JEE Main Mathematics Question (2026) — Solution

Step-by-step solution

The expansion of (1 + x)^ 26 has 27 terms. The middle term is T_ 14 . The coefficient of the middle term is ^ 26 C_ 13 ^ 13 . The expansion of (1 - x)^ 28 has 29 terms. The middle term is T_ 15 . The coefficient of the middle term is ^ 28 C_ 14 (- )^ 14 = ^ 28 C_ 14 ^ 14 . Equating the two coefficients: ^ 26 C_ 13 ^ 13 = ^ 28 C_ 14 ^ 14 Since 0, dividing by ^ 13 gives: = ^ 26 C_ 13 ^ 28 C_ 14 Expanding the combinations using factorials: ^ 28 C_ 14 = 28! 14! 14! = 28 27 26! 14 13! 14 13! = 28 27 14 14 26! 13! 13! ^ 28 C_ 14 = 27 7 ^ 26 C_ 13 Substituting this back: = ^ 26 C_ 13 27 7 ^ 26 C_ 13 = 7 27 Answer: 7 27