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 __________ $$\mathrm{ms}^{-1}$$.

The radius of $$2^{\text {nd }}$$ orbit of $$\mathrm{He}^{+}$$ of Bohr's model is $$r_{1}$$ and that of fourth orbit of $$\mathrm{Be}^{3+}$$ is represented as $$r_{2}$$. Now the ratio $$\frac{r_{2}}{r_{1}}$$ is $$x: 1$$. The value of $$x$$ is ___________.

A potential $$\mathrm{V}_{0}$$ is applied across a uniform wire of resistance $$R$$. The power dissipation is $$P_{1}$$. The wire is then cut into two equal halves and a potential of $$V_{0}$$ is applied across the length of each half. The total power dissipation across two wires is $$P_{2}$$. The ratio $$P_{2}: \mathrm{P}_{1}$$ is $$\sqrt{x}: 1$$. The value of $$x$$ is ___________.