1
MHT CET 2025 22nd April Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $\mathrm{f}(x)=x \cdot \mathrm{e}^{x(1-x)}$, then $\mathrm{f}(x)$ is

A
increasing in $\mathbb{R}$
B
increasing in $\left(\frac{-1}{2}, 1\right)$
C
decreasing in $\mathbb{R}$
D
decreasing in $\left[-\frac{1}{2}, 1\right]$
2
MHT CET 2025 22nd April Morning Shift
MCQ (Single Correct Answer)
+2
-0

The approximate value of $\sqrt[3]{64 \cdot 04}$ is

A
4.00043
B
4.00076
C
4.00083
D
4.00064
3
MHT CET 2025 22nd April Morning Shift
MCQ (Single Correct Answer)
+2
-0

The X and Y intercepts of the tangent to the hyperbola $\frac{x^2}{20}-\frac{y^2}{5}=1$ which is perpendicular to the line $4 x+3 y=7$, are respectively

A
$\frac{-10}{3}, \frac{-5}{3}$
B
$\frac{10}{3}, \frac{-5}{2}$
C
$\frac{10}{3}, \frac{5}{2}$
D
$\frac{10}{3}, \frac{5}{3}$
4
MHT CET 2025 22nd April Morning Shift
MCQ (Single Correct Answer)
+2
-0

If the lines $\frac{x-1}{2}=\frac{y+1}{\mathrm{k}}=\frac{\mathrm{z}}{2}$ and $\frac{x+1}{5}=\frac{y+1}{2}=\frac{\mathrm{z}}{\mathrm{k}}$ are coplanar, then the equation of the plane containing these lines are

A
$x \pm y+z=0$
B
$\quad y \pm z+1=0$
C
$\quad 2 x \pm y=0$
D
$\quad x \pm z+1=0$
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