Two moles of an ideal monatomic gas occupies a volume V at 27oC. The gas expands adiabatically to a volume 2 V. Calculate (a) the final temperature of the gas and (b) change in its internal energy.

One mole of an ideal monoatomic gas is taken along the path ABCA as show in the PV diagram. The maximum temperature attained by the gas along the path BC is given by :

Two moles of helium are mixed with n moles of hydrogen. If {{Cp} \over {Cv}} = {3 \over 2} for the mixture, then the value of n is :

The value closest to the thermal velocity of a Helium atom at room temperature (300 K) in ms-1 is : [kB =1.4 $$\times$$ 10-23 J/K; mHe = 7 $$\times$$ 10 -27 kg ]

Two Carnot engines A and B are operated in series. Engine A receives heat from a reservoir at 600 K and rejects heat to a reservoir at temperature T. Engine B receives heat rejected by engine A and in turn rejects it to a reservoir at 100 K. If the efficiencies of the two energies A and B are represented by $${\eta }_A$$ and $${\eta }_B,$$ respectively, then what is the value of {{{\eta _B}} \over {{\eta _A}}} ?

One mole of an ideal monoatomic gas is compressed isothermally in a rigid vessel to double its pressure at room temperature, $$27^{\circ }C.$$ The work done on the gas will be :

Two identical conducting spheres A and B, carry equal charge. They are separated by a distance much larger than their diameters, and the force between theis F. A third identical conducting sphere, C, is uncharged. Sphere C is first touhed to A, then to B, and then removed. As a result, the force between A and B would be equal to :

A solid ball of radius R has a charge density $$\rho$$ given by $$\rho$$ = $$\rho$$o (1 $$-$$ $$\text{raise}0.5exr/\text{lower}0.25exR$$) for 0 $$\le$$ r $$\le$$ R. The electric field outside the ball is :

A charge $$Q$$ is placed at a distance $$a/2$$ above the center of the square surface of edge a as shown in the figure. The electric flux through the square surface is

A body of mass $$M$$ and charge $$q$$ is connected to spring of spring constant $$k.$$ It is oscillating along $$x$$-direction about its equilibrium position, taken to be at $$x=0,$$ with an amplitude $$A$$. An electric field $$E$$ is applied along the $$x$$-direction. Which of the following statements is correct ?

Three concentric metal shells A, B and C of respective radii a, b and c (a < b < c) have surface charge densities $$+\sigma$$, $$-\sigma$$ and $$+\sigma$$ respectively. The potential of shell B is :

A man in a car at location Q on a straight highway is moving with speed $$\upsilon$$. He decides to reach a point P in a field at a distance d from the highway (point M) as shown in the figure. Speed of the car in the field is half to that on the highway. What should be the distance RM, so that the time taken to reach P is minimum ?

An automobile, travelling at $$40$$ km/h, can be stopped at a distance of $$40$$ m by applying brakes. If the same automobile is travelling at $$80$$ km/h, the minimum stopping distance, in metres, is (assume no skidding) :

The velocity-time graphs of a car and a scooter are shown in the figure. (i) The difference between the distance travelled by the car and the scooter in $$15$$ $$s$$ and (ii) the time at which the car will catch up with the scooter are, respectively.

All the graphs below are intended to represent the same motion. One of them does it incorrectly. Pick it up.

Both the nucleus and the atom of some element arein their respective first excited states. They get de-excted by emitting photons of wavelengths $$\lambda$$N, $$\lambda$$A respectively. The ratio {{{}^\lambda N} \over {{}^\lambda A}}is closest to :

The de-Broglie wavelength ($$\lambda$$B) associated with the electron orbiting in the second excited state of hydrogen atom is related to that in the ground state ($$\lambda$$G) by :

If the de Broglie wavelengths associated with a proton and an $$\alpha$$-particle are equal, then the ratio of velocities of the proton and the $$\alpha$$-particle will be :

Two electrons are moving with non-relativistic speed perpendicular to each other. If corresponding de Broglie wavelength are $${\lambda }_1$$ and $${\lambda }_2,$$ their de Broglie wavelength in the frame of reference attached to their center of masses :

The $$B$$-$$H$$ curve for a ferromagnet is shown in the figure. The ferromagnet is placed inside a long solended with $$1000$$ turns/cm. The current that should be passed in the solended to demagnetise the ferromagnet completely is :