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If |1 1 1a b c a^3b^2c^3|=(a-b)(b-c)(c-a...

If `|1 1 1a b c a^3b^2c^3|=(a-b)(b-c)(c-a)(a+b+c),w h e r ea ,b ,c` are different, then the determinant `|1 1 1(x-a)^2(x-b)^2(x-c)^2(x-b)(x-c)(x-c)(x-a)(x-a)(x-b)|` vanishes when a.`a+b+c=0` b. `x=1/3(a+b+c)` c. `x=1/2(a+b+c)` d. `x=a+b+c`

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CENGAGE ENGLISH-DETERMINANTS-All Questions
  1. Find the following system of equations is consistent, (a+1)^3x+(a+2...

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  2. Prove the identities: |[b^2+c^2,ab, ac],[ba,c^2+a^2,bc],[ca, cb ,a^2+...

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  3. If |1 1 1a b c a^3b^2c^3|=(a-b)(b-c)(c-a)(a+b+c),w h e r ea ,b ,c are...

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  4. Prove that [[1+a^2+a^4, 1+a b+a^2b^2 ,1+a c+a^2c^2],[ 1+a b+a^2b^2, 1+...

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  5. The determinant |y^2-x y x^2a b c a ' b ' c '| is equal to a.|b x+a ...

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  6. If x , y , z are in A.P. , then the value of the determinant |[a+2,...

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  7. Prove that |{:((b+x)(c+x),,(c+x)(a+x),,(a+x)(b+x)),((b+y)(c+y) ,,(c+y)...

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  8. If a+b+c=0, one root of [[a-x, c, b],[c, b-x, a],[ b, a, c-x]]=0 is ...

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  9. Factorize the following |[3,a+b+c,a^3+b^3+c^3],[a+b+c,a^2+b^2+c^2,a^4+...

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  10. Let {D1, D2, D3 ,Dn} be the set of third order determinant that can be...

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  11. If g(x)-(f(x))/((x-a)(x-b)(x-c)),w h e r ef(x) is a polynomial of d...

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  12. If the equation 2x+3y+1=0,3x+y-2=0, and a x+2y-b=0 are consistent, t...

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  13. If w is a complex cube root of unity, then value of =|[a1+b1w, a1w^2+b...

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  14. Let f(x)=|[cos(x+x^2),sin(x+x^2),-cos(x+x^2)],[sin(x-x^2),cos(x-x^2), ...

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  15. Which of the following has/have value equal to zero? |8 2 7 12 3 5 16 ...

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  16. If f(x),g(x)a n dh(x) are three polynomial of degree 2, then prove t...

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  17. If a ,b ,c are in G.P. with common ratio r1a n dalpha,beta,gamma are...

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  18. Show that: |a, b-c,c+b, a+c, b, c-a,a-b,b+a, c|=(a+b+c)(a^2+b^2+c^2)d...

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  19. In triangle A B C , if |1, 1, ,1,cotA/2,cotB/2,cotC/2,tanB/2+tanC/2,ta...

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  20. If a ,b ,c ,d ,e, and fare in G.P. then the value of |((a^2),(d^2),x)...

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