Three vectors $$\overrightarrow{\mathrm{OP}}, \overrightarrow{\mathrm{OQ}}$$ and $$\overrightarrow{\mathrm{OR}}$$ each of magnitude $$\mathrm{A}$$ are acting as shown in figure. The resultant of the three vectors is $$\mathrm{A} \sqrt{x}$$. The value of $$x$$ is _________.

A square loop PQRS having 10 turns, area $$3.6 \times 10^{-3} \mathrm{~m}^2$$ and resistance $$100 \Omega$$ is slowly and uniformly being pulled out of a uniform magnetic field of magnitude $$\mathrm{B}=0.5 \mathrm{~T}$$ as shown. Work done in pulling the loop out of the field in $$1.0 \mathrm{~s}$$ is _________ $$\times 10^{-6} \mathrm{~J}$$.

A liquid column of height $$0.04 \mathrm{~cm}$$ balances excess pressure of a soap bubble of certain radius. If density of liquid is $$8 \times 10^3 \mathrm{~kg} \mathrm{~m}^{-3}$$ and surface tension of soap solution is $$0.28 \mathrm{~Nm}^{-1}$$, then diameter of the soap bubble is __________ $$\mathrm{cm}$$. (if $$\mathrm{g}=10 \mathrm{~m} \mathrm{~s}^{-2}$$ )

A uniform thin metal plate of mass $$10 \mathrm{~kg}$$ with dimensions is shown. The ratio of $$\mathrm{x}$$ and y coordinates of center of mass of plate in $$\frac{n}{9}$$. The value of $$n$$ is ________.