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The value of the determinant |{:(ka,,k^...

The value of the determinant `|{:(ka,,k^(2)+a^(2),,1),(kb,,k^(2)+b^(2),,1),(kc,,k^(2)+c^(2),,1):}|` is

A

`k (a +b) (b +c) (c +a)`

B

`k abc (a^(2) + b^(2) + c^(2))`

C

`k (a -b) (b -c) (c -a)`

D

`k (a + b -c) (b +c -a) (c + a -b)`

Text Solution

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The correct Answer is:
C
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OBJECTIVE RD SHARMA ENGLISH-DETERMINANTS-Exercise
  1. Let A = [(1,sin theta,1),(- sin theta,1,sin theta),(-1,-sin theta,1)],...

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  2. If a,b,c are non-zero real number such that |(bc,ca,ab),(ca,ab,bc),(ab...

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  3. The value of the determinant |{:(ka,,k^(2)+a^(2),,1),(kb,,k^(2)+b^(2)...

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  4. The system of simulataneous equations kx + 2y -z = 1 (k -1) y -2z ...

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  5. The value of the determinant |(1,omega^(3),omega^(5)),(omega^(3),1,ome...

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  6. If a,b,c are non-zero real number such that |(bc,ca,ab),(ca,ab,bc),(ab...

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  7. If the system of equations x + ay + az = 0 bx + y + bz = 0 cx + ...

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  8. The determinant D=|{:(cos(alpha+beta),-sin(alpha+beta),cos2beta),(sina...

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  9. If omega is a cube root of unity, then Root of polynomial is |(x + 1...

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  10. " If " Delta(1) =|{:(x,,b,,b),(a,,x,,b),(a,,a,,x):}|" and " Delta(2)...

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  11. If y= sin px and y(n) is the nth derivative of y, then |{:(y,y(1),y(...

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  12. If |p b c a q c a b r|=0 , find the value of p/(p-a)+q/(q-b)+r/(r-c),\...

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  13. Using properties of determinants, show that |{:(x, p, q), ( p, x, q)...

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  14. The factors of |(x,a,b),(a,x,b),(a,b,x)|, are

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  15. Let omega=-1/2+i(sqrt(3))/2dot Then the value of the determinant |1 1 ...

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  16. If a+b+c=0, one root of |a-x c b c b-x a b a c-x|=0 is x=1 b. x=2 c. ...

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  17. suppose D= |{:(a(1),,b(1),,c(1)),(a(2),,b(2),,c(2)),(a(3),,b(3),,c(3...

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  18. A and B are two non-zero square matrices such that AB = O. Then,

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  19. The roots of the equation |{:(x-1,1,1),(1,x-1,1),(1,1,x-1):}|=0 are

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  20. From the matrix equation AB=AC, we conclude B=C provided.

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