2022-II-24

Ans: A
Rewrite the equation into slope intercept form, we have

$\begin{array}{rcl}
mx +ny & = & 3 \\
ny & = & -mx +3 \\
y & = & \dfrac{-m}{n} x+\dfrac{3}{n}
\end{array}$

I is true. Consider the $y$-intercept of the straight line, we have

$\begin{array}{rcl}
\dfrac{3}{n} & > & 0 \\
n & > & 0
\end{array}$

Consider the slope of the straight line, we have

$\begin{array}{rcl}
\dfrac{-m}{n} & > & 0 \\
-m & > & 0 \\
m & < & 0 \end{array}$

II is true. Consider the $y$-intercept of the straight line, we have

$\begin{array}{rcl}
\dfrac{3}{n} & < & 1 \\ 3 & < & n \\ n & > & 3
\end{array}$

III is not true. Consider the slope of the straight line, we have

$\begin{array}{rcl}
\dfrac{-m}{n} & < & \dfrac{1-0}{0-(-1)} \\ \dfrac{-m}{n} & < & 1 \\ -m & < & n \\ m+n & > & 0
\end{array}$