Question 1 :
Which of the given values of $x$ and $y$ make the following pair of matrices equal.<br>$\displaystyle \begin{bmatrix} 3x+7 & 5 \\ y+1 & 2-3x \end{bmatrix}=\begin{bmatrix} 0 & y-2 \\ 8 & 4 \end{bmatrix}$
Question 3 :
If the area of the triangle formed by $ (0,0), (a,0) $ and $ \left( \dfrac{1}{2} , a \right) $ is equal to $ \dfrac {1}{2} $ sq unit, then the values of $a$ are :
Question 4 :
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 5 :
If the points $(a, 1), (2, -1)$ and $\left(\dfrac{1}{2}, 2\right)$ are collinear, then $a$ is equal to:
Question 7 :
$A$ 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 8 :
The system of equations which can be solved by matrix inversion method have_______.
Question 9 :
The value of k for which $kx+3y-k+3=0$ and $12x+ky=k$, have infinite solutions, is?
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 :
One of the roots of $\begin{vmatrix} x+a & b & c\\ a & x+b & c\\ a & b & x+c \end{vmatrix}=0$ is :<br>
Question 12 :
If $3x+2y=I$ and $2x-y=O$, where $I$ and $O$ are unit and null matrices of order $3$ respectively, then
Question 13 :
If $P=(x_{1}, y_{1}), Q=(x_{2}, y_{2})$ and $R=(x_{3}, y_{3})$ are three points of a triangle in $\mathbb{R}^{2}$. Then, area of a $\triangle PQR$ in terms of determinant of matrix $M=\begin{bmatrix} 1& 1 & 1 \\ x_{1} & x_{2} & x_{3} \\ y_{1} & y_{2} & y_{3}\end{bmatrix}$ is
Question 14 :
The number of solutions of the system of equations $2x+y-z=7   ,   x-3y-2z=1 ,  x+4y-3z=5,$ are 
Question 16 :
For which value of '$k$' the points $(7, -2), (5, 1), (3, k)$ are collinear?
Question 17 :
If $\displaystyle \omega$ is cube root of unity and $\displaystyle x + y + z = a$, $\displaystyle x + \omega y + \omega^{2} z = b$, $\displaystyle x + \omega^{2} y + \omega z = b$ then which of the following is not correct?
Question 18 :
If $x_1, x_2, x_3$ as well as $y_1, y_2, y_3$ are in G.P. with same common ratio, then the points $P(x_1, y_1), Q (x_2, y_2)$ and $R(x_3, y_3)$
Question 19 :
The coordinates of the point $P$ on the line $2x+3y+1=0$ such that $|PA-PB|$ is maximum, where $A(2, 0)$ and $B(0, 2)$ is<br/>
Question 20 :
The values of $\theta $ lying between $\theta =0$ and $\theta =\dfrac {\pi}{2}$ and satisfying the equation<br/>$\begin{vmatrix}<br/>1+\sin ^{2}\theta  & \cos ^{2}\theta  & 4\sin 6\theta \\ <br/>\sin ^{2}\theta  & 1+\cos ^{2}\theta  & 4\sin 6\theta \\ <br/>\sin ^{2}\theta  & \cos ^{2}\theta  & 1+4\sin 6\theta <br/>\end{vmatrix}$<br/>are given by<br/>
