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If x!=y!=za n d|[x,x^2, 1+x^3],[y ,y^2 ,...

If `x!=y!=za n d|[x,x^2, 1+x^3],[y ,y^2 ,1+y^3],[z, z^2, 1+z^3]|=0,` then the value of `x y z` is a.`1` b. `2` c. `-1` d. `2`

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CENGAGE PUBLICATION-DETERMINANTS-All Questions
  1. Show that the determinant |a^2+b^2+c^2 bc+ca+ab bc+ca+ab bc+ca+ab a^2+...

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  2. If x!=0,y!=0,z!=0 and |[1+x,1,1],[1+y,1+2y,1],[1+z,1+z,1+3z]|=0, then ...

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  3. If x!=y!=za n d|[x,x^2, 1+x^3],[y ,y^2 ,1+y^3],[z, z^2, 1+z^3]|=0, th...

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  4. Prove that |2 alpha+beta+gamma+delta alphabeta+gammadelta alpha+beta...

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  5. Solve for x , |[x,-6,-1], [ 2,-3x,x-3], [-3, 2x, x+2]|=0.

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  6. The value of the determinant |{:(1,,1,,1),(.^(m)C(1),,.^(m+1)C(1),...

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  7. Solve the equation |[a-x, c, b], [ c, b-x, a], [b, a, c-x]|=0 where a...

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  8. If a^2+b^2+c^2=-2a n df(x)= |[1+a^2x,(1+b^2)x,(1+c^2)x],[(1+a^2)x,1+b...

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  9. Consider the set A of all determinants of order 3 with entries 0 or 1 ...

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  10. Solve: |[x^2-1, x^2+2x+1, 2x^2+3x+1], [2x^2+x-1, 2x^2+5x-3, 2x^2+4x-3...

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  11. If |[x,3, 6],[ 3, 6,x],[6,x,3]|=|[2,x,7],[x,7, 2],[ 7, 2,x]|=|[4, 5,x]...

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  12. If A1B1C1 , A2B2C2 and A3B3C3 are three digit numbers, each of which ...

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  13. If f^(prime)(x)=|[mx, mx-p, m x+p], [n, n+p, n-p], [mx+2n, m x+2n+p, m...

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  14. If sum(n=1)^nalphan=a n^2+b n ,w h e r ea ,b are constants and alpha...

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  15. The determinant |[x p+y, x, y], [y p+z, y, z],[0,x p+y, y p+z]|=0...

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  16. Using properties of determinant prove that |[a+b+c,-c,-b],[-c, a+b+c,...

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  17. Show that |^x Cr^x C(r+1)^x C(r+2)^y Cr^y C(r+1)^y C(r+2)^z Cr^z C(r+1...

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  18. If omega!=1 is a cube root of unity and x+y+z!=0, then prove that |[x/...

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  19. Statement 1: If the system of equation lambdax+(b-a)y+(c-a)z=0,(a-b)x+...

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  20. If A , Ba n dC are the angels of a triangle, show that |[-1+cos B, c...

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