Undecidability

Which of the following problems are decidable?

Which of the following is/are undecidable?

Which of the following are decidable?

I. Whether the intersection of two regular languages is infinite
II. Whether a given context-free language is regular
III. Whether two push-down automata accept the same language
IV. Whether a given grammar is context-free

Which of the following problems is undecidable? [2007]

Let be the encoding of a Turing machine as a string over ∑= {0, 1}.  Let L = { |M is a Turing machine that accepts a string of length 2014 }. Then, L is

Which of the following problems is undecidable?

Consider three decision problems P1, P2 and P3. It is known that P1 is decidable and P2 is undecidable. Which one of the following is TRUE?

Consider two languages L1 and L2 each on the alphabet ∑. Let f : ∑ → ∑ be a polynomial time computable bijection such that (∀ x) [x ∈ L1 if f(x) ∈ L2]. Further, let f^-1 be also polynomial time computable. Which of the following CANNOT be true?

Consider the following problem X.

Given a Turing machine M over the input alphabet Σ, any
state q of M And a word w∈Σ*, does the computation of M
on w visit the state q? 

Which of the following statements about X is correct?

Consider the following decision problems:

(P1) Does a given finite state machine accept a given string
(P2) Does a given context free grammar generate an infinite 
     number of strings

Which of the following statements is true?