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Question

If p, q, r are in A.P. and x, y, z are in G.P. then xqr.yrp.zpq is equal to


  1. 1
     

  2. xyz
     

  3. x+y+z
     

  4. p+q+r


Solution

The correct option is A

1
 


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

x,y,z are in G.P.
Let R be the common ratio of G.P. then,
y=Rx
z=R2x
Now
xqr,yrp,zpq=xqr(Rx)rp.(R2x)pq
=xqr+rp+pq.Rrp+2p2q=x0.Rp+r2q=x0R0=1

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