Self Studies

Relations and F...

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  • Question 1
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    If f(0)=0,f(1)=1,f(2)=2f\left( 0 \right) = 0,f\left( 1 \right) =1 ,f\left( 2 \right) = 2 and f(x)=f(x2)+f(x3)f\left( x \right) = f\left( {x - 2} \right) + f\left( {x - 3} \right) for x=3,4,5.....x = 3,4,5..... then f(9)=?f\left( 9 \right) = ?

  • Question 2
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    If aRa\ne R and the equation 3(x[x])2+2(x[x])+a2=0-3(x-[x])^2+2(x-[x])+a^2=0 ( where [x][x] denotes the greatest integer x\le x) has no integral solution, then all possible values of a lie in the interval : 

  • Question 3
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    xϵR:14xx+19x30x4<0{x\epsilon R:\frac{14x}{x+1}-\frac{9x-30}{x-4}<0} is equal to 

  • Question 4
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    f:(0, )Rf:\left( 0,\infty  \right) \rightarrow R is continuous. If  F(x)F\left(x\right) is a differentiable function such that F(x)=f(x),x>0F\left(x\right)= f\left(x\right), \forall x>0 and f(x2)=x2+x3 f\left( { x }^{ 2 } \right) ={ x }^{ 2 }+{ x }^{ 3 }, then f(4)f\left(4\right) equals 

  • Question 5
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    If z1a<a,z2a<b,z3a<c\left| { z }_{ 1 }-a \right| <a,\left| { z }_{ 2 }-a \right| <b,\left| { z }_{ 3 }-a \right| <c, (a,b,cR)(a,b,c\in R) then z1+z2+z3\left| { z }_{ 1 }+{ z }_{ 2 }+{ z }_{ 3 } \right| is

  • Question 6
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    The domain of 10x+10x10x10x\dfrac { 10 ^ { x } + 10 ^ { - x } } { 10 ^ { x } - 10 ^ { - x } } is

  • Question 7
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    If RR is the relation from set AA to a set BB and SS is the relation from BB to a set CC, then the relation SoRSoR

  • Question 8
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    A relation R is defined from {2, 3, 4, 5} to {3, 6, 7, 10} by :(x,y)  R  x(x,y)\in\;R\; \rightarrow x is relatively prime to y. Then, domain of R is

  • Question 9
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    Let f(x)=f(x)=max {(1x),(1+x),2},xR\{(1-x), (1+x), 2\}, \forall x\in R. Then?

  • Question 10
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    If f(x)+2f(1x)=x2+2,xRf ( x ) + 2 f ( 1 - x ) = x ^ { 2 } + 2 , \forall x \in R, then find f(x)f ( x )

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