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

$$\int \sqrt{\mathrm{e}^x-1} \mathrm{dx}=$$

A
$\sqrt{\mathrm{e}^x-1}+\tan ^{-1} \sqrt{\mathrm{e}^x-1}+\mathrm{c}$, (where c is constant of integration)
B
$2 \sqrt{\mathrm{e}^x-1}+\tan ^{-1} \sqrt{\mathrm{e}^x-1}+\mathrm{c}$, (where c is constant of integration)
C
$2 \sqrt{\mathrm{e}^x-1}-2 \tan ^{-1} \sqrt{\mathrm{e}^x-1}+\mathrm{c}$, (where c is constant of integration)
D
$2 \sqrt{\mathrm{e}^x-1}-\tan ^{-1} \sqrt{\mathrm{e}^x-1}+\mathrm{c}$, (where c is constant of integration)
2
MHT CET 2024 9th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The value of $\int \frac{\mathrm{d} x}{(x+1)^{3 / 4}(x-2)^{5 / 4}}$ is equal to

A
$4\left(\frac{x+1}{x-2}\right)^{1 / 4}+\mathrm{c}$, where c is a constant of integration.
B
$4\left(\frac{x-2}{x-1}\right)^{1 / 4}+\mathrm{c}$, where c is a constant of integration.
C
$\frac{-4}{3}\left(\frac{x-2}{x+1}\right)^{1 / 4}+\mathrm{c}$, where c is a constant of integration.
D
$\frac{-4}{3}\left(\frac{x+1}{x-2}\right)^{1 / 4}+\mathrm{c}$, where c is a constant of integration.
3
MHT CET 2024 9th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $\int \frac{\cos x-\sin x}{\sqrt{8-\sin 2 x}} d x=a \sin ^{-1}\left(\frac{\sin x+\cos x}{b}\right)+c$ Where c is a constant of integration, then the ordered pair $(\mathrm{a}, \mathrm{b})$ is equal to

A
$(1,3)$
B
$(3,1)$
C
$(-1,3)$
D
$(-3,1)$
4
MHT CET 2024 9th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $\int \mathrm{f}(x) \mathrm{d} x=\psi(x)$, then $\int x^5 \mathrm{f}\left(x^3\right) \mathrm{d} x$ is equal to

A
$\frac{1}{3} x^3 \psi\left(x^3\right)-3 \int x^3 \psi\left(x^3\right) \mathrm{d} x+\mathrm{c}$, (where c is a constant of integration)
B
$\frac{1}{3}\left(x^3 \psi\left(x^3\right)-\int x^3 \psi\left(x^3\right) \mathrm{d} x\right)+\mathrm{c}$, (where c is a constant of integration)
C
$\frac{1}{3} x^3 \psi\left(x^3\right)-\int x^2 \psi\left(x^3\right) \mathrm{d} x+\mathrm{c}$, (where c is a constant of integration)
D
$\frac{1}{3}\left(x^3 \psi\left(x^3\right)-\int x^2 \psi\left(x^3\right) \mathrm{d} x\right)+\mathrm{c}$, (where c is a constant of integration)
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