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If p+q+r=0=a+b+c, then the value of the determinant pa    qb    rcqc    ra    pbrb    pc    qa is

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a
0
b
pa + qb + rc
c
1
d
none of these

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detailed solution

Correct option is A

pa    qb    rcqc    ra    pbrb    pc    qa       =pqra3+b3+c3−3abc−abcp3+q3+r3−3pqr=pqr(a+b+c)a2+b2+c2−ab−bc−ca−abc(p+q+r)p2+q2+r2−pq−qr−pr=0


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If [ ] denotes the greatest integer less than or equal to the real number under consideration, and 1x<0,0y<1,1z<2, then the value of the determinant [x]+1[y][z][x][y]+1[z][x][y][z]+1 is


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