Binomial Theorem 1 Question 9

10. The ratio of the 5th term from the beginning to the 5th term from the end in the binomial expansion of 213+12(3)13 is

(2019 Main, 12 Jan I)

(a) 1:2(6)13

(b) 1:4(16)13

(c) 4(36)13:1

(d) 2(36)13:1

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Answer:

Correct Answer: 10. (c)

Solution:

  1. Since, r th term from the end in the expansion of a binomial (x+a)n is same as the (nr+2) th term from the beginning in the expansion of same binomial.

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

T5T105+2=10C4(21/3)10412(3)1/310C6(21/3)10612(3)1/3=26/3(2(3)1/3)624/3(2(3)1/3)4[Tr+1=nCrxnrar][10C4=10C6]=26/34/3(2(3)1/3)64=22/322323=4(6)2/3=4(36)1/3

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



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