JEE Mains · Maths · STD 11 - 7. binomial theoram
If the term independent of \(x\) in the exapansion of \(\left(\frac{3}{2} x^{2}-\frac{1}{3 x}\right)^{9}\) is \(k,\) then \(18 k\) is equal to
- A \(9\)
- B \(11\)
- C \(5\)
- D \(7\)
Answer & Solution
Correct Answer
(D) \(7\)
Step-by-step Solution
Detailed explanation
\(T _{ r +1}={ }^{9} C _{ r }\left(\frac{3}{2} x ^{2}\right)^{9- r }\left(-\frac{1}{3 x }\right)^{ r }\) \(T _{ r +1}={ }^{9} C _{ r }\left(\frac{3}{2}\right)^{9- r }\left(-\frac{1}{3}\right)^{ r } x ^{18-3 r }\) For independent of x \(18-3 r=0, r=6\)…
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