A thermally insulated vessel contains an ideal gas of molecular mass $$M$$ and ratio of specific heats $$\gamma .$$ It is moving with speed $$v$$ and it's suddenly brought to rest. Assuming no heat is lost to the surroundings, Its temperature increases by:

A Carnot engine operating between temperatures $$T_1$$ and $$T_2$$ has efficiency {1 \over 6}. When $$T_2$$ is lowered by $$62$$ $$K$$ its efficiency increases to {1 \over 3}. Then $$T_1$$ and $$T_2$$ are, respectively:

Two identical charged spheres suspended from a common point by two massless strings of length $$l$$ are initially a distance $$d\left(d<<1\right)$$ apart because of their mutual repulsion. The charge begins to leak from both the spheres at a constant rate. As a result charges approach each other with a velocity $$v$$. Then as a function of distance $$x$$ between them,

The electrostatic potential inside a charged spherical ball is given by $$\varphi =a{r}^2+b$$ where $$r$$ is the distance from the center and $$a,b$$ are constants. Then the charge density inside the ball is:

A water fountain on the ground sprinkles water all around it. If the speed of water coming out of the fountain is v, the total area around the fountain that gets wet is :

An object, moving with a speed of 6.25 m/s, is decelerated at a rate given by : {{dv} \over {dt}} = - 2.5\sqrt v where v is the instantaneous speed. The time taken by the object, to come to rest, would be :

This question has Statement - $$1$$ and Statement - $$2$$. Of the four choices given after the statements, choose the one that best describes the two statements. Statement - $$1$$ : A metallic surface is irradiated by a monochromatic light of frequency $$v>v_0$$ (the threshold frequency). The maximum kinetic energy and the stopping potential are $$K_{\max }$$ and $$V_0$$ respectively. If the frequency incident on the surface is doubled, both the $$K_{\max }$$ anmd $$V_0$$ are also doubled. Statement - $$2$$ : The maximum kinetic energy and the stopping potential of photoelectrons emitted from a surface are linearly dependent on the frequency of incident light.

Two bodies of masses $$m$$ and $$4$$ $$m$$ are placed at a distance $$r.$$ The gravitational potential at a point on the line joining them where the gravitational field is zero is:

This question has a paragraph followed by two statements, Statement $$-1$$ and Statement $$-2$$. Of the given four alternatives after the statements, choose the one that describes the statements. A thin air film is formed by putting the convex surface of a plane-convex lens over a plane glass plane. With monochromatic light, this film gives an interference pattern due to light, reflected from the top (convex) surface and the bottom (glass plate) surface of the film. Statement - $$1$$ : When light reflects from the air-glass plate interface, the reflected wave suffers a phase change of $$\pi .$$ Statement - $$2$$ : The center of the interference pattern is dark.

The transverse displacement $$y(x,t)$$ of a wave on a string is given by $$y\left(x,t\right)=e^{-\left(a{x}^2+b{t}^2+2\sqrt{ab}xt\right)}.$$ This represents $$a:$$

A current $$I$$ flows in an infinitely long wire with cross section in the form of a semi-circular ring of radius $$R.$$ The magnitude of the magnetic induction along its axis is:

A boat is moving due east in a region where the earth's magnetic fields is $$5.0\times 10^{-5}$$ $$N{A}^{-1}{m}^{-1}$$ due north and horizontal. The best carries a vertical aerial $$2$$ $$m$$ long. If the speed of the boat is $$1.50m{s}^{-1},$$ the magnitude of the induced $$emf$$ in the wire of aerial is :

A pulley of radius $$2$$ $$m$$ is rotated about its axis by a force $$F=\left(20t-5t^2\right)$$ newton (where $$t$$ is measured in seconds) applied tangentially. If the moment of inertia of the pulley about its axis of rotation is $$10kg$$-$$m^2$$ the number of rotation made by the pulley before its direction of motion is reversed, is:

A mass $$m$$ hangs with the help of a string wrapped around a pulley on a frictionless bearing. The pulley has mass $$m$$ and radius $$R.$$ Assuming pulley to be a perfect uniform circular disc, the acceleration of the mass $$m,$$ if the string does not slip on the pulley, is:

A thin horizontal circular disc is rotating about a vertical axis passing through its center. An insect is at rest at a point near the rim of the disc. The insect now moves along a diameter of the disc to reach its other end. During the journey of the insect, the angular speed of the disc.

'a’ and `b’ are van der Waals’ constants for gases. Chlorine is more easily liquefied than ethane because

Ozonolysis of an organic compound gives formaldehyde as one of the products. This confirms the presence of :

Which of the following facts about the complex [Cr (NH3)6 ]Cl3 is wrong?

The magnetic moment (spin only) of [NiCl4]2− is

A gas absorbs a photon of 355 nm and emits at two wavelengths. If one of the emissions is at 680 nm, the other is at :