How is the answer valid for following question? 
A closed flask contains water in all its three states solid, liquid
  and vapour at 0 degree Celsius. In this situation, the average kinetic
  energy of water molecules will be
  
  
*
  
*a) the greatest in all the three states
  
*b) the greatest in vapour state
  
*c) the greatest in the liquid state
  
*d) the greatest in the solid state

My opinion: temperature is a measure of average kinetic energy. since they all have same temperature, they all should have same average kinetic energy.
But the answer given is option b) with the explanation "In the three states of matter, the maximum kinetic energy is possessed by the gaseous molecules, so water vapour state has maximum kinetic energy in this situation."
So how is option b) correct?
 A: First of all the triple triple point of water is 0.01C.
Although the temperature of each phase is the same, the internal energy of each phase is not. Since energy in the form of heat is removed from the solid to produce liquid and from the  liquid to produce vapor the internal energy of the solid is the lowest and the vapor the greatest. The internal energy of each phase is the sum of its internal potential and kinetic energies. In liquids and solids there is a significant amount of potential energy associated with the intermolecular forces whereas in vapors most of the internal energy is kinetic.
So I think what they were asking is based on the same mass of each phase at the same temperature. Then the phase that would have the greatest amount of kinetic energy is the vapor phase.
Hope this helps 
A: 
My opinion: temperature is a measure of average kinetic energy

No, that's not what temperature is. Temperature is a measure of the relationship between entropy and total energy for the system: basically, it measures the volume of state space which is made available if a small amount of extra energy $\Delta E$ is added to the system. 
However, there is a very powerful theorem, called the Equipartition Theorem, that applies to any degree of freedom which contributes to the energy of the system via (exclusively) a quadratic form: if there is a phase-space coordinate (say, a velocity $v_1$) such that the total energy of the system can be written as
$$
E_\mathrm{total} = Kv_1^2 + E_\mathrm{remaining},
$$
with $E_\mathrm{remaining}$ completely independent of $v_1$ (though possibly depending on the coordinate $x_1$ whose time derivative is $v_1$), then the equipartition theorem tells us that the average (say, kinetic) energy in that coordinate is strictly proportional to the temperature:
$$
\left< Kv_1^2 \right> = \frac12 k_B T,
$$
with $k_B$ the Boltzmann constant. This is why temperature is often said to be "a measure of average kinetic energy", but this is strictly a secondary result, and not the real definition of temperature.
Nevertheless, the equipartition theorem does apply to the gas-liquid-solid mixture of water at its triple point (which is at 0.01°C, not at 0°C!). The potential-energy content of the three phases is different, so therefore their total internal energies will change from phase to phase, but the average kinetic energy in each phase is still subject to the equipartition theorem, which dictates that it should be the same across all three phases.
Your book's answer looks wrong to me, on that account.
A: I am not sure but I am placing my (obsolete) two cents in, partly for clarifying my own concepts in response to Mr. Pisanty's answer above.
From what I understand, the triple point exhibits a dynamic inter-transition between 3 phases of the same element. But expanding on Mr. Bob  states above, should the variation of internal energy not be accompanied by a variation of kinetic energy also? From a microscopic perspective hydrogen bonds and chemical bonds are constantly being broken and reformed in this state. How should the energy difference of the minimally bond state be subject to quantifcation in comparison to the maximally bonded ice if not for an increase in entropy or disorder of the vapour? This increase in disorder might exhibit itself through randomisation of molecular motion. Is this randomisation not equivalent to an increase in average velocity?
Since the system is non-dissipative, the energy is constant for the sum total across all three phases. But can we conclude that the energy 'share' of each individual  phase is the same as the other two?
E= PdV + TdS.
Despite invariance of maintained temperature and total enthalpy, an increase in dS should lead to variation of E during phase transition resulting in a new energy for the phase. But this is compensated by changes resulting from phase transition for some other molecules also. Mr Pisanty's answer relates the total energy of the flask to an average velocity across the flask. but strictly speaking equipartition should hold only for molecules of each individual phase, i.e molecules of same phase at same temperature have same average velocity. But E of each phase is not constant at all. It is only E(sum across all three phases) that is constant. Otherwise what would be the significance of the triple point? It might just as well be water at 0.01 C in the flask.
I am but an undergrad and would appreciate any comments correcting my visualisation and understanding.
