Which of the following radiations has the least wavelength ?

In the nuclear fusion reaction ${}_1^2H + {}_1^3H \to {}_2^4He + n$ given that the repulsive potential energy between the two nuclei is $$\sim 7.7\times 10^{-14}J$$, the temperature at which the gases must be heated to initiate the reaction is nearly [ Boltzmann's Constant $$k=1.38\times 10^{-23}J/K$$ ]

Which of the following atoms has the lowest ionization potential ?

Which of the following cannot be emitted by radioactive substances during their decay ?

If the binding energy of the electron in a hydrogen atom is $$13.6eV,$$ the energy required to remove the electron from the first excited state of $$L{i}^{++}$$ is

A radioactive sample at any instant has its disintegration rate $$5000$$ disintegrations per minute. After $$5$$ minutes, the rate is $$1250$$ disintegrations per minute. Then, the decay constant (per minute) is

A nucleus with $$Z=92$$ emits the following in a sequence: $\alpha ,{\beta ^ - },{\beta ^ - },\alpha ,\alpha ,\alpha ,\alpha ,\alpha ,{\beta ^ - },{\beta ^ - },\alpha ,{\beta ^ + },{\beta ^ + },\alpha$ Then $$Z$$ of the resulting nucleus is

When a $$U^{238}$$ nucleus originally at rest, decays by emitting an alpha particle having a speed $${}^{\prime }{u}^{\prime },$$ the recoil speed of the residual nucleus is

The wavelengths involved in the spectrum of deuterium $$\left({}_1^{2}D\right)$$ are slightly different from that of hydrogen spectrum, because

During an adiabatic process, the pressure of a gas is found to be proportional to the cube of its absolute temperature. The ratio $$C_p/C_V$$ for the gas is

The earth radiates in the infra-red region of the spectrum. The spectrum is correctly given by

A carnot engine takes $$3\times 10^6$$ cal. of heat from a reservoir at $$627^{\circ }C,$$ and gives it to a sink at $$27^{\circ }C$$. The work done by the engine is

Which of the following parameters does not characterize the thermodynamic state of mattter?

''Heat cannot by itself flow from a body at lower temperature to a body at higher temperature'' is a statement or consequence of :

If the electric flux entering and leaving an enclosed surface respectively is $${\varphi }_1$$ and $${\varphi }_2,$$ the electric charge inside the surface will be

A thin spherical conducting shell of radius $$R$$ has a charge $$q.$$ Another charge $$Q$$ is placed at the center of the shell. The electrostatic potential at a point $$P$$ a distance {R \over 2} from the center of the shell is

Three charges $$-q_1,+q_2$$ and $$-q_3$$ are placed as shown in the figure. The $$x$$-component of the force on $$-q_1$$ is proportional to

A boy playing on the roof of a 10 m high building throws a ball with a speed of 10 m/s at an angle of $$30^{\circ }$$ with the horizontal. How far from the throwing point will the ball be at the height of 10 m from the ground? \left[ {g = 10m/{s^2},\sin 30^\circ = {1 \over 2},\cos 30^\circ = {{\sqrt 3 } \over 2}} \right]

A car, moving with a speed of 50 km/hr, can be stopped by brakes after at least 6 m. If the same car is moving at a speed of 100 km/hr, the minimum stopping distance is

The co-ordinates of a moving particle at any time 't' are given by x = $$\alpha$$t3 and y = βt3. The speed to the particle at time 't' is given by