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

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

A

A.P

B

G.P

C

H.P

D

none of these

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The correct Answer is:
B
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|{:(1,a,b+c),(1,b,c+a),(1,c,a+b):}|=0

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If a, b, c, are real numbers such that |{:(b+c,c+a,a+b),(c+a,a+b,b+c),(a+b,b+c,c+a):}|=0, then show that either a+b+c=0 or, a=b=c.

|{:(" "0," "a,-b),(-a," "0," "c),(" "b,-c," "0):}|=0

If, a,b,c are positive and unequal,show that value of the determinant Delta ={:|( a,b,c),( b,c,a),( c,a,b)|:} is negative

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|{:(b+c,a-c,a-b),(b-c,c+a,b-a),(c-b,c-a,a+b):}|=8abc

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CHHAYA PUBLICATION-DETERMINANT -EXERCISE 2B
  1. If two rows (or two columns ) of a determinant are identical , then ...

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  2. The determinant |{:(a,b,aalpha+b),(b,c,aalpha+c),(aalpha+b,balpha+c,0...

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  3. Given that x=-9 is a root of |{:(x,3,7),(2,x,2),(7,6,x):}|=0 then the ...

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  4. Let p lambda^4+qlambda^3+rlambda^2+slambda+t=|{:(lambda^2+3lambda,lamb...

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  5. The value of theta lying between theta=0 and theta=(pi)/2 and satifyi...

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  6. Evaluate the determinants |{:(1,a,a^2),(1,b,b^2),(1,c,c^2):}| .

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  7. Evaluate the determinants |{:(x+4,x,x),(x,x+4,x),(x,x,x+4):}|

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  8. Let A=|{:(" "1," "sin theta,1),(-sin theta," "1,sintheta),(-1,-sinth...

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  9. Let A be a square matrix of order 3xx3, then |KA| is equal to

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  10. |{:(alpha,beta,gamma),(alpha^2,beta^2,gamma^2),(beta+gamma,gamma+alpha...

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  11. |{:(x,a,b),(a,x,b),(a,b,x):}|

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  12. |{:(2,3,4),(3,4,5),(4,5,6):}|=0

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  13. |{:(a,b,c),(x,y,z),(p,q,r):}|=|{:(x,y,z),(p,q,r),(a,b,c):}|=|{:(y,b,q)...

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  14. |{:(1,omega,omega^2),(omega,omega^2,1),(omega^2,1,omega):}|=0 where om...

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  15. |{:(b+c,a,1),(c+a,b,1),(a+b,c,1):}|=0

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  16. |{:(a-b,1,a),(b-c,1,b),(c-a,1,c):}|=|{:(a,1,b),(b,1,c),(c,1,a):}|

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  17. |{:(a+1,a+4,a+2),(a+2,a+5,a+4),(a+3,a+6,a+6):}|=0

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  18. |{:(" "0," "a,b),(-a," "0,c),(-b,-c,0):}|

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  19. |{:(9,9,12),(1,-3,-4),(1,9,12):}|=0

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  20. |{:(a,a^2,bc),(b,b^2,ca),(c,c^2,ab):}|=|{:(1,a^2,a^3),(1,b^2,b^3),(1,c...

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