1.

In a football championship, 153 matches were played. Every two teams played one match with each other. The number of teams, participating in the championship is …….. .A. 21B. 18C. 17D. 15

Answer» Correct Answer - B
Let total no. of team participated in a championship ben. Since, every team played one match with each other team.
`:. .^(n)C_(2) = 153 rArr (n!)/(2!(n -2)!) = 153`
`rArr (n(n-1)(n-2)!)/(2!(n-2)!) = 153 rArr (n(n-1))/(2) = 153`
`rArr n(n-1) = 306`
`rArr n^(2) - n - 306 = 0`
`rArr n (n -18) + 17 (n -18) = 0`
`rArr n = 18, -17`
n cannot be negative
`:. n != - 17`
`rArr n = 18`


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