In a quadrilateral $ABCD$,the point $P$ divides $DC$ in the ratio $1:2$ and $Q$ is the midpoint of $AC$. If $\overrightarrow{AB}+2\overrightarrow{AD}+\overrightarrow{BC}-2\overrightarrow{DC}=k\overrightarrow{PQ}$,then $k$ is equal to

In the following circuit,find $i_1$ and $i_2$.

The coefficient of apparent expansion of a liquid when determined using two different vessels $A$ and $B$ are $\gamma_1$ and $\gamma_2$ respectively. If the coefficient of linear expansion of vessel $A$ is $\alpha$,the coefficient of linear expansion of vessel $B$ is

In a mass spectrometer used for measuring the masses of ions,the ions are initially accelerated by an electric potential $V$ and then made to describe semicircular paths of radius $R$ using a magnetic field $B$. If $V$ and $B$ are kept constant,the ratio $\left( \frac{\text{charge on the ion}}{\text{mass of the ion}} \right)$ will be proportional to

While a collector to emitter voltage is constant in a transistor,the collector current changes by $8.2 ~mA$ when the emitter current changes by $8.3 ~mA$. The value of forward current ratio is

Assertion : Between any two given energy levels,the number of absorption transitions is always less than the number of emission transitions.
Reason : Absorption transitions start from the lowest energy level only and may end at any higher energy level. But emission transitions may start from any higher energy level and end at any energy level below it.