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QJEEM19Maf146: JEE Main 2019 Mathematics - Class 11 JEEM19Maf146 Solution: Let S be the set of all triangles in the xy-plane, each having…

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 :

Multiple Choice Options

  • A 9
  • B 18
  • C 36
  • D 32

Step-by-Step Verified Solution

JEE Main 2019 (Online) 9th January Evening Slot Mathematics - Permutations and Combinations Question 156 English Explanation

Area = 12{1 \over 2} h. k = 50

h. k = 100

h. k = 22 . 52

Total divisors

= (2 + 1) (2 + 1) = 9

if   h > 0, k > 0

But   h>0,k<0h<0,k>0h<0,k<0

all are possible so that total no. of positive case

9 + 9 + 9 + 9 = 36

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