IPMAT Indore (MCQ) PYQs

A circle of radius $13$ cm touches the adjacent sides AB and BC of a square ABCD at M and N, respectively. If AB = $18$ cm and the circle intersects the other two sides CD and DA at P and Q, respectively, then the area, in sq. cm, of triangle PMD is

On a circular path of radius 6 m a boy starts from a point $A$ on the circumference and walks along a chord $AB$ of length 3 m. He then walks along another chord $BC$ of length 2 m to reach point $C$. The point $B$ lies on the minor arc $AC$. The distance between point $C$ from point $A$ is

In the xy-plane let $A = (- 2, 0), B = (2, 0)$ . Define the set S as the collection of all points C on the circle $x ^ 2 + y ^ 2 = 4$ such that the area of the triangle ABC is an integer. The number of points in the set S is