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Question

Δ1=∣ ∣xbbaxbaax∣ ∣ and Δ2=xbax are the given determinants, then

A
Δ1=3(Δ2)2
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B
ddx(Δ1)=3Δ2
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C
ddx(Δ1)=3(Δ2)2
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D
Δ1=3(Δ2)3/2
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Solution

The correct option is B ddx(Δ1)=3Δ2
Δ1=∣ ∣xbbaxbaax∣ ∣=x(x2ab)b(axab)+b(a2ax)
Δ1=x33abx+ab2+a2b
ddxΔ1=3(x2ab)...(1)
Now, Δ2=xbax=x2ab...(2)
From equation (1) and (2)
ddxΔ1=3Δ2

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