NIMCET 2024 Paper

Put the points in the given line and check the signs. If the signs are same, then the points are on the same side of the line otherwise they are on different sides of the lines.
The first line is $2\mathit{x}+3\mathit{y}-6=0$ and the second line is $2\mathit{x}+3\mathit{y}+6=0$
At point $\left(1,\frac{1}{2}\right)$, the first line is negative, but the second line is positive.
At the point $\left(3,-\frac{1}{2}\right)$, the first line is negative, but the second line is positive.
Only choice (4) is wrong. The first three choices are correct.
both the lines are of opposite signs. Hence this point lies between the lines. Similarly, the point $\left(3,-\frac{1}{2}\right)$ also lies between the lines.