IPMAT Indore 2019 (SA) PYQs

The area of the triangle, formed by the straight lines $y = 0, 12x - 5y = 0,$ and $3x + 4y = 7$ is

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

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