A common emitter amplifier circuit, built using an \(npn\) transistor, is shown in the figure. Its \(dc\) current gain is \(250\), \(R_C = 1\,k\, \Omega \) and \(V_{CC} = 10\,V\). What is the minimum base current for \(V_{CE}\) to reach saturation?.........\(\mu A\)

A time varying potential difference is applied between the plates of a parallel plate capacitor of capacitance \(2.5 \mu \mathrm{~F}\). The dielectric constant of the medium between the capacitor plates is 1 . It produces an instantaneous displacement current of 0.25 mA in the intervening space between the capacitor plates, the magnitude of the rate of change of the potential difference will be _____ \(\mathrm{Vs}^{-1}\).

A square aluminium (shear modulus is \(25 \times 10^{9}\,Nm ^{-2}\) ) slab of side \(60\,cm\) and thickness \(15\,cm\) is subjected to a shearing force (on its narrow face) of \(18.0 \times 10^{4}\,N\). The lower edge is riveted to the floor. The displacement of the upper edge is \(.......\mu\,m\).

You are given that Mass of \({ }_{3}^{7} Li =7.0160\, u\) Mass of \({ }_{2}^{4} He =4.0026\, u\) and Mass of \({ }_{1}^{1} H =1.0079\, u\) When \(20\, g\) of \({ }_{3}^{7} Li\) is converted into \({ }_{2}^{4} He\) by proton capture, the energy liberated, (in \(kWh\) ), is: [Mass of nudeon \(\left.=1\, GeV / c ^{2}\right]\)

A Carnot engine operates between two reservoirs of temperatures \(900\; \mathrm{K}\) and \(300 \;\mathrm{K}\) The engine performs \(1200\; \mathrm{J}\) of work per cycle. The heat energy (in \(\mathrm{J}\) ) delivered by the engine to the low temperature reservoir, in a cycle. is

If three helium nuclei combine to form a carbon nucleus then the energy released in this reaction is _______ \(\times 10^{-2} \mathrm{MeV}\). (Given \(1 \mathrm{u}=931 \mathrm{MeV} / \mathrm{c}^2\), atomic mass of helium \(=4.002603 \mathrm{u}\) )

The frequency of oscillation of a mass \(m\) suspended by a spring is \(v_1\). If the length of the spring is cut to half, the same mass oscillates with frequency \(v_2\). The value of \(v_2/v_1\) is ________.

For a train engine moving with speed of \(20 \;ms ^{-1}\). the driver must apply brakes at a distance of \(500 \;m\) before the station for the train to come to rest at the station. If the brakes were applied at half of this distance, the train engine would cross the station with speed \(\sqrt{ x }\; ms ^{-1}\). The value of \(x\) is \(..............\) (Assuming same retardation is produced by brakes)

A solid ball of radius \(R\) has a charge density \(\rho \) given by \(\rho  = {\rho _0}\left( {1 - \frac{r}{R}} \right)\) for \(0 \leq r \leq R\). The electric field outside the ball is

An inductor \((L = 0.03\;H)\) and a resistor \((R = 0.15 k\Omega )\) are connected in series to a battery of \(15\;V\) \(EMF\) in a circuit shown below. The key \(K_1\) has been kept closed for a long time. Then at \(t = 0\), \(K_1\) is opened and key \(K_2\) is closed simultaneously. At \(t = 1 \;ms\), the current in the circuit will be ........... \(mA\). (\({e^5} \cong 150)\)

In a hydrogen spectrum, \(\lambda\) be the wavelength of first transition line of Lyman series. The wavelength difference will be "a \(\lambda^{\prime}\) between the wavelength of \(3^{\text {rd }}\) transition line of Paschen series and that of \(2^{\text {nd }}\) transition line of Balmer Series where \(a=........\)

A potentiometer wire \(AB\) having length \(L\) and resistance \(12\, r\) is joined to a cell \(D\) of \(emf\) \(\varepsilon \) and internal resistance \(r\). A cell \(C\) having \(emf\) \(\varepsilon /2\) and internal resistance \(3r\) is connected. The length \(AJ\) at which the galvanometer as shown in figure shows no deflection is