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CUET Mathematics 2023 PYQs30 May Shift 3. Free, no login required.

Geometry

Trigonometry

Medium

core

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 :

$\alpha = 0, \beta = \pi$

$\alpha = 0, \beta = \frac{\pi}{2}$

$\alpha = \frac{\pi}{2}, \beta = \pi$

$\alpha = -\frac{\pi}{2}, \beta = \frac{\pi}{2}$

✅ Correct Option: 1

$\tan^{-1}x + \cot^{-1}x = \frac{\pi}{2}$ for all real $x$ . So expression $= \frac{\pi}{2} + \sin^{-1}x$ . Since $\sin^{-1}x \in \left[-\frac{\pi}{2}, \frac{\pi}{2}\right]$ , expression ranges from $0$ to $\pi$ . Hence $\alpha = 0$ , $\beta = \pi$ .

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:

2025: 30 May Shift 1

$\cos^{-1}\left(\cos\frac{7\pi}{6}\right)$ equals:

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:

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:

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:

2025: 30 May Shift 1

Consider $f(x) = \sin(3x) + 4, \forall x \in \mathbb{R}$ . Then

(A) Maximum value of $f(x)$ is 5

(B) Minimum value of $f(x)$ is 3

(C) Maximum value of $f(x)$ is attained at $x = \frac{\pi}{6}$

(D) Minimum value of $f(x)$ is attained at $x = 0$

Choose the correct answer from the options given below:

CUET Mathematics Past Year Questions (Topic-Wise)