Solution:

CAT

Explanation:
1. LOCATE
2. EDUCATE
3. CATER
4. CATTLE

Solution:

See the figure for the answer. Wasn't it a bit tricky?

Solution:

He should draw any chit of paper and before unfolding it, he must eat and swallow the chit. In this manner, to determine the judgment of the god, they will have to look at the other chit which will have 'Guilty' written over it. Thus everyone will believe that the chit which he ate had innocent written over it and thus they will believe that he is innocent.

Solution:

On Your lap.

Solution:

f the last elf is taking some time to answer the question then it shall mean that the elf's before him are all wearing distinct coloured hats. However sufficient time shall be given to the last elf to give the answer.
If he views the similar coloured hats in front of him , he shall quickly tell the answer

Solution:

The answer is 'R'

It represents the gear stick. The number 1-5 represents gears and the last one thus should be reverse i.e. R.

Solution:

-3 -1 1

Explanation:
-3 * 1 * -1 = 3(prime)
-1 - (-3) = 1 -(-1) = 2

Solution:

Birbal drew another line that was larger than the pre-drawn line. Now the pre drawn line was smaller.

Solution:

16-days

In 15-days, he will climb 15-inch and when he climbs 5 inch more, he will be out of the well :-)

Solution:

Colors:
Y B R G
G R B Y
B Y G R
R G Y B


Signs:
x + - /
- / x +
/ - + x
+ x / -

Solution:

Bond was suspicious of the women as one never knocks its own door at the hotel.