In the experiment to determine the galvanometer resistance by half-deflection method, the plot of $$1 / \theta$$ vs the resistance (R) of the resistance box is shown in the figure. The figure of merit of the galvanometer is _________ $$\times 10^{-1} \mathrm{~A} /$$ division. [The source has emf $$2 \mathrm{~V}$$]

The density and breaking stress of a wire are $$6 \times 10^4 \mathrm{~kg} / \mathrm{m}^3$$ and $$1.2 \times 10^8 \mathrm{~N} / \mathrm{m}^2$$ respectively. The wire is suspended from a rigid support on a planet where acceleration due to gravity is $$\frac{1}{3}^{\text {rd }}$$ of the value on the surface of earth. The maximum length of the wire with breaking is _______ $$\mathrm{m}$$ (take, $$\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2$$).

An ac source is connected in given series LCR circuit. The rms potential difference across the capacitor of $$20 \mu \mathrm{F}$$ is __________ V.

A body moves on a frictionless plane starting from rest. If $$\mathrm{S_n}$$ is distance moved between $$\mathrm{t=n-1}$$ and $$\mathrm{t}=\mathrm{n}$$ and $$\mathrm{S}_{\mathrm{n}-1}$$ is distance moved between $$\mathrm{t}=\mathrm{n}-2$$ and $$\mathrm{t}=\mathrm{n}-1$$, then the ratio $$\frac{\mathrm{S}_{\mathrm{n}-1}}{\mathrm{~S}_{\mathrm{n}}}$$ is $$\left(1-\frac{2}{x}\right)$$ for $$\mathrm{n}=10$$. The value of $$x$$ is __________.