CUET Mathematics - Geometry - Trigonometry | Free Questions

Q1:

2026: 31 May Shift 2

Geometry

>

Trigonometry

Hard

Core

The value of $\cos^{-1}\left\{\dfrac{\sin x+\cos x}{\sqrt{2}}\right\}, \dfrac{5\pi}{4} < x < \dfrac{9\pi}{4}$ is :

$x - \dfrac{\pi}{4}$

$\dfrac{\pi}{4} - x$

$\dfrac{9\pi}{4} - x$

$x - \dfrac{9\pi}{4}$

Correct Answer

Option 3

Correct Answer

Explanation

Q2:

2026: 30 May Shift 2

Geometry

>

Trigonometry

Easy

Core

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:

(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 Answer

Option 2

Correct Answer

Explanation

Q3:

2026: 30 May Shift 1

Geometry

>

Trigonometry

Easy

Core

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

15

30

40

10

Correct Answer

Option 3

Correct Answer

Explanation

Q4:

2026: 29 May Shift 2

Geometry

>

Trigonometry

Hard

Core

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:

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

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

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

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

Correct Answer

Option 3

Correct Answer

Explanation

Q5:

2026: 29 May Shift 1

Geometry

>

Trigonometry

Easy

Core

The value of $\tan^{-1}(\sqrt3)-\sec^{-1}(-2)$ is

$\dfrac{\pi}{3}$

0

$-\dfrac{\pi}{3}$

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

Correct Answer

Option 3

Correct Answer

Explanation

Q6:

2026: 26 May Shift 2

Geometry

>

Trigonometry

Easy

Core

Match the LIST-I with LIST-II

	LIST-I		LIST-II
A.	The range of $\sin^{-1} x$	I.	$[-1, 1]$
B.	Domain of $\cos^{-1} x$	II.	$(-\infty, \infty)$
C.	The range of $\tan^{-1} x$	III.	$\left[-\dfrac{\pi}{2}, \dfrac{\pi}{2}\right]$
D.	Domain of $\tan^{-1} x$	IV.	$\left(-\dfrac{\pi}{2}, \dfrac{\pi}{2}\right)$

Choose the correct answer from the options given below:

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

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

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

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

Correct Answer

Option 2

Correct Answer

Explanation

Q7:

2026: 25 May Shift 1

Geometry

>

Trigonometry

Hard

Core

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:

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

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

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

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

Correct Answer

Option 4

Correct Answer

Explanation

Q8:

2026: 22 May Shift 2

Geometry

>

Trigonometry

Medium

Core

$\cos[\tan^{-1}\{\sin(\cot^{-1}x)\}]$ is equal to

$\sqrt{\frac{x^2+1}{x^2+2}}$

$\sqrt{\frac{x^2+2}{x^2+1}}$

$\sqrt{\frac{x}{x^2+2}}$

$\sqrt{\frac{x}{x^2+1}}$

Correct Answer

Option 1

Correct Answer

Explanation

Q9:

2026: 22 May Shift 1

Geometry

>

Trigonometry

Easy

Core

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:

(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 Answer

Option 4

Correct Answer

Explanation

Q10:

2026: 21 May Shift 2

Geometry

>

Trigonometry

Easy

Core

Match the LIST-I with LIST-II

LIST-I (Function)		LIST-II (Range of the principal value branch)
A. $\cos^{-1}x$		I. $\left(-\dfrac{\pi}{2}, \dfrac{\pi}{2}\right)$
B. $\text{cosec}^{-1}x$		II. $(0, \pi)$
C. $\tan^{-1}x$		III. $[0, \pi]$
D. $\cot^{-1}x$		IV. $\left[-\dfrac{\pi}{2}, \dfrac{\pi}{2}\right] - \{0\}$

Choose the correct answer from the options given below:

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

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

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

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

Correct Answer

Option 2

Correct Answer

Explanation

Q11:

2026: 21 May Shift 1

Geometry

>

Trigonometry

Medium

Core

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

5

6

7

9

Correct Answer

Option 3

Correct Answer

Explanation

Q12:

2026: 19 May Shift 2

Geometry

>

Trigonometry

Medium

Core

Which one of the following is TRUE?

$\cot^{-1}1 < \cot 1$

$\cos^{-1}1 > \cos 1$

$\sin^{-1}1 < \sin 1$

$\tan^{-1}1 < \tan 1$

Correct Answer

Option 4

Correct Answer

Explanation

Q13:

2026: 18 May Shift 2

Geometry

>

Trigonometry

Easy

Core

Match the LIST-I with LIST-II

LIST-I Functions	LIST-II Principal value
A. $\sin^{-1}\left(\dfrac{1}{2}\right)$	I. $\dfrac{\pi}{4}$
B. $\sin^{-1}\left(-\dfrac{1}{\sqrt{2}}\right)$	II. $\dfrac{\pi}{6}$
C. $\tan^{-1}(1)$	III. $-\dfrac{\pi}{4}$
D. $\cos^{-1}\left(-\dfrac{1}{2}\right)$	IV. $\dfrac{2\pi}{3}$

Choose the correct answer from the options given below:

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

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

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

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

Correct Answer

Option 2

Correct Answer

Explanation

Q14:

2026: 15 May Shift 1

Geometry

>

Trigonometry

Medium

Core

The value of $\tan\left(\dfrac{1}{2}\cos^{-1}\dfrac{\sqrt5}{3}\right)$ is equal to

$\dfrac{5-\sqrt3}{2}$

$\dfrac{5+\sqrt3}{2}$

$\dfrac{3+\sqrt5}{2}$

$\dfrac{3-\sqrt5}{2}$

Correct Answer

Option 4

Correct Answer

Explanation

Q15:

2026: 14 May Shift 2

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:

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 Answer

Option 1

Correct Answer

Explanation

Q16:

2026: 12 May Shift 2

Geometry

>

Trigonometry

Easy

Core

Match List-I with List-II

List-I (Functions)	List-II (Range, principal value)
(A) $\sin^{-1}x$	(I) $[0,\pi]-\left\{\dfrac{\pi}{2}\right\}$
(B) $\tan^{-1}x$	(II) $\left[-\dfrac{\pi}{2},\dfrac{\pi}{2}\right]-\{0\}$
(C) $cosec^{-1}x$	(III) $\left[-\dfrac{\pi}{2},\dfrac{\pi}{2}\right]$
(D) $\sec^{-1}x$	(IV) $\left(-\dfrac{\pi}{2},\dfrac{\pi}{2}\right)$

Choose the correct answer from the options given below:

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

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

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

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

Correct Answer

Option 2

Correct Answer

Explanation

Q17:

2025: 3 June Shift 2

Geometry

>

Trigonometry

Medium

Core

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

$\frac{\pi}{4}$

$-\frac{\pi}{4}$

$\frac{3\pi}{4}$

$-\frac{3\pi}{4}$

Correct Answer

Option 3

Correct Answer

Explanation

Q18:

2025: 3 June Shift 1

Geometry

>

Trigonometry

Medium

Core

The value of $-\cosec^2(\cot^{-1}y) + \sec^2( \tan^{-1}x)$ is equal to

$x^2 + y^2$

$x^2 - y^2$

$2 + x^2 + y^2$

$2 + x^2 - y^2$

Correct Answer

Option 2

Correct Answer

Explanation

Q19:

2025: 30 May Shift 2

Geometry

>

Trigonometry

Medium

Core

The simplified form of $\tan^{-1}\left(\frac{\cos x}{1+\sin x}\right)$ , $-\frac{\pi}{2} < x < \frac{\pi}{2}$ is

$\frac{\pi}{4} + \frac{x}{2}$

$\frac{\pi}{4} - \frac{x}{2}$

$\frac{\pi}{2} + x$

$\frac{\pi}{4} + x$

Correct Answer

Option 2

Correct Answer

Explanation

Q20:

2025: 30 May Shift 1

Geometry

>

Trigonometry

Medium

Core

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

$\frac{7\pi}{6}$

$\frac{5\pi}{6}$

$-\frac{5\pi}{6}$

$\frac{\pi}{6}$

Correct Answer

Option 2

Correct Answer

Explanation

Q21:

2025: 30 May Shift 1

Geometry

>

Trigonometry

Medium

Applied

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:

(A), (B) and (C) only

(A), (B) and (D) only

(C) and (D) only

(B) and (D) only

Correct Answer

Option 1

Correct Answer

Explanation

Q22:

2025: 29 May Shift 2

Geometry

>

Trigonometry

Medium

Core

The value of $\cos(2\cos^{-1}x + \sin^{-1}x)$ at $x = \frac{1}{5}$ is

$\sqrt{\frac{25}{24}}$

$-\sqrt{\frac{24}{25}}$

$\sqrt{\frac{24}{25}}$

$-\sqrt{\frac{25}{24}}$

Correct Answer

Option 2

Correct Answer

Explanation

Q23:

2025: 27 May Shift 1

Geometry

>

Trigonometry

Hard

Core

Match List-I with List-II

List-I	List-II
(A) $\tan^{-1}\frac{2}{11} + \tan^{-1}\frac{7}{24}$	(I) $\frac{3\pi}{4}$
(B) $\tan^{-1}2 + \tan^{-1}3$	(II) $\pi$
(C) $\tan^{-1}1 + \tan^{-1}2 + \tan^{-1}3$	(III) $\tan^{-1}\frac{1}{2}$
(D) $\tan^{-1}\frac{1}{7} + \tan^{-1}\frac{1}{13}$	(IV) $\tan^{-1}\frac{2}{9}$

Choose the correct answer from the options given below:

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

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

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

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

Correct Answer

Option 2

Correct Answer

Explanation

Q24:

2025: 26 May Shift 2

Geometry

>

Trigonometry

Medium

Core

Arrange the principal values of the following functions in ascending order

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

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

(C) $\tan^{-1}(1)$

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

Choose the correct answer from the options given below:

(A), (B), (C), (D)

(A), (D), (B), (C)

(B), (D), (A), (C)

(D), (A), (B), (C)

Correct Answer

Option 3

Correct Answer

Explanation

Q25:

2025: 22 May Shift 2

Geometry

>

Trigonometry

Medium

Core

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

$\frac{25}{24}$

$\frac{24}{25}$

$\frac{7}{25}$

$\frac{7}{24}$

Correct Answer

Option 4

Correct Answer

Explanation

Q26:

2025: 22 May Shift 1

Geometry

>

Trigonometry

Medium

Core

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

6

11

13

15

Correct Answer

Option 2

Correct Answer

Explanation

Q27:

2025: 22 May Shift 1

Geometry

>

Trigonometry

Medium

Core

The minimum value of the function $f(x) = 3\sin x - 4\cos x, x \in [-4\pi, 4\pi]$ is equal to

0

-4

-5

-7

Correct Answer

Option 3

Correct Answer

Explanation

Q28:

2025: 21 May Shift 2

Geometry

>

Trigonometry

Medium

Core

$\sin^{-1}(\cos\frac{3\pi}{5})$ equals

$\frac{3\pi}{5}$

$\frac{-\pi}{10}$

$\frac{\pi}{10}$

$\frac{-3\pi}{10}$

Correct Answer

Option 2

Correct Answer

Explanation

Q29:

2025: 21 May Shift 1

Geometry

>

Trigonometry

Medium

Core

Match List-I with List-II

List-I	List-II
(Inverse Trigonometric Function)	(Principal Value)
(A) $\sin^{-1}(-\frac{1}{2})$	(I) ${\pi}/{6}$
(B) $\cos^{-1}(-\frac{1}{2})$	(II) $-{\pi}/{6}$
(C) $\tan^{-1}(-\sqrt{3})$	(III) ${2\pi}/{3}$
(D) $\cot^{-1}(\sqrt{3})$	(IV) $-{\pi}/{3}$

Choose the correct answer from the options given below:

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

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

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

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

Correct Answer

Option 3

Correct Answer

Explanation

Q30:

2025: 19 May Shift 1

Geometry

>

Trigonometry

Easy

Common

The maximum value of $\sin x \cdot \cos x$ is:

1

$\frac{1}{2}$

$\frac{1}{4}$

$\sqrt{2}$

Correct Answer

Option 2

Correct Answer

Explanation

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CUET Mathematics Past Year Questions (Topic-Wise)