1
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
$$x \sec ^{-1} x+\log \left|x+\sqrt{x^2+1}\right|+c$$
2
MHT CET 2021 23rd September Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $$\int \frac{\sqrt{x}}{x(x+1)} d x=k \tan ^{-1} m+c$$, (where c is constant of integration), then

A
$$k=1, m=\sqrt{x}$$
B
$$k=2, m=\sqrt{x}$$
C
$$\mathrm{k}=1, \mathrm{~m}=\mathrm{x}$$
D
$$\mathrm{k}=2, \mathrm{~m}=\mathrm{x}$$
3
MHT CET 2021 23rd September Evening Shift
MCQ (Single Correct Answer)
+2
-0

$$\int \frac{d x}{\cos x \sqrt{\cos 2 x}}=$$

A
$$\sin ^{-1}(\tan x)+c$$
B
$$\frac{1}{2} \log \left|\tan \left(\frac{\pi}{4}+x\right)\right|+c$$
C
$$2 \log \left|\frac{1+\tan x}{1-\tan x}\right|+c$$
D
$$\frac{1}{2} \log \left|\frac{1-\tan x}{1+\tan x}\right|+c$$
4
MHT CET 2021 23th September Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $$\int \frac{\sin x}{\sin (x-\alpha)} d x=A x+B \log \sin (x-\alpha)+c$$, then the value of A and B are respectively (where $$\mathrm{c}$$ is a constant of integration)

A
$$\cos \alpha, \sin \alpha$$
B
$$\sin \alpha, \cos \alpha$$
C
$$-\cos \alpha, \sin \alpha$$
D
$$-\sin \alpha, \cos \alpha$$
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