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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

0

B

1

C

2

D

3

Text Solution

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The correct Answer is:
C
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DISHA PUBLICATION-DETERMINANTS-EXERCISE -2 CONCEPT APPLICATOR
  1. If a(n)=(1)/(n+1)+1 then find the vaue of a(1)+a(3)+a(5)

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  2. If [] denotes the greatest integer less than or equal to the real numb...

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

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  4. If a , b , c are non-zero, then the system of equations (alpha+a)x+alp...

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  5. If m is a positive integer and Dr=|2r-1\ ^m Cr1m^2-1 2^m m+1s in^2(...

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  6. If x,y and z are the integers in AP lying between 1 and 9 and x 51, ...

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  7. If omega is a non-real cube root of unity, then Delta = |(a(1) + b(1) ...

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  8. prove that |{:((a-x)^(2),,(a-y)^(2),,(a-z)^(2)),((b-x)^(2),,(b-y)^(2),...

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  9. Evaluate |{:(.^(x)C(1),,.^(x)C(2),,.^(x)C(3)),(.^(y)C(1),,.^(y)C(2),,....

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  10. If |{:(x^(n),x^(x+2),x^(2n)),(1,x^(a),a),(x^(n+5),x^(a+6),x^(2n+5)):}|...

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  11. The value of the determinant |{:(1^(2),2^(2),3^(2),4^(2)),(2^(2),3^(2)...

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  12. The value of the determinant |{:(1 ,(5^(2x)-5^(-2x))^(2),(5^(2x)-5^(-2...

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  13. If a^(2)+b^(2)+c^(2)=-2 and |{:(1+a^(2)x,(1+b^(2))x,(1+c^(2))x),((...

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

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  15. If Sr = alpha^r + beta^r + gamma^r then show that |[S0,S1,S2],[S1,S2,S...

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  16. If f(x) = |{:(cos^(2)x, cosx.sinx, -sin x),(cos x sinx ,sin^(2)x ,cos ...

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  17. the value of the determinant |{:((a(1)-b(1))^(2),,(a(1)-b(2))^(2),,...

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  18. f'(x) = |{:(cos x , x , 1),(2sin x,x^(2),2x),(tan x, x,1):}| . The val...

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  19. If the matrix A = [{:(y+a,b,c),(a,y+b,c),(a,b,y+c):}] has rank 3, then

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  20. If the system of linear equations x1 + 2x2 + 3x3 = 6, x1 + 3x2 + 5x3 =...

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