JEE Mains · Maths · STD 11 - 7. binomial theoram
The smallest natural number \(n,\) such that the coefficient of \(x\) in the expansion of \({\left( {{x^2}\, + \,\frac{1}{{{x^3}}}} \right)^n}\) is \(^n{C_{23}}\) is
- A \(38\)
- B \(58\)
- C \(23\)
- D \(35\)
Answer & Solution
Correct Answer
(A) \(38\)
Step-by-step Solution
Detailed explanation
\({T_{r + 1}}\, = \,\sum\limits_{r = 0}^n {^n{C_r}\,{x^{2n - 2r}}\,.\,{x^{ - 3r}}} \) \(2n - 5r = 1\Rightarrow 2n = 5r + 1\) for \(r = 15, n = 38\) smallest value of \(n\) is \(38\).
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