Question

In the expansion of $(7^{\frac{1}{3}}+{11}^{\frac{1}{9}}{)}^{6561}$,

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

Answer 1

Answer: (A), (B), (C)

there are exactly $730$ rational terms
there are exactly $5832$ irrational terms
the term which involves greatest binomial coefficient is irrational

Total number of rational terms will be
$1+\frac{6561}{L.C.M(3,9)}$
$=1+\frac{6561}{9}$
$=730$
Hence total number of irrational terms will be
Total number of terms-total number of rational terms
$=6562-730$
$=5832$
The middle terms are ${\left(\frac{N+1}{2}\right)}^{th}$ term and ${(\frac{N+1}{2}+1)}^{th}$ term.
Both are irrational.