Question

# In the expansion of (713+1119)6561There are exactly 730 rational termsThere are exactly 5831 irrational terms The term which involves greatest binomial coefficients is irrational The term which involves greatest binomial coefficients is rational

Solution

## The correct options are A There are exactly 730 rational terms C The term which involves greatest binomial coefficients is irrational General term is  6561Cr(76561−r3)11r9. Terms will be rational if r is a multiple of 9.  ∴ r=0,9,18,27,....,6561. Now 6561=0+(n−1)9⇒n=730 Hence, there are 730 rational terms. The greatest binomial coefficients are  6561C6561−12 and 6561C6561+12 ⇒6561C3280 and 6561C3281 Now, 3280 are 3281 are not a multiple of 3; hence, both terms involving greatest binomial coefficients are irrational.

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