1
MHT CET 2024 4th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

The value of $\mathrm{I}=\int \frac{x^2}{(\mathrm{a}+\mathrm{bx})^2} \mathrm{dx}$ is

A
$\frac{1}{b^3}\left[a+b x+2 a \log |a+b x|-\frac{a^2}{a+b x}\right]+c$, (where c is the constant of integration)
B
$\frac{1}{b^3}\left[a+b x-2 a \log |a+b x|+\frac{a^2}{a+b x}\right]+c$, (where c is the constant of integration)
C
$\frac{1}{b^3}\left[a+b x-2 a \log |a+b x|-\frac{a^2}{a+b x}\right]+c$, (where c is the constant of integration)
D
$\frac{1}{b^3}\left[a+b x+2 a \log |a+b x|+\frac{a^2}{a+b x}\right]+c$, (where c is the constant of integration)
2
MHT CET 2024 4th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $I=\int e^{\sin \theta}\left(\log \sin \theta+\operatorname{cosec}^2 \theta\right) \cos \theta d \theta$, then $I$ is equal to

A
$\mathrm{e}^{\sin \theta}\left(\log \sin \theta+\operatorname{cosec}^2 \theta\right)+\mathrm{c}$, (where c is a constant of integration)
B
$\mathrm{e}^{\sin \theta}(\log \sin \theta+\operatorname{cosec} \theta)+\mathrm{c}$, (where c is a constant of integration)
C
$\mathrm{e}^{\sin \theta}(\log \sin \theta-\operatorname{cosec} \theta)+\mathrm{c}$, (where c is a constant of integration)
D
$\mathrm{e}^{\sin \theta}\left(\log \sin \theta-\operatorname{cosec}^2 \theta\right)+\mathrm{c}$, (where c is a constant of integration)
3
MHT CET 2024 4th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

The integral $\int \sec ^{\frac{2}{3}} x \cdot \operatorname{cosec}^{\frac{4}{3}} x \mathrm{~d} x$ is equal to

A
$3(\tan x)^{-\frac{1}{3}}+\mathrm{c}$, (where c is the constant of integration)
B
$-\frac{3}{4}(\tan x)^{\frac{4}{3}}+\mathrm{c},($ where c is the constant of integration)
C
$-3(\cot x)^{\frac{1}{3}}+\mathrm{c},($ where c is the constant of integration)
D
$-3(\tan x)^{\frac{1}{3}}+\mathrm{c}$, (where c is the constant of integration)
4
MHT CET 2024 3rd May Evening Shift
MCQ (Single Correct Answer)
+2
-0

$$\int \frac{\operatorname{cosec} x d x}{\cos ^2\left(1+\log \tan \frac{x}{2}\right)}=$$

A
$\tan \left(1+\log \tan \frac{x}{2}\right)+\mathrm{c}$, where c is a constant of integration.
B
$\frac{1}{2} \tan \left(1+\log \tan \frac{x}{2}\right)+\mathrm{c}$, where c is a constant of integration.
C
$2 \tan \left(1+\log \tan \frac{x}{2}\right)+\mathrm{c}$, where c is a constant of integration.
D
$\frac{1}{4} \tan \left(1+\log \tan \frac{x}{2}\right)+\mathrm{c}$, where c is a constant of integration.
MHT CET Subjects
EXAM MAP