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Relations and F...

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  • Question 1
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    If f(2x+3y,2x7y)=20x f(2x+3y,2x-7y)=20x,then f(x,y) f(x,y) equal to

  • Question 2
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    If f(x)=cos(logx)f(x) = \cos (\log x), then f(x)f(y)12[f(xy)+f(xy)]f(x)\, f(y)\, -\, \displaystyle \frac{1}{2}\, [f\left(\dfrac{x}{y}\right)\, +\, f(xy)] is equal to :

  • Question 3
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    Let AA and BB be two finite sets having mm and nn elements respectively. Then the total number of mapping from AA to BB is:

  • Question 4
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    AA and BB are two sets having 33 and 44 elements respectively and having 22 elements in common. The number of relations which can be defined from AA to BB is

  • Question 5
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    If A={1,2,3},B={1,4,6,9}A=\left\{ 1,2,3 \right\} , B=\left\{ 1,4,6,9 \right\} and RR is a relation from AA to BB defined by 'xx is greater than yy'. Then range of RR is

  • Question 6
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    Let g(x)=1+x[x]g\left( x \right)=1+x-\left[ x \right] and f(x)={1x<00x=01x>0f\left( x \right)=\begin{cases} \begin{matrix} -1 & x<0 \end{matrix} \\ \begin{matrix} 0 & x=0 \end{matrix} \\ \begin{matrix} 1 & x>0 \end{matrix} \end{cases}. Then for all x,f[g(x)]x,f\left[ g\left( x \right) \right] is equal to

  • Question 7
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    If A={1,2,3}A = \left\{1,2,3\right\}, B={1,4,6,9}B = \left\{1,4,6,9\right\} and RR is relation from AA to BB defined by x'x' is greater than y'y'. Then range of RR is

  • Question 8
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    Given the relation R={(1,2),(2,3)}R = \left\{(1,2), (2,3)\right\} on the set A={1,2,3}A = \left\{1,2,3\right\}, the minimum number of ordered pairs which when added to RR make it an equivalence relation is

  • Question 9
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    If A={2,3}A = \left\{2,3\right\} and B={1,2}B = \left\{1,2\right\}, then A×BA \times B is equal to 

  • Question 10
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    Let n(A)=nn(A) = n. Then the number of all relations on AA is

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