If _ r=1 ^ 9 ( r+3 2^r ). ^9C_r = ( 3 2 )^9 - , , N, then ( + )^2 is equal to

JEE Main 2025 Mathematics question

If , , then is equal to

Answer: (3)

Splitting the sum and simplifying using binomial identities gives , , so .

Question ID VK-002643