1
MHT CET 2025 23rd April Evening Shift
MCQ (Single Correct Answer)
+2
-0

The area bounded by the curve $y=x^2+3, y=x, x=3$ and $y$-axis is

A
$\frac{9}{2}$ sq. units
B
18 sq. units
C
$\frac{27}{2}$ sq. units
D
$\frac{27}{3}$ sq. units
2
MHT CET 2025 23rd April Evening Shift
MCQ (Single Correct Answer)
+2
-0

$$ \int\limits_{\frac{-\pi}{2}}^{\frac{\pi}{2}}\left(x^2+\log \left(\frac{\pi-x}{\pi+x}\right) \cdot \cos x\right) d x= $$

A
0
B
$\frac{\pi^3}{12}$
C
$\frac{\pi^2}{2}-4$
D
$\frac{\pi^2}{2}+4$
3
MHT CET 2025 23rd April Evening Shift
MCQ (Single Correct Answer)
+2
-0

$$ \int_0^1 \log \left(\frac{1}{x}-1\right) d x= $$

A
$\frac{1}{2}$
B
1
C
2
D
0
4
MHT CET 2025 23rd April Evening Shift
MCQ (Single Correct Answer)
+2
-0

If the foot of the perpendicular drawn from the origin to a plane is $\mathrm{P}(2,-1,4)$, then the equation of the plane is

A
$2 x+y+4 z-19=0$
B
$x+y+z-5=0$
C
$2 x-2 y-3 z+6=0$
D
$2 x-y+4 z-21=0$

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