Correct Answer - Option 2 : 5k
Concept:
Properties of Determinant:
Any scalar multiplied to a row or a column can be taken out, e.g.
\(\begin{vmatrix} ka_{11} &ka_{12} & ka_{13}\\ a_{21} & a_{22} & a_{23}\\ a_{31} & a_{32} & a_{33} \end{vmatrix}\) = k\(\begin{vmatrix} a_{11} &a_{12} & a_{13}\\ a_{21} & a_{22} & a_{23}\\ a_{31} & a_{32} & a_{33} \end{vmatrix}\) = k[a11(a22 a33 - a23 a32) - a12(a21 a33 - a23 a31) + a13(a21 a32 - a22 a31)]
Calculation
Given \(\begin{vmatrix} p & q & r \\ x & y & z \\ a & b& c \end{vmatrix}\) = 5
Now,
\(\begin{vmatrix} kp & kq &k r \\ x & y & z \\ a & b& c \end{vmatrix}\) = k\(\begin{vmatrix} p & q & r \\ x & y & z \\ a & b& c \end{vmatrix}\)
= 5k