The points `(-a, -b)`, `(0, 0)`, `(a, b)` and `(a^2, ab)` are
(a)  Collinear      (b)  Vertices of a rectangle
(c)  Vertices of an parallelogram     (d)   None of these.

If the vertices of a triangle PQR are rational points, then which of the following points of this triangle may not be rational - (a)   Centroid     (b)   Incenter (c)    Circumcenter     (d)    Orthocenter

The number of solutions of z^2+bar z=0 is (a) 1           (b) 2 (c) 3           (d) 4

The co-ordinates of two fixed points A and B of a triangle ABC are (a,0) and (-a,0) respectively. If variable point C moves such that cot A+ cot B=lamda , (where lamda is a constant) then the locus of point C is:- (1)    y lamda =2a     (2)    y =lamda a     (3)    y a=2lamda     (4)     None of these.

The distance of the point (2,3) from the line x-2y+5=0 measured in a direction parallel to the line x -3y=0 is: (A)   2sqrt(10)     (B)   sqrt(10)     (C)   2sqrt(5)     (D)   None of these

The domain of the function f(x)=sqrt({(-log_0.3(x-1))/(-x^2+3x+18)}) is (a)   [2,6]   (b)   ]2,6[ (b)   [2,6[   (d)  None of these

If a+c+e=0 and b+d=0, then ax^4+bx^3+cx^2+dx+e is exactly divisible by (1)   x+1       (2)  x-1 (3)   Both (1) & (2)       (4)   None of these

If alpha , beta gamma are the roots of the equation x^3+px^2+qx+r=0 , then (1-alpha^2)(1-beta^2)(1-gamma^2) is equal to (a)    (1+q)^2-(p-r)^2    (b)    (1+q)^2+(p+r)^2 (c)    (1-q)^2+(p-r)^2    (d)   none of these

The radical center of the circles x^2+y^2=a^2 , (x-c)^2+y^2=a^2 and x^2+(y-b)^2=a^2 is (A)   (a/2,b/2)   (B)   (b/2,c/2)   (C)   (c/2,b/2)   (D)   None of these

The number of integer values of m , for which the x-coordiante of the point of intersection of the lines 3x+4y=9 and y=mx+1 is also an integer, is (a)    2     (b)   0 (c)    4     (d)   1

If p_(n+1)=sqrt(1/2(1+p_n)) , then cos(sqrt(1-p_0^2)/(p_1p_2p_3...to oo)) (a)   1    (b)   -1    (c)   p_0    (d)   1/p_0     (e)  None of these