Let f(x) =   $cos\left(2ta{n}^{-1}sin\left(co{t}^{-1}\sqrt[]{\frac{1-x}{x}}\right)\right),0<x<1.Then:$

Number of integers in the domain of the function, f(x) = $\sqrt[]{3-2^x-2^{1-x}}$  

Let n(A) = 4 and n(B) = 6, then the number of one- one functions from A to B is

Let f:R→R be a function which satisfies f(x+y)=f(x)+f(y) ∀x,y∈R. If f(1)=2 and g(n)=Σ????f(k), n∈N, then the value of n for which g(n)=20 is
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Let A=(a,b,c) and B=(1,2,3,4). Then the number of elements in the set C={f: A→B | 2∈f(A) and f is not one-one} is

Let f(x) = $min\left\{\left[x-1\right],\left[x-2\right],....,\left[x-10\right]\right\}$ <!-- [if gte mso 9]><xml> </xml><![endif]--> where [t] denotes the greatest integer $\le$ <!-- [if gte mso 9]><xml> </xml><![endif]--> t. Then ${\displaystyle \underset{0}{\overset{10}{\int }}f\left(x\right)dx+{\displaystyle \underset{0}{\overset{10}{\int }}{\left(f\left(x\right)\right)}^{2}dx+{\displaystyle \underset{0}{\overset{10}{\int }}\left|f\left(x\right)\right|dx}}}$ <!-- [if gte mso 9]><xml> </xml><![endif]--> is equal to………..