In a typical combustion engine the workdone by a gas molecule is given by $$W = {\alpha ^2}\beta {e^{{{ - \beta {x^2}} \over {kT}}}}$$, where x is the displacement, k is the Boltzmann constant and T is the temperature. If $$\alpha$$ and $$\beta$$ are constants, dimensions of $$\alpha$$ will be :

If e is the electronic charge, c is the speed of light in free space and h is Planck's constant, the quantity $${1 \over {4\pi {\varepsilon _0}}}{{|e{|^2}} \over {hc}}$$ has dimensions of :

Match List - I with List - II :

	List I		List II
(a)	h (Planck's constant)	(i)	$$[ML{T^{ - 1}}]$$
(b)	E (kinetic energy)	(ii)	$$[M{L^2}{T^{ - 1}}]$$
(c)	V (electric potential)	(iii)	$$[M{L^2}{T^{ - 2}}]$$
(d)	P (linear momentum)	(iv)	$$[M{L^2}{I^{ - 1}}{T^{ - 3}}]$$

Choose the correct answer from the options given below :

The pitch of the screw gauge is 1 mm and there are 100 divisions on the circular scale. When nothing is put in between the jaws, the zero of the circular scale lies 8 divisions below the reference line. When a wire is placed between the jaws, the first linear scale division is clearly visible while 72^nd division on circular scale coincides with the reference line. The radius of the wire is :