Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • The number of rational terms in the binomial expansion of is ____

The number of rational terms in the binomial expansion of \left(4^{\frac{1}{4}}+5^{\frac{1}{6}}\right)^{120}is ________
 

Answers (3)

best_answer

\left(4^{\frac{1}{4}}+5^{\frac{1}{6}}\right)^{120}=\left(2^{\frac{2}{4}}+5^{\frac{1}{6}}\right)^{120}=\left(2^{\frac{1}{2}}+5^{\frac{1}{6}}\right)^{120}

General term

\begin{aligned} &={ }^{120} C_{r}\left(2^{\frac{1}{2}}\right)^{120-r}\left(5^{\frac{1}{6}}\right)^{r} \\ &={ }^{120} C_{r}(2)^{60-\frac{r}{2}}(5)^{\frac{r}{6}} \end{aligned}

For this term to be rational, r should be a multiple of 2 and r should be a multiple of 6

\begin{aligned} &\text { As } \quad 0 \leq r \leq 120 \\ &\Rightarrow r=0,6,12, \ldots 120 \end{aligned}

Total of 21 values of r

Hence, the correct answer is 21.

Posted by

Kuldeep Maurya

View full answer

21

Posted by

Anjali

View full answer

21

Posted by

Anjali

View full answer

Similar Questions

Latest Question