Let Q and W denote the amount of heat given to an ideal gas and the work done by it in an adiabatic process.

In an adiabatic process, we assume that there is no heat exchange between the system and surroundings.

Hence, Q = 0. Also, U = W(when Q = 0), so Q ≠ W holds.

Option (b) is incorrect because due to change in temperature, there is still a change in internal energy and from the first law of thermodynamics, ΔU = W. Hence W ≠ 0.

Option (c) is incorrect because the heat exchange is zero, but the work done in general is not zero.

Hence, the correct answers are option (a) and (d).