Consider a determinant $\Delta=\begin{vmatrix}3a & -a+b & -a+c\\ -b+a & 3b & -b+c\\ -c+a & -c+b & 3c\end{vmatrix}$, then

Match the LIST-I with LIST-II

	LIST-I (Value of $a, b, c$)		LIST-II (Value of $\Delta$)
A.	$a = 0, b = 0, c = 1$	I.	$27$
B.	$a = 0, b = 1, c = 1$	II.	$0$
C.	$a = 0, b = 2, c = -1$	III.	$6$
D.	$a = 1, b = 1, c = 1$	IV.	$-6$

Choose the correct answer from the options given below:

If $A = [a_{ij}]$ is skew symmetric matrix of order 'n', then

If $A = \begin{pmatrix} \cos 2\theta & \sin 2\theta \\ -\sin 2\theta & \cos 2\theta \end{pmatrix}$, then $A^2 =$

If $A=\begin{bmatrix}2 & 3\\1 & 2\end{bmatrix}, I=\begin{bmatrix}1 & 0\\0 & 1\end{bmatrix}$ and $A^2=\alpha A+\beta I$, for some constant $\alpha$ and $\beta$ then the value of $\alpha$ and $\beta$ respectively:

If the points (2, 1), $(-1, 4)$ and (a, 3) are collinear then the value/(s) of a is/(are) :

If area of the triangle formed by A(1, 3), B(0, 0) and C(k, 0) is 3 sq. units, then which of the following is/are TRUE?

A. k = 2

B. k = -2

C. k = 3

D. k = -3

Choose the correct answer from the options given below:

If A and B are two symmetric matrices of the same order, then