At a certain instant, a stationary transverse wave is found to have maximum kinetic energy. The appearance of the string at that instant is:

An ideal gas expands isothermally from a volume $V_1$ to $V_2$ and is then compressed to the original volume $V_1$ adiabatically. The initial pressure is $P_1$ and the final pressure is $P_3$. If the total work done is $W$,then:

Consider a solid insulating sphere of radius $R$ with charge density varying as $\rho = \rho_0 r^2$ (where $\rho_0$ is a constant and $r$ is measured from the centre). Consider two points $A$ and $B$ at distances $x$ and $y$ respectively from the centre,such that $x < R$ and $y > R$. If the magnitudes of the electric fields at points $A$ and $B$ are equal,then:

In how many ways can $3$ letters be posted in $4$ letter-boxes,if all the letters are not posted in the same letter-box?

A $6 \, V$ cell with $0.5 \, \Omega$ internal resistance, a $10 \, V$ cell with $1 \, \Omega$ internal resistance and a $12 \, \Omega$ external resistance are connected in parallel. The current (in ampere) through the $10 \, V$ cell is

Which of the following elements has the least number of electrons in its $M$ shell?