UPSC NDA 2 2019 Mathematics Solved Paper

Concept:A linear equation in two variables always represents a straight line in the $xy$-plane.Explanation:The general equation $Ax + By + C = 0$ has two variable terms: $Ax$ and $By$.If both $A$ and $B$ are zero, the equation reduces to $C = 0$.This is either false (no graph) or an identity (entire plane), not a line.If $A = 0$ but $B \neq 0$, the equation becomes $By + C = 0$, i.e., $y = -C/B$, a horizontal line.If $B = 0$ but $A \neq 0$, the equation becomes $Ax + C = 0$, i.e., $x = -C/A$, a vertical line.If both $A$ and $B$ are non-zero, the line is slanted.Therefore, a straight line is represented only when at least one of $A$ or $B$ is non-zero.Answer:D. only when at least one of a and b is non-zero