All points lying inside the triangle formed by the points $(1, 3)$,$(5, 0)$,and $(-1, 2)$ satisfy which of the following inequalities?

If a straight line $L$ is perpendicular to the line $4x - 2y = 1$ and forms a triangle of area $4 \text{ sq unit}$ with the coordinate axes,then the equation of the line $L$ is

In a $\triangle ABC$ with $\angle A < \angle B < \angle C$,points $D, E, F$ are on the interior of segments $BC, CA, AB$ respectively. Which of the following triangles cannot be similar to $\triangle ABC$?

Let a point $A$ lie between the parallel lines $L_1$ and $L_2$ such that its distances from $L_1$ and $L_2$ are $6$ and $3$ units, respectively. Then the area (in sq. units) of the equilateral triangle $ABC$, where the points $B$ and $C$ lie on the lines $L_1$ and $L_2$ respectively, is:

If the three lines $x - 3y = p$,$ax + 2y = q$,and $ax + y = r$ form a right-angled triangle,then:

The area (in sq units) of the quadrilateral formed by the lines $2x + 3y + 6 = 0$,$2x - 3y + 6 = 0$,$2x + 3y - 6 = 0$,and $2x - 3y - 6 = 0$ is