MCA Entrance Previous Year Question Bank

The equation of the circle passing through $(2,3)$ and $(-1,1)$ with its centre lying on the line $x-3y-11=0$ is

What is the diameter of the largest circle that can be drawn on a chessboard so that its entire circumference gets covered by the black squares and no part of the circumference on any white space, given that the chessboard has black and white squares of size one inch?

The radius of the circle passing through the foci of the ellipse $\frac{x^2}{16}+\frac{y^2}{9}=1$ and having its centre at $(0,3)$ is:

A circle touches the X-axis and also touches another circle with centre at $(0,3)$ and radius $2$. Then the locus of the centre of the first circle is:

If two circles $x^2+y^2+2gx+2fy=0$ and $x^2+y^2+2g^{\prime }x+2f^{\prime }y=0$ touch each other, then which of the following is true?

If the circles $x^2+y^2+2x+2ky+6=0$ and $x^2+y^2+2ky+k=0$ intersect orthogonally, then $k$ is:

If $2x+3y-6=0$ and $9x+6y-18=0$ cuts the axes in concyclic points, then the centre of the circle is:

The circle $x^2+y^2=9$ is contained in the circle $x^2+y^2-6x-8y+25=c^2$ if:

Find the equation of the circle which passes through $(-1,1)$ and $(2,1)$, and having centre on the line $x+2y+3=0$.

The lines $3x-4y+4=0$ and $6x-8y-7=0$ are tangents to the same circle. The radius of this circle is: