A gear train shown in the figure consists of gears P, Q, R and S. Gear Q and gear R are mounted on the same shaft. All the gears are mounted on parallel shafts and the number of teeth of P, Q, R and S are 24, 45, 30 and 80, respectively. Gear P is rotating at 400 rpm. The speed (in rpm) of the gear S is _________ .

A mass $$m$$ is attached to two identical springs having spring constant $$k$$ as shown in the figure. The natural frequency of this single degree of freedom system is

The radius of gyration of a compound pendulum about the point of suspension is $$100$$ mm. The distance between the point of suspension and the centre of mass is $$250$$ mm. Considering the acceleration due to gravity as $$9.81$$ m/s², the natural frequency (in radian/s) of the compound pendulum is _________.

In the Rankine cycle for a system power plant the turbine entry and exit enthalpies are $$2803$$ $$kJ/kg$$ and $$1800$$ $$kJ/kg$$, respectively. The enthalpies of water at pump entry and exit are $$121$$ $$kJ/kg$$ and $$124$$ $$kJ/kg,$$ respectively. The specific steam consumption (in $$kg/kW.h$$) of the cycle is __________.