IPMAT Indore (MCQ) PYQs

If one of the lines given by the equation $2x^2 + axy + 3y^2 = 0$ coincides with one of those given by $2x^2 + bxy - 3y^2 = 0$ and the other lines represented by them are perpendicular then $a^2+b^2 =$

The equation of the straight line passing through the point $M (-5,4)$, such that the portion of it between the axes is divided by the point $M$ into two equal halves, is

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