IPMAT Indore (MCQ) PYQs

The value of $k$ for which the following lines are concurrent is

$x-y-1=0 \newline 2x+3y-12=0 \newline 2x-3y+k=0$

Consider the polynomials $f(x) = ax^2 + bx + c$, where $a > 0, b, c$ are real, $g(x) = -2x$. If $f(x)$ cuts the x-axis at $(-2, 0)$ and $g(x)$ passes through $(a, b)$, then the minimum value of $f(x) + 9a + 1$ is

The maximum distance between the point $(-5, 0)$ and a point on the circle $x^2 + y^2 = 4$ is