Who is that with a neck and no head, two arms and no hands? What is it?

In the Chess Board picture below white army is arranged. You need to add a black army on the board such that no piece is under any threat.
Note: Army comprised of 1 king, 1 queen, 2 rooks, 2 bishops, 2 knights, and 8 pawns.

In the Mexico City area, there are two Houses H1 and H2. Both H1 and H2 have two children each.
In House H1, The boy plays for Mexico Youth academy and the other child plays baseball.
In House H2, The boy Plays soccer for his school in Mexico and they recently have a newborn.

Can you prove that the probability of House-H1 having a girl child is more than that of House-H2?

Is the statement valid that it does not matter how much older a sibling is, eventually the younger one will be half as old as the older one?

I never was there, I am always to be.
You have never ever seen me, not ever you will.
Yet I am the confidence of everyone.

Who Am I?

A Shopkeeper sold a few chickens to four different customers on a particular day. It was such that each customer purchased half of the remaining chickens and half the chicken more.

Can you find out how many chicken were sold by the shopkeeper on that day if we tell you that the fourth customer bought a single chicken ?

What word begins and ends with an E, but has only one letter?

Why did Navjot Singh Sidhu put the new January calendar in the freezer

Find out a multi-digit number that if multiplied by the number 9 or any of its multiplications products (i.e. 18, 27, 36, 45,..) will result in the multiplication factor repeated (n) number of times.

You can hear me, but you can't touch or see me.

What am I?