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If a relation R:AtoAis an equivalence re...

If a relation R:`AtoA`is an equivalence relation then prove that R^-1:A toA is also an equivalence relation.

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USHA PUBLICATION-MODEL QUESTION SET-MODEL QUESTION SET
  1. Solve the pair of these equationsx+y=10,3x+y=12,

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  2. Show that sin^(-1)(1/sqrt(10))+cos^(-1)(2/sqrt5)=pi/4.

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  3. If a relation R:AtoAis an equivalence relation then prove that R^-1:A ...

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  4. Verify that [AB]^T = B^T A^T whereA=[[1,2,3],[3,-2,1]],B=[[1,2],[2,0],...

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  5. Verify that [AB]^T = B^T A^T whereA=[[1,2,3],[3,-2,1]],B=[[1,2],[2,0],...

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  6. alpha = 0.9. The value of beta is

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  7. If Aand B are both symmetric matrices of same oder,then prove that AB...

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  8. If ABC is a triangle, then prove that abs[[tanA,1,1],[1,tanB,1],[1,1,...

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  9. Solve by matrix method 2x+y=5,x-y=1

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  10. Find the point on the curve y^2 - x^2 + 2x - 1 =0 where the tangent ...

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  11. If 2y=x(1+(dy)/(dx)), then show that y(2) is a constant.

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  12. If y=tan^(-1)(cosx/(1+sinx)),then prove that dy/dx=-1/2

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  13. Examine the continuity of the following functions at indicated points....

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  14. If f(x+y)=f(x)f(y)for all real x,y,f(2)=3,f'(0)=1 then what is the val...

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  15. Find the area of the circle x^2+y^2=2ax.

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  16. intdx/(sqrtx-root(3)(x))(x=t^6)

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  17. Solve dy/dx+y/x=xy^2.

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  18. Evaluate int0^2abs(x^2+2x-3)dx

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  19. Evaluateint-2^2[x^2+3x+2]dx.

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  20. Find the point where the line (x-2)/1=y/(-1)=(z-1)/2 meets the plane 2...

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