JEE MAIN - Mathematics (2019 - 12th January Evening Slot - No. 4)
There are m men and two women participating in a chess tournament. Each participant plays two games with every other participant. If the number of games played by the men between themselves exceeds the number of games played between the men and the women by 84, then the value of m is :
12
9
7
11
Explanation
Let m-men, 2-women
mC2 $$ \times $$ 2 = mC1 2C1 . 2 + 84
m2 $$-$$ 5m $$-$$ 84 = 0 $$ \Rightarrow $$ (m $$-$$ 12) (m + 7) = 0
m = 12
mC2 $$ \times $$ 2 = mC1 2C1 . 2 + 84
m2 $$-$$ 5m $$-$$ 84 = 0 $$ \Rightarrow $$ (m $$-$$ 12) (m + 7) = 0
m = 12
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