If the co-efficient of x⁷ and x⁸ in the expansion of $${\left( {2 + {x \over 3}} \right)^n}$$ are equal, then the value of n is equal to _____________.

The relation between time t and distance x for a moving body is given as t = mx² + nx, where m and n are constants. The retardation of the motion is : (When v stands for velocity)

In a simple harmonic oscillation, what fraction of total mechanical energy is in the form of kinetic energy, when the particle is midway between mean and extreme position.

A force $$\overrightarrow F = (40\widehat i + 10\widehat j)N$$ acts on a body of mass 5 kg. If the body starts from rest, its position vector $$\overrightarrow r $$ at time t = 10 s, will be :