The number of points with integral co-ordinates that are interior to the circle \(x^{2}+y^{2}=16\) is : (a) 43 (b) 45 (c) 47 (d) 49

For what values of \(l\) and \(m\), circle \(5\left(x^{2}+y^{2}\right)+b y-m=0\) belongs to the co-axial system determined by the circles $x^{2}+y^{2}+2 x+4 y-6=0\( and \)2\left(x^{2}+y^{2}\right)-x=0 ?$

A square is inscribed in the circle \(x^{2}+y^{2}-10 x-6 y+30=0\) One side of the square is parallel to \(y=x+3\), then one vertex of the square is : (a) \((3,3)\) (b) \((7,3)\) (c) \((6,3-\sqrt{3})\) (d) \((6,3+\sqrt{3})\)

The ends \(A, B\) of a fixed straight line of length ' \(a^{\prime}\) and ends \(A^{\prime}\) and \(B\) ' of another fixed straight line of length ' \(b\) ' slide upon the axis of \(x\) and the axis of \(y\) (one end on axis of \(x\) and the other on axis of \(y\) ). Find the locus of the centre of the circle passing through \(A, B, A^{\prime}\) and \(B\).

Let the base of a triangle lie along the line \(x=a\) and be of length \(2 a .\) The area of this triangle is \(a^{2}\), if the vertex lies on the line :. (a) \(x=-a\) (b) \(x=0\) (c) \(x=\frac{a}{2}\) (d) \(x=2 a\)

An equation of a circle touching the axes of co-ordinates and the line $x \cos \alpha+y \sin \alpha=2$ can be : (a) \(x^{2}+y^{2}-2 g x-2 g y+g^{2}=0 \quad\) where $g=2 /(\cos \alpha+\sin \alpha+1)$ (b) \(x^{2}+y^{2}-2 g x-2 g y+g^{2}=0 \quad\) where $g=2 /(\cos \alpha+\sin \alpha-1)$ (c) \(x^{2}+y^{2}-2 g x+2 g y+g^{2}=0 \quad\) where $g=2 /(\cos \alpha-\sin \alpha+1)$ (d) \(x^{2}+y^{2}-2 g x+2 g y+g^{2}=0 \quad\) where $g=2 /(\cos \alpha-\sin \alpha-1)$