NDA Mathematics Question (2025) — Solution

Step-by-step solution

The general term in the expansion of (1 + x)^ n is given by T_ r+1 = ^ n C_ r x^ r , where the coefficient of x^ r is ^ n C_ r . For an even integer n, the greatest binomial coefficient is the middle term, which is ^ n C_ n/2 . Given n = 100, which is even, the greatest coefficient is ^ 100 C_ 100/2 = ^ 100 C_ 50 . This corresponds to the coefficient of x^ 50 . Answer: The coefficient of x^ 50