In a large building, there are \(15\) bulbs of \(40\ W\), \(5\) bulbs of \(100\ W, 5\) fans of \(80\ W\) and \(1\) heater of \(1\ kW\). The voltage of electric mains is \(220\ V\). The minimum capacity of the main fuse of the building will be ................ \(A\)

The diameter of a sphere is measured using a vernier caliper whose \(9\) divisions of main scale are equal to \(10\) divisions of vernier scale. The shortest division on the main scale is equal to \(1 \mathrm{~mm}\). The main scale reading is \(2 \mathrm{~cm}\) and second division of vernier scale coincides with a division on main scale. If mass of the sphere is \(8.635 \mathrm{~g}\), thedensity of the sphere \(1 \mathrm{~s}\) _______.

The electric field in an electromagnetic wave is given as \(\vec{E}=20 \sin \omega\left(t-\frac{x}{c}\right) \vec{j} NC ^{-1}\) Where \(\omega\) and \(c\) are angular frequency and velocity of electromagnetic wave respectively. The energy contained in a volume of \(5 \times 10^{-4}\, m ^3\) will be \(.....\times 10^{-13}\,J\) (Given \(\varepsilon_0=8.85 \times 10^{-12}\,C ^2 / Nm ^2\) )

How many alpha and beta particles are emitted when Uranium \({ }_{92} U ^{238}\) decays to lead \({ }_{82} Pb ^{206}\) ?

A circular hole of radius \(\frac{R}{4}\) is made in a thin uniform disc having mass \(M\) and radius \(R\), as shown in figure. The moment of inertia of the remaining portion of the disc about an axis passing through the point \(O\) and perpendicular to the plane of the disc is

For a constant collector-emitter voltage of \(8\,V\), the collector current of a transistor reached to the value of \(6\,mA\) from \(4\,mA\), whereas base current changed from \(20\,\mu A\) to \(25\,\mu\,A\) value. If transistor is in active state, small signal current gain (current amplification factor) will be.

The de-Broglie wavelength associated with the electron in the \(n\, = 4\) level is

The drift velocity of electrons for a conductor connected in an electrical circuit is \(V _{ d }\). The conductor in now replaced by another conductor with same material and same length but double the area of cross section. The applied voltage remains same. The new drift velocity of electrons will be

The charge flowing in a conductor changes with time as \(Q ( t )=\alpha t -\beta t ^2+\gamma t ^3\). Where \(\alpha, \beta\) and \(\gamma\) are constants. Minimum value of current is :

A fluid is flowing through a horizontal pipe of varying cross-section, with speed \(v\;ms^{-1}\) at a point where the pressure is \(P\) Pascal. At another point where pressure is \(\frac{ P }{2}\) Pascal its speed is \(V\;ms^{-1}\). If the density of the fluid is \(\rho\, kg\, m ^{-3}\) and the flow is streamline, then \(V\) is equal to

In the circuit shown, charge on the \(5\, \mu F\) capacitor is\(........\mu C\)

A free electron of \(2.6\, {eV}\) energy collides with a \({H}^{+}\) ion. This results in the formation of a hydrogen atom in the first excited state and a photon is released. Find the frequency of the emitted photon. \(\left({h}=6.6 \times 10^{-34}\, {J} {s}\right)\)