The eccentricity of the locus of point `(3h+2,k),` where `(h , k)` lies on the circle `x^2+y^2=1` , is `1/3` (b) `(sqrt(2))/3` (c) `(2sqrt(2))/3` (d) `1/(sqrt(3))`

If cosx=(2cosy-1)/(2-cosy), where x , y in (0,pi) then tan(x/2)cot(y/2) is equal to sqrt(2) (b) sqrt(3) (c) 1/(sqrt(2)) (d) 1/(sqrt(3))

The eccentricity of the conjugate hyperbola of the hyperbola x^2-3y^2=1 is 2 (b) 2sqrt(3) (c) 4 (d) 4/5

The centre of a circle passing through (0,0), (1,0) and touching the CircIe x^2+y^2=9 is a. (1/2,sqrt2) b. (1/2,3/sqrt2) c. (3/2,1/sqrt2) d. (1/2,-1/sqrt2)

Three equal circles each of radius r touch one another. The radius of the circle touching all the three given circles internally is (a) (2+sqrt(3))r (b) ((2+sqrt(3)))/(sqrt(3))r (c) ((2-sqrt(3)))/(sqrt(3))r (d) (2-sqrt(3))r

Consider a branch of the hypebola x^2-2y^2-2sqrt2x-4sqrt2y-6=0 with vertex at the point A. Let B be one of the end points of its latus rectum. If C is the focus of the hyperbola nearest to the point A, then the area of the triangle ABC is (A) 1-sqrt(2/3) (B) sqrt(3/2) -1 (C) 1+sqrt(2/3) (D) sqrt(3/2)+1

The incenter of the triangle with vertices (1,sqrt(3)),(0,0), and (2,0) is (a) (1,(sqrt(3))/2) (b) (2/3,1/(sqrt(3))) (c) (2/3,(sqrt(3))/2) (d) (1,1/(sqrt(3)))

The angle between the lines joining origin to the points of intersection of the line sqrt(3)x+y=2 and the curve y^2-x^2=4 is (A) tan^(-1)(2/(sqrt(3))) (B) pi/6 (C) tan^(-1)((sqrt(3))/2) (D) pi/2

If tangents P Q and P R are drawn from a point on the circle x^2+y^2=25 to the ellipse (x^2)/16+(y^2)/(b^2)=1,(b (a) (sqrt(5))/4 (b) (sqrt(7))/4 (c) (sqrt(7))/2 (d) (sqrt(5))/3

On the line segment joining (1, 0) and (3, 0) , an equilateral triangle is drawn having its vertex in the fourth quadrant. Then the radical center of the circles described on its sides. (a) (3,-1/(sqrt(3))) (b) (3,-sqrt(3)) (c) (2,-1/sqrt(3)) (d) (2,-sqrt(3))

If the area enclosed between the curves y=kx^2 and x=ky^2 , where kgt0 , is 1 square unit. Then k is: (a) 1/sqrt(3) (b) sqrt(3)/2 (c) 2/sqrt(3) (d) sqrt(3)