Match the types/steps involved in organizing a tournament listed in List-I with their correct associations listed in List-II:

$\begin{array}{ll}\text{List-I (Tournament Types)}& \text{List-II (Associations)}\\ \text{(A) Bye}& \text{(I) Advantage given to team not playing the first round}\\ \text{(B) Knock-out}& \text{(II) Team eliminated after first defeat}\\ \text{(C) Number of byes}& \text{(III) Next highest power of 2 − number of teams}\\ \text{(D) Number of teams in upper half (odd teams)}& \text{(IV) (Number of teams + 1)/2}\end{array}$

Choose the correct answer from the options given below:

The correct option is (A)- (I), (B)- (II), (C)- (III), (D)- (IV).

Let us understand and match each concept step-by-step:

1. (A) Bye − (I) Advantage given to team not playing the first round
A "Bye" is a privilege or advantage granted to a team in a tournament. It allows the team to advance directly to the second round without having to play or compete in the first round.

2. (B) Knock-out − (II) Team eliminated after first defeat
A "Knock-out" (or single-elimination) tournament is a type of competition where a team is immediately eliminated from the tournament upon losing a single match. Only the winning team advances to the next round.

3. (C) Number of byes − (III) Next highest power of 2 − number of teams
To ensure a smooth bracket progression in a knock-out tournament, the number of teams participating must be a power of 2. If the number of teams is not a power of 2, byes are given. The formula to calculate the total number of byes is:
$\text{Number of Byes}=2^n-N$
where $2^n$ represents the next highest power of 2 greater than or equal to the total number of teams $N$.

4. (D) Number of teams in upper half (odd teams) − (IV) (Number of teams + 1)/2
When organizing a tournament with an odd number of teams ($N$), the teams are divided into two halves. Since the division is uneven, the upper half receives one extra team. The formula to calculate the number of teams in the upper half is:
$\text{Teams in Upper Half}=\frac{N+1}{2}$
which corresponds to (Number of teams + 1)/2.