UPSC NDA I 2021 Mathematics Solved Paper

Concept
Slope intercept form of a straight line ⇔y=mx+c
Where m is the slope and c is the y-intercept
When two lines are perpendicular, the product of their slope is −1. If m is the slope of a line, then the slope of a line perpendicular to it is −1∕m.
Calculation:
Given equations are, y+px=1 and y−qx=2 which can be written as, y=−px+1 and y=qx+2
So, m1 (slope of 1 st line )=−p and m2 (slope of 2 nd line )=q
As they are perpendicular m1×m2=−1
⇒−pq=−1
⇒pq−1=0