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|(1,log(x)y,log(x)z),(log(y)x,1,log(y)z)...

`|(1,log_(x)y,log_(x)z),(log_(y)x,1,log_(y)z),(log_(z)x,log_(z)y,1)|=`

A

log(xyz)

B

`log(xy+yz+zx)`

C

0

D

`log(x+y+z)`

Text Solution

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The correct Answer is:
C
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AAKASH SERIES-MATRICES -DETERMINANTS- EXERCISE - II
  1. If w is a complex cube root unity then |{:(1,1+w,1+w^(2)),(1+w,1+w^(2)...

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  2. If alpha, beta, gamma are the roots of x^(3)+px+q=0 then |(alpha, beta...

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  3. |(1,log(x)y,log(x)z),(log(y)x,1,log(y)z),(log(z)x,log(z)y,1)|=

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  4. |(1//a,a^(2),bc),(1//b,b^(2),ca),(1//c,c^(2),ab)|=

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  5. Let A=[(5,5 alpha, alpha),(0, alpha, 5 alpha),(0,0,5)] If |A|^(2)=25 t...

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  6. If k gt1, and the determinant of the matrix A^(2), where A=[(k,kalpha,...

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  7. If bc+ca+ab=18, and |(1,a^(2),a^(3)),(1,b^(2),b^(3)),(1,c^(2),c^(3))|=...

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  8. If a,b,c are positive and not all equal then |(a,b,c),(b,c,a),(c,a,b)|

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  9. |(a^(2)+x,ab,ac),(ab,b^(2)+x,bc),(ac,bc,c^(2)+x)|

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  10. Show that A=|{:(-2a,a+b,c+a),(a+b,-2b,b+c),(c+a,c+b,-2c):}|=4(a+b)(b+c...

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  11. If a+b+c=0 and |(a-x,c,b),(c,b-x,a),(b,a,c-x)|=0 then x=

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  12. If |(lamda^(2)+3lamda, lamda-1, lamda+3),(lamda+1, 2-lamda,lamda-4),(l...

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  13. Let |{:(x^(2)+x+1,x+1,2x-3),(3x^(2)-1,x+2,x-1),(x^(2)+5x+1,2x+3,x+4):}...

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  14. If |(a,b,a alpha+b),(b,c, b alpha+c),(a alpha+b, b alpha+c,0)|=0 then

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  15. If a,b,c are the p^(th),q^(th),r^(th) terms in H.P. then |{:(bc,p,1),(...

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  16. If |(3x-8,3,3),(3,3x-8,3),(3,3,3x-8)|=0 then x=0

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  17. If a,b,c are different and |(0,x-a,x-b),(x+a,0,x-c),(x+b,x+c,0)|=0 the...

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  18. If x=-1 is a root of the equation |{:(2-x,3,3),(3,4-x,5),(3,5,4-x):}|=...

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  19. If one of the roots of |(3,5,x),(7,x,7),(x,5,3)|=0 is -10, then the ot...

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  20. If |(x,x+y,x+y+z),(2x,3x+2y,4x+3y+2z),(3x,6x+3y,10x+6y+3z)|=64 then x=

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