Match the LIST-I with LIST-II, LIST-I (Functions), LIST-II (Principal Values), A., ^(-1)(-1/2) + ^(-1)(-1/2), I., -()/3, B., ^(-1)(1/2) + 2^(-1)(1/2), II., (3)/4, C., ^(-1)√3 - ^(-1)(-2), III., ()/2, D., ^(-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-I, C-II, D-III Option 3: A-III, B-II, C-I, D-IV Option 4: A-IV, B-II, C-I, D-III

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

Geometry

Trigonometry

Medium

core

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:

	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.	$\dfrac{2\pi}{3}$

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

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

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

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

✅ Correct Option: 1

A: $-\frac{\pi}{6}+\frac{2\pi}{3}=\frac{\pi}{2}$ (III).

B: $\frac{\pi}{3}+2\cdot\frac{\pi}{6}=\frac{2\pi}{3}$ (IV).

C: $\frac{\pi}{3}-\frac{2\pi}{3}=-\frac{\pi}{3}$ (I).

D: $\pi-\frac{\pi}{4}=\frac{3\pi}{4}$ (II).

2026: 25 May Shift 1

Match the LIST-I with LIST-II

LIST-I Function	LIST-II Value
A. $\tan[\cos^{-1}(\sin(\tan^{-1} 4/3))]$	I. $1/\sqrt2$
B. $\sin\left(2\tan^{-1}\left(\dfrac{3}{4}\right)\right)$	II. 1
C. $\cos\left[\tan^{-1}\left(\dfrac{1}{2}\right)+\tan^{-1}\left(\dfrac{1}{3}\right)\right]$	III. 24/25
D. $\sin\left[\dfrac{\pi}{3} - \sin^{-1}(-1/2)\right]$	IV. 3/4

Choose the correct answer from the options given below:

2026: 21 May Shift 1

Value of $\cot\left\{\frac{\pi}{4} - 2\cot^{-1}3\right\}$ is

2022: 25 May Shift 1

Match List I with List II

Choose the correct answer from the options given below:

2025: 22 May Shift 2

The value of $\cot\left(\cos^{-1}\frac{7}{25}\right)$ is

2025: 13 May Shift 1

The value of $\tan^{-1}(1) + \cos^{-1}\left(-\frac{\sqrt{3}}{2}\right) + \sin^{-1}\left(\frac{1}{2}\right)$ is

2023: 23 May Shift 3

The maximum value of $\sin x + \cos x, x \in R$ is: