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|(a,b,c),(b,c,a),(c,a,b)| =...

`|(a,b,c),(b,c,a),(c,a,b)| =`

A

`a+b+c+a b c`

B

`a^2+b^2+c^2+a b+bc+c a`

C

`3 a b c-a^3-b^3-c^3`

D

`a^3+b^3+c^3-3 a b c`

Text Solution

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The correct Answer is:
C
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HIMALAYA PUBLICATION-MATRICES AND DETERMINANTS-QUESTION BANK
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  2. |[1, x, x^2 ],[1, y, y^2],[1, z, z^2]|=

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  3. |(a,b,c),(b,c,a),(c,a,b)| =

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  4. |[1, a, a^2-b c],[1,b, b^2-c a],[1,c, c^2-a b]|=

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  5. |(b^(2)c^(2),bc,b+c),(c^(2)a^(2),ca,c+a),(a^(2)+b^(2),ab,a+b)|=

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  6. If |[ x+1 ,2 ,3],[1 , x+2,3],[1, 2, x+3]|=0, then x=0 and

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  7. The factors of |[x,a,b],[a,x,b],[a,b,x]|are

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  8. If |[1,2,3],[2,x,3],[3,4,5]|=0 then x=

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  9. The roots of the equation |[0,x,16],[x,5,7],[0,9,x]|= 0 are

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  10. The roots of the equation |[2+x,3,-4],[2,3+x,-4],[2,3,-4+x]|=0 are

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  11. A root of the equation |(0, x-a,x-b),(x+a,0,x-c),(x+b,x+c,0)|=0 is

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  12. The roots of the equation |(x-1,1,1),(1,x-1,1),(1,1,x-1)| = 0 are

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  13. If a+b+c=0 , one root of : |(a-x,c,d),(c,b-x,a),(b,a,c-x)|=0 is :

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  14. The non zero value of x, if |[-x,1,0],[1,-x,1],[0,1,-x]|=0 is

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  15. The factors of |[1,1,1],[x,y,1],[x^2,y^2,1]|are

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  16. The factors of |[x,a,b],[a,x,b],[a,b,x]|are

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  17. If alpha , beta and gammaare roots of the equations x^3+px+q=0 then th...

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  18. |[1^(2),2^(2), 3^(2),4^(2)],[2^(2),3^(2),4^(2),5^(2)],[3^(2),4^(2),5^(...

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  19. The value of [[a,b,c,d],[-a,b,c,d],[-a,-b,c,d],[-a,-b,-c ,d]] is

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  20. If A is a square matrix of order 3 and |A|=8, then |adj A|=

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