Match List-I with List-II, List-I, List-II, (A) Domain of ^(-1)(2x-3), (I) [-1, 0], (B) Domain of ^(-1)(1+2x), (II) [-1, 1], (C) Domain of ^(-1)(2x-1), (III) [1, 2], (D) Domain of ^(-1)(x^2), (IV) [0, 1], Choose the correct answer from the options given below: Option 1: (A) - (IV), (B) - (I), (C) - (II), (D) - (III) Option 2: (A) - (III), (B) - (I), (C) - (IV), (D) - (II) Option 3: (A) - (III), (B) - (IV), (C) - (I), (D) - (II) Option 4: (A) - (IV), (B) - (II), (C) - (III), (D) - (I)

Answer: (A) - (III), (B) - (I), (C) - (IV), (D) - (II). Solution: Both ^(-1) and ^(-1) need their argument in [-1,1]. (A) -1≤2x-3≤1[1,2], (III). (B) -1≤1+2x≤1[-1,0], (I). (C) -1≤2x-1≤1[0,1], (IV). (D) x^2≤1[-1,1], (II).

Geometry

Trigonometry

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Match List-I with List-II

List-I List-II
(A) Domain of $\sin^{-1}(2x-3)$ (I) [-1, 0]
(B) Domain of $\sin^{-1}(1+2x)$ (II) [-1, 1]
(C) Domain of $\cos^{-1}(2x-1)$ (III) [1, 2]
(D) Domain of $\sin^{-1}(x^2)$ (IV) [0, 1]

Choose the correct answer from the options given below:

List-I	List-II
(A) Domain of $\sin^{-1}(2x-3)$	(I) [-1, 0]
(B) Domain of $\sin^{-1}(1+2x)$	(II) [-1, 1]
(C) Domain of $\cos^{-1}(2x-1)$	(III) [1, 2]
(D) Domain of $\sin^{-1}(x^2)$	(IV) [0, 1]

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

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

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

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

✅ Correct Option: 2

Both $\sin^{-1}$ and $\cos^{-1}$ need their argument in $[-1,1]$ .

(A) $-1\le2x-3\le1\Rightarrow[1,2]$ , (III).

(B) $-1\le1+2x\le1\Rightarrow[-1,0]$ , (I).

(D) $x^2\le1\Rightarrow[-1,1]$ , (II).

2026: 30 May Shift 1

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

2022: 10 Aug Shift 1

The value of $\alpha$ is

2023: 15 June Shift 2

Let $\tan^{-1}y = \tan^{-1}x + \tan^{-1}\left(\frac{2x}{1-x^2}\right)$ . Then $y$ is :

2023: 30 May Shift 3

Let $a \leq \tan^{-1} x + \cot^{-1} x + \sin^{-1} x \leq b$ . If $\alpha$ and $\beta$ denote the minimum and maximum possible values of a and b respectively, then :

2025: 22 May Shift 2

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

2025: 13 May Shift 2

Match List-I with List-II

List-I	List-II
(A) $\sin^{-1}(-1)$	(I) $\frac{5\pi}{6}$
(B) $\cot^{-1}(-1)$	(II) $\frac{-\pi}{2}$
(C) $\sec^{-1}\left(\frac{-2}{\sqrt{3}}\right)$	(III) $\frac{\pi}{4}$
(D) $\tan^{-1}(1)$	(IV) $\frac{3\pi}{4}$

Choose the correct answer from the options given below:

Solution

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