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Prove that |{:(x^(2),,x^(2)-(y-z)^(2),,y...

Prove that `|{:(x^(2),,x^(2)-(y-z)^(2),,yz),(y^(2),,y^(2)-(z-x)^(2),,zx),(z^(2),,z^(2)-(x-y)^(2),,xy):}|`
`=(x-y) (y-z) (z-x)(x+y+z) (x^(2)+y^(2)+z^(2))`

A

`(x-y)(y-z)(z-x)sumx`

B

`(x-y)(y-z)(z-x)sumxy`

C

`(x-y)(y-z)(z-x)sumx^2`

D

`(x-y)(y-z)(z-x)(sumx^2)sumx`

Text Solution

Verified by Experts

The correct Answer is:
D
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ML KHANNA-DETERMINANTS -Problem Set (2) (MULTIPLE CHOICE QUESTIONS)
  1. If R be the circum radius of the triangle ABC then the value of R^3...

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  2. If a, b, c are sides of a triangle and |(a^2,b^2,c^2),((a+1)^2,(b+1...

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  3. If A+B+C=pi, show that |(sin^2A,sinAcosA,cos^2A),(sin^2B,sinBcosB,cos...

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  4. If x,y,z are all distinct and |(x,x^2,1+x^3),(y,y^2,1+y^3),(z,z^2,1...

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  5. If |(x+a,a^2,a^3),(x+b,b^2,b^3),(x+c,c^2,c^3)| = 0 , a ne b ne c then ...

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  6. If a,b,c be all distinct and |(a^3-1,b^3-1,c^3-1),(a,b,c),(a^2,b^2,c...

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  7. If a,b,c are different , then the determinant |(1,1,1),((x-a)^2,(x-b...

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  8. If |(x^(lamda),x^(lamda+2),x^(lamda+3)),(y^(lamda),y^(lamda+2),y^(lamd...

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  9. Prove that |{:(x^(2),,x^(2)-(y-z)^(2),,yz),(y^(2),,y^(2)-(z-x)^(2),,zx...

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  10. If a,b,c are negative distinct real numbers then the determinant |(a,b...

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  11. the value of the determinant |(b+c,a-b,a),(c+a,b-c,b),(a+b,c-a,c)| is

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  12. If |(x,y,z),(y,z,x),(z,x,y)|=-(x+y+z)(x+yk+zk^2)(x+yk^2+zk) then k eq...

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  13. If a,b,c are the roots of x^3+px^2+q=0 , then the value of |(a,b,c),(b...

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

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  15. If both n and r be greater than 1 and if Delta=|(""^xCr,""^(n-1)Cr,"...

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  16. If Delta=|(""^(10)C3,""^(10)C4,""^(11)Cn),(""^(11)C5,""^(11)C6,""^(12)...

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  17. If Delta = |(""^(5)C0,""^(5)C3,14),(""^(5)C1,""^(5)C4,1),(""^(5)C2,""^...

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  18. The value of the determinant |(1,1,1),(.^(m)C(1),.^(m +1)C(1),.^(m+2)C...

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  19. The determinant |(y^(2),-xy,x^(2)),(a,b,c),(a',b',c')| is equal to

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  20. |(bc,bc'+b'c,b'c'),(ca,ca'+ac',c'a'),(ab,ab'+a'b,a'b')| is equal to

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