If P=(1,0), Q=(-1,0) and R=(2,0) are three given points, then locus of the point S satisfying the relation SQ2+ SR2 =2SP2, is
A straight line parallel to x-axis
A circle passing through the origin
A circle with the centre at the origin
A straight line parallel to y-axis
If the sum of the distances of a point from two perpendicular lines in a plane is 1, then its locus is
Square
Circle
Straight
Two intersecting lines
If x1, x2, x3 as well as y1, y2, y3, are in G.P. with the same common ratio, then the points (x1,y1), (x2,y2) and (x3, y3).
Lie on a straight line
lie on an ellipse
lie on a circle
are vertices of a triangle
The number of integer values of m, for which the x-coordinate of the point of intersection of the lines 3x + 4y =9 an y= mx+1 is also an integer, is
2
0
4
1
The number of intergral points (integral point means both the coordinates should be integer) exactly in the interior of the triangle with vertices (0,0),(0,21) and (21,0), is
133
190
233
105
Area of the triangle formed by the line x +y=3 and angle bisectors of the pair of straight lines x2 – y2 + 2y=1 is
2 sq. units
4 sq. units
6 sq. units
8 sq. units
Three lines px + qy + r =0, qx + ry +p =0 and rx + py + q =0 are concurrently if
P + q + r =0
P2 + q2 + r2 = pr + rp + pq
P3 + q3 + r3 = 3pqr
None of these
1, 2 and 3
If (P(1,2), Q(4,6), R(5,7) and S(a, b) are the vertices of a parallelogram PQRS, then
a=2, b=4
a=3, b=4
a=2, b=3
a=3, b=5
If the vertices P, Q, R of a triangle PQR are rational points, which of the following points of the triangle PQR is always rational point(s)?
Circumcentre
incentre
centre
Orthocentre
Let L1 be a straight line passing through the origin and L2 be the straight line x +y =1. If the intercepts made by the circle x2 + y2 –x +3y=0 on L1 and L2 are equal , then which of the following equations can represent L1?
X+ y =0
X –y=0
X +7y=0
X –7y=0
2 and 3
1 and 4