1
MHT CET 2021 23rd September Evening Shift
MCQ (Single Correct Answer)
+2
-0

$$\int_\limits1^3\left[\tan ^{-1}\left(\frac{x}{x^2-1}\right)+\tan ^{-1}\left(\frac{x^2-1}{x}\right)\right] d x=$$

A
$$\pi$$
B
$$\frac{\pi}{4}$$
C
$$\frac{\pi}{2}$$
D
$$2 \pi$$
2
MHT CET 2021 23th September Morning Shift
MCQ (Single Correct Answer)
+2
-0

$$\int_\limits0^1|5 x-3| d x=$$

A
$$\frac{13}{10}$$
B
1
C
$$\frac{3}{10}$$
D
$$\frac{1}{2}$$
3
MHT CET 2021 23th September Morning Shift
MCQ (Single Correct Answer)
+2
-0

$$\int_0^{\pi / 2} \frac{\cos x}{3 \cos x+\sin x} d x=$$

A
$$\frac{3 \pi}{20}-\frac{\log 3}{100}$$
B
$$\frac{3 \pi}{10}-\frac{\log 3}{10}$$
C
$$\frac{3 \pi}{20}+\frac{\log 3}{10}$$
D
$$\frac{3 \pi}{20}-\frac{\log 3}{10}$$
4
MHT CET 2021 22th September Evening Shift
MCQ (Single Correct Answer)
+2
-0

$$\int_\limits{\frac{\pi}{6}}^{\frac{\pi}{2}} \frac{\operatorname{cosec} x \cdot \cot x}{1+\operatorname{cosec}^2 x} d x=$$

A
$$\frac{\pi}{4}-\tan ^{-1} 2$$
B
$$\tan ^{-1} 1$$
C
$$\tan ^{-1} 2$$
D
$$\tan ^{-1}\left(\frac{1}{3}\right)$$
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