JEE Mains · Maths · STD 11 - 7. binomial theoram
If the fourth term in the expansion of \(\left(x+x^{\log _{2} x}\right)^{7}\) is \(4480,\) then the value of \(x\) where \(x \in N\) is equal to
- A \(2\)
- B \(4\)
- C \(3\)
- D \(1\)
Answer & Solution
Correct Answer
(A) \(2\)
Step-by-step Solution
Detailed explanation
\({ }^{7} C _{3} x ^{4} x ^{\left(3 \log _{2}^{x}\right)}=4480\) \(\Rightarrow x ^{\left(4+3 \log _{2}^{x}\right)}=2^{7}\) \(\Rightarrow \quad(4+3 t ) t =7 ; t =\log _{2} x\) \(\Rightarrow t =1, \frac{-7}{3} \Rightarrow x =2\)
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