A ratio of the 5th term from the beginning to the 5th term from the end in the binomial expansion of 213+12(3)1310 is 

A ratio of the 5th term from the beginning to the 5th term from the end in the binomial expansion of 213+12(3)1310 is 

  1. A

    1:2(6)13

  2. B

    1:4(16)13

  3. C

    4(36)13:1

  4. D

    2(36)13:1

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    Solution:

    Since, rth term from the end in the expansion of a binomial (r +α)n is same as the (n - r +2)th term from the beginning in the expansion of same binomial.

     Required ratio =T5T105+2=T5T7=T4+1T6+1

     T5T105+2= 10C421/310412(3)1/34 10C621/310612(3)1/36

    Tr+1=nCrxnrar10C4=10C6

    =26/32(3)1/3624/32(3)1/34=26/34/32(3)1/364=22322323=4(6)23=4(36)1/3

    So, the required ratio is. 4(36)1/3:1

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