Match the LIST-I with LIST-II

	LIST-I		LIST-II
A.	A matrix which is both symmetric and skew symmetric	I.	symmetric matrix
B.	All positive integral powers of a symmetric matrix	II.	unit matrix
C.	Positive odd integral powers of a skew-symmetric matrix	III.	null matrix
D.	A square matrix $A = [a_{ij}]_{n\times n}$ with $a_{ij} = \begin{cases}0, & \forall\, i \neq j \\ 1, & \forall\, i = j\end{cases}$	IV.	skew-symmetric matrix

Choose the correct answer from the options given below:

Which of the following are true for the given graph.

(A) Break even point is at x = 10

(B) Break even point is at x = 8

(C) Break even point is at x = 6

(D) Fixed cost is 20

(E) Fixed cost is 0

Choose the correct answer from the options :

Let A be a square matrix. Then,

(A) $A + A^T$ is a symmetric matrix

(B) $A - A^T$ is a skew-symmetric matrix

(C) $AA^T$ is a skew-symmetric matrix

(D) $A^T A$ is a symmetric matrix

Choose the correct answer from the options given below :

If $A = \begin{bmatrix} n & 0 & 0 \\ 0 & n & 0 \\ 0 & 0 & n \end{bmatrix}$ and $B = \begin{bmatrix} a_1 & a_2 & a_3 \\ b_1 & b_2 & b_3 \\ c_1 & c_2 & c_3 \end{bmatrix}$, then AB is equals to :

A die is rolled thrice. What is the probability of getting a number greater than 4 in the first and the second throw of dice and a number less than 4 in the third throw?

If A is a skew symmetric matrix, then $A^2$ is

If A is square matrix of order 3 with $|A| = 3$, then $|4 \text{ adj} A|$ is equal to :