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 \(=1.6 \times 10^{-19}\,C\) )

An observer moves towards a stationary source of sound with a velocity equal to one-fifth of the velocity of sound. The percentage change in the frequency will be \(\dots \;\)%

A particle executes simple harmonic motion and is located at \(x = a, b\)  and  \(c\) at times \(t_0, 2t_0\) and \(3t_0\) respectively. The frequency of the oscillation is

A nucleus at rest disintegrates into two smaller nuclei with their masses in the ratio of \(2: 1\). After disintegration they will move :-

Two capacitors of capacities \(2 {C}\) and \({C}\) are joined in parallel and charged up to potential \({V}\). The battery is removed and the capacitor of capacity \(C\) is filled completely with a medium of dielectric constant \({K}\). The potential difference across the capacitors will now be

The current in an inductor is given by \(\mathrm{I}=(3 \mathrm{t}+8)\) where \(t\) is in second. The magnitude of induced emf produced in the inductor is \(12 \mathrm{mV}\). The selfinductance of the inductor _______ \(\mathrm{mH}\).

Two tubes of radii \(r_1\) and \(r_2\), and lengths \(l_1\) and \(l_2\), respectively, are connected in series and a liquid flows through each of them in streamline conditions. \(P_1\) and \(P_2\) are pressure differences across the two tubes. If \(P_2\) is \(4P_1\) and \(l_2\) is \( \frac{l_1}{4}\) , then the radius \(r_2\) will be equal to

Given below are two statement  Statement \(-I\) : What \(\mu\) amount of an ideal gas undergoes adiabatic change from state \(\left( P _{1}, V _{1}, T _{1}\right)\) to state \(\left( P _{2}, V _{2}, T _{2}\right)\), the work done is \(W =\frac{1 R \left( T _{2}- T _{1}\right)}{1-\gamma}\), where \(\gamma=\frac{ C _{ P }}{ C _{ V }}\) and \(R =\) universal gas constant, Statement \(-II\) : In the above case. when work is done on the gas. the temperature of the gas would rise. Choose the correct answer from the options given below

An insulating thin rod of length \(l\) has a linear charge density \(\rho \left( x \right) = {\rho _0}\,\frac{x}{l}\) on it. The rod is rotated about an axis passing through the origin \((x = 0)\) and perpendicular to the rod. If the rod makes \(n\) rotations per second, then the time averaged magnetic moment of the rod is

A \(9\, V\) battery with internal resistance of \(0.5\,\Omega \) is connected across an infinite network as shown in the figure. All ammeters \(A_1 , A_2, A_3\) and voltmeter \(V\) are ideal. Choose correct statement

A beam of light travelling along \(X\)-axis is described by the electric field \(E _{ y }=900 \sin \omega( t - x / c )\). The ratio of electric force to magnetic force on a charge \(q\) moving along \(Y\)-axis with a speed of \(3 \times 10^{7}\,ms ^{-1}\) will be. [Given speed of light \(=3 \times 10^{8}\,ms ^{-1}\) ]

The acceleration due to gravity on the earth's surface at the poles is \(g\) and angular velocity of the earth about the axis passing through the pole is \(\omega .\) An object is weighed at the equator and at a height \(h\) above the poles by using a spring balance. If the weights are found to be same, then \(h\) is \(:( h << R ,\) where \(R\) is the radius of the earth)

The driver of a bus approaching a big wall notices that the frequency of his bus's horn changes from \(420\, Hz\) to \(490\, Hz ,\) when he hears it after it gets reflected from the wall. Find the speed of the bus (in \(kmh^{-1}\)) if speed of the sound is \(330\, ms ^{-1}\).