GATE | GATE CS 2018 | Question 9

If pqr ≠ 0 and p^{-x} = \frac{1}{q}, q^{-y} = \frac{1}{r}, r^{-z} = \frac{1}{p}, what is the value of the product xyz ?

(A) -1
(B) 1 / pqr
(C) 1
(D) pqr


Answer: (C)

Explanation: Taking logs of given three values,
we get

1/q = p-x -------(1)
1/r = q-y -------(2)
1/p = r-z -------(3)

1/q = p-x
    = r-xz [Putting value of p from (3)]
    = q-xyz  [Putting value of r from (2)]
    = 1 / qxyz

On comparing power of q both sides, we get xyz = 1

So, option (C) is correct.




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