In this figure the resistance of the coil of galvanometer \(G\) is \(2\,\Omega\). The emf of the cell is \(4\,V\). The ratio of potential difference across \(C_1\) and \(C_2\) is:

The work functions of Aluminium and Gold are \(4.1\,eV\) and \(5.1\,eV\) respectively. The ratio of the slope of the stopping potential versus frequency plot for Gold to that of Aluminium is \(.......\)

A plane electromagnetic wave of frequency \(35\  \mathrm{MHz}\) travels in free space along the \(\mathrm{X}\)-direction. At a particular point (in space and time) \(\overrightarrow{\mathrm{E}}=9.6\  \hat{\mathrm{j}} \mathrm{V} / \mathrm{m}\). The value of magnetic field at this point is _______.

Given below are two statements Statement \(-I\) : A point charge is brought in an electric field. The value of electric field at a point near to the charge may increase if the charge is positive. Statement \(-II\) : An electric dipole is placed in a non-uniform electric field. The net electric force on the dipole will not be zero. Choose the correct answer from the options given below 

Three point particles of masses \(1.0\; \mathrm{kg} .1 .5 \;\mathrm{kg}\) and \(2.5\; kg\) are placed at three comers of a right angle triangle of sides \(4.0\; \mathrm{cm}, 3.0 \;\mathrm{cm}\) and \(5.0\; \mathrm{cm}\) as shown in the figure. The center of mass of the system is at a point

If \(K_{1}\) and \(K_{2}\) are the thermal conductivities \(L_{1}\) and \(L _{2}\) are the lengths and \(A _{1}\) and \(A _{2}\) are the cross sectional areas of steel and copper rods respectively such that \(\frac{K_{2}}{K_{1}}=9, \frac{A_{1}}{A_{2}}=2, \frac{L_{1}}{L_{2}}=2\). Then, for the arrangement as shown in the figure. The value of temperature \(T\) of the steel - copper junction in the steady state will be ........... \(^{\circ} C\)

The half life period of radioactive element \({x}\) is same as the mean life time of another radioactive element \(y.\) Initially they have the same number of atoms. Then:

A car covers \(A B\) distance with first one-third at velocity \(v _{1} ms ^{-1}\), second one-third at \(v _{2} ms ^{-1}\) and last one-third at \(v _{3} ms ^{-1}\). If \(v _{3}=3 v _{1}, v _{2}=2 v _{1}\) and \(v _{1}=11\,ms ^{-1}\) then the average velocity of the car is________ \(ms ^{-1} .\)

The point \(A\) moves with a uniform speed along the circumference of a circle of radius \(0.36\, m\) and covers \(30^{\circ}\) in \(0.1\, s\). The perpendicular projection \('P'\) from \('A'\) on the diameter \(MN\) represents the simple harmonic motion of \('P'.\) The restoration force per unit mass when \(P\) touches \(M\) will be ...... \(N\)

A given object takes \(n\) times the time to slide down \(45^{\circ}\) rough inclined plane as it takes the time to slide down an identical perfectly smooth \(45^{\circ}\) inclined plane. The coefficient of kinetic friction between the object and the surface of inclined plane is _______.