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 __________.

In Young's double slit experiment, carried out with light of wavelength $$5000~\mathop A\limits^o$$, the distance between the slits is $$0.3 \mathrm{~mm}$$ and the screen is at $$200 \mathrm{~cm}$$ from the slits. The central maximum is at $$x=0 \mathrm{~cm}$$. The value of $$x$$ for third maxima is __________ $$\mathrm{mm}$$.

A 2A current carrying straight metal wire of resistance $$1 \Omega$$, resistivity $$2 \times 10^{-6} \Omega \mathrm{m}$$, area of cross-section $$10 \mathrm{~mm}^2$$ and mass $$500 \mathrm{~g}$$ is suspended horizontally in mid air by applying a uniform magnetic field $$\vec{B}$$. The magnitude of B is ________ $$\times 10^{-1} \mathrm{~T}$$ (given, $$\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2$$).