The smallest natural number n, such that the coefficient of x in the expansion of \left(\left(\right. x^{2} + \frac{1}{x^{3}} \left.\right)\right)^{n} is nC23, is

Engineering

Mathematics

Introduction to Binomial Theorem

Question

The smallest natural number n, such that the coefficient of x in the expansion of ${(x^{2} + \frac{1}{x^{3}})}^{n}$ is ⁿC₂₃, is

College PredictorLive

Know your College Admission Chances Based on your Rank/Percentile, Category and Home State.

Get your JEE Main Personalised Report with Top Predicted Colleges in JoSA

$T_{r + 1} = {\sum_{r = 0}^{n}}^{n} C_{r} x^{2 n - 2 r} . x^{- 3 r}$

2n – 5r = 1 ⇒ 2n = 5r + 1 for r = 15, n = 38 smallest value of n is 38.