A parallel plate capacitor with plate separation \(5\) \(\mathrm{mm}\) is charged up by a battery. It is found that on introducing a dielectric sheet of thickness \(2 \mathrm{~mm}\), while keeping the battery connections intact, the capacitor draws \(25 \%\) more charge from the battery than before. The dielectric constant of the sheet is _______.

The surface of a metal is illuminated altemately with photons of energies \(E _{1}=4\, eV\) and \(E _{2}=2.5\, eV\) respectively. The ratio of maximum speeds of the photoelectrons emitted in the two cases is \(2 .\) The work function of the metal in \(( eV )\) is\(......ev\)

At room temperature \(\left(27^{\circ} \mathrm{C}\right)\), the resistance of a heating element is \(50 \Omega\). The temperature coefficient of the material is \(2.4 \times 10^{-4}{ }^{\circ} \mathrm{C}^1\). The temperature of the element, when its resistance is \(62 \Omega\) is _______ \({ }^{\circ} \mathrm{C}\).

The maximum vertical height to which a man can throw a ball is \(136\,m\). The maximum horizontal distance upto which he can throw the same ball is \(.....\,m\)

Two factories are sounding their sirens at \(800\, Hz\) . A man goes from one factory to other at a speed of \(2\,m/s\). The velocity of sound is \(320\, m/s\). The number of beats heard by the person in one second will be

A potentiometer \(PQ\) is set up to compare two resistances as shown in the figure. The ameter \(A\) in the circuit reads \(1.0\, A\) when two way key \(K_3\) is open. The balance point is at a length \(l_1\, cm\) from \(P\) when two way key \(K_3\) is plugged in between \(2\) and \(1\) , while the balance point is at a length \(l_2\, cm\) from \(P\) when key \(K_3\) is plugged in between \(3\) and \(1\) . The ratio of two resistances \(\frac{{{R_1}}}{{{R_2}}}\) is found to be

A car is moving with speed of \(150\,km / h\) and after applying the brake it will move \(27\,m\) before it stops. If the same car is moving with a speed of one third the reported speed then it will stop after travelling \(....m\) distance.

The relative error in the determination of the surface area of a sphere is \(\alpha \). Then the relative error in the determination of its volume is

Two trains ' \(A\) ' and ' \(B\) ' of length ' \(l\) ' and ' \(4 l\) ' are travelling into a tunnel of length ' \(L\) ' in parallel tracks from opposite directions with velocities \(108\,km / h\) and \(72\,km / h\), respectively. If train '\(A\)' takes \(35\,s\) less time than train ' \(B\) ' to cross the tunnel then, length ' \(L\) ' of tunnel is \(...........\,m\) \(\text { (Given } L=60 l \text { ) }\)

A galvanometer with its coil resistance \(25\,\Omega \) requires a current of  \(1\,mA\)  for its full deflection. In order to construct an ammeter to read up to a current of \(2\,A,\)  the approximate value of the shunt resistance should be

Two charges of \(-4 \ \mu \mathrm{C}\) and \(+4\  \mu \mathrm{C}\) are placed at the points \(A(1,0,4) \mathrm{m}\) and \(B(2,-1,5) \mathrm{m}\) located in an electric field \(\vec{E}=0.20 \hat{\mathrm{i}} \mathrm{V} / \mathrm{cm}\). The magnitude of the torque acting on the dipole is \(8 \sqrt{\alpha} \times 10^{-3} \mathrm{Nm}\), Where \(\alpha=\)___________

A physical quantity \(Q\) is found to depend on quantities \(a, b, c\) by the relation \(Q=\frac{a^4 b^3}{c^2}\). The percentage error in \(a\), \(b\) and \(c\) are \(3 \%, 4 \%\) and \(5 \%\) respectively. Then, the percentage error in \(\mathrm{Q}\) is _______.

In the circuit shown below, maximum zener diode current will be \(.....mA\)