An oscillating \(LC\) circuit consists of a \(75\,mH\) inductor and a \(1.2\,\mu F\) capacitor. If the maximum charge to the capacitor is \(2.7\,\mu C\). The maximum current in the circuit will be \(...........\,mA\).

As per the given figure, two plates \(A\) and \(B\) of thermal conductivity \(K\) and \(2 K\) are joined together to form a compound plate. The thickness of plates are \(4.0 \,cm\) and \(2.5 \,cm\) respectively and the area of cross-section is \(120 \,cm ^{2}\) for each plate. The equivalent thermal conductivity of the compound plate is \(\left(1+\frac{5}{\alpha}\right) K\), then the value of \(\alpha\) will be_______

The mass number of nucleus having radius equal to half of the radius of nucleus with mass number \(192\) is _______.

A metal wire of resistance \(3\,\Omega \) is elongated to make a uniform wire of double its previous length. The new wire is now bent and the ends joined to make a circle. If two points on this circle make an angle \(60^o\) at the centre, the equivalent resistance between these two points will be

In figure, the optical fiber is \(I = 2\,m\) long and has a diameter of \(d = 20\,\mu \,m\). If a ray of light is incident on one end of the fiber at angle \({\theta _1} = {40^o}\) , the number of reflection it makes before emerging from the other end is close to

Two known resistance of \(R \Omega\) and \(2 R \Omega\) and and one unknown resistance \(X \Omega\) are connected in a circuit as shown in the figure. If the equivalent resistance between points A and B in the circuit is \(X \Omega\), then the value of X is _________ \(\Omega\).

The electric field between the two parallel plates of a capacitor of \(1.5 \mu \mathrm{F}\) capacitance drops to one third of its initial value in \(6.6 \mu \mathrm{s}\) when the plates are connected by a thin wire. The resistance of this wire is _______ \(\Omega\). (Given, \(\log 3=1.1)\)

The equation of state for a gas is given by \(PV = nRT + \alpha V\), where \(n\) is the number of moles and \(\alpha \) is a positive constant. The initial temperature and pressure of one mole of the gas contained in a cylinder are \(T_o\) and \(P_o\) respectively. The work done by the gas when its temperature doubles isobarically will be

A parallel plate capacitor is made of two circular plates separated by a distance \(5\ mm\) and with a dielectric of dielectric constant \(2.2\) between them. When the electric field in the dielectric is \(3 \times 10^4\) \( Vm^{-1}\) the charge density of the positive plate will be close to

Light ray incident along a vector \(\vec{AO}\) \((\vec{AO} = 2\hat{i}-3\hat{j})\) emerges out along vector \(\vec{OB}\) \((\vec{OB} = C\hat{i}-4\hat{j})\) as shown in the figure below. The value of \(C\) is ________.

For a body executing \(S.H.M. :\) \((a)\) Potential energy is always equal to its \(K.E.\) \((b)\) Average potential and kinetic energy over any given time interval are always equal. \((c)\) Sum of the kinetic and potential energy at any point of time is constant. \((d)\) Average \(K.E.\) in one time period is equal to average potential energy in one time period. Choose the most appropriate option from the options given below:

The pitch and the number of divisions, on the circular scale, for a given screw gauge are \(0.5\,mm\) and \(100\) respectively. When the screw gauge is fully tightened without any object, the zero of its circular scale lies \(3\) divisions below the mean line. The readings of the main scale and the circular scale for a thin sheet, are \(5.5\,mm\) and \(48\) respectively, the thickness of this sheet is

Water of volume \(2\, L\) in a closed container is heated with a coil of \(1\,kW\). While water is heated, the container loses energy at a rate of \(160\, J/s\) . In how much time will the temperature of water rise from \(27\,^oC\) to \(77\,^oC\) ? (Specific heat of water is \(4.2\, kJ/kg\) and that of the container is negligible)