NDA Mathematics Question (2025) — Solution

Step-by-step solution

Converting the given binary numbers to decimal: x = (1111)_2 = 1 2^3 + 1 2^2 + 1 2^1 + 1 2^0 = 15 y = (1001)_2 = 1 2^3 + 0 2^2 + 0 2^1 + 1 2^0 = 9 z = (110)_2 = 1 2^2 + 1 2^1 + 0 2^0 = 6 Observing the relationship between x, y, and z: y + z = 9 + 6 = 15 = x x - y - z = 0 Using the algebraic identity, if a + b + c = 0, then a^3 + b^3 + c^3 - 3abc = 0. Substituting a = x, b = -y, and c = -z: x + (-y) + (-z) = 0 x^3 + (-y)^3 + (-z)^3 - 3(x)(-y)(-z) = 0 x^3 - y^3 - z^3 - 3xyz = 0 In binary representation, 0 is (0)_2. Answer: (0)_2