If the $p t h$ $q t h$ and $r t h$ terms of G.P. are $X,$ $Y,$ $Z,$ respectively, then $x^{q - r} y^{r - p} z^{p - q} =$

x y z

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p q r

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0

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1

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Solution

The correct option is A $1$
$a =$ first term $t =$ Common ratio

$t_{p} = X = a t^{p - 1}$

$t_{q} = Y = a t^{q - 1}$

$t_{r} = Z = a t^{r - 1}$

$X^{q - r} . Y^{r - p} . Z^{p - q}$

$= {(\frac{x}{Z})}^{q} (\frac{Y}{x}) {(\frac{Z}{y})}^{p}$

$= (t)^{p - r} . (t)^{q - p} . (t)^{r - q} = t^{o} = 1$

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