JEE Main 2019MathematicsStraight LinesMediumMCQ

JEE Main 2019 — Straight Lines Question with Solution

JEE Main 2019 (09 Jan Shift 2)

Question

Let S be the set of all triangles in the xy -plane, each having one vertex at the origin and the other two vertices lie on coordinate axes with integral coordinates. If each triangle in S has area 50 sq. units, then the number of elements in the set S is:

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Show full solutionCorrect option: A
Correct answer
A36

Step-by-step explanation

Since the vertex of given triangle is O (origin) and other two vertices A and B lies on the coordinate axes, hence triangle must be a right-angled triangle.

Area =12x.y                        ( x, y∈I)

As per given condition

12x.y=50⇒x. y=100

Possible ordered pairs of x, y when ∆ formed in 1st quadrant are 9 i. e. 1,100, 2,50, 4,25, 5,20, 10,10, 25, 4, 50, 2, 100,1

∆ can be formed in any of the quadrants, hence total number of cases 9×4=36.

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About this question

This is a previous-year question from JEE Main 2019, covering the Straight Lines chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.