\(n\) identical waves each of intensity \(I_0\) interfere with each other. The ratio of maximum intensities if the interference is \((i)\) coherent and \((ii)\) incoherent is :

A Zener diode of breakdown voltage \(10 \mathrm{~V}\) is used as a voltage regulator as shown in the figure. The current through the Zener diode is _______.

The electron in a hydrogen atom first jumps from the third excited state to the second excited state and subsequently to the first excited state. The ratio of the respective wavelengths, \(\lambda _1/\lambda _2\), of the photons emitted in this process is

A wire of resistance \(R\) and radius \(r\) is stretched till its radius became \(r / 2\). If new resistance of the stretched wire is \(xR\), then value of \(x\) is _______.

A coaxial cable consists of an inner wire of radius \('a'\) surrounded by an outer shell of inner and outer radii ' \({b}\) ' and '\(c\)' respectively. The inner wire carries an electric current is, which is distributed uniformly across cross-sectional area. The outer shell carries an equal current in opposite direction and distributed uniformly. What will be the ratio of the magnetic field at a distance \({x}\) from the axis when \((i)\) \({x}<{a}\) and \((ii)\) \({a}<{x}<{b}\) ?

Take the mean distance of the moon and the sun from the earth to be \(0.4 \times 10^6\,km\) and \(150 \times 10^6\,km\) respectively. Their masses are \(8 \times 10^{22}\, kg\) and \(2 \times 10^{30}\, kg\) respectively. The radius of the earth is \(6400\, km\). Let \(\Delta {F_1}\) be the difference in the forces exerted by the moon at the nearest and farthest points on the earth and \(\Delta {F_2}\) be the difference in the force exerted by the sun at the nearest and farthest points on the earth. Then, the number closest to \(\frac{{\Delta {F_1}}}{{\Delta {F_2}}}\) is

Match List\(-I\) with List\(-II\).

List\(-I\)	List\(-II\)
\((A)\) Angular momentum	\((I)\) \(\left[ ML ^2 T ^{-2}\right]\)
\((B)\) Torque	\((II)\) \(\left[ ML ^{-2} T ^{-2}\right]\)
\((C)\) Stress	\((III)\) \(\left[ ML ^2 T ^{-1}\right]\)
\((D)\) Pressure gradient	\((IV)\) \(\left[ ML ^{-1} T ^{-2}\right]\)

Choose the correct answer from the options given below:

For a short dipole placed at origin \(O\), the dipole moment \(P\) is along \(x\)-axis, as shown in the figure. If the electric potential and electric field at A are \(\mathrm{V}_0\) and \(\mathrm{E}_0\), respectively, then the correct combination of the electric potential and electric field, respectively, at point \(B\) on the \(y\)-axis is given by...

If momentum \((P),\) area \((A)\) and time \((T)\) are taken to be the fundamental quantities then the dimensional formula for energy is :

For a given gas at \(1\,atm\) pressure, \(rms\) speed of the molecules is \(200\,m/s\) at \(127\,^oC.\) At \(2\,atm\) pressure and at \(227\,^oC,\) the \(rms\) speed of the molecules will be

Suppose you have taken a dilute solution of oleic acid in such a way that its concentration becomes \(0.01 \,cm ^{3}\) of oleic acid per \(cm ^{3}\) of the solution. Then you make a thin film of this solution (monomolecular thickness) of area \(4\, cm ^{2}\) by considering \(100\) spherical drops of radius \(\left(\frac{3}{40 \pi}\right)^{\frac{1}{3}} \times 10^{-3}\, cm .\) Then the thickness of oleic acid layer will be \(x \times 10^{-14} \,m\). Where \(x\) is ...... .

Figure shows a circuit that contains four identical resistors with resistance \(R =2.0\, \Omega,\) two identical inductors with inductance \(L =2.0 \,mH\) and an ideal battery with \(e m f E =9 \,V .\) The current \('i'\) just after the switch \('S'\) is closed will be .... \(A\)

In an experiment, a small steel ball falls through a Iiquid at a constant speed of \(10\, cm/s\). If the steel ball is pulled upward with a force equal to twice its effective weight, how fast will it move upward ? ......... \(cm/s\)