IPMAT Indore (MCQ) PYQs

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

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

The circle $x^2 + y^2 - 6x - 10y + k = 0$ does not touch or intersect the coordinate axes. If the point $(1, 4)$ does not lie outside the circle, and the range of $k$ is $(a, b]$, then $a + b$ is