An inductor of \(0.5\,mH\), a capacitor of \(20\,\mu\,F\) and resistance of \(20\,\Omega\) are connected in series with a \(220\,V\) ac source. If the current is in phase with the emf, the amplitude of current of the circuit is \(\sqrt{x} A\). The value of \(x\) is -

Given below are two statements :
Statement-I : The equivalent emf of two nonideal batteries connected in parallel is smaller than either of the two emfs.
Statement-II : The equivalent internal resistance of two nonideal batteries connected in parallel is smaller than the internal resistance of either of the two batteries.
In the light of the above statements, choose the correct answer from the options given below.

Given are statements for certain thermodynamic variables,
(A) Internal energy, volume (V) and mass (M) are extensive variables.
(B) Pressure (P), temperature (T) and density ( \(\rho\) ) are intensive variables.
(C) Volume (V), temperature (T) and density ( \(\rho\) ) are intensive variables.
(D) Mass (M), temperature (T) and internal energy are extensive variables.

Choose the correct answer from the options given below :

To establish an instantaneous current of \(2\,A\) through a \(1\,\mu F\) capacitor ; the potential difference across the capacitor plates should be changed at the rate of

A triangular shaped wire carrying \(10 A\) current is placed in a uniform magnetic field of \(0.5\,T\), as shown in figure. The magnetic force on segment \(CD\) is \(....N\) \((\) Given \(BC = CD = BD =5\,cm )\).

A diatomic gas, having \(C_{p}=\frac{7}{2} R\) and \(C _{ v }=\frac{5}{2} R ,\) is heated at constant pressure. The ratio \(dU : dQ : dW :\)

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 :

In a cuboid of dimension \(2 L \times 2 L \times L\), a charge \(q\) is placed at the centre of the surface ' \(S\) ' having area of \(4 L ^2\). The flux through the opposite surface to ' \(S\) ' is given by

In an electromagnetic wave the electric field vector and magnetic field vector are given as \(\vec{E}=E_{0} \hat{i}\) and \(\vec{B}=B_{0} \hat{k}\) respectively. The direction of propagation of electromagnetic wave is along.

In an experiment on photoelectric effect, a student plots stopping potential \(V_0\) against reciprocal of the wavelength \(\lambda \) of the incident light for two different metals \(A\) and \(B\). These are shown in the figure Looking at the graphs, you can most appropriately say that