Solution:

Pi(pi-symbol) + Rate (of acceleration)
= Pirate

Solution:

step 3 is wrong

Solution:

Six.

There are only five colors, so six socks guarantee that two will be the same color.

Solution:

Rhea will open just one present.
Cindy|Y - Y is the 25th alphabet
Duk|E - E is the 5th alphabet
Joh|N - N is the fifteenth alphabet
Rhe|A - A is the first alphabet

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:

The stranger said that he thought the room was his. If so, he must have had the keys to the room and thus he must not have knocked.

Solution:

It can be solved as below.

Solution:

7 Races.

Solution:

The women is a of short stature. She can't reach the upper elevator buttons, but can push is with his umbrella.

Solution:

TIF56

Explanation:
The password is formed as:
T (5th letter of Shruti)
I (5th letter of Arshika)
F(1st letter of Friday)
5(5th day of week)
6(Length of Friday)

Similarly, we will pick the 1st letter for Monday and 3rd letter for Wednesday.

Solution:

White should move the rook from
A1 to D1 and hence complete the castling move.