Evaluate the determinant: $\left| \begin{array}{ccc} a_1 & m a_1 & b_1 \\ a_2 & m a_2 & b_2 \\ a_3 & m a_3 & b_3 \end{array} \right|$

If $A_1B_1C_1, A_2B_2C_2, A_3B_3C_3$ are three-digit numbers,each of which is divisible by $k$,and $\Delta = \begin{vmatrix} A_1 & B_1 & C_1 \\ A_2 & B_2 & C_2 \\ A_3 & B_3 & C_3 \end{vmatrix}$,then $\Delta$ is divisible by:

If $a, b, c$ are unequal,what is the condition that the value of the following determinant is zero? $\Delta = \left| \begin{array}{ccc} a & a^2 & a^3 + 1 \\ b & b^2 & b^3 + 1 \\ c & c^2 & c^3 + 1 \end{array} \right|$

If $x, y, z$ are all positive and are the $p$-th, $q$-th, and $r$-th terms of a geometric progression respectively, then the value of the determinant $\left|\begin{array}{lll} \log x & p & 1 \\ \log y & q & 1 \\ \log z & r & 1 \end{array}\right|$ equals:

If $\Delta = \begin{vmatrix} a + x & b & c \\ b & x + c & a \\ c & a & x + b \end{vmatrix}$,which of the following is a factor for the above determinant?

If $\left| \begin{array}{ccc} a^2 & b^2 & c^2 \\ (a + \lambda)^2 & (b + \lambda)^2 & (c + \lambda)^2 \\ (a - \lambda)^2 & (b - \lambda)^2 & (c - \lambda)^2 \end{array} \right| = k\lambda \left| \begin{array}{ccc} a^2 & b^2 & c^2 \\ a & b & c \\ 1 & 1 & 1 \end{array} \right|, \lambda \neq 0$,then $k$ is equal to