If _1= vmatrix 1&p&q 1&q&r 1&r&p vmatrix and _2= vmatrix 1&1&1 &r&p &p&q vmatrix where p q r, then _1+ _2 is

NDA 2022 Mathematics question

If and where , then is

Answer: (C)

Expanding, \Delta_1 = (pq-r^2)-p(p-r)+q(r-q) = -(p^2+q^2+r^2-pq-qr-rp) and \Delta_2 = (qr-p^2)-(q^2-pr)+(pq-r^2) = -(p^2+q^2+r^2-pq-qr-rp).

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Question ID VK-029292