To raise the temperature of a certain mass of gas by \(50^{\circ} C\) at a constant pressure, \(160\) calories of heat is required. When the same mass of gas is cooled by \(100^{\circ} C\) at constant volume, \(240\) calories of heat is released. How many degrees of freedom does each molecule of this gas have (assume gas to be ideal) \(?\)

Assuming in forward bias condition there is a voltage drop of 0.7 V across a silicon diode, the current through diode \(D _1\) in the circuit is ___________mA . (Assume all diodes in the given circuit are identical)

Given below are two statements: Statement \(I\) : A time varying electric field is a source of changing magnetic field and vice-versa. Thus a disturbance in electric or magnetic field creates \(EM\) waves. Statement \(II\) : In a material medium. The \(EM\) wave travels with speed \(v =\frac{1}{\sqrt{\mu_{0} \varepsilon_{0}}}\). In the light of the above statements, choose the correct answer from the options given below

The relative permittivity of distilled water is \(81 .\) The velocity of light in it will be \(....\,\times 10^{7}\,{m} / {s}\) \(\left(\right.\) Given \(\left.\mu_{r}=1\right)\)

The distance travelled by a particle is related to time \(t\) as \(x =4 t ^2\). The velocity of the particle at \(t =\) \(5 s\) is \(.........ms^{-1}\)

A steel rod has a radius of \(20\,mm\) and a length of \(2.0\,m\). A force of \(62.8\,kN\) stretches it along its length. Young's modulus of steel is \(2.0 \times 10^{11}\,N / m ^2\). The longitudinal strain produced in the wire is \(..........\times 10^{-5}\)

A bicycle tyre is filled with air having pressure of \(270\,kPa\) at \(27^{\circ}\,C\). The approximate pressure of the air in the tyre when the temperature increases to \(36^{\circ}\,C\) is \(............kPa\)

A uniform thin rod \(AB\) of length \(L\) has linear mass density \(\mu \left( x \right) = a + \frac{{bx}}{L}\) , where \(x\) is measured from \(A\). If the \(CM\) of the rod lies at a distance of \(\left( {\frac{7}{12}} \right)L\) from \(A\), then \(a\) and \(b\) are related as

The speed of a transverse wave passing through a string of length \(50 \;cm\) and mass \(10\,g\) is \(60\,ms ^{-1}\). The area of cross-section of the wire is \(2.0\,mm ^{2}\) and its Young's modulus is \(1.2 \times 10^{11}\,Nm ^{-2}\). The extension of the wire over its natural length due to its tension will be \(x \times 10^{-5}\; m\). The value of \(x\) is \(...\)

A metal plate of area \(1\times10^{-4}\, m^2\) is illuminated by a radiation of intensity \(16\, m\,W/m^2\). The work function of the metal is \(5\,eV\). The energy of the incident photons is \(10\, eV\) and only \(10\%\) of it produces photo electrons. The number of emitted photo electrons per second and their maximum energy, respectively, will be : \([1\, eV = 1.6\times10^{-19}\, J]\)