JEE Mains · Maths · STD 11 - 7. binomial theoram
If the maximum value of the term independent of \(t\) in the expansion of \(\left( t ^{2} x ^{\frac{1}{5}}+\frac{(1- x )^{\frac{1}{10}}}{ t }\right)^{15}, x \geq 0\), is \(K\), then \(8\,K\) is equal to \(....\)
- A \(6006\)
- B \(6005\)
- C \(6007\)
- D \(6008\)
Answer & Solution
Correct Answer
(A) \(6006\)
Step-by-step Solution
Detailed explanation
\(\left( t ^{2} x ^{\frac{1}{5}}+\frac{(1- x )^{\frac{1}{10}}}{ t }\right)^{15}\) \(T_{r+1}={ }^{15} C_{r}\left(t^{2} x^{\frac{1}{5}}\right)^{15-r} \cdot \frac{(1-x)^{\frac{r}{10}}}{t^{r}}\) For independent of \(t\), \(30-2 r-r=0\) \(r =10\) So, Maximum value of…
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