1
MHT CET 2023 10th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The displacement '$$\mathrm{S}$$' of a moving particle at a time $$t$$ is given by $$S=5+\frac{48}{t}+t^3$$. Then its acceleration when the velocity is zero, is

A
12
B
20
C
16
D
24
2
MHT CET 2023 10th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $$\bar{a}$$ and $$\bar{b}$$ are two unit vectors such that $$\bar{a}+2 \bar{b}$$ and $$5 \bar{a}-4 \bar{b}$$ are perpendicular to each other, then the angle between $$\bar{a}$$ and $$\bar{b}$$ is

A
$$\frac{\pi}{3}$$
B
$$\frac{\pi}{6}$$
C
$$\frac{\pi}{4}$$
D
$$\frac{2 \pi}{3}$$
3
MHT CET 2023 10th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The value of $$\tan ^{-1}(1)+\cos ^{-1}\left(-\frac{1}{2}\right)+\sin ^{-1}\left(-\frac{1}{2}\right)$$ is

A
$$\frac{5 \pi}{6}$$
B
$$\frac{\pi}{2}$$
C
$$\frac{2 \pi}{3}$$
D
$$\frac{3 \pi}{4}$$
4
MHT CET 2023 10th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

$$\int_\limits 0^\pi \frac{x \tan x}{\sec x+\cos x} d x= $$

A
$$\frac{\pi}{8}$$
B
$$-\frac{\pi^2}{8}$$
C
$$\frac{\pi^2}{4}$$
D
$$-\frac{\pi^2}{4}$$
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