1
MHT CET 2024 16th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

$$\int \frac{\mathrm{e}^{\tan ^{-1} x}}{1+x^2}\left[\left(\sec ^{-1} \sqrt{1+x^2}\right)^2+\cos ^{-1}\left(\frac{1-x^2}{1+x^2}\right)\right] \mathrm{d} x,$$ where $x>0$ is

A
$\left(\tan ^{-1} x\right) \mathrm{e}^{\tan ^{-1} x}+\mathrm{c}$, where c is a constant of integration.
B
$\left(\tan ^{-1} x\right)^2 \mathrm{e}^{\tan ^{-1} x}+\mathrm{c}$, where c is a constant of integration.
C
$2\left(\tan ^{-1} x\right) \mathrm{e}^{\tan ^{-1} x}+\mathrm{c}$, where c is a constant of integration.
D
$2\left(\tan ^{-1} x\right)^2 \mathrm{e}^{\tan ^{-1} x}+\mathrm{c}$, where c is a constant of integration.
2
MHT CET 2024 16th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The equation of plane through the point $(2,-1,-3)$ and parallel to lines $\frac{x-1}{3}=\frac{y+2}{2}=\frac{z}{-4}$ and $\frac{x}{2}=\frac{y-1}{-3}=\frac{z-2}{2}$ is

A
$8 x+14 y+13 z-37=0$
B
$8 x-14 y-13 z-34=0$
C
$8 x-14 y-13 z+37=0$
D
$8 x+14 y+13 z+37=0$
3
MHT CET 2024 16th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The co-ordinates of the foot of perpendicular, drawn from the point $(-2,3)$ on the line $3 x-y-1=0$ are

A
$(-1,2)$
B
$(1,-2)$
C
$(-1,-2)$
D
$(1,2)$
4
MHT CET 2024 16th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The value of $\tan ^{-1}(-\sqrt{3})-\sin ^{-1}\left(\frac{1}{\sqrt{2}}\right)+\cos ^{-1}\left(\frac{-1}{2}\right)$ is

A
$\frac{-\pi}{4}$
B
$\frac{4 \pi}{3}$
C
$\frac{\pi}{12}$
D
$\frac{7 \pi}{12}$
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