1
MHT CET 2023 10th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

Let $$\mathrm{f}: \mathrm{R} \rightarrow \mathrm{R}$$ and $$\mathrm{g}: \mathrm{R} \rightarrow \mathrm{R}$$ be continuous functions. Then the value of the integral $$\int_\limits{\frac{-\pi}{2}}^{\frac{\pi}{2}}[\mathrm{f}(x)+\mathrm{f}(-x)][\mathrm{g}(x)-\mathrm{g}(-x)] \mathrm{d} x$$ is

A
$$\pi$$
B
1
C
$$-1$$
D
0
2
MHT CET 2023 10th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

$$\int_\limits 0^\pi \frac{x \tan x}{\sec x+\cos x} d x= $$

A
$$\frac{\pi}{8}$$
B
$$-\frac{\pi^2}{8}$$
C
$$\frac{\pi^2}{4}$$
D
$$-\frac{\pi^2}{4}$$
3
MHT CET 2023 10th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

$$\int_\limits0^1 \cos ^{-1} x d x=$$

A
$$-$$1
B
0
C
1
D
2
4
MHT CET 2023 10th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $$\int_\limits0^{\frac{1}{2}} \frac{x^2}{\left(1-x^2\right)^{\frac{3}{2}}} \mathrm{~d} x=\frac{\mathrm{k}}{6}$$, then the value of $$\mathrm{k}$$ is

A
$$2 \sqrt{3}-\pi$$
B
$$2 \sqrt{3}+\pi$$
C
$$3 \sqrt{2}+\pi$$
D
$$3 \sqrt{2}-\pi$$
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