NIMCET 2013 — Mathematics PYQ

Step 1: Use the property of a line passing through a point

If a line $ax+by+c=0$ passes through a point $(x_1,y_1)$, then the coordinates of that point must satisfy the equation of the line.

Given point: $(1,-2)$

Substituting $x=1$ and $y=-2$ into the equation:

Step 2: Rearrange the equation

To see the relationship between $a,b,$ and $c$, isolate the middle term:

Step 3: Identify the Progression

In an Arithmetic Progression (A.P.), if three numbers $a,b,c$ are in A.P., the common difference is constant:

Since our derived equation $a+c=2b$ matches the condition for an Arithmetic Progression exactly, we can conclude that $a,b,c$ are in A.P.

Correct Option: 1. A.P.