In each of the following questions two equations are given. Solve these equations and give answer : (i) (x^2 - 15\sqrt{3}x + 162 = 0) (ii) (y^2 - 9\sqrt{2}y + 36 = 0)

For equation (i): x^2 - 15√3 x + 162 = 0. The roots are x = [15√3 ± √(675 - 648)]/2 = [15√3 ± √27]/2 = [15√3 ± 3√3]/2. Roots are x = 18√3/2 = 9√3 ≈ 15.59 and x = 12√3/2 = 6√3 ≈ 10.39. For equation (ii): y^2 - 9√2 y + 36 = 0. Using quadratic formula: y = [9√2 ± √(162 - 144)]/2 = [9√2 ± √18]/2 = [9√2 ± 3√2]/2. Roots are y = 12√2/2 = 6√2 ≈ 8.49 and y = 6√2/2 = 3√2 ≈ 4.24. Both roots of x (≈15.59, ≈10.39) are greater than both roots of y (≈8.49, ≈4.24). So x > y always. Option B is correct.