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Question

Find n in the binomial [32+133]n if the ratio of the 7th term from beginning to the 7th term from the end is 16

A
n=7
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B
n=8
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C
n=9
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D
n=10
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Solution

The correct option is C n=9
The total number of terms in binomial expansion are (n+1),
Therefore, 7th term from last will be (n5)th term.
Given,
T7Tn5=16
nC6(2)13(n6)(3)13(6)nCn6(2)13(6)(3)13(n6)=16
n!6!(n6)!(n6)!6!n!(2)13(n12)(3)13(6n+6)=16
(6)13(n12)=(6)1
Equating the powers,
n12=3
So, n=9.

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