In the expansion of x3−1x2n,n∈N, if the sum of the coefficients of x5 and x10is 0, then n is

In the expansion of x31x2n,nN, if the sum of the coefficients of x5 and x10is 0, then n is

  1. A

    25

  2. B

    20

  3. C

    15

  4. D

    None of these

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    Solution:

    x31r2n
    General term Tr+1=n!r!(nr)!(1)nrx5n2n
    If 5r2n=5, then 5r=2n+5 or r=2n5+1
    If 5r2n=10, then 5r=2n+10 or r=2n5+2
    x5 and x10 terms occurs if n=5k
    Given that sum of x5 and x10 is zero.
    5k!(2k+1)!(3k1)!5k!(2k+2)!(3k2)!=0
    or  13k112k+2=0
    or   k=3n=15

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