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without expanding prove that [22-24]
`|{:(7,12,-3),(9,14,-1),(8,13,-2):}|=0`

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CHHAYA PUBLICATION-DETERMINANT -EXERCISE 2B
  1. If a ,b ,c are in A.P , show that , |{:(x+1,x+2,x+a),(x+2,x+3,x+b),(x+...

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  2. If A,B,C , are the angles of a triangles, show that, |{:(sin^2A,coaA,1...

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  3. without expanding prove that [22-24] |{:(7,12,-3),(9,14,-1),(8,13,-2...

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  4. |{:(1,bc,bc(b+c)),(1,ca,ca(c+a)),(1,ab,ab(a+b)):}|=0

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  5. |{:(logx xyz,logxy,logxz),(logyxyz,1,logyz),(logzxyz,logzy,1):}|=0

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  6. if |{:(a+ib,c+id),(-c+id,a-ib):}|xx|{:(alpha-ibeta,gamma-idelta),(-gam...

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  7. |{:(-a(b^2+c^2-a^2)," "2b^3," "2c^3),(" ...

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  8. 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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  9. 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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  10. Show that , |{:((a^2+b^2)/c," "c," "c),(" "a,(b^2+c^2)/a," "a),(" "b,"...

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

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

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

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

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

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

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  20. 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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