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The term idependent of 'x' in the expans...

The term idependent of `'x'` in the expansion of `(9x-(1)/(3sqrt(x)))^(18)`, `x gt 0` , is `alpha` times the corresponding binomial coefficient. Then `'alpha'` is

A

`3`

B

`(1)/(3)`

C

`-(1)/(3)`

D

`1`

Text Solution

Verified by Experts

The correct Answer is:
D
`(d)` `T_(r+1)=^(18)C_(r )*(9x)^(18-r)*(-1)^(r )*((x)^(-r//2))/(3^(r ))`
`T_(r+1)=^(18)C_(r )*9^(18-r)*((-1)^(r ))/(3^(r ))*x^(18-(3r)/(2))`
`:.18-(3r)/(2)=0`
`impliesr=12`
According to question `"^(18)C_(12)*(9^(6))/(3^(12))=alpha*^(18)C_(12)`.
`impliesalpha=1`
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