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Let (r+1)th terms in the expansion of `(2x^(3)-(1)/(3x^(3)))^(10) " is " T_(r+1)`. <br> `T_(r+1)=^(10)C_(r)(2x^(3))^(10-r)(-(1)/(3x^(3)))^(r)` <br> `=^(10)C_(r).2^(10-r).x^(30-3r).((-1)^r)/(3^(r).x^(3r))` <br> `=^(10)C_(r).(2^(10-r).(-1))/(3^(r)).x^(30-6r)` <br> Let 30 -6r =6 <br> `rArr " "6r =24` <br> `rArr " "r=4` <br> `:.` coefficient of `x^(6)=^(10)C_(4).(2^(10-4)(-1)^(4))/(3^(4))` <br> `(|ul10)/(|ul6|ul4)xx(64)/(81)` <br> `(7xx8xx9xx10)/(24)xx(64)/(81)` <br> `(4480)/(27).`**Introduction**

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