JEE Main Mathematics Question (2026) — Solution

Step-by-step solution

The given equation is a + b + 2c = 22, where a, b, c are non-negative integers. This can be rewritten as a + b = 22 - 2c. Since a 0 and b 0, we must have 22 - 2c 0, which gives c 11. Since c is a non-negative integer, the possible values for c are 0, 1, 2, , 11. For a fixed value of c, the number of non-negative integer solutions to the equation a + b = 22 - 2c is given by (22 - 2c) + 1 = 23 - 2c. The total number of solutions n(A) is the sum of the number of solutions for each possible value of c: n(A) = _ c=0 ^ 11 (23 - 2c) n(A) = 23 + 21 + 19 + + 1 This is an arithmetic progression with 12 terms, first term 1, and last term 23. n(A) = 12 2 (1 + 23) = 6 24 = 144 Answer: 144