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UPSC NDA I 2016 Mathematics Solved Paper

Question Numbers: 50-51

Given that logx y, logz x, logy z are in GP, xy

z = 64

and x3, y3, z3 are in AP.

Question : 51 of 120

Marks: +1, -0

xy yz and zx are

Solution:

Concept:

x = y = z

, then the three terms

xy

yz

, and

zx

become equal.

Explanation:

Given that

x

y

, and

z

are equal, we have

xy = yz = zx

All three terms are identical, say

a

In an arithmetic progression (AP), the common difference is

a - a = 0

In a geometric progression (GP), the common ratio is

a / a = 1

Since both conditions are satisfied, the terms are in both AP and GP.

Answer:

C. In both AP and GP

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