JEE MAIN - Mathematics (2019 - 9th January Evening Slot - No. 14)
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 :
9
18
36
32
Explanation
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Area = $${1 \over 2}$$ h. k = 50
h. k = 100
h. k = 22 . 52
Total divisors
= (2 + 1) (2 + 1) = 9
if h > 0, k > 0
But $${\matrix{ {h > 0,} & {k < 0} \cr {h < 0,} & {k > 0} \cr {h < 0,} & {k < 0} \cr } }$$
all are possible so that total no. of positive case
9 + 9 + 9 + 9 = 36
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