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the determinant |{:(a,,b,,aalpha+b),(b,,...

the determinant `|{:(a,,b,,aalpha+b),(b,,c,,balpha+c),(aalpha+b,,balpha+c,,0):}|=0` is equal to zero if

A

a,b,c are in A.P.

B

a,b,c are in G.P.

C

`alpha` is a root of the equation `ax^2 + bx+c=0`

D

`(x-alpha)` is a factor of `ax^2 + 2bx +c`

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The correct Answer is:
B, D
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ML KHANNA-DETERMINANTS -Self Assessment Test
  1. the determinant |{:(a,,b,,aalpha+b),(b,,c,,balpha+c),(aalpha+b,,balpha...

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  2. If a != b != c, are value of x which satisfies the equation |(0,x -a...

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

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  4. |(1,1,1),(a,b,c),(a^3,b^3,c^3)|=

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  5. |(1/a,a^2,bc),(1/b,b^2,ca),(1/c,c^2,ab)|=

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  6. If x=-9 is a root of |(x,3,7),(2,x,2),(7,6,x)|=0 then other two roots ...

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  7. The solution of the equation |(x,2,-1),(2,5,x),(-1,2,x)| = 0 are

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  8. The roots of the equation |(0,x,16),(x,5,7),(0,9,x)| = 0 are

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  9. |(a+b,b+c,c+a),(b+c,c+a,a+b),(c+a,a+b,b+c)|=k|(a,b,c),(b,c,a),(c,a,b)|...

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  10. A root of the equation |(3-x,-6,3),(-6,3-x,3),(3,3,-6-x)| = 0

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  11. If |(-a^2,ab,ac),(ab,-b^2,bc),(ac,bc,-c^2)|=ka^2b^2c^2 , then k =

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  12. If omega!=1 is a cube root of unity and Delta=|(x+omega^(2),omega,1)...

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  13. |((a^x+a^(-x))^2,(a^x-a^(-x))^(2),1),((b^x+b^(-x))^2,(b^x-b^(-x))^(2),...

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  14. The number of values of k which the linear equations 4x+ky+2z=0 kx...

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  15. The value of k for which the set of equationsx + ky + 3z=0, 3x + ky – ...

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  16. If x + y +z=0, 4x+3y -z=0 and 3x + 5y +3z=0 is the given system of equ...

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  17. The system of equations x + y + z=2, 3x – y +2z=6 and 3x + y +z=-18 ha...

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  18. The system of equations x+y+z=6, x+2y + 3z= 10, x+2y + lamdaz=mu has n...

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  19. The system of linear equations x1 + 2x2 + x3 = 3, 2x1 + 3x2 + x3 = 3...

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  20. Let a,b,c be such that b(a+c) ne 0 . If |(a,a+1,a-1),(-b,b+1,b-1),(c...

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