a. At first the cart had only potential energy. After pushing, when it starts moving, the potential energy is converted into kinetic energy. Hemce this is correct.
b. Initially cart was at rest which means that momentum was zero. But when it starts moving momentum becomes greater than zero. Hence, this is incorrect .
c. Work done is force times displacement. Since both force and displacement is non zero, so person does some work. Hence this is correct.
d. Since no loss of energy takes place through dissipation, so the total energy remains constant. Hence this is correct.
Hope it helps.
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