Is it possible for a DFA to have less states than its equivalent NFA? Number of transitions does not matter. If possible also give an example.
Theoretically yes, that NFA could have 9001 unreachable stats that are completely useless.
If you expect that NFA to be connected (common sense) then if you allow epsilon-moves you can have a huge useless cykle.
If you rephrase your question to:
Lets consider any Language and its 'smallest' (min number of states) NFA with $\epsilon$-moves and its 'samllest' DFA then the answer is no and the reason is simple.
any DFA is also NFA (names does not suggest that though). therefore if we take a 'smallest' NFA and then manage find equivalent DFA that is 'smaller' that would contradict previous NFA being smallest.
No. There are infinitely many NFA that are equivalent to any given DFA – it does not make sense to speak of "a DFA and its equivalent NFA". Moreover, every DFA is a very predictable NFA.