If $\left[\begin{array}{rrr}1 & 2 & x \\ 4 & -1 & 7 \\ 2 & 4 & -6\end{array}\right]$ is a singular matrix,then $x$ is equal to

The least count of a stopwatch is $\frac{1}{5} \, s$. The time of $20$ oscillations of a pendulum is measured to be $25 \, s$. The maximum percentage error in the measurement of time will be ..... $\%$

Two spheres of equal masses,one of which is a thin spherical shell and the other a solid sphere,have the same moment of inertia about their respective diameters. The ratio of their radii will be

Two liquids $A$ and $B$ have $P_A^o$ and $P_B^o$ in the ratio of $1 : 3$ and the ratio of number of moles of $A$ and $B$ in the liquid phase are $1 : 3$. The mole fraction of $A$ in the vapour phase in equilibrium with the solution is equal to:

The force constant of a wire is $k$ and that of another wire is $2k$. When both the wires are stretched through the same distance,then the work done is:

The surface of a metal is illuminated with light of wavelength $400 \, nm$. The kinetic energy of the ejected photoelectrons is found to be $1.68 \, eV$. The work function of the metal is .................. $eV$ $(hc = 1240 \, eV-nm)$.