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Question

If a,b and care non zero numbers, then Δ=∣ ∣ ∣b2c2bcb+cc2a2cac+aa2b2aba+b∣ ∣ ∣ is equal to

A
abc
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B
a2b2c2
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C
ab+bc+ca
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D
None of these
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Solution

The correct option is C None of these
Multiplying R1 by a,R2 by b and R3 by c, we have
Δ=1abc∣ ∣ ∣ab2c2abcab+aca2bc2abcbc+aba2b2cabcac+bc∣ ∣ ∣=a2b2c2abc∣ ∣bc1ab+acac1bc+abab1ac+bc∣ ∣=abc∣ ∣ ∣bc1abac1abab1ab∣ ∣ ∣{by C3C3+C1}=abc.ab∣ ∣bc11ca11ab11∣ ∣=0, [Since C2C3].
Trick : Put a=1, b=2, c=3 and check it.

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