I have no doors but I have keys, I have no rooms but I have space, you can enter but you can’t leave! What am I?

I have lakes with no water, mountains with no stone and cities with no buildings. What am I?

What jumps when it walks and sits when it stands?

What can you hold in your right hand, but never in your left hand?

Pronounced as 1 letter, And written with 3, 2 letters there are, and 2 only in me. I’m double, I’m single, I’m black blue and grey, I’m read from both ends, and the same either way. What am I?

Which alphabet is a part of our body?

No matter how little or how much you use me, you change me every month. What am I?

You may enter, but you may not come in. I have space, but no room. I have keys, but open no lock. What am I?

Eight of us go fourth, not back, to protect our king from an attack. What are we?

A chess tournament is taking place on knock-out terms (the one who loses the match is out of the game).
(a) If 10 matches are played in total, how many players participated?
(b) If 20 players took part in the tournament, how many matches were played?