`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)`1//2` d) `1/(sqrt(2))`

An ellipse is drawn with major and minor axis of length 10 and 8 respectively. Using one focus a centre, a circle is drawn that is tangent to ellipse, with no part of the circle being outside the ellipse. The radius of the circle is (A) sqrt3 (B) 2 (C) 2sqrt2 (D) sqrt5

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

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

If two different tangents of y^2=4x are the normals to x^2=4b y , then (a) |b|>1/(2sqrt(2)) (b) |b| 1/(sqrt(2)) (d) |b|<1/(sqrt(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

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))

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

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

If one root x^2-x-k=0 is square of the other, then k= a. 2+-sqrt(5) b. 2+-sqrt(3) c. 3+-sqrt(2) d. 5+-sqrt(2)

Let A B C D be a tetrahedron such that the edges A B ,A Ca n dA D are mutually perpendicular. Let the area of triangles A B C ,A C Da n dA D B be 3, 4 and 5sq. units, respectively. Then the area of triangle B C D is 5sqrt(2) b. 5 c. (sqrt(5))/2 d. 5/2