Three identical resistors with resistance \(R=12 \Omega\) and two identical inductors with sell inductance \(L=5 mH\) are connected to an ideal battery with emf of 12 V as shown in figure. The current through the battery long after the switch has been closed will be _________ A.

A ball of mass \(0.5 \; kg\) is dropped from the height of \(10 \; m\). The height, at which the magnitude of velocity becomes equal to the magnitude of acceleration due to gravity, is \(\dots \; m\). (Use \(g =10 \; m / s ^{2}\)).

If \(917 \mathring A\) be the lowest wavelength of Lyman series then the lowest wavelength of Balmer series will be .......\(\mathring A\).

Match List-I with List-II.

List-I (Physical Quantity)	List-II (Dimensional Formula)
(A) Coefficient of viscosity	(I) [ML0T-3]
(B) Intensity of wave	(II) [ML-2T-2]
(C) Pressure gradient	(III) [M-1LT2]
(D) Compressibility	(IV) [ML-1T-1]

Choose the correct answer from the options given below :

The specific heats, \(C_P\) and \(C_V\) of a gas of diatomic molecules, \(A\), are given (in units of \(J\, mol^{-1}\, K^{-1}\)) by \(29\) and \(22\), respectively. Another gas of diatomic molecules \(B\), has the corresponding values \(30\) and \(21\). If they are treated as ideal gases, then

The electric field in a region is given by \(\overrightarrow{ E }=\frac{2}{5} E _{0} \hat{ i }+\frac{3}{5} E _{0} \hat{ j }\) with \(E _{0}=4.0 \times 10^{3}\, \frac{ N }{ C } .\) The flux of this field through a rectangular surface area \(0.4 \,m ^{2}\) parallel to the \(Y - Z\) plane is ....... \(Nm ^{2} C ^{-1}\)

A heat engine operates between a cold reservoir at temperature \({T}_{2}=400\, {K}\) and a hot reservoir at temperature \({T}_{1} .\) It takes \(300 \,{J}\) of heat from the hot reservoir and delivers \(240\, {J}\) of heat to the cold reservoir in a cycle. The minimum temperature of the hot reservoir has to be \(....{K}\)

The \(rms\) speeds of the molecules of Hydrogen, Oxygen and Carbondioxide at the same temperature are \({V}_{{H}}, {V}_{0}\) and \({V}_{{C}}\) respectively then

A beam of monochromatic light is used to excite the electron in \(Li ^{++}\)from the first orbit to the third orbit. The wavelength of monochromatic light is found to be \(x \times 10^{-10} \; m\). The value of \(x\) is \(\dots.\) [Given hc \(=1242 \; eV nm ]\)

In a meter bridge experiment resistances are connected as shown in the figure. Initially resistance \(P\, = 4\,\Omega \) and the neutral point \(N\) is at \(60\,cm\) from \(A\). Now an unknown resistance \(R\) is connected in series to \(P\) and the new position of the neutral point is at \(80\,cm\) from \(A\) . The value of unknown resistance \(R\) is

In a collinear collision, a particle with an initial speed \(v_0\) strikes a stationary particle of the same mass. If the final total kinetic energy is \(50\%\) greater than the original kinetic energy, the magnitude of the relative velocity between the two particles, after collision, is:

A current of \(2\,A\) flows through a wire of crosssectional area \(25.0\,mm ^2\). The number of free electrons in a cubic meter are \(2.0 \times 10^{28}\). The drift velocity of the electrons is \(...............\times 10^{-6}\,ms ^{-1}\) (given, charge on electron \(=1.6 \times 10^{-19}\,C\) )