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KVPY Sample Paper KVPY Stream-SX Model Paper-30

  • question_answer
    Let f be a function defined from \[{{R}^{+}}\to {{R}^{+}}\]. 'If \[{{(f(xy))}^{2}}=x{{(f(y))}^{2}}\] for all positive numbers x and y and \[f(2)=6\], then \[f(50)\] is equal to

    A) 10

    B) 30   

    C) 40

    D) 50

    Correct Answer: B

    Solution :

    Put \[x=25,\]     \[y=2\]
    \[{{(f(50))}^{2}}=25{{(f(2))}^{2}}\]
    \[=25{{(6)}^{2}}\]\[\Rightarrow f(50)=5\times 6=30\]


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