I am looking for a word that change both gender and number when i add the letter 'S'.

What Word am I Looking For ?

Find the mistake in the below maths equations

A = 2
A(A-1) = 2(A-1)
A2-A = 2A-2
A2-2A = A-2
A(A-2) = A-2
A = 1

Only one colour, but not one size,
Stuck at the bottom, yet easily flies.
Present in sun, but not in rain,
Doing no harm, and feeling no pain.
What is it?

Why is the Hole below a Lock?

Below rebus represent famous DiCaprio movie. Can you name it?

While preparing the table for dinner, wife came up with an idea to tease his mathematician husband. She asked her husband to pick nine toothpicks and make ten without breaking any toothpick.

The husband was also smart and did it within seconds. How ?

At a Society election for president, precisely 963 votes were cast.
There is a total of 4 candidates that participate in the election.

The winning candidate exceeds the opponents by 53, 79 and 105 votes.

How many votes do each candidate gets?

If all Goats are Sheep and all Sheep are Deers, are all Deers Goats ?

Today is a very icy and cold morning in Newcastle. Mr Shearer, an office bus driver arrived to pick up the employees from the last stop. Shearer suddenly remembers that he needs to pick a newly joined 4miles to the north. Mr Shearer lost his direction compass, a few minutes later Shearer is able to figure that he is moving in the correct direction i.e. north. How did Shearer know that he is moving in the correct direction?

Look at this sequence from top to bottom. What is the next number in the sequence?
1
11
21
1211
111221
312211