Question 1 :
$A$ and $B$ are two non-zero square matrices such that $AB = 0$. Then
Question 2 :
The inverse of a skew symmetric matrix of odd order is_____.
Question 4 :
If $P=\begin{bmatrix} 1 & c & 3\\ 1 & 3 & 3\\ 2 & 4 & 4\end{bmatrix}$ is the adjoint of a $3\times 3$ matrix Q and det.(Q)$=4$, then c is equal to.
Question 5 :
The points (2, -3), (4,3) and (5, k/2) are on the same straight line. The value(s) of k is (are):
Question 6 :
Let ${D_1}$ = $\begin{vmatrix}a & b & a+b\\ c & d & c+d\\ a & b & a-b\end{vmatrix}$ and ${D_2}$= $\begin{vmatrix}a & c & a+c\\ b & d & b+d\\ a & c & a+b+c\end{vmatrix}$ then the value of $\frac{{{D_1}}}{{{D_2}}}$ where $b \ne 0$ and $ad \ne bc,$ is
Question 7 :
If $\begin{vmatrix}<br/>cos(A+B) & -sin(A+B) &cos2B \\ <br/> sin A& cos A &sin B \\ <br/> -cos A& sin A & cos B<br/>\end{vmatrix}$ =0 then B=<br/><br/><br/>
Question 9 :
$A$ and $B$ are two points and $C$ is any point collinear with $A$ and $B$. IF $AB=10$, $BC=5$, then $AC$ is equal to:
Question 10 :
If $-9$ is a root of the equation $\begin{vmatrix} x & 3 & 7 \\ 2 & x & 2 \\ 7 & 6 & x \end{vmatrix}=0$, then the other two roots are
Question 11 :
$D\mathrm{e}\mathrm{t} \left\{\begin{array}{lll}<br>2 & 45 & 55\\<br>1 & 29 & 32\\<br>3 & 68 & 87<br>\end{array}\right\}=\ldots.$ .<br>
Question 12 :
The value of $\begin{vmatrix}<br/>1990 & 1991 &1992 \\ <br/> 1991&1992 &1993 \\ <br/>1992 & 1993& 1994<br/>\end{vmatrix}$ is equal to 
Question 13 :
Matrix $A = \left[ {\begin{array}{*{20}{c}}x & 3 & 2\\1 & y & 4\\2 & 2 & z\end{array}} \right] $, if $xyz = 60$ and $8x + 4y + 3z = 20$, then $A(adj A)$ is equal to
Question 14 :
If $A = \begin{bmatrix}5 & 2 \\ 3 & 1\end{bmatrix}$, then $A^{-1}$ =
Question 15 :
The value of the determinant $\left| \begin{matrix} -a & b & c \\ a & -b & c \\ a & b & -c \end{matrix} \right| $ is equal to-
Question 16 :
If $\begin{vmatrix} 6i & -3i & 1\\ 4 & 3i & -1 \\ 20 & 3 & i\end{vmatrix}=x+iy$, then<br>
Question 18 :
If A is a singular matrix, then A (adj A) is a
Question 19 :
If $\left|( {adj\,A}) \right| = 81,$ for $3 \times 3$ matrix, then det $A$ is equal to 
Question 20 :
If $\displaystyle{\left| {_2^{4\,}\,\,_1^1} \right|^2} = \left| {_1^3\,\,_x^2} \right| - \left| {_{ - 2}^x\,\,_1^3} \right|,$ then $x$=
Question 21 :
If abc $\neq $0 and if $\begin{vmatrix}<br/>a & b & c\\ <br/>b & c & a\\ <br/>c & a & b<br/>\end{vmatrix}$ = 0 then $\dfrac{a^{3}+b^{3}+c^{3}}{abc}$ 
Question 22 :
If the area of the triangle with vertices $(2, 5), (7, k)$ and $(3, 1)$ is $10$, then find the value of $k$.<br>
Question 23 :
The determinant $\begin{vmatrix}a & b & a\alpha +b\\ b & c & b\alpha +c\\ a\alpha +b & b\alpha +c & 0\end{vmatrix}$ is equal to zero, if.
Question 24 :
$\begin{vmatrix}<br>x^{2}+3 &x-1 &x+3 \\ <br>x+3 & -2x &x-4 \\ <br> x-3& x+4 & 3x<br>\end{vmatrix}$ $=px^{4}+qx^3+rx^{2}+sx+t,$ then $t = $
Question 25 :
If $A=\begin{bmatrix} 2 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 2 \end{bmatrix}$, then value of ${A}^{-1}$ is
Question 26 :
If $D =$ $\displaystyle \left | \begin{matrix}1 & 1 & 1\\ 1& 1+x &1 \\ 1 & 1 &1+y \end{matrix} \right |$ <br> $\displaystyle x\neq 0,y\neq 0,$ then D is divisible by<br>
Question 27 :
If $\begin{bmatrix} e^t &e^{-t}\cos t &e^{-t}\sin t \\e^t & -e^{-t}\cos t-e^{-t}\sin t & -e^{-t}\sin t+e^{-t}\cos t \\ e^t & 2e^{-t}\sin t & -2e^{-t}\cos t \end{bmatrix}$ Then $A$ is -
Question 28 :
Let $X=\begin{bmatrix} { x }_{ 1 } \\ { x }_{ 2 } \\ { x }_{ 3 } \end{bmatrix};A=\begin{bmatrix} 1 & -1 & 2 \\ 2 & 0 & 1 \\ 3 & 2 & 1 \end{bmatrix}$ and $B=\begin{bmatrix} 3 \\ 1 \\ 4 \end{bmatrix}$. If $AX=B$, then $X$ is equal to
Question 29 :
$A_{3*3}$ is a non - singular matrix $\Rightarrow A^{2}\left ( AdjA \right )=$
Question 30 :
Find the value of the following determinant:<br/>$\begin{vmatrix}\displaystyle \frac{-4}{7} & \displaystyle \frac{-6}{35}\\ 5 & \displaystyle \frac{-2}{5}\end{vmatrix}$
Question 31 :
Two points $(a, 0)$ and $(0, b)$ are joined by a straight line. Another point on this line is
Question 32 :
Let the matrix A and B be defined as $A =\begin{vmatrix} 3 & 2 \\ 2 & 1 \end{vmatrix}$ and $B = \begin{vmatrix} 3 & 1 \\ 7 & 3 \end{vmatrix}$ then the value of Det.$(2A^9B^{-1})$, is
Question 33 :
If A is a square matrix of order $n$ then adj $\left ( adj A \right )$ is equal to
Question 34 :
If $\displaystyle \:A= \left [ \begin{matrix}5 &2 \\3 &1 \end{matrix} \right ],$ then $\displaystyle \:A^{-1}= $
Question 36 :
If $\begin{vmatrix} x & 2 \\ 18 & x \end{vmatrix}=\begin{vmatrix} 6 & 2 \\ 3x & 6 \end{vmatrix}$, then $x$ is equal to
Question 37 :
If A is a non singular matrix then which of the following is not true:
Question 38 :
If $\begin{bmatrix} x & 1 & 1\\ 2 & 3 & 4\\ 1 & 1 & 1\end{bmatrix}$ has no inverse, then $x=$
Question 39 :
Find the value of the following determinant:<br/>$\begin{vmatrix}3\sqrt{6} & -4\sqrt{2}\\ 5\sqrt{3} & 2\end{vmatrix}$
Question 40 :
If $a, b, c$ are non-zero and different from $1$, then the value of $\begin{vmatrix}\log_a 1 & \log_a b & \log_ac\\ \log_a \left( \dfrac{1}{b} \right ) & \log_b 1 &\log_a \left( \dfrac{1}{c} \right ) \\ \log_a \left( \dfrac{1}{c}\right ) & \log_a c & \log_c 1\end{vmatrix}$ is<br/>
Question 41 :
If $a+b+c\neq 0$ and $\begin{vmatrix} a & b & c \\ b & c & a \\ c & a & b \end{vmatrix}=0$, then, $a=b=c$.
Question 42 :
Let $\omega\neq{1}$ be a cube root of unity and $S$ be the set of all non-singular matrices of the form $ \begin{bmatrix} 1 & a & b \\ \omega & 1 & c \\ { \omega }^{ 2 } & \omega & 1 \end{bmatrix}$Where each of $a,\ b$ and $c$ is either $\omega$ or ${\omega}^{2}$. Then the number of distinct matrices in the set $S$ is
Question 43 :
The value of k for which $kx+3y-k+3=0$ and $12x+ky=k$, have infinite solutions, is?
Question 44 :
If $a, b, c$ are in $A.P.$ then $\begin{vmatrix} x+1 & x+2 & x+a \\ x+2 & x+3 & x+b \\ x+3 & x+4 & x+c \end{vmatrix}=$
Question 45 :
Find the value of $x$ in $\begin{vmatrix} 2 & 4 \\ 5 & 1 \end{vmatrix}=\begin{vmatrix} 2x & 4 \\ 6 & x \end{vmatrix}$.
Question 46 :
If $\begin{vmatrix} \ sinx &  \ cos x & \ cosx \\ \ cosx & \ sinx & \ cosx \\ \ cosx & \ cosx & \ sinx \end{vmatrix} = 1 $ in the interval $ \frac{- \pi}{2} \leq x \leq \frac{\pi}{2}, $ then  $ \ tanx$ is 
Question 47 :
If the matrix $\begin{bmatrix}<br/>\cos\theta &\sin \theta &0 \\ <br/>\sin \theta & \cos \theta & 0\\ <br/> 0&0 & 1<br/>\end{bmatrix}$ is singular, then  $\theta =$ 
Question 48 :
If $\omega$ is a cube root of unity and $\Delta=\begin{vmatrix}1 & 2\omega \\ \omega & \omega^2\end{vmatrix}$, then $\Delta^2$ is equal to<br>
Question 49 :
The value of the determinant $\begin{vmatrix}1 & a & a^2-bc\\ 1 & b & b^2-ca\\ 1 & c & c^2-ab\end{vmatrix}$ is<br>
Question 50 :
If each element of a $3 \times 3$ matrix is multiplied by $3$, then the determinant of the newly formed matrix is
