1
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
$$\frac{x^2}{2}-\frac{9}{4} \frac{1}{x^4}+\frac{5}{4}$$
2
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
$$\frac{4}{3}$$
3
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
4
MHT CET 2022 11th August Evening Shift
+2
-0

The area (in sq. units) of the region described by $$A=\left\{(x, y) / x^2+y^2 \leq 1\right.$$ and $$\left.y^2 \leq 1-x\right\}$$ is

A
$$\left(\frac{\pi}{2}+\frac{2}{3}\right)$$
B
$$\left(\frac{\pi}{2}+\frac{4}{3}\right)$$
C
$$\left(\frac{\pi}{2}-\frac{4}{3}\right)$$
D
$$\left(\frac{\pi}{2}-\frac{2}{3}\right)$$
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