1
MHT CET 2024 15th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The value of the integral $\int_0^{\frac{\pi}{2}} \frac{\sqrt{\cot x}}{\sqrt{\cot x}+\sqrt{\tan x}} \mathrm{dx}$ is

A
$\frac{\pi}{4}$
B
$\frac{\pi}{2}$
C
$\frac{\pi}{8}$
D
$2 \pi$
2
MHT CET 2024 15th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

$$\int_0^{\frac{\pi}{4}} \frac{\sec ^2 x}{(1+\tan x)(2+\tan x)} d x=$$

A
$\log \left(\frac{3}{4}\right)$
B
$\frac{1}{3} \log \left(\frac{4}{3}\right)$
C
$\log \left(\frac{4}{3}\right)$
D
$\frac{1}{4} \log \left(\frac{3}{4}\right)$
3
MHT CET 2024 15th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

After $t$ seconds, the acceleration of a particle, which starts from rest and moves in a straight line is $\left(8-\frac{\mathrm{t}}{5}\right) \mathrm{cm} / \mathrm{s}^2$, then velocity of the particle at the instant, when the acceleration is zero, is

A
$160 \mathrm{~cm} / \mathrm{s}$
B
$80 \mathrm{~cm} / \mathrm{s}$
C
$320 \mathrm{~cm} / \mathrm{s}$
D
$480 \mathrm{~cm} / \mathrm{s}$
4
MHT CET 2024 15th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

The value of integral $\int_\limits{-2}^0\left(x^3+3 x^2+3 x+5+(x+1) \cos (x+1)\right) d x$ is equal to

A
0
B
6
C
4
D
1
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