Failed to connect to MySQL: Access denied for user 'examnext_online'@'localhost' (using password: YES) The term independent of x in the expansion of `(9x-1/(3sqrtx))^18`, x > 0, is `alpha` time the corresponding binomial coefficient. Then `alpha` is - Sarthaks eConnect

The term independent of x in the expansion of `(9x-1/(3sqrtx))^18`, x > 0, is `alpha` time the corresponding binomial coefficient. Then `alpha` is :

The term independent of x in the expansion of `(9x-1/(3sqrtx))^18`, x > 0, is `alpha` time the corresponding binomial coefficient. Then `alpha` is :

A.

3

B.

`1/3`

C.

`-1/3`

D.

1

Solution

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Best answer

`T_(r+1)=18C_rxx(9x)^(18-r)xx(-1)^rxx((x)^(-r/2))/3^r`

`T_(r+1)=18C_rxx9^(18-r)xx(-1)^2/3^rxx x^18-(3r)/2`

`18-(3r)/2=0`

`r=12`

`18C_12xx9^6/3^12=alphaxx18C_12`

`alpha=1`