In an experiment to find \(emf\) of a cell using potentiometer, the length of null point for a cell of emf \(1.5\,V\) is found to be \(60\,cm\). If this cell is replaced by another cell of \(emf\; E\). the length-of null point increases by \(40\,cm\). The value of \(E\) is \(\frac{x}{10} V\). The value of \(x\) is \(............\)

The two thin coaxial rings, each of radius \('a'\) and having charges \(+{Q}\) and \(-{Q}\) respectively are separated by a distance of \('s'.\) The potential difference between the centres of the two rings is :

An electron, a proton and an alpha particle having the same kinetic energy are moving in circular orbits of radii \(r_e,r_p\) and \({r_\alpha }\) respectively in a uniform magnetic field \(B\). The relation between \(r_e,r_p\) and \(\;{r_\alpha }\) is

For three low density gases \(A, B, C\) pressure versus temperature graphs are plotted while keeping them at constant volume, as shown in the figure. The temperature corresponding to the point ' \(K\) ' is \(...........\,{}^{\circ}\,C\)

For extrinsic semiconductors; when doping level is increased;

Match the LIST-I with LIST-II.

LIST-I	LIST-II
(A) \(_0^1n + _{92}^{235}U \rightarrow _{54}^{140}Xe + _{38}^{94}Sr + 2_0^1n\)	(I) Chemical reaction
(B) \(2H_2 + O_2 \rightarrow 2H_2O\)	(II) Fusion with +ve Q value
(C) \(_1^2H + _1^2H \rightarrow _2^3He + _0^1n\)	(III) Fission
(D) \(_1^1H + _1^3H \rightarrow _1^2H + _1^2H\)	(IV) Fusion with -ve Q value

Choose the correct answer from the options given below :

A tennis ball (treated as hollow spherical shell) starting from \(O\) rolls down a hill. At point \(A\) the ball becomes air borne leaving at an angle of \(30^o\) with the horizontal. The ball strikes the ground at \(B\). What is the value of the distance \(AB\) ? (Moment of inertia of a spherical shell of mass \(m\) and radius \(R\) about its diameter .......... \(m\). \(= \frac {2}{3}\,mR^2\))

Given below are two statements : Statement-I: When a capillary tube is dipped into a liquid, the liquid neither rises nor falls in the capillary. The contact angle may be \(0^{\circ}\). Statement-II: The contact angle between a solid and a liquid is a property of the material of the solid and liquid as well : In the light of above statement, choose the correct answer from the options given below.

In the experimental setup of meter bridge shown in the figure, the null point is obtained at a distance of \(40\,cm\) from \(A\). If a \(10\,\Omega \) resistor is connected in series with \(R_1\), the null point shifts by \(10\,cm\). The resistance that should be connected in parallel with \(\left( {{R_1} + 10} \right)\,\Omega \) such that the null point shifts back to its initial position is .............. \(\Omega\)

The total number of turns and cross-section area in solenoid is fixed. However, its length \(L\) is varied by adjusting the separation between windings. The inductance of solenoid will be proportional to

Water flows into a large tank with flat bottom at the rate of \({10^{ - 4}}\,{m^3}{s^{ - 1}}\). Water is also leaking out of a hole of area \(1\, cm^2\) at its bottom. If the height of the water in the tank remains steady, then this height is........ \(cm\)