2. Sample Papers
  3. KVPY

KVPY Sample Paper KVPY Stream-SX Model Paper-17

  • question_answer
    If \[{{\log }_{2}}(a+b)+{{\log }_{2}}(c+d)\ge 4,\] where a, b, c, d are positive numbers. Then the minimum value of the expression \[a+b+c+d\]is

    A) 2

    B) 4

    C) 8

    D) 16

    Correct Answer: C

    Solution :

    \[{{\log }_{2}}(a+b)+{{\log }_{2}}(c+d)\ge 4\]\[\Rightarrow \]\[{{\log }_{2}}\{(a+b)(c+d)\}\ge 4\]
    \[\Rightarrow \]\[(a+b)(c+d)\ge {{2}^{4}}\]
    But \[A.M\ge G.M.\]
    \[\therefore \]\[\frac{(a+b)+(c+d)}{2}\ge \sqrt{(a+b)(c+d)}={{2}^{2}}\]
    \[\therefore \]\[a+b+c+d\ge 8.\]


You need to login to perform this action.
You will be redirected in 3 sec spinner