IPMAT Indore (MCQ) PYQs

Let the circle $x^2 + y^2 = 2ax + 2by$ intersect the x-axis at point $A(\alpha, 0)$ and y-axis at point $B(0, \beta)$, where $\alpha\beta \neq 0$. If the point $C(p, q)$ lies on the chord AB, then $\frac{p+\alpha}{a} + \frac{q+\beta}{b}$ equals

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

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