An electric appliance supplies \(6000\, {J} / {min}\) heat to the system. If the system delivers a power of \(90\, {W}\). How long (in \(sec\)) it would take to increase the internal energy by \(2.5 \times 10^{3}\, {J}\) ?

Six point charges are kept \( 60^{\circ} \) apart from each other on the circumference of a circle of radius R as shown in figure. The net electric field at the centre of the circle is __________ .
(\( \epsilon \) is permittivity of free space)

\(7\) mole of certain monoatomic ideal gas undergoes a temperature increase of \(40 K\) at constant pressure. The increase in the internal energy of the gas in this process is\(....J\) (Given \(R =8.3 JK ^{-1} mol ^{-1}\) )

In a Young's double slit experiment, the intensities at two points, for the path difference \(\frac{\lambda}{4}\) and \(\frac{\lambda}{3}\) ( \(\lambda\) being the wavelength of light used) are \(I_1\) and \(I_2\) respectively. If \(I_0\) denotes the intensity produced by each one of the individual slits, then \(\frac{ I _1+ I _2}{ I _0}=..............\)

In the given circuit, the current through zener diode is......\(mA\)

Consider a circular disc of radius 20 cm with centre located at the origin. A circular hole of radius 5 cm is cut from this disc in such a way that the edge of the hole touches the edge of the disc. The distance of centre of mass of residual or remaining disc from the origin will be ________.

The electrostatic force \(\left(\vec{F}_1\right)\) and magnetic force \(\left(\vec{F}_2\right)\) acting on a charge \(q\) moving with velocity \(v\) can be written _______.

A circular coil of radius \(8.0 \,{cm}\) and \(20\) turns is rotated about its vertical diameter with an angular speed of \(50\, {rad} {s}^{-1}\) in a uniform horizontal magnetic field of \(3.0 \times 10^{-2}\, {T}\). The maximum \(emf\) induced the coil will be \(\ldots \ldots \ldots \times 10^{-2}\) \(volt\) (rounded off to the nearest integer)

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

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 clock has \(75 \mathrm{~cm}, 60 \mathrm{~cm}\) long second hand and minute hand respectively. In \(30\) minutes duration the tip of second hand will travel \(x\) distance more than the tip of minute hand. The value of \(x\) in meter is nearly _______. (Take \(\pi=3.14\) )