If $A, B$ and $C$ are three singular matrices given by $A=\left[\begin{array}{ll}1 & 4 \\ 3 & 2 a\end{array}\right], B=\left[\begin{array}{ll}3 b & 5 \\ a & 2\end{array}\right]$ and $C=\left[\begin{array}{cc}a+b+c & c+1 \\ a+c & c\end{array}\right]$, then the value of $a b c$ is :

The value of $\begin{vmatrix}2 & 3 & 4\\5 & 6 & 8\\6x & 9x & 12x\end{vmatrix}$ is

The value of $\Delta = \begin{vmatrix} 2\sin40^\circ & 2\sin50^\circ \\ -3\cos40^\circ & 3\cos50^\circ \end{vmatrix}$ is:

If A is a square matrix such that $A^2=A$ and $I$ is identity matrix of same order, then $(2I+A)^3-19A$ is equal to:

If $\begin{vmatrix}x&2\\18&x\end{vmatrix} = \begin{vmatrix}6&2\\18&6\end{vmatrix}$, then x equals:

If $A=\begin{bmatrix}k & 2\\2 & k\end{bmatrix}$ such that $\lvert A^3 \rvert = 125$ then which of the following statements are TRUE?

(A) $\lvert k.adj(3A) \rvert = 405$

(B) $\lvert k.adj(3A) \rvert = 2025$

(C) $\lvert adj(3A) \rvert = 95$

(D) $\lvert adj(3A) \rvert = 45$

Choose the correct answer from the options given below:

If $\begin{vmatrix} 1 & -2 & 5 \\ 2 & \lambda & -1 \\ 0 & 4 & 2\lambda \end{vmatrix} = 86$, the sum of the values of $\lambda$ is: