Decide major product for first order elimination reaction This is my own created question.


The favourable thing for (c) to be a major product is  conjugation of double bonds and highly acidic nature of hydrogen (resulting in elimination of hydrogen at a higher rate) adjacent to carbonyl group (credit $-$ Rover). According to information I have the above reaction is most probably reversible in nature.
(b) should be major product as per mechanism I have given. So which will be the major (or only) product. You may take high temperature conditions if temperature is required as we are doing elimination reaction.
The product that you have drawn is very unlikely to be the major product of a mixed aldol condensation. The actual major product in said reaction would be (assuming I get the substrates right) would be as follows:



However, your question is a valid one if we take this out of consideration. Now, If we consider just the elimination reaction and your reaction conditions, your mechanism is correct. However, if this reaction were to take place via E2, the rate determining step would be that of the removal of the hydrogen and this would mean that the product formed would be (c). In case of E1, (b) would be the major product since the rate determining step is that of the formation of the carbocation.