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If a,b,c are all different and the equat...

If a,b,c are all different and the equations `ax+a^(2)y+(a^(3)+1)z=0, bx+b^(2)y+(b^(3)+1)z=0, cx+c^(2)y+(c^(3)+1)z=0` have a nonzero solution , then

A

`abc+1=0`

B

`abc-1=0`

C

`a^(2)+b^(2)+c^(2)=ab+bc+ca`

D

`a^(3)+b^(3)+c^(3)+3abc=0`

Text Solution

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The correct Answer is:
A
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DIPTI PUBLICATION ( AP EAMET)-MATRICES-EXERCISE 1D MCQ (LINEAR EQUATIONS)
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  5. The equation x+y+z=6, x+2y+3z=10, x+2y+lamdaz=mu have unique solution ...

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  6. The system of equations x+y+z=6, x+2y+3z=10,x+2y+lamdaz=mu is inconsis...

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  7. The system of equations x+ky+3z=0, 3x+ky-2z=0, 2x+3y-4z=0 has a non t...

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  8. The system of linear equations x+y+z=2, 2x+y-z=3, 3x+2y+kz=4 has a uni...

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  9. If the system of equation x+y=6,x+2y+lamdaz=0, x+2y+3z=0 has no soluti...

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  10. If the system of equations x+2y+z=12,3x+y+2z=5,2x+lamday+2z=18 has non...

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  11. The system of equations 3x-y+4z=3, x+2y-3z=-2,6x+5y+lamdaz=-3 has non ...

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  12. If the system of equation ax+y+z=0, x+by+z=0, x+y+cz=0,(a,b,c!=1) has ...

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  13. If the system of linear equations x+2ay+az=0, x+3by+bz=0,x+4ch+cz=0 ha...

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  14. The number of real values of t such that the system of homogeneous equ...

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  15. Given that a alpha^(2)+2b alpha +c!=0 and that the system of equations...

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  16. If a,b,c are all different and the equations ax+a^(2)y+(a^(3)+1)z=0, b...

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  17. The system of equations (sin 3 theta) x - y+z=0,(cos 2 theta)x+4y+3z=0...

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  18. The System of equation -2x-y+z=a,x-2y+z=b,x+y-2z=c is inconsistent if

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  19. The system of equations -2x+y+z=a,x-2y+z=b,x+y-2z=c is consistent if

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  20. If the system of equations ax+y+z=0, x+by+z=0, x+y+cz=0 has a nontrivi...

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