Question 1 :
The distance between the points (sin x, cos x) and (cos x -sin x) is

Question 2 :
The condition for the points (x,y), (-2,2) and (3,1) to be collinear is

Question 3 :
The points $(a, 0), (0, b)$ and $(1, 1)$ will be collinear if

Question 4 :
Consider a triangle ABC, whose vertical are $A(-2,1), B(1, 3) and C(x,y)$ .If C is a moving point such that area of $\Delta ABC$ is constant,then locus of C is:

Question 5 :
Harmonic conjugate of the point $C(5, 1)$ with respect to the point $A(2, 10)$ and $B(6, -2)$ is?

Question 6 :
Find the inclination of the line passing through (-5, 3) and (10, 7)

Question 8 :
The slope of the line joining the point (-8,-3)and (8,3) is

Question 9 :
The centroid of the triangle with vertices (2,6), (-5,6) and (9,3) is

Question 11 :
The length of the segment of the straight line passing through $(3,3)$ and $(7,6)$ cut off by the coordinate axes is

Question 12 :
If $\left| \begin{array} { l l l } { x _ { 1 } } &amp; { y _ { 1 } } &amp; { 1 } \\ { x _ { 2 } } &amp; { y _ { 2 } } &amp; { 1 } \\ { x _ { 3 } } &amp; { y _ { 3 } } &amp; { 1 } \end{array} \right| = \left| \begin{array} { l l l } { a _ { 1 } } &amp; { b _ { 1 } } &amp; { 1 } \\ { a _ { 2 } } &amp; { b _ { 2 } } &amp; { 1 } \\ { a _ { 3 } } &amp; { b _ { 3 } } &amp; { 1 } \end{array} \right|$<br/>&#160;then two triangles with vertices $\left( x _ { 1 } , y _ { 1 } \right) , \left( x _ { 2 } , y _ { 2 } \right) , \left( x _ { 3 } , y _ { 3 } \right)$ and $\left( a _ { 1 } , b _ { 1 } \right) , \left( a _ { 2 } , b _ { 2 } \right) , \left( a _ { 3 } , b _ { 3 } \right)$ are

Question 13 :
The orthocentre of the triangle $ABC$ is $B$ and the circumstances is $S(a,b)$. If $A$ is the origin, then the coordinates of $C$ are:

Question 14 :
Which of the following points are $10$ units from the origin?

Question 15 :
If the tangent to the curve $y=x\log { x } $ at $\left( c,f\left( x \right) \right) $ is parallel to the line-segment joining $A\left(1,0\right)$ and $B\left(e,e\right)$, then c=...... .

Question 16 :
Given three vertices of a triangle whose coordinates are A (1, 1), B (3, -3) and (5, -3) Find the area of the triangle

Question 20 :
$A(0, 0), B(7, 2), C(7, 7)$ and $D(2, 7)$ are the vertices of a quadrilateral. The respective slopes of diagonals $AC$ and $BD$ are&#160;<br/>

Question 22 :
Which of the following is perpendicular to the line x/3 + y/4 = 1?

Question 23 :
Find the distance between the following pair of points.<br/>$(5, 7)$ and the origin

Question 25 :
The slope of the line passing through the points $A(-2, 1)$ and $B(0, 3)$ is:<br/>

Question 26 :
The points (2, 5) and (5, 1) are the two opposite vertices of a rectangle. If the other two vertices are points on the straight line $y = 2x + k$, then the value of k is

Question 28 :
Find a point on the y-axis which is equidistant from (3, 2) and (-5, -2).<br>

Question 29 :
Which of the following are the co-ordinates of the centre of the circle that passes through $P(6, 6), Q(3, 7)$ and $R(3, 3)$?

Question 30 :
What is the value of k, if the line $\displaystyle 2x-3y=k$ passes through the origin.