The ratio of powers of two motors is $$\frac{3 \sqrt{x}}{\sqrt{x}+1}$$, that are capable of raising $$300 \mathrm{~kg}$$ water in 5 minutes and $$50 \mathrm{~kg}$$ water in 2 minutes respectively from a well of $$100 \mathrm{~m}$$ deep. The value of $$x$$ will be

Two bodies are having kinetic energies in the ratio 16 : 9. If they have same linear momentum, the ratio of their masses respectively is :

When a resistance of $$5 ~\Omega$$ is shunted with a moving coil galvanometer, it shows a full scale deflection for a current of $$250 \mathrm{~mA}$$, however when $$1050 ~\Omega$$ resistance is connected with it in series, it gives full scale deflection for 25 volt. The resistance of galvanometer is ____________ $$\Omega$$.

A fish rising vertically upward with a uniform velocity of $$8 \mathrm{~ms}^{-1}$$, observes that a bird is diving vertically downward towards the fish with the velocity of $$12 \mathrm{~ms}^{-1}$$. If the refractive index of water is $$\frac{4}{3}$$, then the actual velocity of the diving bird to pick the fish, will be __________ $$\mathrm{ms}^{-1}$$.