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

An open tank with a square bottom is to contain 4000 cubic cm . of liquid. The dimensions of the tank so that the surface area of the tank is minimum, is

A
side $=20 \mathrm{~cm}$, height $=10 \mathrm{~cm}$
B
side $=10 \mathrm{~cm}$, height $=20 \mathrm{~cm}$
C
side $=10 \mathrm{~cm}$, height $=40 \mathrm{~cm}$
D
side $=20 \mathrm{~cm}$, height $=05 \mathrm{~cm}$
2
MHT CET 2025 22nd April Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $x$ is real, then the difference between the greatest and least values of $\frac{x^2-x+1}{x^2+x+1}$ is

A
$\frac{10}{3}$
B
$\frac{8}{3}$
C
$\frac{5}{3}$
D
$\frac{1}{3}$
3
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 $\left[-\frac{1}{2}, 1\right]$
4
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
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