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UPSC NDA I 2016 Mathematics Solved Paper

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For the next two (2) items that follow :
Given that logxy,logzx,logyz are in G.P,xyz=64 and x3,y3,z3 are in AP.

[NDA I 2016]

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Question : 51

Total: 120

Which one of the following is correct?
xy , yz and zx are

in AP only
in GP only
in both Ap and GP
neither in Ap nor in GP

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