GATE CSE 2018 | Question: GA-7

Question

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

• A. $-1$
• B. $\dfrac{1}{pqr}$
• C. $1$
• D. $pqr$

Comments

got 1

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same here ans should be 1

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you have type wrong question

p−x=1/q

q−y=1/r

r−z=1/p

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pqr !=0, p^-x = 1/q, q^-y = 1/r, r^-z = 1/p

Taking log both sides,

-x(log p) = -log q,

-y(log q) = -log r,

-z(log r) = -log p

=> x = log q/ log p

=> y = log r/ log q

=> z = log p/ log r

multiplying x,y and z,

(x)(y)(z) = 1

Answer 1

Simplest way possible! 

Answer 2

c.