Relations and F...

If $$D$$ be subset of the set of all rational numbers which can be expressed as terminating decimals, then $$D$$ is closed under the binary operations of:

If $$a\ast b={ a }^{ 3 }+{ b }^{ 3 }$$ on $$z$$, then $$\left( 1\ast 2 \right) \ast 0=........$$

If $$f : R - \left \{\dfrac {3}{5}\right \}\rightarrow R - \left \{\dfrac {3}{5}\right \}; f(x) = \dfrac {3x + 1}{5x - 3}$$, then ___________.

If a language of natural numbers has a binary regularly of $$0$$ and $$1$$, then which one of the following strings represents the natural number $$7$$?

The number of binary operations on $$\left\{ 1,2,3,4 \right\} $$ is ______.

Suppose that $$g\left( x \right) =1+\sqrt { x }$$ and $$f\left( g\left( x \right)  \right) =3+2\sqrt { x } +x$$, then $$f\left( x \right)$$ is

$$f(x)=x^{3}+4x+5$$
$$\int_{0}^{5} f^{-1}(x)dx=$$

Let $$f:N\times N\rightarrow N-\left\{ 1 \right\} $$ be defined as $$f(m,n)=m+n$$, then function $$f$$ is ______.

$$f:R \to R,f\left( x \right) = \dfrac {{x^2} + 2x + c}{{x^2} + 4x + c}$$ is onto only if

$$f: R\rightarrow R$$ is defined by $$f(x)=x^2-5x$$. Then the inverse image set of $$\{-6\}$$ is?