Question 1 :
Points $(6, 8), (3, 7), (-2, -2)$ and $(1, -1)$ are joined to form a quadrilateral. What will be the structure of the quadrilateral?

Question 2 :
If the distance between the points $\left( {a\,\cos {{48}^ \circ },0} \right)$ and $\left( {\,0,a\,\cos {{12}^ \circ }} \right)$ is d,then ${d^2} - {a^2} = $

Question 3 :
In which quadrant or on which axis each of the following points lie?<br>$(- 3, 5), (4, -1), (2, 0), (2, 2), ( -3, -6)$<br><br>

Question 4 :
Which of the following is true for the points $X$ and $Y$ if the co-ordinates of the mid-points $P$ of $\overline {XY}$ are $(-2, 3)$?

Question 5 :
If points $( - 7,5 ) \text { and } \left( \alpha , \alpha ^ { 2 } \right)$ lie on the opposite sides of the line $5 x - 6 y - 1 = 0$ then

Question 6 :
Points $(3, - 1)$ and $(6, 1)$ lie on the line represented by the equation $px\, +\, qy\, =\, 9,$&#160;find the values of $p$ and $q$.

Question 7 :
If a point $P$ has coordinates $(3,4)$ in a coordinate system $X'OX\leftrightarrow Y'OY$, and if $O$ has coordinates $(4,3)$ in another system ${X}_{1}'{O}_{1}{X}_{1}\leftrightarrow {Y}_{1}'{O}_{1}{Y}_{1}$ with $X'OX\parallel {X}_{1}'{O}_{1}{X}_{1}$, then the coordinates of $P$ in the new system ${X}_{1}'{O}_{1}{X}_{1}\leftrightarrow {Y}_{1}'{O}_{1}{Y}_{1}$ is ________________

Question 8 :
Coordinates of $P$ and $Q$ are $(4, - 3)$ and $(- 1, 7)$. The abscissa of a point $R$ on the line segment $PQ$, such that&#160;$\displaystyle \frac { PR }{ PQ } =\frac { 3 }{ 5 }&#160;$ is :

Question 9 :
If the points $( 2,0 ) , ( 0,1 ) , ( 4,5 ) \text { and } ( 0 , c )$ are concyclic then the value of $c$ is

Question 10 :
The abscissa of two points A and B are the roots of the equation&#160;${x^2} + 2ax - {b^2}$ and their ordinates are the root of the equation&#160;${x^2} + 2px - {q^2}=0$. the equation of the circle with AB as diameter is&#160;

Question 11 :
The lines $x + y = | a&#160;|$&#160;and $a x - y = 1$ intersect each other in the first quadrant. Then the set of all possible values of $a$ in the interval are

Question 12 :
State True or False.The point $(-x, -y)$ lies in the first quadrant where x &lt; 0, y &lt; 0.

Question 13 :
$C$ is a point on the line segment joining the points $A(2,-3,4)$ and $B(8,0,10)$. If the value of $y$-coordinate of $C$ is $-2$, then the $z-$coordinate of $C$ is

Question 15 :
State true or falseThe abscissa of two points is $0$.Line joining them is Y axis

Question 16 :
Let $A(1,1,0), B(1,2,1)$ and $C(-2,2,-1)$ be three points then equation of plane is

Question 19 :
If &#160;each of the vertices of a triangle has integral co-ordinates then the triangle may be&#160;

Question 20 :
If the coordinates of vertices of atriangle is always rational then the triangle cannot be

Question 21 :
Let a, b, c and d be non-zero numbers. If the point of intersection of the lines $4ax+2ay+c=0$and $5bx+2by+d=0$lies in the fourth quadrant and is equidistant from the two axes then

Question 22 :
The abscissa of a point on the curve $xy=(a+x)^{2}$, the normal cuts off numerically equal intercepts from the coordinate axes, is

Question 23 :
Sate true or falseLine joining them is parallel to Y axis<br/>(i) $(4, 2)$<br/>(ii) $(4, -5)$<br/>(iii) $(4, 0)$<br/>(iv) $(4, -2)$<br/>

Question 24 :
The points $A(2a ,4a) , B(2a,6a)$ and$C(2a + \sqrt 3 a,5a)$ (when a&gt;0) are vertices of

Question 25 :
If ${x_1},{x_2},{x_3}$ as well as ${y_1},{y_2},{y_3}$ are in&#160;<b>G.P.&#160;</b> with same common ratio, then the points&#160;<b></b>$P\left( {{x_1},{y_1}} \right)$, $Q\left( {{x_2},{y_2}} \right)$&#160;and $R\left( {{x_3},{y_3}} \right)$&#160;

Question 26 :
Find the number of points of X-axis which are at a distance 'c' units $(c &lt; 3)$ from $(2, 3)$.

Question 27 :
A line has the equation $x =-2y +z$. If $(3, 2)$ is a point on the line, what is $z$?

Question 28 :
If the points $(k, 2 - 2k), (1 - k, 2k)$ and $(-k -4, 6 - 2k)$ be collinear the possible value(s) of $k$ is/are