	(II) $-\frac{\pi}{4}$
(C) $y=cosec^{-1}(-\sqrt2)$	(III) $-\frac{\pi}{6}$
(D) $y=\cos^{-1}\left(-\frac{1}{\sqrt2}\right)$	(IV) $\frac{2\pi}{3}$

(A) - (III), (B) - (IV), (C) - (I), (D) - (II)

(A) - (IV), (B) - (III), (C) - (II), (D) - (I)

(A) - (IV), (B) - (III), (C) - (I), (D) - (II)

(A) - (III), (B) - (IV), (C) - (II), (D) - (I)

✅ Correct Option: 4

$\sin^{-1}\left(-\frac{1}{2}\right)=-\frac{\pi}{6}$ , so (A)-(III).

Since the range of $\cot^{-1}$ is $(0,\pi)$ , $\cot^{-1}\left(-\frac{1}{\sqrt3}\right)=\frac{2\pi}{3}$ , so (B)-(IV).

$cosec^{-1}(-\sqrt2)=-\frac{\pi}{4}$ gives (C)-(II), and $\cos^{-1}\left(-\frac{1}{\sqrt2}\right)=\frac{3\pi}{4}$ gives (D)-(I).

2025: 3 June Shift 2

The value of $\tan^{-1}(2) + \tan^{-1}(3)$ is equal to

2024: 16 May Shift 1

If $\tan ^{-1}\left(\frac{2}{3^{-x}+1}\right)=\cot ^{-1}\left(\frac{3}{3^{x}+1}\right)$ , then which one of the following is true ?

2023: 23 May Shift 3

The simplest form of $\tan^{-1} \frac{\sqrt{1+x^2} - 1}{x}$ , $x \neq 0$ is:

2026: 29 May Shift 2

Match the LIST-I with LIST-II

	LIST-I		LIST-II
A.	If $\cos^{-1}\alpha + \cos^{-1}\beta + \cos^{-1}\gamma = 3\pi$ then $\alpha(2\beta+\gamma) + \beta(2\gamma+\alpha) + \gamma(2\alpha+\beta)$ equals	I.	$1$
B.	The value of $\tan^2(\sec^{-1}4) + \cot^2(\text{cosec}^{-1}5)$ is	II.	$9$
C.	If $\sin\left(\cos^{-1}\dfrac{2}{5} + \sin^{-1}x\right) = 1$ then $10x$ equals	III.	$4$
D.	The length of the interval of domain of $\sin^{-1}2x$ is	IV.	$39$

Choose the correct answer from the options given below:

2025: 19 May Shift 1

Match List-I with List-II

List-I	List-II
(A) $\cos^{-1} x + \cos^{-1}(-x)$	(I) $\frac{\pi}{3}$
(B) $\text{cosec}^{-1}(-x) + \sec^{-1}(-x)$	(II) $-\frac{\pi}{3}$
(C) $\tan^{-1}\sqrt{3} - \sec^{-1}(-2)$	(III) $\pi$
(D) $\tan^{-1}\left(\tan\frac{4\pi}{3}\right)$	(IV) $\frac{\pi}{2}$

Choose the correct answer from the options given below:

2022: 16 July Shift 2

The value of $\text{cosec}^{-1}(-2) - 2\sec^{-1}(-2)$ is equal to:

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