If ^ 11 C_1 2 + ^ 11 C_2 3 + + ^ 11 C_9 10 = nm with gcd(n, m) = 1, then n + m is equal to ________.

JEE Main 2024 Mathematics question

If with gcd(n, m) = 1, then n + m is equal to .

Answer: 2041

Integrating (1 + x)¹¹ = Σ ¹¹Cᵣxʳ from 0 to 1 gives (2¹² − 1)/12 = Σ_{r=0}^{11} ¹¹Cᵣ/(r + 1). Removing the terms r = 0, 10 and

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Question ID VK-016915