Questions about sentence completion exercise
Hello, I just did sentence completion exercise today.
And I have some questions that I don't exactly understand.
So anybody can explain it to me? Thank you!

1. It is going to be ........
a) very hot indeed
b) hot indeed
(The correct answer is a. very hot indeed)
Q : Why can't I answer b. hot indeed? I think that's also reasonable.

2. That idea has been ..... for years.
a) died
b) dead
(The correct answer is b. dead)
Q : Why is the answer a. died incorrect? since has been+V3 (if I don't get it wrong :P)

3. His latest book is ………… than his last one.
a) quite more interesting
b) a lot more interesting
b) dead
(The correct answer is b. a lot more interesting)
Q : Why is the answer a. quite more interesting incorrect? But if I choose a. is it possible?

4. I think she is ……………………
a) a bit fool
b) a bit of a fool
(The correct answer is b. a bit of a fool)
Why?

Question

Questions about sentence completion exercise
Hello,  I just did sentence completion exercise today. 
And I have some questions that I don't exactly understand. 
So anybody can explain it to me? Thank you!

1. It is going to be ........
a) very hot indeed
b) hot indeed
(The correct answer is a. very hot indeed)
Q : Why can't I answer b. hot indeed? I think that's also reasonable.

2. That idea has been ..... for years.
a) died
b) dead
(The correct answer is b. dead)
Q : Why is the answer a. died incorrect? since has been+V3 (if I don't get it wrong :P)

3. His latest book is ………… than his last one.
a) quite more interesting
 b) a lot more interesting
b) dead
(The correct answer is b. a lot more interesting)
Q : Why is the answer a. quite more interesting incorrect? But if I choose a. is it possible?

4. I think she is ……………………
a) a bit fool
 b) a bit of a fool
(The correct answer is b. a bit of a fool)
Why?

Answer

1. I call this a bad question. We normally say "very hot indeed", but "hot indeed" is simply uncommon.

2. It's not a passive sentence, so "dead" (adjective) is correct. Also, "to die" can't exist in passive form.

3. "Quite" is not possible here. It's a very vague word for describing degree, so only "a lot more interesting" makes sense.

4. "A bit of a fool" is the only correct option. The other expression we use is "a bit foolish" (ie. "foolish" being an adjective).