The number of electric lines that emerge from a finite charge $+q$ is _____

Two balls of charge \(q_1\) and \(q_2\) initially have a velocity of the same magnitude and direction. After a uniform electric field has been applied during a certain time, the direction of the velocity of the first ball changes by \(60^{\circ}\), and the velocity magnitude is reduced by half. The direction of the velocity of the second ball changes thereby by \(90^{\circ}\).
In what proportion will the velocity of the second ball change? Determine the magnitude of the charge-to-mass ratio for the second ball if it is equal to \(k_1\) for the first ball. The electrostatic interaction between the balls should be neglected.

When the temperature of a body increases from \(T\) to \(T+\Delta T\), its moment of inertia increases from \(I\) to \(I+\Delta I\). If \(\alpha\) is the coefficient of linear expansion of the material of the body, then \(\frac{\Delta I}{I}\) is (neglect higher orders of \(\alpha\) )

In an experiment on photoelectric emission from a metallic surface, wavelength of incident light is \(2 \times 10^{-7} \mathrm{~m}\) and stopping potential is \(2.5 \mathrm{~V}\). The threshold frequency of the metal (in \(\mathrm{Hz}\) ) approximately (charge of electron \(e=1.6 \times 10^{-19} \mathrm{C}\), Planck's constant \(\left.h=6.6 \times 10^{-34} \mathrm{~J}-\mathrm{s}\right)\)

If the ratio of amplitudes of two interfering waves is \(4: 3\), then the ratio of maximum and minimum intensity is

The masses of neutron, proton and deutron in amu are 1.00893, 1.00813 and 2.01473, respectively. The packing fraction of the deutron in amu is

A bomb at rest explodes into three parts of equal mass. If the momentum of two parts are \(-2 p \hat{\mathbf{i}}\) and \(p \hat{\mathbf{j}}\), find the magnitude of momentum of the third part.

The locus of the variable point \(\mathrm{z}=\mathrm{x}+\mathrm{iy}\) whose amplitude is always equal to \(\theta\), is

The temperature of a body is measured both in \({ }^{\circ} \mathrm{C}\) and \({ }^{\circ} \mathrm{F}\). A graph is plotted with \({ }^{\circ} \mathrm{F}\) on \(X\)-axis and \({ }^{\circ} \mathrm{C}\) on \(Y\)-axis. Then, the cosine of angle between the graph and the \(X\)-axis is

The area (in sq units) of the region bounded by \(x=-1, x=2, y=x^2+1\) and \(y=2 x-2\) is

The correct order of decomposition temperature of \(\mathrm{MgCO}_3\) \((\mathrm{X}) . \mathrm{BaCO}_3(\mathrm{Y}), \mathrm{CaCO}_3(\mathrm{Z})\) is

\(X_2\) is used in the refining of Ti metal by van Arkel method. \(Y_2\) does not liberate \(\mathrm{O}_2\) from water and does not form \(\mathrm{HY}\) and \(\mathrm{HOY}\) with water. \(X_2\) and \(Y_2\) are respectively

The center of ellipse \(x^2+2 y^2-4 x+12 y+14=0\) is