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Find a positive value of m for which the...

Find a positive value of m for which the coefficient of `x^2` in the expansion of `(1+x)^m` is 6.

Text Solution

Verified by Experts

The correct Answer is:
`m=4`
`(1+x)^(m) = .^(m) C_(0) + .^(m)C _(1) x + .^(m) C_(2)x^(2) + ...+ .^(m) C_(m)x^(m).`
` :. .^(m) C _(2) =6 rArr (m(m-1))/(2!)= 6 rArr m^(2) - m - 12 = 0 rArr (m-4) (m+3) = 0 rArr m= 4.`
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