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If f(alpha) = |{:(1,alpha,alpha^2),(alph...

If `f(alpha) = |{:(1,alpha,alpha^2),(alpha,alpha^2,1),(alpha^2,1,alpha):}|` , then find the value of `f(3^(1/3))` .

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`-4`
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CHHAYA PUBLICATION-DETERMINANT -EXERCISE 2B
  1. Show that |{:(x-3,x-4,x-alpha),(x-2,x-3,x-beta),(x-1,x-2,x-gamma):}|=0...

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  2. If a, b, c, are real numbers such that |{:(b+c,c+a,a+b),(c+a,a+b,b+c...

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  3. Show that , |{:((a^2+b^2)/c," "c," "c),(" "a,(b^2+c^2)/a," "a),(" "b,"...

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  4. prove that , |{:(1,1+a,1+a+b),(2,3+2a,4+3a+2b),(3,6+3a,10+6a+3b):}|=1

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  5. if f(x) =|{:(sinx,cosx,tanx),(x^3,x^2,x),(2x,1,1):}| then show that li...

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  6. If 5 is one root of the equation |{:(x,3,7),(2,x,-2),(7,8,x):}|=0 then...

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  7. If y =sinpx and yn is the nth derivative of y , then find the value...

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  8. If |{:(1+ax,1+bx,1+cx),(1+a1x,1+b1x,1+c1x),(1+a2x,1+b2x,1+c2x):}|=A0+A...

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  9. Evaluate: |{:(1,1,1),(1,omega^2,omega),(1,omega,omega^2):}| (where ome...

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  10. If |{:(-a^2," "ab," "ac),(" "ab,-b^2," "bc),(" "ac," "bc,-c^2):}|=lamb...

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  11. If |{:(10(c(4)),10(c(5)),11(c(m))),(11(c(6)),11(c(7)),12(c(m+2))),(12(...

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  12. If l,m and n are real numbers such that l^2+m^2+n^2=0 , then show t...

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  13. If f(x)= |{:(1,x,x+1),(2x,x(x-1),x(x+1)),(3x(x-1),x(x-1)(x-2),x(x+1)(x...

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  14. If omega ne 1 is a cube root of unity , then find the value of |{:(...

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  15. If alpha is a cube root of unity , then find the value of |{:(alpha...

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  16. If f(alpha) = |{:(1,alpha,alpha^2),(alpha,alpha^2,1),(alpha^2,1,alpha)...

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  17. Without expanding prove that, |{:(b^2c^2,bc,b+c),(c^2a^2,ca,c+a),(a^2b...

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  18. Show that, |{:(a^2+10,ab,ac),(ab,b^2+10,bc),(ca,bc,c^2+10):}| is divis...

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  19. If D1 =|{:(1,1,1),(1,omega,omega^2),(1,omega^2,omega):}| and D2= |{:(1...

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  20. Using properties of determinants porve that, |{:(x,x^2,1+px^3),(y,y^2,...

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