The value of $\sqrt{p^{-1} q} \cdot \sqrt{q^{-1} r} \cdot \sqrt{r^{-1} p}$ is
(a) $-1$
(b) 0
(C) 1
(d) 2
$\sqrt{p^{-1} q} \cdot \sqrt{q^{-1} r} \cdot \sqrt{r^{-1} p}=\left(p^{-1} q\right)^{\frac{1}{2}} \cdot\left(q^{-1} r\right)^{\frac{1}{2}} \cdot\left(r^{-1} p\right)^{\frac{1}{2}}$
$=\left(p^{-\frac{1}{2}} q^{\frac{1}{2}}\right) \cdot\left(q^{-\frac{1}{2}} r^{\frac{1}{2}}\right) \cdot\left(r^{-\frac{1}{2}} p^{\frac{1}{2}}\right)$
$=p^{-\frac{1}{2}+\frac{1}{2}} q^{\frac{1}{2}-\frac{1}{2}} r^{\frac{1}{2}-\frac{1}{2}}$
$=p^{0} q^{0} r^{0}$
$=1$
$\therefore$ The value of $\sqrt{p^{-1} q} \cdot \sqrt{q^{-1} r} \cdot \sqrt{r^{-1} p}$ is equal to 1 .
Hence, the correct option is (c).
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