$A$ homogeneous equation of second degree in $x$ and $y$ represents which of the following?

$\left|\begin{array}{ccc}a-b-c & 2a & 2a \\ 2b & b-c-a & 2b \\ 2c & 2c & c-a-b\end{array}\right|$ is equal to

The number of triangles that can be formed by choosing the vertices from a set of $12$ points,seven of which lie on the same straight line,is

$A$ line passing through the point of intersection of $x+y=4$ and $x-y=2$ makes an angle $\tan ^{-1}\left(\frac{3}{4}\right)$ with the $x$-axis. It intersects the parabola $y^{2}=4(x-3)$ at points $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$ respectively. Then, $|x_{1}-x_{2}|$ is equal to

Which of the following liquid mixtures shows a positive deviation from Raoult's law?

Which pair of oxides is acidic in nature?