1
MHT CET 2023 10th May Morning Shift
+2
-0

Area of the region bounded by the curve $$y=\sqrt{49-x^2}$$ and $$\mathrm{X}$$-axis is

A
$$49 \pi$$ sq. units
B
$$\frac{49 \pi}{2}$$ sq. units
C
$$\frac{49 \pi}{4}$$ sq. units
D
$$98 \pi$$ sq. units
2
MHT CET 2023 9th May Evening Shift
+2
-0

If $$\mathrm{f}^{\prime}(x)=x-\frac{5}{x^5}$$ and $$\mathrm{f}(1)=4$$, then $$\mathrm{f}(x)$$ is

A
$$\frac{x^2}{2}+\frac{9}{4} \frac{1}{x^4}+\frac{5}{4}$$
B
$$\frac{x^2}{2}-\frac{5}{4} \frac{1}{x^4}+\frac{9}{4}$$
C
$$\frac{x^2}{2}+\frac{5}{4} \frac{1}{x^4}+\frac{9}{4}$$
D
$$\frac{x^2}{2}-\frac{9}{4} \frac{1}{x^4}+\frac{5}{4}$$
3
MHT CET 2023 9th May Evening Shift
+2
-0

The area (in sq. units) bounded by the curve $$y=x|x|, \mathrm{X}$$-axis and the lines $$x=-1$$ and $$x=1$$ is

A
$$\frac{2}{3}$$
B
$$\frac{1}{3}$$
C
1
D
$$\frac{4}{3}$$
4
MHT CET 2023 9th May Morning Shift
+2
-0

The area (in sq. units) of the region $$\mathrm{A}=\left\{(x, y) / \frac{y^2}{2} \leq x \leq y+4\right\}$$ is

A
30
B
$$\frac{53}{3}$$
C
16
D
18
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