If x, y, z are in arithmetic progression with common difference d, x ≠ 3d,

Question

If x, y, z are in arithmetic progression with common difference d, x \(\neq\) 3d, and the determinant of the matrix \(\begin{bmatrix} 3 & 4\sqrt{2} & x \\[0.3em] 4 & 5\sqrt{2} & y \\[0.3em] 5 & k & z \end{bmatrix}\) is zero, then the value of k² is

(1) 72

(2) 12

(3) 36

(4) 6

Answer 1

Answer is (1)