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KVPY Sample Paper KVPY Stream-SX Model Paper-12

  • question_answer
    The integers\[x,y\]and \[z\]each are perfect square and \[x>y>z>0.\]If \[x,y,z\]from an A.P. then the smallest possible value of \[x\]is

    A) 39

    B) 31

    C) 41

    D) 49

    Correct Answer: D

    Solution :

    Let \[x={{a}^{2}},y={{b}^{2}},z={{c}^{2}}\]. Then \[2{{b}^{2}}={{a}^{2}}+{{c}^{2}}\]since \[b\]is at least 2, consider the value of \[b\]from 2 onwards. The first such value occur when \[b\]=5(and then \[a=7,c=1\])so, the least possible value of \[x={{a}^{2}}=49\]


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