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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 10Cr⋅210−r23r5 This is rational if 10−r is even or zero and r is multiple of 5 or r is zero So, if r=5 then 10−r is not even if r=10 then 10−r=0 if r=0 then 10−r=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 =10C0⋅25+10C10⋅32=41

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