Question

If p, q, r are in A.P. and x, y, z are in G.P. then $x^{q-r}.y^{r-p}.z^{p-q}$ is equal to

• A. 1
• B. xyz
• C. x+y+z
• D. p+q+r

Answer 1

The correct option is A

1

p, q, r are in A.P.
$\therefore 2q=p+r$

x,y,z are in G.P.
Let R be the common ratio of G.P. then,
$y=Rx$
$z=R^{2}x$
Now
$x^{q-r},y^{r-p},z^{p-q}=x^{q-r}(Rx{)}^{r-p}.(R^{2}x{)}^{p-q}$
$=x^{q-r+r-p+p-q}.R^{r-p+2p-2q}=x^0.R^{p+r-2q}=x^0{R}^0=1$