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Determine whether the following operatio...

Determine whether the following operation on the set R is associative and commutative `a ** b = (a + b)/2 ` for all `a, b in R`.

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SHARAM PUBLICATION-MODEL QUESTION PAPER -1-EXERCISE
  1. If f(x) = cos(logex) then show that f(x).f(y)-1/2[f(xy) + f(x/y)]=0

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  2. Let R={(a, a^(3)): a is a prime number less than 5) be a relation. Fin...

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  3. Determine whether the following operation on the set R is associative ...

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  4. Solve cos(tan^-1x) = sin(cot^-1 (3/4))

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  5. Write the solution of the following LPP Maximise Z=x+y Subject to ...

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  6. If A=[{:(3,1),(-1,2):}] then prove that A^(2)-5A+7I=O

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

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  8. Solve for x, |{:(15-2x,11,10),(11-3x,17,16),(7-x,14,13):}|=0

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  9. Find the inverse of the matrix [{:(2,5),(1,3):}]

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  10. Find the value of [[1,a,b+a],[1,b,c+a],[1,c,a+b]].

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

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  12. Show that f(x)=|x| is continuous at x=0 but not deferentiable at x=0.

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  13. If sin y=(2t)/(1 + t^2),cos x= 1/(sqrt(1+t^2)) then show that (dy)/(dx...

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  14. Find the interval where the function f(x) = sin x + cos x, x in [0, 2p...

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  15. Show that no two normals to a parabola are parallel.

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  16. int(cos2x-cos2alpha)/(cosx-cosalpha)dx

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  17. Integrate: int0^(3/2)[x^2]dx

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  18. Solve : (x+y)dy +(x-y)dx = 0.

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

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

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