Question 1 :
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 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 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 :
The value of k for which $kx+3y-k+3=0$ and $12x+ky=k$, have infinite solutions, is?
Question 7 :
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 8 :
The system of equations which can be solved by matrix inversion method have_______.
Question 9 :
Two points $(a, 0)$ and $(0, b)$ are joined by a straight line. Another point on this line is
Question 10 :
If the points $(a, 1), (2, -1)$ and $\left(\dfrac{1}{2}, 2\right)$ are collinear, then $a$ is equal to:
Question 11 :
If $A, B, C$ are collinear points such that $A(3, 4), C(11, 10)$ and $AB = 2.5$ then point $B$ is
Question 12 :
If the lines $2\mathrm{x}-\mathrm{a}\mathrm{y}+1 =0$,$\ 3\mathrm{x}-\mathrm{b}\mathrm{y}+1 =0$,$\ 4\mathrm{x}-\mathrm{c}\mathrm{y}+1 =0$ are concurrent then $a,b,c$ are in ?<br/><br/>.<br/>
Question 13 :
If $|A| = 3$ and $A^{-1} = \begin{bmatrix}3 & -1\\ \dfrac {-5}{3} & \dfrac {2}{3}\end{bmatrix}$ then $adj\ A = ?$<br>
Question 14 :
If three points $(k, 2k), (2k, 3k), (3, 1)$ are collinear, then $k$ is equal to:<br/>
Question 15 :
If $\begin{vmatrix}<br>x_{1} & y_{1} &1 \\ <br>x_{2} & y_{2} &1 \\ <br> x_{3}&y_{3} & 1<br>\end{vmatrix}$ = $\begin{vmatrix}<br>1 & 1 &1 \\ <br>b_{1} & b_{2} &b_{3} \\ <br> a_{1}&a_{2} & a_{3}<br>\end{vmatrix}$ then the two triangles whose vertices are $(x_{1},y_{1}),(x_{2},y_{2}),(x_{3},y_{3})$ and $ (a_{1},b_{1}),(a_{2},b_{2}),(a_{3},b_{3})$ are<br><br>
Question 16 :
The straight lines $\mathrm{x}+2\mathrm{y}-9=0,3\mathrm{x}+5\mathrm{y}-5=0$ and $\mathrm{a}\mathrm{x}+\mathrm{b}\mathrm{y}-1=0$ are concurrent if the straight line $22\mathrm{x}-35\mathrm{y}-1=0$ passes through the point <br><br>
Question 17 :
The number of values of $\theta \in (0,\pi )$ for which the system of linear equations<br>x+3y+7z=0<br>x+4y+7z=0<br>$(\sin { 3\theta } )x+(\cos { 2\theta } )y+2z=0$<br>has a non trivial solution is :
Question 18 :
Solve the system of equations<br>$\quad x+y+z = 6 \\ \quad x+2y+3z = 14 \\ \quad x+4y+7z = 30$
Question 19 :
If the points $(k, 2k),\ ( 3k, 3k)$ and $(3, 1)$ are collinear then the value of $k$ is 
Question 21 :
If the points $(-2, -5), (2, -2), (8, a)$ are collinear, then the value of $a$ is ________.
Question 22 :
Number of values of $a$ for which the lines $2x+y-1=0, ax+3y-3=0, 3x+2y-2=0$ are concurrent is<br><br>
Question 23 :
If the points $(2,5),(4,6)$ and $(a,a)$ are collinear, then the value of $a$ is equal to
Question 24 :
The area of a triangle, whose vertices are $(3, 2), (5, 2)$ and the point of intersection of the lines $x = a$ and $y = 5$, is $3$ square units. What is the value of $a$?
Question 26 :
If $S$ is the set of distinct values of '$b$' for which the following system of linear equations<br/> $x+y+z=1$, <br/>$x+ay+z=1$, <br/>$ax+by+z=0$ <br/>has no solution, then $S$ is<br/>
Question 27 :
Find the correct option regarding given points $(1, 2), (2, 4)$ and $(3, 6)$ <br/>
Question 28 :
What is the area of the triangle formed by the points $(a,c+a), \displaystyle \left ( a^{2},c^{2} \right )$ and $(-a, c-a)$?
Question 29 :
If the points $(a, 0), (0, b)$ and $(1, 1)$ are collinear, then $\displaystyle \frac{1}{a} + \frac{1}{b}$ equal to -<br/>
Question 30 :
Find the value of $x$ and $y$ that satisfy the equations.<br>$\left[\begin{matrix}3 & -2 \\ 3 & 0 \\ 2 & 4\end{matrix}\right]\left[\begin{matrix} y & y \\ x & x\end{matrix}\right] = \left[\begin{matrix}3 & 3\\3y & 3y\\10 & 10\end{matrix}\right]$
Question 31 :
The system of equations , $ ax+y+z = a-1 $ , $x+ay+z = a-1 $, $x+y+az = a-1 $has no solution, if a is 
Question 32 :
If the points $(a, 1), (1, b)$ and $(a -1, b -1)$ are collinear, $\alpha ,\beta $ are respectively the arithmetic and geometric means of $a$ and $b $, then $4\alpha -\beta^{2}$ is equal to<br>
Question 33 : Use the product of two matrices $A$ and $B$, where $A=\left[\begin{matrix}-5&1&3\\7&1&-5\\1&-1&1\end{matrix}\right]$ and $ B = \left[\begin{matrix}1&1&2\\3&2&1\\2&1&3\end{matrix}\right]$ to solve the following system of linear equations, <div>$x+y+2z=1$; </div><div>$3x+2y+z=7$; </div><div>$2x+y+3z=2$, <span>for $x, y$ and $z$.</span></div>
Question 34 :
Consider three points ${P}=(-\sin(\beta-\alpha), -\cos\beta) , {Q}=(\cos(\beta-\alpha), \sin\beta)$ and ${R}=(\cos(\beta-\alpha +\theta), \sin(\beta-\theta))$ , where $0< \alpha,\ \beta,\ \theta <\displaystyle \frac{\pi}{4}$. Then<br>
Question 36 :
If the lines $\mathrm{x}+\mathrm{p}\mathrm{y}+\mathrm{p}=0,\ \mathrm{q}\mathrm{x}+\mathrm{y}+\mathrm{q}=0$ and $\mathrm{r}\mathrm{x}+\mathrm{r}\mathrm{y}+1 =0 (\mathrm{p},\mathrm{q}, \mathrm{r}$ being distinct and $ \neq$ 1) are concurrent, then the value of<br/>$\displaystyle \frac{p}{p-1}+\frac{q}{q-1}+\frac{r}{r-1}=$<br/>
Question 37 :
If $A$ is $4\times 4$ matrix and if $\left| \left| A \right| adj\left( \left| A \right| A \right) \right| ={ \left| A \right| }^{ n }$, then $n$ is
Question 38 :
The system of equations<br>$\alpha x+y+z=\alpha -1\\ x+\alpha y+z=a-1\\ x+y+\alpha z=a-1$<br>has infinite solutions, if $\alpha$ is
Question 39 :
The system of equations<br>$\alpha x+y+z=\alpha -1$<br>$x+\alpha y+z=\alpha -1$<br>$x+ y+\alpha z=\alpha -1$<br> has infinite solutions, if $\alpha $ is
Question 40 :
 Points (a, 0), (0, b) and (1, 1)are collinear, if: <br/>
Question 42 :
If the lines $p_{1}x+q_{1}y=1,p_{2}x+q_{2}y=1 $ and $ p_{3}x+q_{3}y=1$ be concurrent, then the points $(p_{1},q_{1}),(p_{2},q_{2})$ and $(p_{3},q_{3})$ ,<br>
Question 43 :
If $\omega$ is a cube root of unity and $x+ y + z = a, x + \omega y + \omega^2 z = b, x + \omega^2 y + \omega z = c$, then $x = $ ............
Question 44 :
The vertices of the triangle $ABC$ are $(2, 1, 1), (3, 1, 2), (-4, 0, 1)$. The area of triangle is
Question 45 :
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 46 :
If $f'(x)=\begin{vmatrix} mx & mx-p & mx+p \\ n & n+p & n-p \\ mx+2n & mx+2n+p & mx+2n-p \end{vmatrix}$, then $y=f(x)$ represents
Question 47 :
If $a,b,c$ are non-zeros, then the system of equations $(\alpha +a)x+\alpha y+\alpha z=0,\quad \alpha x+(\alpha +b)y+\alpha z=0,\quad \alpha x+\alpha y+(\alpha +c)z=0\quad $ has a non-trivial solution if <br>
Question 48 :
$(x_1 - x_2)^2 + (y_1 - y_2)^2 = a^2$;<br>$(x_2 - x_3)^2 + (y_2 - y_3)^2 = b^2$;<br>$(x_3 - x_1)^2 + (y_3 - y_1)^2 = c^2$;<br>then find $4 \begin{vmatrix}x_1 & y_1 & 1\\ x_2 & y_2 & 1\\ x_3 & y_3 & 1\end{vmatrix}^2 = $
Question 50 :
System of equations<br/>$x + 2y + z = 0, 2x + 3y- z = 0 $ and $(tan\theta) x + y -3z = 0$ has non-trivial solution then number of value(s) of $\theta \epsilon (-\pi,\pi)$ is equal to?<br/><br/><br/>
