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KVPY Sample Paper KVPY Stream-SX Model Paper-11

  • question_answer
    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

    Correct Answer: D

    Solution :

    Let \[A(\alpha ,0)\] and \[B\,(0,\beta )\] be the vectors of the given triangle AOB
    \[\Rightarrow \]   \[\left| a\beta  \right|=100\]
    \[\Rightarrow \] Number of triangles
    \[=4\times \] (number of divisors of 100)
    \[=4\times 9=36.\]


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