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Find the value of the determinant |{:(a^...

Find the value of the determinant `|{:(a^2,a b, a c),( a b,b^2,b c), (a c, b c,c^2):}|`

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If a,b,c are positive and unequal, show that value of the determinant Delta=|{:(a,b,c),(b,c,a),(c,a,b):}| is negative

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Using the properties of determinants, prove the following |{:((b+c)^2,a^2,a^2),(b^2,(c+a)^2,b^2),(c^2,c^2,(a+b)^2):}|=2abc(a+b+c)^3

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ALLEN -DETERMINANTS-All Questions
  1. Find the minors and cofactors of elements '-3^(prime),\ \ ^(prime)5^(p...

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  2. Prove that: |{:(a, b, c), (x, y, z), (p, q, r):}|=|{:(y, b, q), (x, ...

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  3. Find the value of the determinant |{:(a^2,a b, a c),( a b,b^2,b c), (a...

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  4. If |3^2+k4^2 3^2+3+k4^2+k5^2 4^2+4+k5^2+k6^2 5^2+5+k|=0 then the value...

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  5. Prove that abs((a,a,x),(m,m,m),(b,x,b))=m(x-a)(x-b)

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  6. Let alpha "and " beta be the roots of the equation ax^(2)+bx+c=0. Let ...

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  7. Prove that |{: (1,alpha,alpha^2), (alpha,alpha^2, 1),(alpha^2, 1,alpha...

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

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

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

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

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

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

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

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

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

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

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  20. 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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