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Find the coefficient of x^(6) in the exp...

Find the coefficient of `x^(6)` in the expansion of `(2x^(3)-(1)/(3x^(3)))^(10)`

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The correct Answer is:
N/a
Let (r+1)th terms in the expansion of `(2x^(3)-(1)/(3x^(3)))^(10) " is " T_(r+1)`.
`T_(r+1)=^(10)C_(r)(2x^(3))^(10-r)(-(1)/(3x^(3)))^(r)`
`=^(10)C_(r).2^(10-r).x^(30-3r).((-1)^r)/(3^(r).x^(3r))`
`=^(10)C_(r).(2^(10-r).(-1))/(3^(r)).x^(30-6r)`
Let 30 -6r =6
`rArr " "6r =24`
`rArr " "r=4`
`:.` coefficient of `x^(6)=^(10)C_(4).(2^(10-4)(-1)^(4))/(3^(4))`
`(|ul10)/(|ul6|ul4)xx(64)/(81)`
`(7xx8xx9xx10)/(24)xx(64)/(81)`
`(4480)/(27).`
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Knowledge Check

  • Find the coefficient of x^(4) in the expansion of (2x^(2)+(3)/(x^(3)))^(7)

    A
    `""^(7)C_(2)2^(5)3^(3)`
    B
    `""^(7)C_(2)2^(5)3^(2)`
    C
    `""^(7)C_(2)3^(5)2^(2)`
    D
    `""^(7)C_(2)2^(5)3^(2)`

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