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Question

The numerically greatest term in the expansion of (3+2x)14 when x=4/5 is

A
4th term
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B
5th term
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C
6th term
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D
7th term
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Solution

The correct option is B 6th term
We know that in expansion of (x+y)n
Tr+1Tr=(nr+1)ryx
Let Tr+1 be the greatest term
|Tr+1Tr|=14r+1r|2x3|
|Tr+1Tr|=15rr|815|
|Tr+1Tr|=1208r15r
For greatest term,
|Tr+1Tr|1
1208r15r1
23r120
r=5
So, the greatest term is Tr+1
T5+1=14C5(3)9(2x)5

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