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Question

If s=p+q+r, then value of ∣ ∣s+rpqrs+pqrps+q∣ ∣ is ________.

A
s3
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B
2s3
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C
2s2
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D
3s3
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Solution

The correct option is A 2s3
given s=p+q+r

∣ ∣s+rpqrs+pqrps+q∣ ∣

computing C1C1+C2+C3

=∣ ∣s+r+p+qpqr+s+p+qs+pqr+p+s+qps+q∣ ∣

substituting s=p+q+r

=∣ ∣2spq2ss+pq2sps+q∣ ∣ =2s×∣ ∣1pq1s+pq1ps+q∣ ∣

computing R2R2R1 abd R3R3R1

=2s×∣ ∣1pq0s000s∣ ∣

now computing determinant , we get
=2s×s2=2s3

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