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Question

If xa, yb, zc and
∣ ∣ayzxbzxyc∣ ∣=0
then value of x+axa+y+byb+z+czc is

A
0
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B
1
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C
1
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D
2
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Solution

The correct option is C 1
Given ∣ ∣ayzxbzxyc∣ ∣=0

a(bcyz)y(xcxz)+z(xyxb)=0

abcayzxyz+xyz+xyzxbz=0

(x+a)(yb)(zc)+(y+b)(xa)(zc)+(z+c)(xa)(yb)+(xa)(yb)(zc)=0

x+axa+y+byb+z+czc=1

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