1
MHT CET 2024 10th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

$$\int \frac{\sqrt{x}}{x+1} d x=$$

A
$\left(2 \sqrt{x}-\tan ^{-1} \sqrt{x}\right)+\mathrm{c}$, where c is a constant of integration.
B
$2\left(\sqrt{x}-\tan ^{-1} \sqrt{x}\right)+\mathrm{c}$, where c is a constant of integration.
C
$\left(2 \sqrt{x}+\tan ^{-1} \sqrt{x}\right)+\mathrm{c}$, where c is a constant of integration.
D
$2\left(\sqrt{x}+\tan ^{-1} \sqrt{x}\right)+\mathrm{c}$, where c is a constant of integration.
2
MHT CET 2024 10th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

The equation of the normal to the curve $y=x \log x$, which is parallel to the line $2 x-2 y+3=0$, is

A
$x+y=3 \mathrm{e}^{-2}$
B
$x-y=3 \mathrm{e}^{-2}$
C
$ x-y=3 \mathrm{e}^2$
D
$x+y=3 \mathrm{e}^2$
3
MHT CET 2024 10th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

$$\int \frac{1+\sin (\log x)}{1+\cos (\log x)} d x=$$

A
$x^2 \tan \left(\frac{\log x}{2}\right)+c$, where $c$ is a constant of integration.
B
$x \tan \left(\log \left(\frac{x}{2}\right)\right)+\mathrm{c}$, where c is a constant of integration.
C
$x^3 \log \left(\frac{\tan x}{2}\right)+\mathrm{c}$, where c is a constant of integration.
D
$x \cdot \tan \left(\frac{\log x}{2}\right)+\mathrm{c}$, where c is a constant of integration.
4
MHT CET 2024 10th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $\mathrm{w}=\frac{-1+i \sqrt{3}}{2}$, where $\mathrm{i}=\sqrt{-1}$, then the value of $\left(3+w+3 w^2\right)^4$ is

A
16
B
$-16$
C
16w
D
16w$^2$
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