JEE MATHEMATICS MCQ: PERMUTATIONS

1 Hard

1 of 1

Analyzing +4 | -1

Ten persons numbered

1,2,3, \ldots, 10

play a chess tournament, each player playing against every player exactly one game. It is known that no game ends in a draw. Let

w_1, w_2, w_3, \ldots, w_{10}

be the number of games won by player

1,2,3, \ldots, 10

respectively and

l_1, l_2, l_3, \ldots

l_{10}

be the number of games lost by the players

1,2,3, \ldots

, 10 respectively, then

View answer and explanation

Correct option: C

\Sigma w_i^2=\Sigma l_i^2

Option C (

\Sigma w_i^2=\Sigma l_i^2

) is correct because in a tournament where each game has a winner and a loser, the sum of the squares of the wins equals the sum of the squares of the losses.

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