Hi, I need help with part B. Please show all the work, thanks.

Decidability 1. Which of the following problems is decidable? Why? a) Given a TM M and a string y, does M ever write the symbol # on its tape on input y? b) Given a context free grammar G over (a, b), does G generate all the strings of the anguage fa, b* of length s 381? c) Given a context free grammar G over (a, b), does G generate all the strings of the language (a, b* of length greater than 381? d) Given a TM M, are there infinitely many TMs M' accepting the same enumerable set A L(M)