Question 1 :
If $A$ and $B$ are square matrices such that $AB = I$ and $BA = I$, then $B$ is<br/>
Question 2 :
If order of $A+B$ is $n \times n$, then the order of $AB$ is
Question 3 :
If order of a matrix is $3 \times 3$, then it is a
Question 4 :
What is the order of the product $ \begin{bmatrix} x &  y & z \end{bmatrix} \begin{bmatrix} a & h & g \\ h & b & f \\ g & f & c \end{bmatrix} \begin{bmatrix} x \\ y \\ z \end{bmatrix}$ ?
Question 5 :
If a matrix has $13$ elements, then the possible<br>dimensions (orders) of the matrix are
Question 7 :
Let $L$ denote the set of all straight lines in a plane, Let a relation $R$ be defined by $lRm$, iff $l$ is perpendicular to $m$ for all $l \in L$. Then, $R$ is
Question 8 :
Given the relation R= {(1,2), (2,3) } on the set {1, 2, 3}, the minimum number of ordered pairs which when added to R make it an equivalence relation is
Question 9 :
$N$ is the set of positive integers. The relation $R$ is defined on N x N as follows: $(a,b) R (c,d)\Longleftrightarrow ad=bc$ Prove that
Question 10 :
If $f: A \rightarrow B$is a bijective function and if n(A) = 5, then n(B) is equal to
Question 11 :
The relation $R$ in $N\times N$ such that $(a,b)R(c,d)\Leftrightarrow a+d=b+c$ is
Question 12 :
Find number of all such functions $y = f(x)$ which are one-one?
Question 13 :
Consider the following two binary relations on the set $A = \left \{a, b, c\right \} : R_{1} = \left \{(c, a), (b, b), (a, c), (c, c), (b, c), (a, a)\right \}$<br>and $R_{2} = \left \{(a, b), (b, a), (c, c), (c, a), (a, a), (b, b), (a, c)\right \}$ Then<br>
Question 14 :
Which of the following is not an equivalence relation on $Z$?
Question 15 :
Let N denote the set of all natural numbers and R a relation on $N\times N$. Which of the following is an equivalence relation?
Question 16 :
Find the value of the following determinant:<br/>$\begin{vmatrix}3\sqrt{6} & -4\sqrt{2}\\ 5\sqrt{3} & 2\end{vmatrix}$
Question 17 :
<i></i>What is the determinant of the matrix $\left [\begin{matrix} 3& 6\\ -1 & 2\end {matrix} \right]$?<br/>
Question 18 :
$x = \left| \begin{gathered}   - 1\,\,\,\,\,\, - 2\,\,\,\,\,\,\, - 2 \hfill \\  \,\,\,2\,\,\,\,\,\,\,\,\,\,1\,\,\,\,\,\,\, - 2 \hfill \\  \,\,\,2\,\,\,\,\,\, - 2\,\,\,\,\,\,\,\,\,\,1 \hfill \\ \end{gathered}  \right|$, then $x=$
Question 19 :
$\displaystyle \Delta = \begin{vmatrix}1 & \log_{x}y  & \log_{x}z \\ \log_{y}x & 1 & \log_{y}z \\ \log _{z}x  &\log _{z}y  & 1\end{vmatrix}$ is equal to <br/> <br/>
Question 20 :
Find the value of $x$ in $\begin{vmatrix} 2 & 4 \\ 5 & 1 \end{vmatrix}=\begin{vmatrix} 2x & 4 \\ 6 & x \end{vmatrix}$.