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Prove that the following. [[a,b,c],[a^2,...

Prove that the following. `[[a,b,c],[a^2,b^2,c^2],[bc,ca,ab]]`=(b-c)(c-a)(a-b)(bc+ca+ab)

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MODERN PUBLICATION-TEST PAPER 9-EXERCISE
  1. Let A={1,2,3,...,9) and R be the relation on A xx A defined by (a, b) ...

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  2. If A=[{:(1,-2,2),(3,1,-1):}]andB=[{:(2,4),(1,2),(3,-1):}] , then veri...

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  3. Prove that the following. [[a,b,c],[a^2,b^2,c^2],[bc,ca,ab]]=(b-c)(c-a...

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  4. If A=[{:(-1,3,5),(1,-3,-5),(-1,3,5):}], then find A^(3)-A^(2).

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  5. Prove that [[b^2c^2, bc,b+c],[c^2a^2,ca,c+a],[a^2b^2,ab,a+b]] = 0

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  6. Find "a" and "b" such that the function f(x)={3ax+b, if x>1 11 if x=1 ...

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  7. If y= tan^-1 x then prove that (1+x^2) y(2) + 2xy(1) =0. Differentiate...

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  8. Find the point (S) on the curve x=(3at)/(1+t^2), y=(3at^2)/(1+t^2) whe...

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  9. Find the intervals in which the function y=(lnx)/(x) is increasing and...

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  10. Evaluate int (x+1)dx/sqrt(x^2+2x-3))

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  11. Evaluate: int(0)^(2π) dx/(1+e^sin x).

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  12. Solve: (1+x^2)dy/dx+2xy-x^3=0

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  13. If the sum of two unit vectors is a unit vectors find the magnitude of...

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  14. Prove by vector method that in аny ∆ АВС. а=Ь cos С +с cos В.

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  15. Find the equation of the plane passing through (1, 3,4), (2, 1.-1) an...

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  16. Obtain the co-ordinates of the foot of the perpendicular drawn from th...

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  17. Let A=Rxx R and be the binary operation on A defined by (a, b) *(c,d) ...

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  18. Prove that f:X rarr Y is injective iff for all subsets A,B of X,f(A n...

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  19. Use matrix product [(1,-1,2),(0,2,-3),(3,-2,4)] [(-2,0,1),(9,2,-3),(6,...

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  20. Prove that the following. [[b^2+c^2,ab,ac],[ab,c^2+a^2,bc],[ca,cb,a^2+...

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