1
MHT CET 2023 14th May Morning Shift
+2
-0

If $$\mathrm{f}^{\prime}(x)=\tan ^{-1}(\sec x+\tan x),-\frac{\pi}{2} < x < \frac{\pi}{2}$$ and $$f(0)=0$$, then $$\mathrm{f}(1)$$ is

A
$$\frac{\pi+1}{4}$$
B
$$\frac{\pi+2}{4}$$
C
$$\pi+\frac{1}{4}$$
D
$$\frac{\pi-1}{4}$$
2
MHT CET 2023 14th May Morning Shift
+2
-0

The area bounded by the curves $$y=(x-1)^2, y=(x+1)^2$$ and $$y=\frac{1}{4}$$ is

A
$$\frac{1}{3}$$ sq. units.
B
$$\frac{2}{3}$$ sq. units.
C
$$\frac{1}{4}$$ sq. units.
D
$$\frac{1}{5}$$ sq. units.
3
MHT CET 2023 13th May Evening Shift
+2
-0

If a curve $$y=a \sqrt{x}+b x$$ passes through the point $$(1,2)$$ and the area bounded by the curve, line $$x=4$$ and $$X$$-axis is 8 sq units, then

A
$$a=3, b=-1$$
B
$$a=3, b=1$$
C
$$a=-3, b=1$$
D
$$a=-3, b=-1$$
4
MHT CET 2023 13th May Morning Shift
+2
-0

The area (in sq. units) of the region bounded by curves $$y=3 x+1, y=4 x+1$$ and $$x=3$$ is

A
$$\frac{7}{2}$$
B
$$\frac{9}{5}$$
C
$$\frac{9}{2}$$
D
$$\frac{7}{5}$$
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