$A$ man $2 \, m$ high walks at a uniform speed of $5 \, m/h$ away from a lamp post $6 \, m$ high. The rate at which the length of his shadow increases is

$A$ tank in the shape of a rectangular parallelepiped has a volume of $27 \ m^3$. This tank is filled with water such that the rate of change of the water level is thrice the rate of change of the water quantity falling into the tank. The height of the tank (in meters) is:

The distance travelled by a particle moving in a straight line in time $t$ is $s = \sqrt{at^2 + bt + c}$. The acceleration of the particle is

If the rate of change of $x$ is more than the rate of change of $y$ on the curve $x^3 = 12y$ for $x > 0$,then $x$ lies in the interval:

The displacement of a particle in time $t$ is given by $s = 2t^2 - 3t + 1$. The acceleration is

If a particle moves such that the displacement $s$ is proportional to the square of the velocity $v$ acquired,then its acceleration is