Solution:

Letter "D"

The sequence "JFMAMJJASON" represents the first letter of each month in a calendar year. Following the pattern, the next letter in the sequence should be "D" for December. So, the complete sequence for a calendar year would be:

J - January
F - February
M - March
A - April
M - May
J - June
J - July
A - August
S - September
O - October
N - November
D - December

Therefore, "D" is the next letter in the sequence.

Solution:

The clerk said that every day the password is CHANGED. Changed is the password.

Solution:

They used the planks in the manner that is shown in the figure.

Solution:

At first, there were 2 apples on the tree. After the wind blew, one apple fell on the ground. So there where no apples on the tree and there were no apples on the ground.
*apples => more than one apple

Another solution(non tricky one)
The wind blew so hard that the apples fell of the tree and blew along the ground.

Solution:

Hhe hung herself using big Ice slabs , which are now now melted and hence puddle of water.

Solution:

The attached picture gives away the solution. If you can find another solution, do send us yours.

Solution:

Costa

Explanation:
c + 1 characters-> d
o + 2 characters-> q
s + 3 characters-> v
t + 4 characters-> x
a + 5 characters-> f

=> dqvxf = costa

Solution:

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

Solution:

28 =>1+2+4+7+14

cannot be 1 (as number cannot be included)

Solution:

It can surely be true because it is not mentioned that it was raining.

Solution:

2100 miles.

Each vowel equivalent to 500 and each consonant equivalent to -200