1
MHT CET 2021 24th September Morning Shift
MCQ (Single Correct Answer)
+2
-0

$$\int \frac{\mathrm{dx}}{32-2 \mathrm{x}^2}=\mathrm{A} \log (4-\mathrm{x})+\mathrm{B} \log (4+\mathrm{x})+\mathrm{c}$$, then the values of $$\mathrm{A}$$ and $$\mathrm{B}$$ are respectively (where c is a constant of integration)

A
$$\frac{-1}{8}, \frac{1}{8}$$
B
$$\frac{1}{8}, \frac{-1}{8}$$
C
$$\frac{-1}{16}, \frac{1}{16}$$
D
$$\frac{1}{8}, \frac{1}{8}$$
2
MHT CET 2021 24th September Morning Shift
MCQ (Single Correct Answer)
+2
-0

$$\int \cos ^3 x \cdot e^{\log (\sin x)} d x=$$

A
$$\frac{-e^{\sin x}}{4}+c$$
B
$$\frac{-\cos ^4 x}{4}+c$$
C
$$\frac{-\sin ^4 x}{4}+c$$
D
$$\frac{e^{\sin x}}{4}+c$$
3
MHT CET 2021 24th September Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $$\int \frac{(\cos x-\sin x)}{8-\sin 2 x} d x=\frac{1}{p} \log \left[\frac{3+\sin x+\cos x}{3-\sin x-\cos x}\right]+c$$, then $$p=$$ (where $$\mathrm{c}$$ is a constant of integration)

A
12
B
$$\frac{1}{6}$$
C
6
D
3
4
MHT CET 2021 23rd September Evening Shift
MCQ (Single Correct Answer)
+2
-0

$$\int \sec ^{-1} x d x=$$

A
$$x \sec ^{-1} x+\log \left|x+\sqrt{x^2-1}\right|+c$$
B
$$x \sec ^{-1} x-\log \left|x+\sqrt{x^2-1}\right|+c$$
C
$$x \sec ^{-1} x-\log \left|x+\sqrt{x^2+1}\right|+c$$
D
$$x \sec ^{-1} x+\log \left|x+\sqrt{x^2+1}\right|+c$$
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