Suppose $A$ and $B$ are two points on the line $2x-y+3=0$ and $P(1,2)$ is a point such that $PA=PB$. Then,the mid-point of $AB$ is

An ideal gas of mass $m$ in a state $A$ goes to another state $B$ via three different processes as shown in the figure. If ${Q_1}, {Q_2}$ and ${Q_3}$ denote the heat absorbed by the gas along the three paths,then

$A$ circular disc of radius $R$ is removed from a bigger circular disc of radius $2R$ such that the circumferences of the discs touch. The centre of mass of the new disc is at a distance $\alpha R$ from the centre of the bigger disc. The value of $\alpha$ is

Zero growth means:

$Ge$ and $Si$ diodes conduct at $0.3\,V$ and $0.7\,V$ respectively. In the following figure,if the $Ge$ diode connection is reversed,the value of $V_0$ changes by.....$V$.

$A$ musical instrument $P$ produces sound waves of frequency $n$ and amplitude $A_P$. Another musical instrument $Q$ produces sound waves of frequency $\frac{n}{4}$. The waves produced by $P$ and $Q$ have equal energies. If the amplitude of waves produced by $P$ is $A_P$,the amplitude of waves produced by $Q$ will be: (in $A_P$)