Two resistors \(2 \Omega\) and \(3 \Omega\) are connected in the gaps of bridge as shown in figure. The null point is obtained with the contact of jockey at some point on wire XY . When an unknown resistor is connected in parallel with \(3 \Omega\) resistor, the null point is shifted by 22.5 cm toward Y . The resistance of unknown resistor is _________ \(\Omega\).

A cylinder with fixed capacity of \(67.2\, lit\) contains helium gas at \(STP\). The amount of heat needed to raise the temperature of the gas by \(20\,^oC\) is ..... \(J\) [Given that \(R = 8.31\, J\, mol^{-1}\, K^{-1}\)]

If \(X\) and \(Y\) are the inputs, the given circuit works as _______.

Considering the Bohr model of hydrogen like atoms, the ratio of the ratio of the radius \(5^{\text {th}}\) orbit of the electron in \(\mathrm{Li}^{2+}\) and \(\mathrm{He}^{+}\) is _______.

A uniform rectangular thin sheet \(ABCD\) of mass \(M\) has length \(a\) and breadth \(b\), as shown in the figure. If the shaded portion \(HBGO\) is cut off, the coordinates of the centre of mass of the remaining portion will be

In an electrical circuit, a battery is connected to pass \(20\, C\) of charge through it in a certain given time. The potential difference between two plates of the battery is maintained at \(15\, V\). The work done by the battery is ........... \(J\).

As shown in the figure, two infinitely long, identical wires are bent by \(90^o\) and placed in such a way that the segments \(LP\) and \(QM\) are along the \(x-\) axis, while segments \(PS\) and \(QN\) are parallel to the \(y-\) axis. If \(OP = OQ = 4\, cm\), and the magnitude of the magnetic field at \(O\) is \(10^{-4}\, T\), and the two wires carry equal current (see figure), the magnitude of the current in each wire and the direction of the magnetic field at \(O\) will be \((\mu_ 0 = 4\pi \times10^{-7}\, NA^{-2})\)

A galvanometer has a \(50\) \(division\) scale. Battery has no internal resistance. It is found that there is deflection of \(40\) \(divisions\) when \(R = 2400\,\Omega \). Deflection becomes \(20\) \(divisions\) when resistance taken from resistance box is \(4900\,\Omega \) . Then we can conclude

In a medium the speed of light wave decreases to \(0.2\) times to its speed in free space The ratio of relative permittivity to the refractive index of the medium is \(x: 1\). The value of \(x\) is \(...........\) (Given speed of light in free space \(=3 \times 10^8 m s ^{-1}\) and for the given medium \(\mu_{ r }=1\) )

An electron in the hydrogen atom initially in the fourth excited state makes a transition to \(\mathrm{n}^{\text {th }}\) energy state by emitting a photon of energy 2.86 eV. The integer value of \(n\) will be ____.

A rod with circular cross-section area \(2\,cm ^2\) and length \(40\,cm\) is wound uniformly with \(400\) turns of an insulated wire. If a current of \(0.4\,A\) flows in the wire windings, the total magnetic flux produced inside windings is \(4\,\pi \times 10^{-6}\,Wb\). The relative permeability of the rod is (Given : Permeability of  vacuum \(\left.\mu_0=4 \pi \times 10^{-7} \;NA ^{-2}\right)\)

If a source of electromagnetic radiation having power \(15 kW\) produces \(10^{16}\) photons per second, the radiation belongs to a part of spectrum is.(Take Planck constant \(h =6 \times 10^{-34}\,Js\) )

A long cylindrical vessel is half filled with a liquid. When the vessel is rotated about its own vertical axis, the liquid rises up near the wall. If the radius of vessel is \(5\,cm\) and its rotational speed is \(2\) rotations per second, then the difference in the heights between the centre and the sides, in \(cm,\) will be