1
MHT CET 2024 4th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The Solution set of the equation $\sin ^2 \theta-\cos \theta=\frac{1}{4}$ in the interval $[0,2 \pi]$ is

A
$\left\{\frac{\pi}{6}, \frac{5 \pi}{6}\right\}$
B
$\left\{\frac{\pi}{3}, \frac{5 \pi}{3}\right\}$
C
$\left\{\frac{\pi}{3}, \frac{2 \pi}{3}\right\}$
D
$\left\{\frac{2 \pi}{3}, \frac{4 \pi}{3}\right\}$
2
MHT CET 2024 3rd May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The number of all values of $\theta$ in the interval $\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$ satisfying the equation $(1-\tan \theta)(1+\tan \theta) \sec ^2 \theta+2 \tan ^2 \theta=0$ is

A
1
B
0
C
2
D
infinitely many.
3
MHT CET 2024 3rd May Morning Shift
MCQ (Single Correct Answer)
+2
-0

Let $S=\left\{x \in(-\pi, \pi) \mid x \neq 0, \pm \frac{\pi}{2}\right\}$. The sum of all distinct solutions of the equation $\sqrt{3} \sec x+\operatorname{cosec} x+2(\tan x-\cot x)=0$ in the set S is equal to

A
$-\frac{7 \pi}{9}$
B
$-\frac{2 \pi}{9}$
C
0
D
$\frac{5 \pi}{9}$
4
MHT CET 2024 3rd May Morning Shift
MCQ (Single Correct Answer)
+2
-0

The number of roots of the equation, $(81)^{\sin ^2 x}+(81)^{\cos ^2 x}=30$ in the interval $[0, \pi]$, is equal to

A
4
B
3
C
8
D
2
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