IPMAT Indore (MCQ) PYQs

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

Let ABCD be a rectangle with AB = 72 cm and BC = 30 cm. A circle passing through points A and C cuts the side AB at P such that AP = 56 cm. The radius, in cm, of the circle is

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