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Question

If the sixth term from the beginning is equal to the sixth term from the end in the expansion of (21/5+31/5)n, then the sum of the rational terms in the expansion is

A
13499
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B
15499
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C
17599
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D
11199
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Solution

The correct option is B 15499
In the expansion of (21/5+31/5)n,
Tr+1=nCr(21/5)nr(31/5)r

Given that T6=Tn4
nC5(2n/56)=nCn5(63n/5)
6n/5=36
n=10

Tr+1=10Cr(2)10r5(3)r5
The term will be rational only when r=0,5,10
Sum of rational terms =T1+T6+T11
=10C022+10C523+10C1019
=4+168+19
=15499

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