If the lines $${{x - 2} \over 1} = {{y - 3} \over 1} = {{z - 4} \over { - k}}$$ and $${{x - 1} \over k} = {{y - 4} \over 2} = {{z - 5} \over 1}$$ are coplanar, then $$k$$ can have :

Diameter of a plano-convex lens is $$6$$ $$cm$$ and thickness at the center is $$3mm$$. If speed of light in material of lens is $$2 \times {10^8}\,m/s,$$ the focal length of the lens is

A diode detector is used to detect an amplitude modulated wave of $$60\% $$ modulation by using a condenser of capacity $$250$$ picofarad in parallel with a load resistance $$100$$ kilo $$ohm.$$ Find the maximum modulated frequency which could be detected by it.

In a hydrogen like atom electron make transition from an energy level with quantum number $$n$$ to another with quantum number $$\left( {n - 1} \right)$$. If $$n > > 1,$$ the frequency of radiation emitted is proportional to :