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If S is a set of all rational numbers ex...

If S is a set of all rational numbers except 1 and `**` be defined on S by `a ** b = a + b-ab` for all `a, b in s` then prove that `**`is commutative as well as associative.

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If S is a set of all rational numbers except 1 and ** be defined on S by a ** b = a + b-ab for all a, b in s then prove that ** is a binary operation.

If S is the set of all rational numbers except 1 and * be defined on S by a**b =a+b-ab , for all a, b in S . Prove that (i) * is a binary operation on S. (ii) * is commutative as well as associative.

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SHARAM PUBLICATION-MODEL QUESTION PAPER -16-EXERCISE
  1. Show that the relation R on the set A of real numbers defined as R = {...

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  2. If S is a set of all rational numbers except 1 and ** be defined on S ...

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  3. If S is a set of all rational numbers except 1 and ** be defined on S ...

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  4. Prove that cot^(-1)7+cot^(-1)8+cot^(-1)18=cot^(-1)3

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  5. Solve the following LPP graphically Maximize, Z=20x+30y Subject to...

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  6. Verify that A=[[a,b],[c,d]] satisfies the equation A^2-(a+d)A+(ad-bc...

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  7. If the matrix A is such that [[1,-1],[2,3]]A=[[-4,1],[7,7]], find A.

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  8. Show that (a+1) is a factor of abs([(a+1),2,3],[1,a+1,3],[3,-6,a+1])

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  9. Solve : |[x-a, 0, 0],[a, x-b, 0],[a, b, x-c]|=0

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  10. For what value of k is the function defined by {(k(x^2+2),when xle0),(...

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  11. If sin y = x sin (a + y) then show that (dy)/(dx)=(sin^2(a+y))/(sina)

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  12. Find (dy)/(dx) when y=x^(siny)

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  13. Find the interval in which the function f(x) = 3x^4- 4x^3- 12x^2+ 5 is...

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  14. Find two numbers whose sum is 24 and product is maximum.

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  15. Integrate: intx(e^x)/((1+x)^2)dx

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  16. Integrate :inttan^-1x/(1+x^2)dx

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  17. Evaluate int0^(pi/2)(sqrt(cosx))/(sqrt(sinx)+sqrt(cosx))dx

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  18. Find the area bounded by the line y = 2x, x- axis and the ordinate x =...

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  19. Solve 2y^3(dy)/(dx)=ax

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  20. Find [veca vecb vecc] when veca= hati -2hatj + 3hatk, vecb=2hati+ hatj...

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