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If the following equations x+y-3 = 0, (1...

If the following equations `x+y-3 = 0, (1+lamda)x + (2+lamda) y - 8 = 0, x-(1+lamda)y + (2+lamda) = 0` are consistent then the value of `lamda` is

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ALLEN -DETERMINANTS-All Questions
  1. Prove that |{: (1,alpha,alpha^2), (alpha,alpha^2, 1),(alpha^2, 1,alpha...

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  2. Find the nature of solution for the given system of equation: x+2y+3...

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  3. If the following equations x+y-3 = 0, (1+lamda)x + (2+lamda) y - 8 = 0...

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  4. If the system of equation x+lambday+1=0,\ lambdax+y+1=0\ &\ x+y+lambda...

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  5. The value of determinant |a-bb-cc-a b-cc-a a-b c-a a-bb-c| is equal to...

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  6. Solve the following integration int (3 sin x cos^(2)x-sin^(3)x)dx

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  7. The value of the determinant |{:(-a, b, c), (a,-b, c), (a, b,-c):}| is...

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  8. For any "Delta"A B C the value of determinant |sin^2\ \ A cot A1sin^2B...

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  9. If a1, a2 an ,\ a(n+1) are in GP and a1>0AAI ,\ t h e n |loganloga(n+2...

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  10. If A+B+C=pi,\ t h e n\ |"sin"(A+B+C) sinB cosC -sinB 0 tanA "cos"(A+B)...

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  11. The number of real values of x satisfying |(x,3x+2,2x-1),(2x-1,4x,3x+1...

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  12. If p^(th),q^(th)and r^(th) tern of G.P are a,b and c respectively then...

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  13. If a1, a2 an ,\ a(n+1) are in GP and a1>0AAI ,\ t h e n |loganloga(n+2...

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  14. If p x^4+q x^3+r x^2+s x+t=|[x^2+3x, x-1, x+3],[x+1, 2-x, x-3], [x-3...

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  15. For positive numbers x ,\ y\ a n d\ z the numerical value of the deter...

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  16. If a ,\ b ,\ c >0\ a n d\ x ,\ y ,\ z in R , then the determinant |\ ...

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  17. For a non-co real a,b and c |((a^2+b^2)/c,c,c),(a,(b^2+c^2)/a,a),(b,b,...

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  18. The equation |((1+x)^2,(1-x)^2,-(2+x^2)),(2x+1,3x,1-5x),(x+1,2x,2-3x)...

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  19. Let a determinant is given by A=|[a,b,c],[p,q,r],[x,y,z]| and suppose ...

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  20. If a!=b!=c\ and\ |{:(a, b, c), (a^2,b^2,c^2), (b+c, c+a, a+b):}|=0 the...

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