MHT CET PYQs for Trigonometric Identities with Solutions: Practice MHT CET Previous Year Questions

Educational Content Expert | Updated on - Nov 26, 2025

Trigonometric Identities is an important topic in the Mathematics section in MHT CET exam. Practising this topic will increase your score overall and make your conceptual grip on MHT CET exam stronger.

This article gives you a full set of MHT CET PYQs for Trigonometric Identities with explanations for effective preparation. Practice of MHT CET Mathematics PYQs including Trigonometric Identities questions regularly will improve accuracy, speed, and confidence in the MHT CET 2026 exam.

MHT CET PYQs for Trigonometric Identities with Solutions

1.
If $n = 100!$ , then what is the value of the following? $\frac{1}{\log_{2} n} + \frac{1}{\log_{3} n} + \frac{1}{\log_{4} n} + \dots \dots + \frac{1}{\log_{100} n}$
- (A) $0$
- (B) $1$
- (C) $2$
- (D) $3$
View Solution
2.
Evaluate the integral: \[ \int \frac{1}{\sin^2 2x \cdot \cos^2 2x} \, dx \]
- $ \frac{1}{2} \tan 2x $
- $ \frac{1}{2} \cot 2x $
- $ \frac{1}{4} \cot 2x $
- $ \frac{1}{4} \tan 2x $
View Solution
3.
The area of the region bounded by the curve $y = x^{2}$ and the line $y = 16$ is:
- (A) $\frac{32}{3}$ sq.units
- (B) $\frac{256}{3}$ sq.units
- (C) $\frac{64}{3}$ sq.units
- (D) $\frac{128}{3}$ sq.units
View Solution
4.
If $ \tan^{-1} (\sqrt{\cos \alpha}) - \cot^{-1 (\cos \alpha) = x $, then what is $ \sin \alpha $?}
- $ \tan \left( \frac{x}{2} \right) $
- $ \cot \left( \frac{x}{2} \right) $
- $ \cot^2 \left( \frac{x}{2} \right) $
- $ \tan^2 \left( \frac{x}{2} \right) $
View Solution
5.
If $ \tan(\pi \cos x) = \cot(\pi \sin x) $, then what is $ \sin \left( \frac{\pi}{2} + x \right) $?
- $ \frac{1}{2} $
- $ \frac{1}{\sqrt{2}} $
- $ -\frac{1}{2} $
- $ -\frac{1}{\sqrt{2}} $
View Solution
6.
If $2 x^{3} - 3 y^{2} = 7$ , what is $\frac{d y}{d x}$ equal to $(y \neq 0)$ :
- (A) $\frac{x^{2}}{2 y}$
- (B) $\frac{x}{2 y}$
- (C) $\frac{x^{2}}{y}$
- (D) None of the above
View Solution
7.
If $2 \sin \left( \theta + \frac{\pi}{3}\right) = \cos \left( \theta -\frac{\pi}{6}\right) , $ then $\tan \, \theta = $
- $\sqrt{3}$
- $- \frac{1}{\sqrt{3}}$
- $\frac{1}{\sqrt{3}}$
- $- \sqrt{3}$
View Solution
8.
Given the equation: \[ 81 \sin^2 x + 81 \cos^2 x = 30 \] Find the value of $ x $.
- $ x = \frac{\pi}{4} $
- $ x = \frac{\pi}{6} $
- $ x = \frac{\pi}{3} $
- $ x = \frac{\pi}{2} $
View Solution
9.
Find the equation of the line passing through $(- 3, 5)$ and perpendicular to the line through the points $(2, 5) (- 3, 6)$ .
- (A) $x + y + 20 = 0$
- (B) $x - y + 20 = 0$
- (C) $x + 5 y + 20 = 0$
- (D) $5 x - y + 20 = 0$
View Solution
10.
$\frac{\sin 7 x + 6 \sin 5 x + 17 \sin 3 x + 12 \sin x}{\sin 6 x + 5 \sin 4 x + 12 \sin 2 x}$ equals:
- (A) $\sin x$
- (B) $2 \sin x$
- (C) $\cos x$
- (D) $2 \cos x$
View Solution
11.
Jobs arrive at a facility at an average rate of $5$ in an $8$ hour shift. The arrival of the jobs follows Poisson distribution. The average service time of a job on the facility is $40$ minutes. The service time follows exponential distribution. Idle time (in hours) at the facility per shift will be _______.
- (A) $\frac{5}{7}$
- (B) $\frac{14}{3}$
- (C) $\frac{7}{5}$
- (D) $\frac{10}{3}$
View Solution
12.
If $A = [\begin{array}{cc} \cos 2 θ & - \sin 2 θ \\ \sin 2 θ & \cos 2 θ \end{array}]$ and $A + A^{T} = I$ Where $I$ is the unit matrix of $2 \times 2$ and $A^{T}$ is the transpose of $A$ , then the value of $θ$ is equal to:
- (A) $\frac{3 π}{2}$
- (B) $π$
- (C) $\frac{π}{3}$
- (D) $\frac{π}{6}$
View Solution
13.
Value of $\cos (- 1230^{\circ}) \times \cot (- 315^{\circ})$ is:
- (A) $\frac{- \sqrt{3}}{2}$
- (B) $\frac{2}{\sqrt{3}}$
- (C) $\frac{1}{2}$
- (D) $- \frac{1}{2}$
View Solution

View more MHT CET Questions

SHARE ON FACEBOOK SHARE ON TWITTER

Categories	State
General	800
Women	800
sc	600
pwd	600
Others	600

MHT CET PYQs for Trigonometric Identities with Solutions: Practice MHT CET Previous Year Questions

MHT CET PYQs for Trigonometric Identities with Solutions

1.
If $n = 100!$ , then what is the value of the following? $\frac{1}{\log_{2} n} + \frac{1}{\log_{3} n} + \frac{1}{\log_{4} n} + \dots \dots + \frac{1}{\log_{100} n}$

2.
Evaluate the integral: \[ \int \frac{1}{\sin^2 2x \cdot \cos^2 2x} \, dx \]

3.
The area of the region bounded by the curve $y = x^{2}$ and the line $y = 16$ is:

4.
If \( \tan^{-1} (\sqrt{\cos \alpha}) - \cot^{-1 (\cos \alpha) = x \), then what is \( \sin \alpha \)?}

5.
If \( \tan(\pi \cos x) = \cot(\pi \sin x) \), then what is \( \sin \left( \frac{\pi}{2} + x \right) \)?

6.
If $2 x^{3} - 3 y^{2} = 7$ , what is $\frac{d y}{d x}$ equal to $(y \neq 0)$ :

7.
If $2 \sin \left( \theta + \frac{\pi}{3}\right) = \cos \left( \theta -\frac{\pi}{6}\right) , $ then $\tan \, \theta = $

8.
Given the equation: \[ 81 \sin^2 x + 81 \cos^2 x = 30 \] Find the value of \( x \).

9.
Find the equation of the line passing through $(- 3, 5)$ and perpendicular to the line through the points $(2, 5) (- 3, 6)$ .

10.
$\frac{\sin 7 x + 6 \sin 5 x + 17 \sin 3 x + 12 \sin x}{\sin 6 x + 5 \sin 4 x + 12 \sin 2 x}$ equals:

12.
If $A = [\begin{array}{cc} \cos 2 θ & - \sin 2 θ \\ \sin 2 θ & \cos 2 θ \end{array}]$ and $A + A^{T} = I$ Where $I$ is the unit matrix of $2 \times 2$ and $A^{T}$ is the transpose of $A$ , then the value of $θ$ is equal to:

13.
Value of $\cos (- 1230^{\circ}) \times \cot (- 315^{\circ})$ is:

Fees Structure

Structure based on different categories

Comments

SUBSCRIBE TO OUR NEWS LETTER

MHT CET PYQs for Trigonometric Identities with Solutions

1.If n=100!, then what is the value of the following?1log2⁡n+1log3⁡n+1log4⁡n+……+1log100⁡n

2.Evaluate the integral: \[ \int \frac{1}{\sin^2 2x \cdot \cos^2 2x} \, dx \]

3.The area of the region bounded by the curve y=x2 and the line y=16 is:

4.If \( \tan^{-1} (\sqrt{\cos \alpha}) - \cot^{-1 (\cos \alpha) = x \), then what is \( \sin \alpha \)?}

5.If \( \tan(\pi \cos x) = \cot(\pi \sin x) \), then what is \( \sin \left( \frac{\pi}{2} + x \right) \)?

6.If 2x3−3y2=7, what is dydx equal to (y≠0):

7.If $2 \sin \left( \theta + \frac{\pi}{3}\right) = \cos \left( \theta -\frac{\pi}{6}\right) , $ then $\tan \, \theta = $

8.Given the equation: \[ 81 \sin^2 x + 81 \cos^2 x = 30 \] Find the value of \( x \).

9.Find the equation of the line passing through (−3,5) and perpendicular to the line through the points (2,5)(−3,6).

10.sin⁡7x+6sin⁡5x+17sin⁡3x+12sin⁡xsin⁡6x+5sin⁡4x+12sin⁡2x equals:

12.If A=[cos⁡2θ−sin⁡2θsin⁡2θcos⁡2θ] and A+AT=I Where I is the unit matrix of 2×2 and AT is the transpose of A, then the value of θ is equal to:

13.Value of cos⁡(−1230∘)×cot⁡(−315∘) is:

Fees Structure

Structure based on different categories

Comments

SUBSCRIBE TO OUR NEWS LETTER

1.
If $n = 100!$ , then what is the value of the following? $\frac{1}{\log_{2} n} + \frac{1}{\log_{3} n} + \frac{1}{\log_{4} n} + \dots \dots + \frac{1}{\log_{100} n}$

2.
Evaluate the integral: \[ \int \frac{1}{\sin^2 2x \cdot \cos^2 2x} \, dx \]

3.
The area of the region bounded by the curve $y = x^{2}$ and the line $y = 16$ is:

4.
If \( \tan^{-1} (\sqrt{\cos \alpha}) - \cot^{-1 (\cos \alpha) = x \), then what is \( \sin \alpha \)?}

5.
If \( \tan(\pi \cos x) = \cot(\pi \sin x) \), then what is \( \sin \left( \frac{\pi}{2} + x \right) \)?

6.
If $2 x^{3} - 3 y^{2} = 7$ , what is $\frac{d y}{d x}$ equal to $(y \neq 0)$ :

7.
If $2 \sin \left( \theta + \frac{\pi}{3}\right) = \cos \left( \theta -\frac{\pi}{6}\right) , $ then $\tan \, \theta = $

8.
Given the equation: \[ 81 \sin^2 x + 81 \cos^2 x = 30 \] Find the value of \( x \).

9.
Find the equation of the line passing through $(- 3, 5)$ and perpendicular to the line through the points $(2, 5) (- 3, 6)$ .

10.
$\frac{\sin 7 x + 6 \sin 5 x + 17 \sin 3 x + 12 \sin x}{\sin 6 x + 5 \sin 4 x + 12 \sin 2 x}$ equals:

12.
If $A = [\begin{array}{cc} \cos 2 θ & - \sin 2 θ \\ \sin 2 θ & \cos 2 θ \end{array}]$ and $A + A^{T} = I$ Where $I$ is the unit matrix of $2 \times 2$ and $A^{T}$ is the transpose of $A$ , then the value of $θ$ is equal to:

13.
Value of $\cos (- 1230^{\circ}) \times \cot (- 315^{\circ})$ is: