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If A=N xx N and * is a binary operation...

If `A=N xx N` and * is a binary operation on A defined by `(a, b) ** (c, d)=(a+c, b+d)`. Show that * is commutative and associative. Also, find identity element for * on A, if any.

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ARIHANT PRAKASHAN-VERY SIMILAR TEST 1 -Section B
  1. Solve the following LPP. Maximise: Z = 5x + 3y Subject to: 5x +2...

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  2. Let f ,g: R rarr R be two functions defined as f(x) = |x| +x and g(x) ...

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  3. If A=N xx N and * is a binary operation on A defined by (a, b) ** (c,...

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  4. Solve for x, tan^(-1)(x-1)+tan^(-1)x +tan^(-1)(x+1) =tan^(-1)3x.

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  5. In bag A, there are 5 white and 8 red balls, in bag B, 7 white and 6 ...

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  6. Prove the following : [[x+4,2x,2x],[2x,x+4,2x],[2x,2x,x+4]]-(5x+4)(4-x...

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  7. If A=[(2,0,1),(2,1,3),(1,-1,0)], then find A^(2)-5A+4I and hence find ...

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  8. If A= [{:(1,-1),(2,-1):}],B=[{:(a,1),(b,-1):}]and(A+B)^(2)=A^(2)+B^(2)...

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  9. A box contains 4 orange and 4 green balls, another box contains 3 oran...

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  10. If y=sin^(-1)(2x sqrt(1-x^(2))), then find (dy)/(dx) and determine its...

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  11. If y=(x+(1)/(x+(1)/(x+ . . .oo))) find (dy)/(dx), the rhs being a vali...

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  12. Find a point on the curve y=(x-2)^(2) at which the tangent is parall...

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  13. Find the intervals in which the following functions is increasing or d...

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  14. Examine the applicability of mean value theorem for the function f(...

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  15. Evaluate the integral int(0)^(2pi)(1)/(1+e^(sinx))dx.

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  16. Evaluate int log (1+x^2)dx

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  17. Find the area of the region enclosed by the curve y=x e^(x^(2), the ...

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  18. Solve (dy)/(dx)+2y =6e^(x).

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  19. Find the differential equation of the family of curves given by x^(2...

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  20. Prove by vector method that the diagonals of a parallelogram bisect ea...

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