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The determinant : |(a,b,aalpha+b),(b,c...

The determinant :
`|(a,b,aalpha+b),(b,c,balpha+c),(aalpha+b,balpha+c,0)|=0` if :

A

a,b,c are in A.P

B

a,b,c are in G.P or `(x-alpha)` is a factor of `ax^2+2bx+c`

C

a,b,c are in H.P

D

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

Text Solution

Verified by Experts

The correct Answer is:
D
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MODERN PUBLICATION-DETERMINANTS -Multiple Choice Questions - LEVEL - II
  1. 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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  2. If A+B+C = pi , then the value of |(sin(A+B+C), sinB,cosC),(-sinB,0,ta...

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  3. The determinant : |(a,b,aalpha+b),(b,c,balpha+c),(aalpha+b,balpha+c,...

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  4. Dk=|(1,n,n),(2k,n^2+n+1,n^2+n),(2k-1,n^2,n^2+n+1)| and sum(k=1)^nDk=56...

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  5. The parameter on which the value of the determinant |[1, a, a^2],[...

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  6. Given a,b,c are in A.P. Then determinant : |(x+1,x+2,x+a),(x+2,x+3,x...

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  7. If A=|(1+cosalpha,1+sinalpha,1),(1+cosbeta,1+sinbeta,1),(1,1,1)|ne0 , ...

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  8. If a , b, c are all different from zero and |(1+a,1,1),(1,1+b,1),(1,...

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  9. If the system of equations : x + 4ay+az =0, x + 3by+ bz = 0 , x + 2cy ...

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  10. The value of the determinant : |(1,1,1),(""^mC1,""^(m+1)C1,""^(m+2)C...

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  11. If A, B and C are the angles of a triangle and |(1,1,1),(1+sinA,1+sinB...

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  12. If, p,q,r are negative distinct real numbers , then the determinant De...

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  13. The value of the determinant : Delta=|(a^2,a,1),(cosnx,cos(n+1)x,co...

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  14. If alpha, beta and gamma are real numbers, then : Delta=|(1,cos(beta...

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  15. If sin2x=1 , then |(0,cosx,-sinx),(sinx,0,cosx),(cosx,sinx,0)| equals...

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  16. If Deltar= |[2r-1, mCr,1],[m^2-1,2^m,m+1],[m^2+m+1,2^m+1,m+2]|, then s...

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  17. The value of theta satisfying : |(sin3theta,-2,3),(cos2theta,8,-7),(...

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  18. Let f(x)=|(cosx,sinx,cosx),(cos2x,sin2x,2cos2x),(cos3x,sin3x,3cos3x)| ...

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  19. If the system of equations x+ay+az=0 , bx+y+bz=0 , cx +cy +z=0 where a...

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  20. Delta1=|(x,b,a),(a,x,b),(a,a,x)|,Delta2=|(x,b),(a,x)| are the given d...

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