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1
MHT CET 2024 9th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $\int \frac{d x}{\sqrt[3]{\sin ^{11} x \cos x}}=-\left(\frac{3}{8} f(x)+\frac{3}{2} g(x)\right)+c$ then

A
$\mathrm{f}(x)=\tan ^{\frac{-8}{3}} x, \mathrm{~g}(x)=\tan ^{\frac{-2}{3}} x$, (where c is a constant of integration)
B
$\mathrm{f}(x)=\tan ^{\frac{8}{3}} x, \mathrm{~g}(x)=\tan ^{\frac{-2}{3}} x$, (where c is a constant of integration)
C
$\mathrm{f}(x)=\tan ^{\frac{-8}{3}} x, \mathrm{~g}(x)=\tan ^{\frac{2}{3}} x$, (where c is a constant of integration)
D
$\mathrm{f}(x)=\tan ^{\frac{8}{3}} x, \mathrm{~g}(x)=\tan ^{\frac{2}{3}} x$, (where c is a constant of integration)
2
MHT CET 2024 9th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

$\int \frac{x^4+x^2+1}{x^2-x+1} d x$ is equal to

A
$\frac{x^3}{3}-\frac{x^2}{2}+x+\mathrm{c}$, (where c is a constant of integration)
B
$\frac{x^3}{3}+\frac{x^2}{2}+x+\mathrm{c}$, (where c is a constant of integration)
C
$\frac{x^3}{3}-\frac{x^2}{2}-x+\mathrm{c}$, (where c is a constant of integration)
D
$\frac{x^3}{3}+\frac{x^2}{2}-x+\mathrm{c}$, ( where c is a constant of integration)
3
MHT CET 2024 9th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

The value of $I=\int \frac{(x-1) \mathrm{e}^x}{(x+1)^3} \mathrm{dx}$ is

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

The value of $\int \frac{\mathrm{d} x}{x^2\left(x^4+1\right)^{\frac{3}{4}}}$ is

A
$\frac{\left(x^4+1\right)^{\frac{1}{4}}}{x}+\mathrm{c}$, where c is a constant of integration.
B
$\left(x^4+1\right)^{\frac{1}{4}}+\mathrm{c}$, where c is a constant of integration.
C
$\frac{-\left(x^4+1\right)^{\frac{1}{4}}}{x}+\mathrm{c}$, where c is a constant of integration.
D
$-\left(x^4+1\right)^{\frac{1}{4}}+c$, where $c$ is a constant of integration.
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