$∣ ∣ ∣ ∣ \begin{matrix} a - b & b - c & c - a x - y & y - z & z - x p - q & q - r & r - p \end{matrix} ∣ ∣ ∣ ∣$

a(x+y+z)+b(p+q+r)+c

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abc+xyz+pqr

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None of these

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Solution

The correct option is B \N
$∣ ∣ ∣ ∣ \begin{matrix} a - b & b - c & c - a x - y & y - z & z - x p - q & q - r & r - p \end{matrix} ∣ ∣ ∣ ∣ = ∣ ∣ ∣ ∣ \begin{matrix} 0 & b - c & c - a 0 & y - z & z - x 0 & q - r & r - p \end{matrix} ∣ ∣ ∣ ∣$
[by $C_{1} \to C_{1} + C_{2} + C_{3}$ ]

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Question 4(iii)
Divide as directed
$52 p q r (p + q) (q + r) (r + p) \div 104 p q (q + r) (r + p)$

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