A machine gun fires n bullets per second and the mass of each bullet is m. If v is the speed of each bullet, then the force exerted on the machine gun is:

Force is calculated by dividing the change in momentum by the change in time.
Assuming the bullet's initial velocity is u=0 and its final velocity is v

Therefore,

A single bullet's change in momentum is: $\Delta P_1$
Therefore, a change in momentum equals: $\Delta P_1=mv-0=mv$
The number of shots fired in one second is n.
As a result, the bullets' change in momentum in a second equals: $\Delta P=n\Delta P_1=mnv$
Therefore,
based on how speed is defined.
The machine gun experiences equivalent force to; $F=\frac{\Delta P}{\Delta t}$
On entering the data we obtain.
$F=\frac{mnv}{1}=mnv$

Hence, the correct answer is option A.