1
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)
2
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.
3
MHT CET 2024 3rd May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The value of $\int \sin \sqrt{x} \mathrm{dx}$ is equal to

A
$\sin \sqrt{x}-2 \sqrt{x} \cos \sqrt{x}+c$, where $c$ is a constant of integration.
B
$2 \cos \sqrt{x}-2 \sqrt{x} \sin \sqrt{x}+\mathrm{c}$, where c is a constant of integration.
C
$\cos \sqrt{x}-2 \sqrt{x} \sin \sqrt{x}+c$, where $c$ is a constant of integration.
D
$2 \sin \sqrt{x}-2 \sqrt{x} \cos \sqrt{x}+c$, where $c$ is a constant of integration.
4
MHT CET 2024 3rd May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $\mathrm{f}\left(\frac{x-4}{x-2}\right)=2 x+1, x \in \mathbb{R}-\{1,-2\}$, then $\int \mathrm{f}(x) \mathrm{d} x$ is equal to

A
$5 x-4 \log (x-1)+\mathrm{c}$, where c is constant of integration.
B
$x-4 \log (x-1)+c$, where $c$ is constant of integration.
C
$5 x+4 \log (x-1)+\mathrm{c}$, where c is constant of integration.
D
$5 x+\log (x-1)+\mathrm{c}$, where c is constant of integration.
MHT CET Subjects
EXAM MAP