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A language accepted by Deterministic Push down automata is closed under which of the following?

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1.
Consider the following languages.

L1 = {ai bj ck | i = j, k ? 1}
L1 = {ai bj | j = 2i, i ? 0}
Which of the following is true?
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2.
Let LD  be the set of all languages accepted by a PDA by final state and LF  the set of all languages accepted by empty stack. Which of the following is true?

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3.
PDA can be represented with the help of
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4.
In a pushdown automaton P=(Q,?,?,?,q0,F), a transition of the form,
where p,q?Q, a???{?}, X,Y,???{?}, represents
(q,Y) ? ?(p,a,X)
Consider the following pushdown automaton over the input alphabet ?={a,b} and stack alphabet ?={#,A}.
The number of strings of length 100 accepted by the above pushdown automaton is ___________ . 
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5.
If L1 and L2 are context free languages and R a regular set, one of the languages below is not necessarily a context free language, which one?
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