AP EAMCET · Maths · Binomial Theorem
The number of all possible values of k for which the expansion \((\sqrt{x}+\sqrt[k]{y})^{10}\) will have exactly nine irrational terms is
- A 3
- B 4
- C 5
- D 6
Answer & Solution
Correct Answer
(C) 5
Step-by-step Solution
Detailed explanation
Total number of terms \(= 10+1 = 11\). Exactly nine irrational terms means exactly \(= 11-9 = 2\) rational terms. The general term is \(T_{r+1} = \binom{10}{r} (\sqrt{x})^{10-r} (\sqrt[k]{y})^r = \binom{10}{r} x^{\frac{10-r}{2}} y^{\frac{r}{k}}\). For a term to be rational,…
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