Match List - I with List - II., List - I, List - II, (A) ^(-1)√3 - ^(-1)(-2), (I) (3)/4, (B) ^(-1)((-1)/√3), (II) -()/3, (C) ^(-1)(-1/√2), (III) ()/2, (D) ^(-1)(1/2) + ^(-1)(1/2), (IV) (2)/3, Choose the correct answer from the options given below : Option 1: (A) - (IV), (B) - (I), (C) - (III), (D) - (II) Option 2: (A) - (III), (B) - (II), (C) - (IV), (D) - (I) Option 3: (A) - (I), (B) - (III), (C) - (IV), (D) - (II) Option 4: (A) - (II), (B) - (IV), (C) - (I), (D) - (III)

Answer: (A) - (II), (B) - (IV), (C) - (I), (D) - (III). Solution: (A) ()/3 - (2)/3 = -()/3, matches II. (B) ^(-1)(-1/√3) = - ()/3 = (2)/3, matches IV. (C) ^(-1)(-1/√2) = (3)/4, matches I. (D) ()/3+()/6 = ()/2, matches III.

Geometry

Trigonometry

Medium

Match List - I with List - II.

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

Choose the correct answer from the options given below :

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

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

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

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

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

✅ Correct Option: 4

(A) $\frac{\pi}{3} - \frac{2\pi}{3} = -\frac{\pi}{3}$ , matches II. (B) $\cot^{-1}(-\frac{1}{\sqrt{3}}) = \pi - \frac{\pi}{3} = \frac{2\pi}{3}$ , matches IV. (C) $\cos^{-1}(-\frac{1}{\sqrt{2}}) = \frac{3\pi}{4}$ , matches I. (D) $\frac{\pi}{3}+\frac{\pi}{6} = \frac{\pi}{2}$ , matches III.

2022: 30 Aug Shift 1

$\sin^{-1}(1 - x) - 2\sin^{-1}x = \frac{\pi}{2}$ , than $x$ is equal to

(a) $0$

(b) $1$

(d) $2$

Choose the most appropriate answer from the options given below:

2026: 14 May Shift 2

Match the LIST-I with LIST-II

	LIST-I (Functions)		LIST-II (Principal Values)
A.	$\sin^{-1}\left(-\dfrac{1}{2}\right) + \cos^{-1}\left(-\dfrac{1}{2}\right)$	I.	$-\dfrac{\pi}{3}$
B.	$\cos^{-1}\left(\dfrac{1}{2}\right) + 2\sin^{-1}\left(\dfrac{1}{2}\right)$	II.	$\dfrac{3\pi}{4}$
C.	$\tan^{-1}\sqrt{3} - \sec^{-1}(-2)$	III.	$\dfrac{\pi}{2}$
D.	$\cos^{-1}\left(-\dfrac{1}{\sqrt{2}}\right)$	IV.	$\dfrac{2\pi}{3}$

Choose the correct answer from the options given below:

2025: 26 May Shift 2

Arrange the principal values of the following functions in ascending order

(A) $\cosec^{-1}(2)$

(B) $\tan^{-1}(-\sqrt{3})$

(D) $\tan^{-1}\left(\cos\frac{3\pi}{7}\right)$

Choose the correct answer from the options given below:

2022: 25 May Shift 1

Match List I with List II

LIST I	LIST II
A. $\sin^{-1} x + \cos^{-1} x, x \in [-1,1]$	I. $-\frac{\pi}{2}$
B. $\tan^{-1} \sqrt{3} - \cot^{-1}(-\sqrt{3})$	II. $-\frac{\pi}{6}$
C. $\cos^{-1}\left(\cos\frac{13\pi}{6}\right)$	III. $\frac{\pi}{2}$
D. $\sin^{-1}\left(-\frac{1}{2}\right)$	IV. $\frac{\pi}{6}$

Choose the correct answer from the options given below:

2022: 16 July Shift 2

Match List I with List II

List I (Functions)	List II (Principal value branches)
A. $f(x) = \cos^{-1} x$	I. $[0, \pi]$
B. $f(x) = \tan^{-1} x$	II. $[0, \pi] - \left\{\frac{\pi}{2}\right\}$
C. $f(x) = \text{cosec}^{-1} x$	III. $\left[-\frac{\pi}{2}, \frac{\pi}{2}\right] - \{0\}$
D. $f(x) = \sec^{-1} x$	IV. $\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$

Choose the correct answer from the options given below:

2026: 30 May Shift 1

The value of $2\sec^2(\tan^{-1}2)+3\text{cosec}^2(\cot^{-1}3)$ is:

Solution

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