1
COMEDK 2024 Afternoon Shift
MCQ (Single Correct Answer)
+1
-0

$$ \text { If } y=\sin ^{-1}(\sqrt{\sin x}) \text {, then } \frac{d y}{d x} \text { equals } $$

A
$$ \frac{1}{2} \sqrt{1-\operatorname{cosec} x} $$
B
$$ \frac{1}{2} \sqrt{1-\sin x} $$
C
$$ \frac{1}{2} \sqrt{1+\operatorname{cosec} x} $$
D
$$ \frac{1}{2} \sqrt{1+\sin x} $$
2
COMEDK 2024 Afternoon Shift
MCQ (Single Correct Answer)
+1
-0

$$ \text { If } \alpha=\tan ^{-1}\left(\tan \frac{5 \pi}{4}\right) \text { and } \beta=\tan ^{-1}\left(-\tan \frac{2 \pi}{3}\right) \text { then } $$

A
$$ 3 \alpha=4 \beta $$
B
$$ \alpha-\beta=\frac{7 \pi}{12} $$
C
$$ 4 \alpha=3 \beta $$
D
$$ \alpha+\beta=-\frac{7 \pi}{12} $$
3
COMEDK 2024 Morning Shift
MCQ (Single Correct Answer)
+1
-0

Evaluate : $$\cos ^{-1}\left[\cos \left(-680^{\circ}\right)\right]+\sin ^{-1}\left[\sin \left(-600^{\circ}\right)\right]-\cos ^{-1}\left(\sin 270^{\circ}\right)$$

A
$$\frac{14 \pi}{9}$$
B
$$-\frac{5 \pi}{9}$$
C
$$-\frac{4 \pi}{9}$$
D
$$\pi$$
4
COMEDK 2024 Morning Shift
MCQ (Single Correct Answer)
+1
-0

$$ \text { The value of } \sin ^{-1}\left[\cot \left(\frac{1}{2} \tan ^{-1} \frac{1}{\sqrt{3}}+\cos ^{-1} \frac{\sqrt{12}}{4}+\sin ^{-1} \frac{1}{\sqrt{2}}\right)\right] $$ is

A
$$ \frac{\pi}{6} $$
B
$$ \frac{\pi}{2} $$
C
$$ \frac{\pi}{4} $$
D
0
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