`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))`

(a) sqrt(175) (b) 2sqrt(112) (c) sqrt(125) (d) 5sqrt(119)

The value of the definite integral int_0^(pi/2)sqrt(tanx)dx is (a) sqrt(2)pi (b) pi/(sqrt(2)) (c) 2sqrt(2)pi (d) pi/(2sqrt(2))

The equation of four circles are (x+-a)^2+(y+-a)^2=a^2 . The radius of a circle touching all the four circles is (a) (sqrt(2)+2)a (b) 2sqrt(2)a (c) (sqrt(2)+1)a (d) (2+sqrt(2))a

If center of a regular hexagon is at the origin and one of the vertices on the Argand diagram is 1+2i , then its perimeter is 2sqrt(5) b. 6sqrt(2) c. 4sqrt(5) d. 6sqrt(5)

Length of the latus rectum of the parabola sqrt(x) +sqrt(y) = sqrt(a) is (a) a sqrt(2) (b) (a)/(sqrt(2)) (c) a (d) 2a

The minimum vertical distance between the graphs of y=2+sinx and y=cosx is (a) 2 (b) 1 (c) sqrt(2) (d) 2-sqrt(2)

Let C be a circle with two diameters intersecting at an angle of 30^0dot A circle S is tangent to both the diameters and to C and has radius unity. The largest radius of C is (a) 1+sqrt(6)+sqrt(2) (b) 1+sqrt(6)-sqrt(2) (c) sqrt(6)+sqrt(2)-11 (d) none of these

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

A rectangle is inscribed in an equilateral triangle of side length 2a units. The maximum area of this rectangle can be (a) sqrt(3)a^2 (b) (sqrt(3)a^2)/4 a^2 (d) (sqrt(3)a^2)/2

A square is inscribed in the circle x^2+y^2-2x+4y+3=0 . Its sides are parallel to the coordinate axes. One vertex of the square is (a) (1+sqrt(2),-2) (b) (1-sqrt(2),-2) (c) (1,-2+sqrt(2)) (d) none of these