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Context free grammar is not closed under:

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1.
Context sensitive language can be recognized by a :
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2.
Let L1 be regular language, L2 be a deterministic context free language and L3 a recursively enumerable language, but not recursive. Which one of the following statements is false?
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3.
For the correct answer strings to above question, how many derivation trees are there?
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4. 
Consider the following languages:
I. {ambncpdq ? m + p = n + q, where m, n, p, q ? 0}
II. {ambncpdq ? m = n and p = q, where m, n, p, q ? 0}
III. {ambncpdq ? m = n = p and p ? q, where m, n, p, q ? 0}
IV. {ambncpdq ? mn = p + q, where m, n, p, q ? 0}
Which of the above languages are context-free?
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5.
Are ambiguous grammar context free?
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