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If f(x)= |1 x x+1 2x x(x-1)(x+1)x3x(x-1)...

If `f(x)= |1 x x+1 2x x(x-1)(x+1)x3x(x-1)x(x-1)(x-2)(x+1)x(x-1)|` then `f(500)` is equal to a. `0` b. `1` c. `500` d. `-500`

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CENGAGE PUBLICATION-DETERMINANTS-All Questions
  1. Prove that the value of each the following determinants is zero: |[(a^...

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  2. The value of the determinant |(1^2, 2^2, 3^2, 4^2) ,(2^2, 3^2 ,4^2,5^2...

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  3. If f(x)= |1 x x+1 2x x(x-1)(x+1)x3x(x-1)x(x-1)(x-2)(x+1)x(x-1)| then f...

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  4. Prove that the value of each the following determinants is zero: |[l...

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  5. If the system of equations x-k y-z=0, k x-y-z=0,x+y-z=0 has a nonzero ...

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  6. Show that |[1,1+p,1+p+q],[2,3+2p,1+3p+2q],[3,6+3p,1+6p+3q]|= 1

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  7. By using properties of determinants. Show that: |1+a^2-b^2; 2ab; -2b: ...

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  8. Which of the following values of alpha satisfying the equation |(1+alp...

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  9. Show that: |[3a,-a+b,-a+c],[-b+a,3b,-b+c],[-c+a,-c+b,3c]|=3(a+b+c)(a b...

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  10. If the system of equations x+a y=0,a z+y=0,a n da x+z=0 has infinite s...

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  11. If |[6i,-3i,1],[ 4, 3i,-1],[ 20, 3,i]|=x+i y , then a.x=3,y=1 b. x=1,y...

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  12. The value of |y z z xx y p2p3r1 1 1|,w h e r ex ,y ,z are respectively...

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  13. Prove that |((beta+gamma-alpha-delta)^4,(beta+gamma-alpha-delta)^2,1),...

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  14. Prove that the value of each the following determinants is zero: |s...

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  15. The number of values of k for which the system of the equations (k+1)x...

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  16. Prove that |[b+c ,a-b, a] ,[c+a, b-c ,b],[ a+b, c-a, c]|=3abc-a^3-b^3-...

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  17. " if " |{:(a^(2),,b^(2),,c^(2)),((a+1)^(2),,(b+1)^(2),,(c+1)^(2)),((a-...

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  18. Statement 1: "Delta"= |[m y+n z, m q+n r, m b+n c],[k z-m x, k r-m ...

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  19. Prove that |[1, 1, 1]; [a, b, c]; [ bc+a^2, ac+b^2, ab+c^2]|=2(a-b)(b...

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  20. If =|sin theta cos var phi sin theta sin var phi cos theta cos theta c...

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