1
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
$$\frac{3 \pi}{20}-\frac{\log 3}{10}$$
2
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
$$\tan ^{-1}\left(\frac{1}{3}\right)$$
3
MHT CET 2021 22th September Evening Shift
MCQ (Single Correct Answer)
+2
-0

$$\int_\limits0^2|2 x-3| d x=$$

A
$$\frac{3}{10}$$
B
$$\frac{5}{2}$$
C
$$\frac{10}{3}$$
D
$$\frac{2}{5}$$
4
MHT CET 2021 22th September Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $$\int_\limits0^a \sqrt{\frac{a-x}{x}} d x=\frac{k}{2}$$, then $$k=$$

A
$$\pi \mathrm{a}$$
B
$$\frac{\pi \mathrm{a}}{2}$$
C
$$\frac{5 \pi \mathrm{a}}{2}$$
D
$$\frac{3 \pi \mathrm{a}}{2}$$
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