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If f:XrightarrowY is onto, then prove th...

If `f:XrightarrowY` is onto, then prove that `f(f^(-1)(B))=B` for all `BsubseteqY`.

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USHA PUBLICATION-MODEL QUESTION SET-MODEL QUESTION SET
  1. Evaluate int0^1frac[ln(1+x)][1+x^2]dx

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  2. Solve xfrac[dy][dx]+y=x^4

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  3. If f:XrightarrowY is onto, then prove that f(f^(-1)(B))=B for all Bsub...

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  4. Prove that f:X rarr Y is injective iff f^(-1) (f(A)) = "A for all" A s...

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  5. Prove that cos^(-1)(frac[b+acosx][a+bcosx])=2tan^(-1)(sqrt(frac[a-b][a...

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  6. Prove that the measure of the angle between two main diagonals of a cu...

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  7. Show that the shortest distance between the lines x+a=2y=-12z and x=y+...

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  8. If e^(y//x)=(x)/(a+bx) then show that x^(3)(d)/(dx)((dy)/(dx))=(x(dy)/...

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  9. Find the extreme values of the function f(x)=x^2e^(-x^2) and show that...

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  10. Shows that the triangle of greatest area that can be inscribed in a ci...

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  11. Find the inverse of [(1,1,2),(0,1,2),(1,2,1)] using elementary operati...

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  12. If [[x,x^2,x^3-1],[y,y^2,y^3-1],[z,z^2,z^3-1]]=0 then prove that xyz...

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  13. If A [[1,2,0],[1,1,0],[-1,4,0]],B=[[1,2,3],[1,1,-1],[1,1,1]]"and"C=[[1...

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  14. Let f:RrightarrowR be defined as f(x)=3x. Then f is one-one and onto

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  15. Let f:RrightarrowR be defined as f(x)=3x. Then f is one-one and onto

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  16. Let f:RrightarrowR be defined as f(x)=3x. Then f is one-one and onto

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  17. Let f:RrightarrowR be defined as f(x)=3x. Then f is one-one and onto

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  18. Find the number of binary operations on the set {a,b}.

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  19. If A, B are symmetric matrices of same order, then find AB-BA.

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  20. Let A be square matrix of order 3times3, then find abs(KA) where, k is...

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