Concept:1). In the expansion of (x + y)n, the term having the greatest coefficient is the middle term.2). When n is even, the middle term is \(\displaystyle \frac{n+2}{2}\) and the greatest coefficient is nCn/23). When n is odd, the middle term is \(\displaystyle \frac{n+1}{2}\) or \(\displaystyle \frac{n+3}{2}\) and the greatest coefficient is \(\displaystyle ^nC_{\frac{n-1}{2}}\) or \(\displaystyle ^nC_{\frac{n+1}{2}}\)4). rth term for the binomial expression, (x + y)n, Tr = nCr-1 xn-r-1 yr-1Calculation:The given expansion is (x + y)10Statement I: Among all the coefficients of the terms, the coefficient of the 6th term has the highest valueThe value of n is 10 which is even. So, the term having the greatest coefficient is the \(\displaystyle \frac{n+2}{2}\) = \(\displaystyle \frac{10+2}{2}\) = 6? The coefficient of the 6th term has the highest value.Statement II: The coefficient of the 3rd term is equal to the coefficient of the 9th term.We know that, \(^nC_r=\frac{n!}{r!(n-r)!}\)The coefficient of the 3rd term, T3 = 10C2 = \(\frac{10!}{8!.2!}\)The coefficient of the 9th term, T9 = 10C8 = \(\frac{10!}{8!.2!}\) ? Coefficient of the 3rd term = Coefficient of the 9th term.? Both Statement I and II are correct.