1
MHT CET 2024 15th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $\mathrm{f}(x)=x^3-10 x^2+200 x-10$, then

A
$\mathrm{f}(x)$ is decreasing in $(-\infty, 10]$ and increasing in $[10, \infty)$
B
$f(x)$ is increasing in $(-\infty, 10]$ and decreasing in $[10, \infty)$
C
$\mathrm{f}(x)$ is increasing throughout real line
D
$\mathrm{f}(x)$ is decreasing throughout real line
2
MHT CET 2024 15th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

Twenty meters of wire is available for fencing off a flower-bed in the form of a circular sector. Then the maximum area (in sq.m) of the flowerbed is

A
30
B
12.5
C
25
D
10
3
MHT CET 2024 15th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

A ladder 5 m in length is leaning against a wall. The bottom of the ladder is pulled along the ground away from the wall, at the rate of $2 \mathrm{~m} / \mathrm{sec}$. How fast is the height on the wall decreasing when the foot of the ladder is 4 m away from the wall?

A
$\frac{4}{3} \mathrm{~m} / \mathrm{sec}$
B
$\frac{2}{3} \mathrm{~m} / \mathrm{sec}$
C
$\frac{5}{3} \mathrm{~m} / \mathrm{sec}$
D
$\frac{8}{3} \mathrm{~m} / \mathrm{sec}$
4
MHT CET 2024 11th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $y=\mathrm{a} \log x+\mathrm{b} x^2+x$ has its extreme values at $x=-1$ and $x=2$, then the value of $\left(\frac{a}{b}+\frac{b}{a}\right)$ is

A
$-\frac{7}{4}$
B
$-\frac{15}{4}$
C
$-\frac{17}{4}$
D
$-\frac{5}{4}$
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