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

If $y=\sin ^2\left(\cot ^{-1} \sqrt{\frac{1+x}{1-x}}\right)$, then $\frac{\mathrm{d} y}{\mathrm{~d} x}$ has the value

A
$\frac{-1}{2}$
B
$\frac{1}{2}$
C
$-1$
D
$1$
2
MHT CET 2024 10th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If the line $\frac{x-1}{2}=\frac{y+1}{3}=\frac{z-1}{4}$ and $\frac{x-3}{1}=\frac{y-\mathrm{k}}{2}=\frac{\mathrm{z}}{1}$ intersect, then the value of k is

A
$\frac{3}{2}$
B
$\frac{9}{2}$
C
$-\frac{2}{9}$
D
$-\frac{3}{2}$
3
MHT CET 2024 10th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

Inverse of the matrix $\left[\begin{array}{cc}0.8 & -0.6 \\ 0.6 & 0.8\end{array}\right]$ is

A
$\left[\begin{array}{cc}0.8 & 0.6 \\ -0.6 & 0.8\end{array}\right]$
B
$\left[\begin{array}{ll}-0.8 & 0.6 \\ -0.6 & 0.8\end{array}\right]$
C
$\left[\begin{array}{cc}-0.8 & -0.6 \\ 0.6 & 0.8\end{array}\right]$
D
$\left[\begin{array}{cc}8 & -6 \\ 6 & 8\end{array}\right]$
4
MHT CET 2024 10th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

$\int \frac{\mathrm{d} x}{\sqrt{\mathrm{e}^x-1}}=2 \tan ^{-1}(\mathrm{f}(x))+\mathrm{c}$ where $x>0$ and c is a constant of integration, then $\mathrm{f}(x)$ is

A
$\mathrm{e}^x-1$
B
$\sqrt{\mathrm{e}^x-1}$
C
$\mathrm{e}^x+1$
D
$\sqrt{\mathrm{e}^x+1}$
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