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If a,b, and c are all different and if ...

If a,b, and c are all different and if
`|{:(a,a^(2),1+a^(3)),(b,b^(2),1+b^(3)),(c,c^(2),1+c^(3)):}|`=0 Prove that abc =-1.

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|(1,a^(2)+bc,a^(3)),(1,b^(2)+ac,b^(3)),(1,c^(2)+ab,c^(3))|=-(a-b)(b-c)(c-a)(a^(2)+b^(2)+c^(2))

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ARIHANT MATHS-DETERMINANTS -Exercise (Questions Asked In Previous 13 Years Exam)
  1. If a,b, and c are all different and if |{:(a,a^(2),1+a^(3)),(b,b^(2...

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

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  3. The system of equations alphax+y+z=alpha-1, x+alphay+z=alpha-1 ...

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  4. If a1,a2,a3,.....an.... are in G.P. then the determinant Delta=|[logan...

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  5. If D =|{:(1,1,1),(1,1+x,1),(1,1,1+y):}|"for" " "xne0,yne0 then D is

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  6. Consider the system of equations x-2y+3z=-1 -x+y-2z=k x-3y+4z=1 ...

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  7. Let a,b,c, be any real number. Suppose that there are real numbers x,y...

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  8. Let a,b,c be such that b(a+c)ne 0. If |{:(,a,a+1,a-1),(,-b,b+1,b-1),(,...

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  9. If f(theta)=|{:(1,tantheta,1),(-tantheta,1,tantheta),(-1,-tantheta,1):...

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  10. The number of values of k which the linear equations 4x+ky+2z=0 kx...

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  11. If the trivial solution is the only solution of the system of equation...

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  12. The number of values of k, for which the system of equations (k""+"...

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  13. If alpha,beta!=0 , and f(n)""=alpha^n+beta^n and |3 1+f(1)1+f(2)1+f(1)...

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  14. The set of the all values of lamda for which the system of linear equa...

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

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  16. The system of linear equations x+lambday-z=0 lambdax-y-z=0 x+y-l...

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  17. The total number of distinct x in R for which |[x, x^2, 1+x^3] , [2x,...

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  18. Let a,lambda,mu in R, Consider the system of linear equations ax+2y=la...

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  19. If S is the set of distinct values of ' b for which the following syst...

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