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Question

If 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=3Δ23/2
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Solution

The correct option is C ddx(Δ1)=3Δ2
Given, Δ1=∣ ∣xbbaxbaax∣ ∣ and Δ2=xbax
Δ1=x33abx+ab2+a2b
and Δ2=x2ab
Now, ddx(Δ1)=3(x2ab)
Hence, ddx(Δ1)=3Δ2

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