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Question

If p+q+r=a+b+c=0, then the determinant ∣∣ ∣∣paqbrcqcrapbrbpcqa∣∣ ∣∣ equals.

A
0
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B
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C
pa+qb+rc
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D
pa+qb+rc+a+b+c
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Solution

The correct option is D 0
determinant of matrix =pa(qra2p2bc)qb(q2caprb2)+rc(pqc2r2ab)

=pqr(a3+b3+c3)abc(p3+q3+r3)

=pqr(3abc)abc(3pqr) ......(as when a+b+c=0,a3+b3+c3=3abc)

=0

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