1
AP EAPCET 2024 - 23th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

$$ \begin{aligned} & \sin ^2 18^{\circ}+\sin ^2 24^{\circ}+\sin ^2 36^{\circ}+\sin ^2 42^{\circ}+\sin ^2 78^{\circ} \\ & +\sin ^2 90^{\circ}+\sin ^2 96^{\circ}+\sin ^2 102^{\circ}+\sin ^2 138^{\circ}+\sin ^2 162^{\circ} \text { is } \\ & \text { equal to } \end{aligned} $$

A
$\frac{11}{2}$
B
$\frac{9}{2}$
C
5
D
4
2
AP EAPCET 2024 - 23th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
If $A B$ and $C$ are the angles of a triangle, then $\frac{\sin A+\sin B+\sin C}{\sin ^2 \frac{A}{2}-\sin ^2 \frac{B}{2}+\sin ^2 \frac{C}{2}-1}$ is equal to
A
$-2 \tan \frac{B}{2}$
B
$-2 \cot \frac{B}{2}$
C
$2 \tan \frac{B}{2}$
D
$2 \cot \frac{B}{2}$
3
AP EAPCET 2024 - 23th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
The general solution of $\cot \frac{x}{2}-\cot x=\operatorname{cosec} \frac{x}{2}$ is
A
$\left\{\left.2 n \pi+\frac{\pi}{3} \right\rvert\, n \in z\right\}$
B
$\left\{\left.4 n \pi+\frac{\pi}{3} \right\rvert\, n \in z\right\}$
C
$\left\{\left.2 n \pi+\frac{2 \pi}{3} \right\rvert\, n \in z\right\}$
D
$\left\{\left.4 n \pi \pm \frac{2 \pi}{3} \right\rvert\, n \in z\right\}$
4
AP EAPCET 2024 - 23th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

If $0 < x < \frac{1}{2}$ and $\alpha=\sin ^{-1} x+\cos ^{-1}\left(\frac{x}{2}+\frac{\sqrt{3-3 x^2}}{2}\right)$, then $\tan \alpha+\cot \alpha$ is equal to

A
$\frac{4}{\sqrt{3}}$
B
$4 \sqrt{3}$
C
$\frac{4 x}{1-x^2}$
D
$x \sqrt{1-x^2}$
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