The radius of the circle `ax^2 + (2a-3) y^2 - 4x - 7 = 0` is : (A) 1 (B) `5/3` (C) `4/3` (D) 3

The radical centre of three circles : x^2 + y^2 + x + 2y + 3 = 0, x^2 + y^2 + 2x + 4y + 5 = 0 and x^2 + y^2 - 7x - 8y - 9 = 0 is : (A) (- 2/3, - 2/3) (B) (1/3, 1/3) (C) (1/4, 1/4) (D) (0, 0)

The equation of the locus of points which are equidistant from the points (2,-3) and (3,-2) is (A) x+y=0 (B) x+y=7 (C) 4x+4y=38 (D) x+y=1

The plane x+2y-z=4 cuts the sphere x^2+y^2+z^2-x+z-2=0 in a circle of radius (A) sqrt(2) (B) 2 (C) 1 (D) 3

The plane x+2y-z=4 cuts the sphere x^2+y^2+z^2-x+z-2=0 in a circle of radius (A) 3 (B) 1 (C) 2 (D) sqrt(2)

The radical centre of the circles x^(2)+y^(2)=9 , x^(2)+y^(2)-2x-2y-5=0 , x^(2)+y^(2)+4x+6y-19=0 is A) (0,0) (B) (1,1) (C) (2,2) (D) (3,3)

If d_(1)&d_(2) are the longest and shortest distances of (4,-3) to the circle x^(2)+y^(2)+4x-10y-7=0 then G.M of d_(1) and d_(2) is

The radius of the circle which touches circle (x+2)^(2)+(y-3)^(2)=25 at point (1,-1) and passes through (4,0) is (a) 4 (b) 5 (c) 3 (d) 8

The radius of the circle which touches the co- ordinates axes and the line 3x+4y=12 is 1 (b) 2 (c) 3 (d) 6

The normal to the parabola y^2 = 4ax from the point (5a, 2a) are (A) y=x-3a (B) y=-2x+12a (C) y=-3x+33a (D) y=x+3a

The radius of the circle passing through the foci of the ellipse (x^(2))/(16)+(y^(2))/(9) and having its center (0,3) is 4(b)3(c)sqrt(12) (d) (7)/(2)