TS EAMCET · Maths · Binomial Theorem
The sixth term in the expansion of \(\left(3-\sqrt{\frac{17}{4}+3 \sqrt{2}}\right)^{10}\) is a
- A positive rational number
- B negative rational number
- C positive irrational number
- D negative irrational number
Answer & Solution
Correct Answer
(D) negative irrational number
Step-by-step Solution
Detailed explanation
We have, \[ \left(3-\sqrt{\frac{17}{4}+3 \sqrt{2}}\right)^{20} \Rightarrow T_6=-{ }^{20} C_5(3)^5\left(\frac{17}{4}+3 \sqrt{2}\right)^{5 / 2} \] \(\therefore \mathrm{r}_6=\) negative irrational number
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