The radius of the circle passing through the points `(1, 2), (5, 2) and (5, -2)` is : (A) `5sqrt(2)` (B) `2sqrt(5)` (C) `3sqrt(2)` (D) `2sqrt(2)`

Simplify : (i) (5+sqrt(5))(5-sqrt(5)) (ii) (3+2sqrt(2))(3-2sqrt(2))

If |z-4/2z|=2 then the least of |z| is (A) sqrt(5)-1 (B) sqrt(5)-2 (C) sqrt(5) (D) 2

Simplify: (i) (5+\ sqrt(5))\ (5-\ sqrt(5)) (ii) (3+2sqrt(2))\ (3-2sqrt(2))

Direction cosines of a line which passes through the points (1,2,3) and (-3,4,1) is A) (4/(2sqrt6), -2/(2sqrt6), 2/(2sqrt6)) B) (4/(2sqrt6), -2/(2sqrt6), -2/(2sqrt6)) C) (4/(2sqrt6), 4/(2sqrt6), 2/(2sqrt6)) D) (-4/(2sqrt6), 1/(2sqrt6), -2/(2sqrt6))

Radius of the circle that passes through the origin and touches the parabola y^2=4a x at the point (a ,2a) is (a) 5/(sqrt(2))a (b) 2sqrt(2)a (c) sqrt(5/2)a (d) 3/(sqrt(2))a

The length of the tangent of the curve y=x^(2)+1 at (1 ,3) is (A) sqrt(5) (B) 3sqrt(5) (C) 1/2 (D) 3(sqrt(5))/(2)

Add 2sqrt(2)+5sqrt(3) and sqrt(2)-3sqrt(3) .

The length of the chord of the parabola y^2=x which is bisected at the point (2, 1) is (a) 2sqrt(3) (b) 4sqrt(3) (c) 3sqrt(2) (d) 2sqrt(5)

The length of the perpendicular drawn from the point P(3,4,5) on y-axis is a. 3sqrt(2) b. 5 c. sqrt(113) d. 5sqrt(2) e. sqrt34

Simplify: (sqrt(5)-2)/(sqrt(5)+2)-(sqrt(5)+\ 2)/(sqrt(5)-\ 2)