How many Byes will be given if 19 teams are participating in a Knock-Out Tour nament?

The correct option is 13.

To find the number of byes given in a knock-out tournament, we use the following step-by-step mathematical logic:

1. Identify the total number of participating teams, denoted by N.
Here, N = 19.

2. Determine the next highest power of 2 that is greater than or equal to the total number of teams (N).
The powers of 2 are: 2, 4, 8, 16, 32, 64, and so on.
For 19 teams, the next highest power of 2 is 32 (which is 2⁵).

3. Calculate the number of byes using the formula:
Number of Byes = Next power of 2 - Total number of teams

Applying the values to the formula:

$\text{Number of Byes}=32-19=13$

Therefore, 13 byes will be given in the tournament.