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Question

lf p,q,r are distinct, then (q−r)x+(r−p)y+(p−q)=0 and (q3−r3)x+(r3−p3)y+(p3−q3)=0 represents the same line if

A
p+q+r=0
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B
p=q=r
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C
p2+q2+r2=0
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D
p3+q3+r3=0
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Solution

The correct option is D p+q+r=0
Given
L1:(qr)x+(rp)y+(pq)=0

L2:(q3r3)x+(r3p3)y+(p3q3)=0
If these two lines represent the same line, then the coefficients should be in the same ratios.
qrq3r3=rpr3p3=pqp3q3

1q2+qr+r2=1r2+rp+p2=1p2+pq+q2

q2+r2+qr=r2+p2+pr
q2p2=r(pq)
(p+q)=rp+q+r=0
Hence, option A is the correct answer.

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