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Question

In the expansion of (713+1119)6561,

A
there are exactly 730 rational terms
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B
there are exactly 5832 irrational terms
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C
the term which involves greatest binomial coefficient is irrational
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D
the term which involves greatest binomial coefficients is rational
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Solution

The correct options are
A there are exactly 730 rational terms
B there are exactly 5832 irrational terms
D the term which involves greatest binomial coefficient is irrational
Total number of rational terms will be
1+6561L.C.M(3,9)
=1+65619
=730
Hence total number of irrational terms will be
Total number of terms-total number of rational terms
=6562730
=5832
The middle terms are (N+12)th term and (N+12+1)th term.
Both are irrational.

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