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Question

For some αϵR, if αxpx=αyqy=αzrz and p,q,r are in A.P., then


A

x, y, z are in H.P.

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B

x, y, z are in G.P.

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C

x2,y2,z2 are in A.P.

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D

No such relation in x, y, z

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Solution

The correct option is A

x, y, z are in H.P.


Let αxpx=αyqy=αzrz=λ

p=αxλx,q=αyλy,r=αzλz

Given, 2q=p+r2αλy2λ=αλx1λ+αλz1λ

2y=1x+1z


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