Skew Symmetric Matrix

Q. 3. Consider two sets A={a, b, c}, B={e, f}. If maximum number of total releation from A to B; symmetric releation from A to A and From B to B are l, m, n respectively, then the value of 2l+ m-n

Q. If A and B be 2 sets such that n(A) = 15, n(B)= 25 then number of possible value of symmetric difference of A and B is

Q. If A and B are symmetric matrices then (AB + BA) is a matrix and (AB - BA) is a matrix.

1. skew - symmetric
2. symmetric
3. null
4. identity

Q. If A is a skew-symmetric matrix of order 3, then the matrix $A^4$ is

1. skew symmetric
2. symmetric
3. diagonal
4. none of those

Q.

If A is a square matric $\left[\begin{array}{ccc}1& 2& 3\\ 4& 5& 6\\ 7& 8& 9\end{array}\right]$ then A - $A^T$ is symmetric.

1. True

2. False

Q. Two cubes have their face painted as either red or blue color. 1st cube has 5 faces red and 1 face blue. The Probability that both the faces show same color on rolling is $\frac{1}{2}$. How many red faces are present on the $2^{nd}$ cube.

1. 4
2. 3
3. 6
4. 2

Q. If both $A-\frac{1}{2}I$ and $A+\frac{1}{2}I$ are orthogonal matrices, then

1. $A$ is orthogonal
2. $A^2=\frac{3}{4}I$
3. $A$ is skew-symmetric
4. none of these

Q. The number of $4\times 4$ skew symmetric matrices that can be formed using exactly four $0$'s, six $3$'s and six $-3$'s is

Q. If U={1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, A={1, 2, 3, 4, 5}, A symmetric difference B={1, 2, 3, 4} then find n[B-A].

Q. The symmetric difference of A and B is
(a) $\left(A-B\right)\cap \left(B-A\right)$
(b) $\left(A-B\right)\cup \left(B-A\right)$
(c) $\left(A\cup B\right)-\left(A\cap B\right)$
(d) $\left\{\left(A\cup B\right)-A\right\}\cup \left\{\left(A\cup B\right)-B\right\}$

Q. The matrix $X$ for which $\left[\begin{array}{cc}1& -4\\ 3& -2\end{array}\right]X=\left[\begin{array}{cc}-16& -6\\ 7& 2\end{array}\right],$ is

1. $\left[\begin{array}{cc}-2& 4\\ -3& 1\end{array}\right]$
2. $\left[\begin{array}{cc}6& 2\\ \frac{11}{2}& 2\end{array}\right]$
3. $\left[\begin{array}{cc}-16& -6\\ 7& 2\end{array}\right]$
4. $\left[\begin{array}{cc}-\frac{1}{5}& \frac{2}{5}\\ -\frac{3}{10}& \frac{1}{5}\end{array}\right]$

Q.

In how many ways a 4 letter code can be formed from the letters of English alphabet with at least one symmertric letters of the english alphabet?

Q. $\mathrm{If}\left(\begin{array}{cc}2& 9\\ 6& 8\end{array}\right]\mathrm{is}\mathrm{expressed}\mathrm{as}\mathrm{the}\mathrm{sum}\mathrm{of}a\mathrm{symmetric}\mathrm{and}a\mathrm{skew}\mathrm{symmetric}\mathrm{matrix},\mathrm{then}\mathrm{those}\mathrm{are}$

1. $\left(\begin{array}{cc}2& \frac{15}{2}\\ \frac{15}{2}& 8\end{array}\right]\mathrm{and}\left(\begin{array}{cc}0& \frac{3}{2}\\ -\frac{3}{2}& 0\end{array}\right]$
2. $\left(\begin{array}{cc}4& 5\\ 3& 8\end{array}\right]\mathrm{and}\left(\begin{array}{cc}3& 2\\ 1& 0\end{array}\right]$
3. None of these

Q. Matrices of order $3\times 3$ are formed using the elements of set $A=\{-3,-2,-1,0,1,2,3\}.$ Then the probability that matrices are either symmetric or skew-symmetric, is

1. $\frac{1}{7^6}+\frac{1}{7^3}$
2. $\frac{1}{7^6}+\frac{1}{7^3}-\frac{1}{7^8}$
3. $\frac{1}{7^3}+\frac{1}{7^8}$
4. $\frac{1}{7^3}+\frac{1}{7^6}-\frac{1}{7^9}$

Q. Let A and B are two non-singular square matrices, $A^T$ and $B^T$ are the transpose matrices of A and B respectively, then which of the following is correct

1. $B^{T}AB$ is symmetric matrix if and only if A is symmetric
2. $B^{T}AB$ is symmetric matrix if and only if B is symmetric
3. $B^{T}AB$ is skew symmetric matrix for every matrix A
4. $B^{T}AB$ is skew symmetric matrix if B is skew symmetric

Q. If N=√5328/961, then (31×N) is

Q. The symmetric difference of A = {1, 2, 3} and B = {3, 4, 5} is
(a) {1, 2}
(b) {1, 2, 4, 5}
(c) {4, 3}
(d) {2, 5, 1, 4, 3}

Q.

If A and B are two square matrices which are skew symmetric then $(AB{)}^T$ equals to

1. AB
2. BA
3. -AB
4. -BA