Relations and F...

Total number of equivalence relations defined in the set $$S=\left\{a, b, c\right\}$$ is?

A function $$y=f(x)$$ satisfies $$f"(x)=-\dfrac{1}{x^2}-\pi^2\sin(\pi x);f'(2)=\pi+\dfrac{1}{2}$$ and $$f(1)=0$$, the value of $$f\left(\dfrac{1}{2}\right)$$ is 

Which of the following is always true

$$f:\left( { - \infty ,\infty } \right) \to \left( {0,1} \right]$$ defined by $$f\left( x \right) = \frac{1}{{{x^2} + 1}}$$ is 

The values of $$a$$ and $$b$$ such that $$f$$ and $$f'$$ are continuous, are

Let $$X=\left\{ x \epsilon {R};\cos(\sin\ x)=\sin(\cos\ x)\right\}$$. The number of elements in $$X$$ is 

Let f(x) be a polynomial function such that $$f(x)+f(\dfrac{1}{x})=f(x).f(\dfrac{1}{x})$$ and $$ f(3)=82$$, then the value of $$f(5)$$, is 

If $$f^2(x)\cdot f\left(\dfrac{1-x}{1+x}\right)=x^{3},\ x\neq -1$$ and $$f(x)\neq 0$$ then the value of $$\left\{ f\left( -2 \right) \right\}$$ (the fractional part of $$f(x)$$ is equal to)

If $$\phi\left(x\right)=\phi\left(1\right)=2$$, then $$\phi\left(3\right)$$ equals

Let $$g$$ be a function that is differentiable throughout an open interval containing the origin.
Suppose $$g$$ has the following properties
$$g\left( x+y \right) =\left\{ g\left( x \right) +g\left( y \right)  \right\} \div \left\{ 1-g\left( x \right) g\left( y \right)  \right\}$$ for all real numbers $$x,\ y$$ and $$x+y$$ in the domain of $$g$$.
$$\displaystyle \lim _{ h\rightarrow 0 }{ \dfrac { g\left( h \right)  }{ h } =1 }$$.
Then $$g(0)$$ has value equal to