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
$$-\sin \alpha, \cos \alpha$$
MHT CET Subjects
EXAM MAP
Medical
NEETAIIMS
Graduate Aptitude Test in Engineering
GATE CSEGATE ECEGATE EEGATE MEGATE CEGATE PIGATE IN
Civil Services
UPSC Civil Service
Defence
NDA
Staff Selection Commission
SSC CGL Tier I
CBSE
Class 12