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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=

A
1
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B
2
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C
1
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D
None of the above
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Solution

The correct option is A.1

Let d be the common difference of A.P. and r(0), the common ratio of G.P,

Since, p,q,r are in AP

q=p+d....(1)

r=p+2d..(ii)$

Subtracting, (ii) from (i), we get,

qr=d....(iii)

rp=2d....(iv) [From (ii)]

pq=d....(v) [From (i)]

Also, x,y,z are in GP with common ratio r

y=xr...(vi) and z=xr2....(vii)

xqr.yrp.zpq=xd(xr)2d(xr2)d [From (iii),(iv),(v),(vi) and (vii)]

=xd+2ddr2d2d

=x0r0=1

Hence,xqr.yrp.zpq=1




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