JEE Mains · Maths · STD 11 - 7. binomial theoram
The number of positive integers \(k\) such that the constant term in the binomial expansion of \(\left(2 x^{3}+\frac{3}{x^{k}}\right)^{12}, x \neq 0\) is \(2^{8} \cdot \ell\), where \(\ell\) is an odd integer, is......
- A \(20\)
- B \(9\)
- C \(2\)
- D \(70\)
Answer & Solution
Correct Answer
(C) \(2\)
Step-by-step Solution
Detailed explanation
\(\left(2 x^{3}+\frac{3}{x^{k}}\right)^{12}\) \(t _{ r +1}={ }^{12} C _{ r }\left(2 x ^{3}\right)^{ r }\left(\frac{3}{ x ^{ k }}\right)^{12- r }\) \(x ^{3 r -(12- r ) k } \rightarrow constant\) \(\therefore 3 r -12 k + rk =0\) \(\Rightarrow k =\frac{3 r }{12- r }\)…
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