JEE Main Mathematics Question (2026) — Solution

Step-by-step solution

Using the property ^ n C_ r = ^ n C_ n-r , the given expression can be written as: ^ 30 C_ r + 3 ^ 30 C_ r-1 + 3 ^ 30 C_ r-2 + ^ 30 C_ r-3 This expression represents the coefficient of x^r in the expansion of: (1+x)^ 30 + 3x(1+x)^ 30 + 3x^2(1+x)^ 30 + x^3(1+x)^ 30 Taking (1+x)^ 30 common, we get: (1+x)^ 30 (1 + 3x + 3x^2 + x^3) = (1+x)^ 30 (1+x)^3 = (1+x)^ 33 The coefficient of x^r in (1+x)^ 33 is ^ 33 C_ r . Comparing this with ^ m C_ r , we get m = 33. Answer: 33