JEE Mains · Maths · STD 11 - 6. permutation and combination
Let \(S\) be the set of all triangle 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
- A \(9\)
- B \(18\)
- C \(32\)
- D \(36\)
Answer & Solution
Correct Answer
(D) \(36\)
Step-by-step Solution
Detailed explanation
Let \(A( \propto ,0)\) and \(B(0,\beta )\) be the vectors of the given triangle \(AOB\) \( \Rightarrow \,|\alpha \beta | = 100\) \( \Rightarrow \) Number of triangles \(=4\times \) (numbers of divisors of \(100\)) \(=4\times 9=36\)
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