The current in the following circuit is

A particle of mass '$$m$$' collides with another stationary particle of mass '$$M$$'. A particle of mass '$$\mathrm{m}$$' stops just after collision. The coefficient of restitution is

An air filled parallel plate capacitor has a capacity $$2 \mathrm{~pF}$$. The sepeartion of the plates is doubled and the interspace between the plates is filled with dielectric material, then the capacity is increased to $$6 ~\mathrm{pF}$$. The dielectric constant of the material is

A black body has maximum wavelength '$$\lambda_{\mathrm{m}}$$' at temperature $$2000 \mathrm{~K}$$. Its corresponding wavelength at temperature $$3000 \mathrm{~K}$$ will be