The maximum height is reached in $5$ seconds by a stone thrown vertically upwards and moving under the equation $10s = 10ut - 49t^2$,where $s$ is in metres and $t$ is in seconds. The value of $u$ is ........ $m/sec$.

$A$ horse runs along a circle with a speed of $20 \, km/hr$. $A$ lantern is at the centre of the circle. $A$ fence is along the tangent to the circle at the point at which the horse starts. The speed with which the shadow of the horse moves along the fence at the moment when it covers $1/8$ of the circle is (in $km/hr$):

If $pv = 81$,then $\frac{dp}{dv}$ at $v = 9$ is equal to

The equation of motion of a particle moving along a straight line is $s = 2t^3 - 9t^2 + 12t$,where the units of $s$ and $t$ are $cm$ and $sec$. The acceleration of the particle will be zero after:

The rate of change of the area of a circle with respect to its radius $r$ at $r = 2 \text{ cm}$ is:

The displacement $x$ of a particle at time $t$ is given by $x = At^2 + Bt + C$, where $A, B, C$ are constants and $v$ is the velocity of the particle. Then the value of $4Ax - v^2$ is: