Relations and F...

If $$f(x)$$ is invertible and twice differentiable function satisfying
$$\int _{ 0 }^{ f\left( x \right)  }{ f^{ -1 }\left( 1 \right) dt,\forall x\in R }$$ and $$f^{ \prime  }\left( 0 \right)=1$$ then $$f^{ \prime  }\left( 1 \right)$$ can be-

If the expansion in powers of x of the function $$\frac{1}{(1-ax)(1-bx)}$$ is $$a_{0}+a_{1}x+a_{2}x^{2}+a_{3}x^{3}+...., $$ then $$a_{n}$$ is

If $$f(x)=\dfrac{7^{1}+\ln x}{x^{\ln 7}}$$ then $$f(2015)=$$

Let $$f\left( x \right) =1+\sqrt { x } $$ and $$g\left( x \right) =\dfrac { 2x }{ { x }^{ 2 }+1 } $$, then

If $$n(A)=3,n(B)=4$$ and $$f:A\rightarrow B,$$ Then 

The number of real solutions of the equation $$f(x)=0$$, where $$f(x)=(x-1)^{3}+(x-2)^{3}+(x-3)^{3}$$, is

The set of values of $$x$$ for which $$f(x)=x^{12}-x^{9}+x^{4}-x+1>0$$ is 

If f(x + ay, x - ay) = axy then f(x,y) is equal to

Let F(x) = $$= \int e^{sin^{-1}x}(1-\frac{x}{\sqrt{1-x^{2}}})dx$$ and $$ F(0) = 1, $$ If $$ F(1/2) = \frac{k\sqrt{3}e^{\pi /6}}{\pi }, $$ then the value of k is 

If $$f(x)={ \left( \dfrac { { x }^{ l } }{ { x }^{ m } }  \right)  }^{ l+m }{ \left( \dfrac { { x }^{ m } }{ { x }^{ nd} }  \right)  }^{ m+n }{ \left( \dfrac { { x }^{ n } }{ { x }^{ l } }  \right)  }^{ n+l }$$, then $$f'(x)$$ is equal to