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Question

For the expansion of (2+315)10, which of the following is (are) TRUE?

A
Sum of rational terms is 41
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B
There are two rational terms.
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C
There are four rational terms.
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D
Sum of rational terms is 61
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Solution

The correct options are
A Sum of rational terms is 41
B There are two rational terms.
General term (r+1)th term is
10Cr210r23r5
This is rational if 10r is even or zero and r is multiple of 5 or r is zero
So,
if r=5 then 10r is not even
if r=10 then 10r=0
if r=0 then 10r=10 an even number
So, this will be rational only if r=0,10
So number of rational terms is 2
Sum of rational terms =10C025+10C1032=41

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