Which of the following represents a points in an Argand pane, equidistant from the roots of the equation `(z+1)^4=16 z^4?` `(0,0)` b. `(-1/3,0)` c. `(1/3,0)` d. `(0,2/(sqrt(5)))`

The point in the xy-plane which is equidistant from the points (2,0,3),(0,3,2) and (0,0,1) is

Which of the following sets of points form an equilateral triangle? (a) (1,0),(4,0),(7,-1) (b) (0,0),(3/2,4/3),(4/3,3/2) (c) (2/3,0),(0,2/3),(1,1) (d) None of these

Which of the following is not the root of the equation |[x,-6,-1],[ 2,-3x,x-3],[-3, 2x,x+2]|=0? a. 2 b. 0 c. 1 d. -3

The common roots of the equation Z^3+2Z^2+2Z+1=0 and Z^1985+Z^100+1=0 are

If z_1a n dz_2 are the complex roots of the equation (x-3)^3+1=0,t h e nz_1+z_2 equal to a. 1 b. 3 c. 5 d. 7

A is a point on either of two lines y+sqrt(3)|x|=2 at a distance of 4/sqrt(3) units from their point of intersection. The coordinates of the foot of perpendicular from A on the bisector of the angle between them are (a) (-2/(sqrt(3)),2) (b) (0,0) (c) (2/(sqrt(3)),2) (d) (0,4)

The number of roots of the equation xsinx=1,x in [-2pi,0)uu(0,2pi] is 2 (b) 3 (c) 4 (d) 0

If the angles of elevation of the top of a tower from three collinear points A, B and C, on a line leading to the foot of the tower, are 30^0 , 45^0 and 60^0 respectively, then the ratio, AB : BC, is : (1) sqrt(3):1 (2) sqrt(3):sqrt(2) (3) 1:sqrt(3) (4) 2"":""3

If z^3+(3+2i)z+(-1+i a)=0 has one real root, then the value of a lies in the interval (a in R) a. (-2,1) b. (-1,0) c. (0,1) d. (-2,3)

Let P=0 be the equation of a plane passing through the line of intersection of the planes 2x-y=0a n d3z-y=0 and perpendicular to the plane 4x+5y-3z=8. Then the points which lie on the plane P=0 is/are a. (0,9,17) b. (1//7,21//9) c. (1,3,-4) d. (1//2,1,1//3)