If x, y, z are in arithmetic progression with common difference d, x ≠ 3d, and the determinant of the matrix [ 3 4 2 x 4 5 2 y 5 k z ] is zero, then the value of k² is:

Matrices and Determinants: JEE Main 2021 Mathematics question

JEE Main 2021 · 17 Mar, Evening shift · Q4464

JEE Main 202117 Mar, Evening shiftMathematicsMediumMatrices and Determinants245× since 2002

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

\ne

3d, and the determinant of the matrix

\left[ {\matrix{ 3 & {4\sqrt 2 } & x \cr 4 & {5\sqrt 2 } & y \cr 5 & k & z \cr } } \right]

is zero, then the value of k² is :

JEE Main 2021 · 17 Mar, Evening shift · Q4464

JEE Main 202117 Mar, Evening shiftMathematicsMediumMatrices and Determinants245× since 2002

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

\ne

3d, and the determinant of the matrix

\left[ {\matrix{ 3 & {4\sqrt 2 } & x \cr 4 & {5\sqrt 2 } & y \cr 5 & k & z \cr } } \right]

is zero, then the value of k² is :