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

If the line, $\frac{x-3}{2}=\frac{y+2}{1}=\frac{z+4}{3}$ lies in the plane, $\ell x+m y-z=9$, then $\ell^2+m^2$ is equal to

A
$\frac{124}{49}$
B
$\frac{123}{49}$
C
$\frac{121}{49}$
D
$\frac{122}{49}$
2
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.
3
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
$x+y=3 \mathrm{e}^2$
4
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.
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