\(AC\) alternating emf \(\mathrm{E}=110 \sqrt{2} \sin 100 \mathrm{t}\) volt is applied to a capacitor of \(2 \mu \mathrm{F}\), the rms value of current in the circuit is _______ \(\mathrm{mA}\).

The atomic hydrogen emits a line spectrum consisting of various series. Which series of hydrogen atomic spectra is lying in the visible region?

A ball rolls off the top of a stairway with horizontal velocity \(\mathrm{u}\). The steps are \(0.1 \mathrm{~m}\) high and \(0.1 \mathrm{~m}\) wide. The minimum velocity \(\mathrm{u}\) with which that ball just hits the step \(5\) of the stairway will be \(\sqrt{\mathrm{x}} \mathrm{ms}^{-1}\) where \(\mathrm{x}=\) _______ [use \(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2\) ].

An ideal battery of \(4\, V\) and resistance \(R\) are connected in series in the primary circuit of a potentiometer of length \(1\, m\) and resistance \(5\,\Omega \) . The value of \(R\), to give a difference of \(5\, mV\) across \(10\, cm\) of potentiometer wire, is: ................ \(\Omega\)

A free neutron decays into a proton but a free proton does not decay into neutron. This is because

A body of mass \(M\) at rest explodes into three pieces, in the ratio of masses \(1: 1: 2\). Two smaller pieces fly off perpendicular to each other with velocities of \(30 \,ms ^{-1}\) and \(40 \,ms ^{-1}\) respectively. The velocity of the third piece will be ............... \(\,ms ^{-1}\)

Two equal positive point charges are separated by a distance \(2 a\). The distance of a point from the centre of the line joining two charges on the equatorial line (perpendicular bisector) at which force experienced by a test charge \(q_0\) becomes maximum is \(\frac{a}{\sqrt{x}}\). The value of \(x\) is \(................\)

The internal energy \((U),\) pressure \((P)\) and volume \(( V )\) of an ideal gas are related as \(U =\) \(3 P V+4\). The gas is :-

Two point charges \(2 q\) and \(q\) are placed at vertex \(A\) and centre of face CDEF of the cube as shown in figure. The electric flux passing through the cube is :

Let \(N_{\beta}\) be the number of \(\beta \) particles emitted by \(1\) gram of \(Na^{24}\) radioactive nucler (half life \(= 15\, hrs\)) in \(7.5\, hours\), \(N_{\beta}\) is close to (Avogadro number \(= 6.023\times10^{23}\,/g.\, mole\))

A reversible engine has an efficiency of \(\frac{1}{4}\). If the temperature of the sink is reduced by \(58^{\circ} {C}\), its efficiency becomes double. Calculate the temperature of the sink. (In \(^{\circ} {C}\))

A parallel plate air capacitor is connected to a battery. The plates are pulled apart at uniform speed \(v\). If \(x\) is the separation between the plates at any instant, then the time rate of change of electrostatic energy of the capacitor is proportional to \(x^\alpha\), where \(\alpha\) is _____.

The self produced \(emf\) of a coil is \(25\,volts\). When the current in it is changed at uniform rate from \(10\,A\) to \(25\, A\) in \(1\,s\), the change in the energy of the inductance is......\(J\)