CUET Mathematics - Geometry - Trigonometry | Free Questions - Page 2

Q1:

2025: 19 May Shift 1

Geometry

>

Trigonometry

Medium

Core

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:

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

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

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

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

Correct Answer

Option 2

Correct Answer

Explanation

Q2:

2025: 16 May Shift 1

Geometry

>

Trigonometry

Medium

Core

Match List-I with List-II

List-I	List-II
Inverse Trigonometric function	Principal values of arguments
(A) $sin^{-1}\left(\frac{-1}{2}\right)$	(I) $\frac{-\pi}{3}$
(B) $cos^{-1}\left(\frac{-1}{2}\right)$	(II) $\frac{3\pi}{4}$
(C) $tan^{-1}(-\sqrt{3})$	(III) $\frac{-\pi}{6}$
(D) $sec^{-1}(-\sqrt{2})$	(IV) $\frac{2\pi}{3}$

Choose the correct answer from the options given below:

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

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

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

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

Correct Answer

Option 1

Correct Answer

Explanation

Q3:

2025: 15 May Shift 1

Geometry

>

Trigonometry

Medium

Core

For the principal value branch, the value of $\sin\left(\frac{\pi}{2} - \sin^{-1}\left(-\frac{\sqrt{3}}{2}\right)\right)$ is

$\frac{1}{\sqrt{2}}$

$\frac{\sqrt{3}}{2}$

$\frac{1}{2}$

$-\frac{\sqrt{3}}{2}$

Correct Answer

Option 3

Correct Answer

Explanation

Q4:

2025: 14 May Shift 2

Geometry

>

Trigonometry

Medium

Core

For $x \in [-1,1]$ , if $4\sin^{-1}x + \cos^{-1}x = \pi$ then $x$ is equal to

$-\frac{1}{2}$

$\frac{1}{2}$

$\frac{\sqrt{3}}{2}$

$\frac{-\sqrt{3}}{2}$

Correct Answer

Option 2

Correct Answer

Explanation

Q5:

2025: 14 May Shift 1

Geometry

>

Trigonometry

Medium

Core

for $|x| < 1$ , $sin (tan^{-1}x)$ equal to

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

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

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

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

Correct Answer

Option 4

Correct Answer

Explanation

Q6:

2025: 13 May Shift 2

Geometry

>

Trigonometry

Medium

Core

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:

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

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

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

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

Correct Answer

Option 1

Correct Answer

Explanation

Q7:

2025: 13 May Shift 1

Geometry

>

Trigonometry

Medium

Core

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

$\frac{5\pi}{4}$

$\frac{\pi}{4}$

$\frac{5\pi}{12}$

$\frac{7\pi}{12}$

Correct Answer

Option 1

Correct Answer

Explanation

Q8:

2024: 16 May Shift 1

Geometry

>

Trigonometry

Medium

Core

If $\tan ^{-1}\left(\frac{2}{3^{-x}+1}\right)=\cot ^{-1}\left(\frac{3}{3^{x}+1}\right)$ , then which one of the following is true ?

There is no real value of x satisfying the above equation.

There is one positive and one negative real value of $x$ satisfying the above equation.

There are two real positive values of x satisfying the above equation.

There are two real negative values of $x$ satisfying the above equation.

Correct Answer

Option 2

Correct Answer

Explanation

Q9:

2023: 23 May Shift 3

Geometry

>

Trigonometry

Easy

Core

The principal value of $\cot^{-1}\left(-\frac{1}{\sqrt{3}}\right)$

$\frac{\pi}{3}$

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

$\frac{1}{\sqrt{3}}$

$\frac{2\pi}{3}$

Correct Answer

Option 4

Correct Answer

Explanation

Q10:

2023: 23 May Shift 3

Geometry

>

Trigonometry

Medium

Core

The simplest form of $\tan^{-1}\left\{\frac{x}{\sqrt{a^2 - x^2}}\right\}$ is, where $-a < x < a$ .

$\tan^{-1}\frac{x}{a}$

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

$a \tan^{-1}\frac{x}{a}$

$\sin^{-1}\frac{x}{a}$

Correct Answer

Option 4

Correct Answer

Explanation

Q11:

2023: 23 May Shift 3

Geometry

>

Trigonometry

Easy

Core

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

2

$\sqrt{2}$

$\frac{1}{\sqrt{2}}$

Not known

Correct Answer

Option 2

Correct Answer

Explanation

Q12:

2023: 23 May Shift 3

Geometry

>

Trigonometry

Medium

Core

The simplest form of $\tan^{-1} \frac{\sqrt{1+x^2} - 1}{x}$ , $x \neq 0$ is:

$\tan^{-1} x$

$x$

$\frac{1}{2} \tan^{-1} x$

$\sqrt{1+x^2}$

Correct Answer

Option 3

Correct Answer

Explanation

Q13:

2023: 22 May Shift 3

Geometry

>

Trigonometry

Easy

Core

The principal value of $\cot^{-1}\left(\frac{-1}{\sqrt{3}}\right)$ is :

$-\frac{2\pi}{3}$

$\frac{2\pi}{3}$

$\frac{\pi}{3}$

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

Correct Answer

Option 2

Correct Answer

Explanation

Q14:

2023: 30 May Shift 3

Geometry

>

Trigonometry

Easy

Core

If $\sin^{-1} x + \sin^{-1} y = \frac{2\pi}{3}$ , then the value of $\cos^{-1} x + \cos^{-1} y$ is :

$\frac{\pi}{2}$

$\frac{\pi}{3}$

$\frac{2\pi}{3}$

$\frac{\pi}{6}$

Correct Answer

Option 2

Correct Answer

Explanation

Q15:

2023: 30 May Shift 3

Geometry

>

Trigonometry

Easy

Core

The maximum value of $(\sin x)(\cos x)$ is :

1

$\frac{1}{2}$

$\frac{1}{4}$

$\sqrt{2}$

Correct Answer

Option 2

Correct Answer

Explanation

Q16:

2023: 30 May Shift 3

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 Answer

Option 1

Correct Answer

Explanation

Q17:

2023: 15 June Shift 2

Geometry

>

Trigonometry

Easy

Core

Match List - I with List - II.

List - I	List - II
(A) Range of $y = \text{cosec}^{-1}x$	(I) $R - (-1, 1)$
(B) Domain of $\sec^{-1}x$	(II) $(0, \pi)$
(C) Domain of $\sin^{-1}x$	(III) $[-1, 1]$
(D) Range of $y = \cot^{-1}x$	(IV) $\left[\frac{-\pi}{2}, \frac{\pi}{2}\right] - \{0\}$

Choose the correct answer from the options given below :

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

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

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

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

Correct Answer

Option 2

Correct Answer

Explanation

Q18:

2023: 15 June Shift 2

Geometry

>

Trigonometry

Medium

Core

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

$\frac{3x - x^3}{1 - 3x^2}$

$\frac{3x + x^3}{1 - 3x^2}$

$\frac{3x - x^3}{1 + 3x^2}$

$\frac{3x + x^3}{1 + 3x^2}$

Correct Answer

Option 1

Correct Answer

Explanation

Q19:

2022: 17 Aug Shift 2

Geometry

>

Trigonometry

Easy

Core

The value of $\sin\left[\frac{\pi}{2} - \sin^{-1}\left(-\frac{\sqrt{3}}{2}\right)\right]$ is :

$\frac{1}{2}$

$\frac{1}{\sqrt{2}}$

$\frac{\sqrt{3}}{2}$

$-\frac{\sqrt{3}}{2}$

Correct Answer

Option 1

Correct Answer

Explanation

Q20:

2022: 17 Aug Shift 2

Geometry

>

Trigonometry

Medium

Core

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 :

(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 Answer

Option 4

Correct Answer

Explanation

Q21:

2022: 6 Aug Shift 2

Geometry

>

Trigonometry

Medium

Core

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

$\frac{\pi}{6}$

$\frac{\pi}{3}$

$\frac{\pi}{2}$

$\frac{5\pi}{12}$

Correct Answer

Option 4

Correct Answer

Explanation

Q22:

2022: 6 Aug Shift 2

Geometry

>

Trigonometry

Easy

Core

The Principal value of $\cos^{-1} \left( -\frac{1}{2} \right)$ is:

$\frac{\pi}{3}$

$\frac{2\pi}{3}$

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

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

Correct Answer

Option 2

Correct Answer

Explanation

Q23:

2022: 4 Aug Shift 1

Geometry

>

Trigonometry

Medium

Core

Match List - I with List - II

List - I	List - II
A. $\tan^{-1}\left(\tan\frac{7\pi}{6}\right)$	I. $\frac{5\pi}{6}$
B. $\tan^{-1}\left(\tan\frac{8\pi}{6}\right)$	II. $\frac{\pi}{2}$
C. $\tan^{-1}\frac{1}{\sqrt{3}} + cosec^{-1}\frac{2}{\sqrt{3}}$	III. $\frac{\pi}{6}$
D. $\cos^{-1}\left(\cos\frac{5\pi}{6}\right)$	IV. $\frac{\pi}{3}$

Choose the correct answer from the options given below:

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

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

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

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

Correct Answer

Option 3

Correct Answer

Explanation

Q24:

2022: 4 Aug Shift 1

Geometry

>

Trigonometry

Easy

Core

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

9

5

10

15

Correct Answer

Option 4

Correct Answer

Explanation

Q25:

2022: 10 Aug Shift 1

Geometry

>

Trigonometry

Easy

Core

Two men on either side of a pole of 30 m high observe its top at angles of elevation $\alpha$ and $\beta$ respectively. The distance between the two men is $40\sqrt{3}$ m and the distance between the first man at A and the pole is $30\sqrt{3}$ m.

Based on the above information, answer the question:

The value of $\alpha$ is

$\frac{\pi}{3}$

$\frac{\pi}{4}$

$\frac{\pi}{6}$

$\frac{\pi}{8}$

Correct Answer

Option 3

Correct Answer

Explanation

Q26:

2022: 10 Aug Shift 1

Geometry

>

Trigonometry

Easy

Core

Two men on either side of a pole of 30 m high observe its top at angles of elevation $\alpha$ and $\beta$ respectively. The distance between the two men is $40\sqrt{3}$ m and the distance between the first man at A and the pole is $30\sqrt{3}$ m.

Based on the above information, answer the question:

$\tan(\alpha + \beta) =$

$\sqrt{3} + \frac{1}{\sqrt{3}}$

$\sqrt{3} - \frac{1}{\sqrt{3}}$

$2\sqrt{3} - 1$

Infinite (does not exist)

Correct Answer

Option 4

Correct Answer

Explanation

Q27:

2022: 10 Aug Shift 1

Geometry

>

Trigonometry

Easy

Core

Two men on either side of a pole of 30 m high observe its top at angles of elevation $\alpha$ and $\beta$ respectively. The distance between the two men is $40\sqrt{3}$ m and the distance between the first man at A and the pole is $30\sqrt{3}$ m.

Based on the above information, answer the question:

Area of $\triangle ABD$ is

$150\sqrt{3} \, m^2$

$900\sqrt{3} \, m^2$

$450\sqrt{3} \, m^2$

$100\sqrt{3} \, m^2$

Correct Answer

Option 3

Correct Answer

Explanation

Q28:

2022: 10 Aug Shift 1

Geometry

>

Trigonometry

Easy

Core

Two men on either side of a pole of 30 m high observe its top at angles of elevation $\alpha$ and $\beta$ respectively. The distance between the two men is $40\sqrt{3}$ m and the distance between the first man at A and the pole is $30\sqrt{3}$ m.

Based on the above information, answer the question:

$\angle ABC$ is equal to:

$\frac{\pi}{4}$

$\frac{\pi}{6}$

$\frac{\pi}{2}$

$\frac{\pi}{3}$

Correct Answer

Option 3

Correct Answer

Explanation

Q29:

2022: 10 Aug Shift 1

Geometry

>

Trigonometry

Medium

Core

Two men on either side of a pole of 30 m high observe its top at angles of elevation $\alpha$ and $\beta$ respectively. The distance between the two men is $40\sqrt{3}$ m and the distance between the first man at A and the pole is $30\sqrt{3}$ m.

Based on the above information, answer the question:

The value of $\frac{1}{AB^2} + \frac{1}{BC^2}$ is:

$\frac{1}{BD^2}$

$\frac{1}{AD^2}$

$\frac{1}{CD^2}$

$\frac{1}{AC^2}$

Correct Answer

Option 1

Correct Answer

Explanation

Q30:

2022: 30 Aug Shift 1

Geometry

>

Trigonometry

Medium

Core

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

(a) $0$

(b) $1$

(c) $\frac{1}{2}$

(d) $2$

Choose the most appropriate answer from the options given below:

(a) and (b) only

(a) and (c) only

(a) only

(c) only

Correct Answer

Option 3

Correct Answer

Explanation

CUET Mathematics: GeometryTrigonometry. Free, no login required.

Q1:

Q2:

Q3:

Q4:

Q5:

Q6:

Q7:

Q8:

Q9:

Q10:

Q11:

Q12:

Q13:

Q14:

Q15:

Q16:

Q17:

Q18:

Q19:

Q20:

Q21:

Q22:

Q23:

Q24:

Q25:

Q26:

Q27:

Q28:

Q29:

Q30:

CUET Mathematics Past Year Questions (Topic-Wise)