The sides of an equilateral triangle are increasing at the rate of $2 \, cm/sec$. The rate at which the area increases,when the side is $10 \, cm$ is:

$A$ closed conical vessel is filled with water fully and is placed with its vertex down. The water is let out at a constant speed. After $21 \, min$,it was found that the height of the water column is half of the original height. How much more time in minutes does it require to empty the vessel?

If the sides of a triangle vary slightly in such a way that its circumradius remains constant,then $\frac{da}{\cos A} + \frac{db}{\cos B} + \frac{dc}{\cos C}$ is equal to

$OA$ and $OB$ are two roads enclosing an angle of $120^{\circ}$. $X$ and $Y$ start from '$O$' at the same time. $X$ travels along $OA$ with a speed of $4 \text{ km/h}$ and $Y$ travels along $OB$ with a speed of $3 \text{ km/h}$. The rate at which the shortest distance between $X$ and $Y$ is increasing after $1 \text{ h}$ is

If a metallic circular plate of radius $50 \, cm$ is heated so that its radius increases at the rate of $1 \, mm$ per hour,then the rate at which the area of the plate increases (in $cm^2/hour$) is (in $\pi$)

The equation of motion of a particle is $s = at^2 + bt + c$. If the displacement after $1 \text{ s}$ is $20 \text{ m}$,velocity after $2 \text{ s}$ is $30 \text{ m/s}$,and the acceleration is $10 \text{ m/s}^2$,then: