A charge particle of $$2 ~\mu \mathrm{C}$$ accelerated by a potential difference of $$100 \mathrm{~V}$$ enters a region of uniform magnetic field of magnitude $$4 ~\mathrm{mT}$$ at right angle to the direction of field. The charge particle completes semicircle of radius $$3 \mathrm{~cm}$$ inside magnetic field. The mass of the charge particle is __________ $$\times 10^{-18} \mathrm{~kg}$$

A light of energy $$12.75 ~\mathrm{eV}$$ is incident on a hydrogen atom in its ground state. The atom absorbs the radiation and reaches to one of its excited states. The angular momentum of the atom in the excited state is $$\frac{x}{\pi} \times 10^{-17} ~\mathrm{eVs}$$. The value of $$x$$ is ___________ (use $$h=4.14 \times 10^{-15} ~\mathrm{eVs}, c=3 \times 10^{8} \mathrm{~ms}^{-1}$$ ).

A thin cylindrical rod of length $$10 \mathrm{~cm}$$ is placed horizontally on the principle axis of a concave mirror of focal length $$20 \mathrm{~cm}$$. The rod is placed in a such a way that mid point of the rod is at $$40 \mathrm{~cm}$$ from the pole of mirror. The length of the image formed by the mirror will be $$\frac{x}{3} \mathrm{~cm}$$. The value of $$x$$ is _____________.

A small particle moves to position $$5 \hat{i}-2 \hat{j}+\hat{k}$$ from its initial position $$2 \hat{i}+3 \hat{j}-4 \hat{k}$$ under the action of force $$5 \hat{i}+2 \hat{j}+7 \hat{k} \mathrm{~N}$$. The value of work done will be __________ J.