`A B C D` is a square of unit area. A circle is tangent to two sides of `A B C D` and passes through exactly one of its vertices. The radius of the circle is (a) `2-sqrt(2)` (b) `sqrt(2)-1` (c) `sqrt(2)-1/2` (d) `1/(sqrt(2))`

The line 2x-y+1=0 is tangent to the circle at the point (2, 5) and the center of the circle lies on x-2y=4. The radius of the circle is (a) 3sqrt(5) (b) 5sqrt(3) (c) 2sqrt(5) (d) 5sqrt(2)

The value of sqrt(3-2\ sqrt(2)) is (a) sqrt(2)-1 (b) sqrt(2)+1 (c) sqrt(3)-sqrt(2) (d) sqrt(3)+\ sqrt(2)

The rationalisation factor of sqrt(3) is (a) -sqrt(3) (b) 1/(sqrt(3)) (c) 2sqrt(3) (d) -2sqrt(3)

Maximum value of |z+1+i|, where z in S is (a) sqrt(2) (b) 2 (c) 2sqrt(2) (d) 3sqrt(2)

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

Two equal circles of radius r intersect such that each passes through the centre of the other. The length of the common chord of the circles is sqrt(r) (b) sqrt(2)\ r\ A B (c) sqrt(3)\ r\ (d) (sqrt(3))/2\ r

int_0^(sqrt(2)) [x^2] dx is equal to (A) 2-sqrt(2) (B) 2+sqrt(2) (C) sqrt(2)-1 (D) sqrt(2)-2

A circle S of radius ' a ' is the director circle of another circle S_1,S_1 is the director circle of circle S_2 and so on. If the sum of the radii of all these circle is 2, then the value of ' a ' is (a) 2+sqrt(2) (b) 2-1/(sqrt(2)) (c) 2-sqrt(2) (d) 2+1/(sqrt(2))

1/(sqrt(9)-\ sqrt(8)) is equal to: (a) 3+2sqrt(2) (b) 1/(3+2sqrt(2)) (c) 3-2sqrt(2) (d) 3/2-\ sqrt(2)

The value of sin(1/4sin^(-1)((sqrt(63))/8)) is (a) 1/(sqrt(2)) (b) 1/(sqrt(3)) (c) 1/(2sqrt(2)) (d) 1/(3sqrt(3))