If 21x = 79x, what is the value of x?

Which of the following words don't belong in the group and why?
CORSET, COSTER, SECTOR, ESCORT, COURTS

What number when divided in half becomes zero?

A bomb goes off.
Carnage.
One person, only a few feet away, survives! How can this be?

A convention is held where all the big logicians are summoned. The master places a band on everyone's forehead. Now all of them can see others bands but can't see his own. Then they are told that there are different colours of bands. All the logicians sit in circle and they are further explained that a bell will ring at regular intervals. The moment when a logician knew the colour of band on his forehead, he will leave at the next bell. If anyone leaves at the wrong bell, he will be disqualified.

The master assures the logicians that the puzzle will not be impossible for anyone of them. How will the logicians manage ?

The dirtier I get, the whiter I look. Who am I?

If I put in one canary per cage, I have one bird too many. If I put in two canaries per cage, I have one cage too many. How many cages and canaries do I have?

Analyze and find the missing item in the sequence:
16, 06, 68, 88, __, 98

A spy was in Canada trying to steal insider information on how to set up new Maple Syrup factories in their country. He was introduced to the operations manager of the biggest factory in Canada. However, the manager was suspicious and decided to test him with a question before he trusted him. So he asked, “What would you be sure to find in the middle of Toronto?” The spy thought fast and came up with an answer for the manager. What was his answer?

Speaking of rivers, a man calls his dog from the opposite side of the river. The dog crosses the river without getting wet, and without using a bridge or boat. How?