1.

If the number ofterms in the expansion (1+2x-3y+4z)^(n) is 286, then find thecoefficient of term containing xyz.

Answer»


Solution :Number of term in the expansion
`= .^(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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