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If the number ofterms in the expansion (1+2x-3y+4z)^(n) is 286, then find thecoefficient of term containing xyz. |
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Answer» `= .^(n+4-1)C_(4-1) = .^(n+3)C_(3) = ((n+3)(n+2)(n+1))/(3!)` ACCORDING to the question, `((n+3)(n+2)(n+1))/(3!) = 286` `:. n = 10` So, theterm containing `(xyz)` is `(10!)/(7!!!!!!!!) (1)^(7) (2x)^(1) (-3y)^(1)(4Z)^(1)` `= -17280 xyz`. THEREFORE, the requiredcoefficient is `- 17280`. |
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