The volume of an ideal gas increases 8 times and temperature becomes (1/4) of initial temperature during a reversible change. If there is no exchange of heat in this process (\( \Delta Q=0 \)) then identify the gas from the following options:

The amplitude of a damped oscillator decreases to \(0.9\) times its original magnitude in \(5\ s\). In another \(10\ s\) it will decrease to \(\alpha \) times its original magnitude, where  \(\alpha \) equals

The machine as shown has \(2\) rods of length \(1\, m\) connected by a pivot at the top. The end of one rod is connected to the floor by a stationary pivot and the end of the other rod has a roller that rolls along the floor  in a slot As the roller goes back and forth, a \(2\, kg\) weight moves up and down. If the roller is moving towards right at a constant speed, the weight moves up with a

The equivalent resistance between \(A\) and \(B\) of the network shown in figure

The specific heat of water \(=4200\, J\, kg ^{-1}\, K ^{-1}\) and the latent heat of ice \(=3.4 \times 10^{5}\, J\, kg ^{-1}.\) \(100\) grams of ice at \(0^{\circ} C\) is placed in \(200\, g\) of water at \(25^{\circ} C\). The amount of ice that will melt as the temperature of water reaches \(0^{\circ} C\) is close to (in \(grams\)) 

A plane electromagnetic wave of frequency \(20\,MHz\) propagates in free space along \(x\)-direction. At a particular space and time, \(\overrightarrow{ E }=6.6 \hat{ j } V / m\). What is \(\overrightarrow{ B }\) at this point?

Taking the wavelength of first Balmer line in hydrogen spectrum (\( n = 3\) to \(n = 2\) ) as \(660\,nm ,\) the wavelength of the \(2^{nd}\) Balmer line ( \(n =4\) to \(n = 2\) ) will be....\(nm\)

In the Young's double slit experiment, the distance between the slits varies in time as \({d}({t})={d}_{0}+{a}_{0}\, sin\omega \,t\) ; where \({d}_{0}, \omega\) and \(a_{0}\) are constants. The difference between the largest fringe width and the smallest fringe width obtained over time is given as :

Particle \(A\) of mass \(m_{A}=\frac{m}{2}\) moving along the \(x-\)axis with velocity \(v_{0}\) collides elastically with another particle \(B\) at rest having mass \(m _{ B }=\frac{ m }{3}\) If both particles move along the \(x-\)axis after the collision, the change \(\Delta \lambda\) in \(de-\)Broglie wavelength of particle \(A,\) in terms of its \(de-\)Broglie wavelength \(\left(\lambda_{0}\right)\) before collision is

A soap bubble of radius \(3\, {cm}\) is formed inside the another soap bubble of radius \(6\, {cm}\). The radius of an equivalent soap bubble which has the same excess pressure as inside the smaller bubble with respect to the atmospheric pressure is .......... \({cm}\) 

A loop of flexible wire of irregular shape carrying current is placed in an external magnetic field. Identify the effect of the field on the wire.

Two polarisers \(P_1\) and \(P_2\) are placed in such a way that the intensity of the transmitted light will be zero. A third polariser \(P_3\) is inserted in between \(P_1\) and \(\mathrm{P}_2\), at the particular angle between \(\mathrm{P}_2\) and \(\mathrm{P}_3\). The transmitted intensity of the light passing the through all three polarisers is maximum. The angle between the polarisers \(\mathrm{P}_2\) and \(\mathrm{P}_3\) is :