Question 1: Palette 1/19

TS-EAMCET 2025 MCQ

If $a, b$ are real numbers and $\alpha$ is a real roots of $x^2+12+3 \sin (a+b x)+6 x=0$, then the value of $\cos (a+b \alpha)$ for the least positive value of $a+b \alpha$ is

A

-1

B

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

C

$\frac{1}{2}$

D

0

Question 2: Palette 2/19

TS-EAMCET 2025 MCQ

If $0 \leq A, B \leq \frac{\pi}{4}$ and $\cot A+\cot B+\tan A+ \tan B=\cot A \cot B-\tan A \tan B$, then $\sin (A+B)=$

A

0

B

$\frac{1}{2}$

C

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

D

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

Question 3: Palette 3/19

TS-EAMCET 2025 MCQ

Number of solutions of the equation $\tan ^2 x+3 \cot ^2 x=2 \sec ^2 x$ lying in the interval $[0,2 \pi]$ is

A

3

B

4

C

5

D

6

Question 4: Palette 4/19

TS-EAMCET 2025 MCQ

If $2 \sin \theta+3 \cos \theta=2$ and $\theta \neq(2 n+1) \frac{\pi}{2}$, then $\sin \theta+\cos \theta=$

A

$5 / 13$

B

$3 / 5$

C

$7 / 13$

D

$4 / 5$

Question 5: Palette 5/19

TS-EAMCET 2025 MCQ

If $x \in(-\pi, \pi)$, then the number of solutions of the equation $2 \sin x \sin 3 x \sin 5 x+\sin 5 x \cos 4 x=0$ is

A

14

B

12

C

13

D

9

Question 6: Palette 6/19

TS-EAMCET 2025 MCQ

If $\cos \alpha+\cos \beta+\cos \gamma=0=\sin \alpha+\sin \beta+\sin \gamma$, then $\sin 2 \alpha+\sin 2 \beta+\sin 2 \gamma=$

A

$\cos (\alpha+\beta)+\cos (\beta+\gamma)+\cos (\gamma+\alpha)$

B

$\cos ^2 \alpha+\cos ^2 \beta+\cos ^2 \gamma$

C

$\sin ^2 \alpha+\sin ^2 \beta+\sin ^2 \gamma$

D

$\cos (2 \alpha-\beta-\gamma)+\cos (2 \beta-\gamma-\alpha)+\cos (2 \gamma-\alpha-\beta)$

Question 7: Palette 7/19

TS-EAMCET 2025 MCQ

Number of solutions of the equation $\sin ^2 \theta+2 \cos ^2 \theta-\sqrt{3} \sin \theta \cos \theta=2$ lying in the interval ( $-\pi, \pi$ ) is

A

2

B

3

C

4

D

5

Question 8: Palette 8/19

TS-EAMCET 2025 MCQ

$1+\cos x+\cos ^2 x+\cos ^3 x+\ldots$ to $\infty=4+2 \sqrt{3}$, then $x=$

A

$\frac{n \pi}{6}$

B

$(4 n \pm 1) \frac{\pi}{3}$

C

$(12 n \pm 1) \frac{\pi}{6}$

D

$(3 n \pm 1) \frac{\pi}{3}$

Question 9: Palette 9/19

TS-EAMCET 2025 MCQ

$\alpha, \beta$ are the roots of the equation $\sin ^2 x+b \sin x+c=0$. If $\alpha+\beta=\frac{\pi}{2}$, then $b^2-1=$

A

$C$

B

$2 c$

C

$C^2$

D

$4 c^2$

Question 10: Palette 10/19

TS-EAMCET 2025 MCQ

The general solution of the equation $\sqrt{6-5 \cos x+7 \sin ^2 x}-\cos x=0$ also satisfies the equation

A

$\tan x+\cot x=2$

B

$\cot x+\operatorname{cosec} x=1$

C

$\tan x+\sec x=1$

D

$\sec x+\operatorname{cosec} x=2$

Question 11: Palette 11/19

TS-EAMCET 2024 MCQ

Suppose, $\theta_{1}$ and $\theta_{2}$ are such that $\left(\theta_{1}-\theta_{2}\right)$ lies in 3rd or 4th quadrant. If $\sin \theta_{1}+\sin \theta_{2}=-\frac{21}{65}$ and $\cos \theta_{1}+\cos \theta_{2}=-\frac{27}{65}$, then $\cos \left(\frac{\theta_{1}-\theta_{2}}{2}\right)=$

A

$\frac{3}{\sqrt{150}}$

B

$\frac{3}{\sqrt{130}}$

C

$-\frac{3}{\sqrt{130}}$

D

$-\frac{3}{\sqrt{150}}$

Question 12: Palette 12/19

TS-EAMCET 2024 MCQ

If $A$ is the solution set of the equation $\cos ^{2} x=\cos ^{2} \frac{\pi}{6}$ and $B$ is the solution set of the equation $\cos ^{2} x=\log _{16} P$ where, $P+\frac{16}{P}=10$, then, $B-A=$

A

$\left\{x \in R / x=2 n \pi \pm \frac{\pi}{4}, 2 n \pi \pm \frac{\pi}{3} n=0,12,3 \ldots\right\}$

B

$\left\{x \in R / x=2 n \pi \pm \frac{\pi}{3}, 2 n \pi \pm \frac{2 \pi}{3} n=0,1,2,3 \ldots\right\}$

C

$\left\{x \in R / x=2 n \pi \pm \frac{\pi}{6}, 2 n \pi \pm \frac{\pi}{12} n=0,1,2,3 \ldots\right\}$

D

$\left\{x \in R / x=2 n \pi \pm \frac{\pi}{8}, 2 n \pi \pm \frac{\pi}{16} n=0,1,2,3 \ldots\right\}$

Question 13: Palette 13/19

TS-EAMCET 2024 MCQ

If $\tan A+\tan B+\cot A+\cot B=\tan A \tan B-\cot A \cot B$ and $0^{\circ} < A+B<270^{\circ}$, then $A+B=$

A

$45^{\circ}$

B

$135^{\circ}$

C

$150^{\circ}$

D

$225^{\circ}$

Question 14: Palette 14/19

TS-EAMCET 2024 MCQ

The equation that is satisfied by the general solution of the equation $4-3 \cos ^2 \theta=5 \sin \theta \cos \theta$ is

A

$7 \sin ^2 \theta+3 \cos ^2 \theta=4$

B

$\sin ^2 \theta-2 \cos \theta+\frac{1}{4}=0$

C

$\cot \theta-\tan \theta=\sec \theta$

D

$1+\sin ^2 \theta=3 \cos ^2 \theta$

Question 15: Palette 15/19

TS-EAMCET 2024 MCQ

The solution set of the equation $\cos ^2 2 x+\sin ^2 3 x=1$ i

A

$\left\{x \left\lvert\, x=n \pi+\frac{\pi}{2}\right., n \in Z\right\}$

B

$\left\{x \left\lvert\, x=2 n \pi \pm \frac{\pi}{4}\right., n \in Z\right\}$

C

$\left\{x \left\lvert\, x=\frac{n \pi}{5}\right., n \in Z\right\}$

D

$\left\{x \left\lvert\, x=n \pi+(-1)^n \frac{n \pi}{6}\right., n \in Z\right\}$

Question 16: Palette 16/19

TS-EAMCET 2024 MCQ

If the period of the function $f(x)=2 \cos (3 x+4)-3 \tan (2 x-3)+5 \sin (5 x)-7$ is $k$, then

A

$\sin \frac{k}{8}=\frac{1}{2}$

B

$\cos \frac{k}{6}=\frac{1}{\sqrt{2}}$

C

$\tan \frac{k}{3}=-\sqrt{3}$

D

$\sec \frac{k}{2}=2$

Question 17: Palette 17/19

TS-EAMCET 2024 MCQ

The number of solutions of the equation $\sin 7 \theta-\sin 3 \theta=\sin 4 \theta$ that lie in the interval $(0, \pi)$, is

A

6

B

3

C

4

D

5

Question 18: Palette 18/19

TS-EAMCET 2020 MCQ

The general solution of the equation $(\sqrt{3}-1) \sin \theta+(\sqrt{3}+1) \cos \theta=2$ is

A

$2 n \pi \pm \frac{\pi}{4}+\frac{\pi}{12}$

B

$n \pi+(-1)^n \frac{\pi}{4}+\frac{\pi}{12}$

C

$2 n \pi \pm \frac{\pi}{4}-\frac{\pi}{12}$

D

$n \pi+(-1)^n \frac{\pi}{4}-\frac{\pi}{12}$

Question 19: Palette 19/19

TS-EAMCET 2020 MCQ

The solution set of the trigonometric equation $\tan \theta+5 \cot \theta=\sec \theta$ is

A

$\left\{\frac{\theta}{\theta}=2 n \pi \pm \frac{\pi}{3}, n \in \mathbf{Z}\right\}$

B

$\left\{\frac{\theta}{\theta}=n \pi+(-1)^n \frac{\pi}{2}, n \in \mathbf{Z}\right\}$

C

$\left\{\frac{\theta}{\theta}=n \pi+\frac{\pi}{6}, n \in \mathbf{Z}\right\}$

D

$\phi$