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Let A={1,2,3,...,9) and R be the relatio...

Let A={1,2,3,...,9) and R be the relation on A `xx` A defined by (a, b) R (c,d), if a+d=b+c for (a, b), (c,d) in A `xx` A. Prove that R is an equivalence relation and also obtain the equivalence class (2,5).

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MODERN PUBLICATION-TEST PAPER 9-EXERCISE
  1. Let A=N xx N and let* be a binary operation on A defined by (a, b) * (...

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  2. A factory uses three different respurce for the manufacture of two dif...

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  3. Let A={1,2,3,...,9) and R be the relation on A xx A defined by (a, b) ...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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