MHT CET 2024 15th May Evening Shift | Application of Derivatives Question 13 | Mathematics

The equation of motion of a particle is $s=a t^2+b t+c$. If the displacement after 1 second is 20 m , velocity after 2 seconds is $30 \mathrm{~m} / \mathrm{sec}$ and the acceleration is $10 \mathrm{~m} / \mathrm{sec}^2$, then

$\mathrm{a}+\mathrm{c}=2 \mathrm{~b}$

$\mathrm{a}+\mathrm{c}=\mathrm{b}$

$\mathrm{a}-\mathrm{c}=\mathrm{b}$

$\mathrm{a+c=3 b}$

MHT CET 2024 15th May Morning Shift

MCQ (Single Correct Answer)

-0

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

$\mathrm{f}(x)$ is decreasing in $(-\infty, 10]$ and increasing in $[10, \infty)$

$f(x)$ is increasing in $(-\infty, 10]$ and decreasing in $[10, \infty)$

$\mathrm{f}(x)$ is increasing throughout real line

$\mathrm{f}(x)$ is decreasing throughout real line

MHT CET 2024 15th May Morning Shift

MCQ (Single Correct Answer)

-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

12.5

MHT CET 2024 15th May Morning Shift

MCQ (Single Correct Answer)

-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?

$\frac{4}{3} \mathrm{~m} / \mathrm{sec}$

$\frac{2}{3} \mathrm{~m} / \mathrm{sec}$

$\frac{5}{3} \mathrm{~m} / \mathrm{sec}$

$\frac{8}{3} \mathrm{~m} / \mathrm{sec}$

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