Absolute zero & Kinetic/Internal Energy. (A level)?

You're right...it ISN'T possible.... that's why absolute zero has not been achieved ( and it never will be).

There is always a minimum of energy associated with some quantum system: the bond between atoms in a molecule can be modeled as a harmonic oscillator, which has a minimum energy hw/2, and this energy does not depend on temperature. So even at the very lowest physically possible energy, the gas still has some internal energy and hence a temperature.

A gas can have a minimum internal energy, but it cannot be 0.

all the expressions are the part of theories in thermodynamics and according to theory at absolute temperature internal and kinetic energy is zero.

all these things are according to theory
nobody knows whether it is possible or not
scientist are trying to achieve it
but for a common man answer is "not possible"

No one answered. You are screwed for your test. You should have asked your teacher lol! (edit: during the writing of this answer, two other people answered. However, they are only half-right. I explain below.)

Due to quantum physics and quantum theory (which is above where you probably are for your test), you are correct that a stationary object is not possible, because quantum theory states that no particle of matter (or antimatter) is present at the same place at the same time. This is also true when related to the Big Bang Theory which states that the universe is constantly expanding, and when it stops expanding it will begin contracting.

However, this does not actually answer your question, because it is most likely far beyond your scope.

What is certainly relevant to you, is that an absolute zero is not theoretically possible (partly as a result of the aforementioned quantum theory). In this case you would be correct that a molecule cannot be stationary. However, the question does not ask whether absolute zero is actually possible, it states that according to physics, if absolute zero were to theoretically occur, then would a molecule be stationary?

The answer, to the best of my knowledge, is Yes. In the event of actually reaching Absolute Zero, if it were theoretically possible, then a molecule would be completely at rest with zero kinetic energy. This is why it is literally called "absolute" "zero". I do not mean that sarcastically.

It is also true that a particle cannot, according to quantum theory, ever reach a true absolute zero.

What you need to look at is whether the questions is asking you about a REAL absolute zero, which is meant for the sake of principle and understanding, since it is theoretically impossible to reach -- or if they are referring to a factual standpoint.

My advice is that:
A) If the question is referring the the principle of a REAL absolute zero, then the answer is ZERO kinetic energy.

or

B) If the question is asking from a perspective of attainable absolute zero, which is very close but not quite there, then the answer is most likely what the textbook says, because a true absolute zero is not possible. This is why it is best to say "minimum" kinetic energy - because in real life (not theory), ZERO is not possible.

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Note: I would verify this with your teacher, if you have not yet taken the final. Even if you have taken the final, still verify what they are asking. However, to the best of my knowledge, the information I have given you above is correct.

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A easier way to understand why a matter cannot be "absolutely at rest" is:
there is gravitational force acting on any matter in any universe.
And the gravitational force from any direction can NOT be cancelled, so the matter must be dragged even if it is rotating on its own.

YES U ARE RIGHT THAT AT ABSOLUTE TEMPERATURE i'e AL ZERO KELVIN THE MOLECULES HAVE LEAST OR ZERO K.E. THIS MEANS VELOCITY IS ALSO ZERO AND MOLECULES OF GAS DO NOT MOVE AT ALL OR THEY ARE IN STATE OF REST. ALSO U MIGHT BE AWARE OF FACT THAT ZERO KELVIN IS UN ACHIEVABLE.