Relations and F...

The numbers system which uses alphabets as well as numbers is-

Number of one-one functions from A to B where $$n(A)=4, n(B)=5$$.

If is a binary operation such that $$a * b = a^2 + b^2$$ then $$3 * 5$$ is 

If a binary operation is defined $$a\star b=a^b$$ then 2$$\star 2$$ is equal to:

Let $$f(x)=x^ {135}+x^ {125}-x^ {115}+x^ {5}+1$$. If $$f(x)$$ divided by $$x^ {3}-x$$, then the remainder is some function of $$x$$ say $$g(x)$$. Then $$g(x)$$ is an:-

If $$  f : R \rightarrow R  $$ be given by $$  f(x)=\left(3-x^{3}\right)^{\dfrac{1}{3}},  $$ then $$fof(x)$$ is

Let : $$R\rightarrow R$$ defined as $$f\left( x \right) =\dfrac { x\left( x+1 \right) \left( { x }^{ 4 }+1 \right) +{ 2x }^{ 4 }+{ x }^{ 2 }+2 }{ { x }^{ 2 }+x+1 } $$

Let f : $$R\rightarrow R$$ be a function defined by f(x) = $${ x }^{ 3 }+{ x }^{ 2 }+3x+sin\times .$$ Then f is.

A function $$f$$ from the set of natural numbers to integers defined by $$f(n)=\begin{cases} \cfrac { n-1 }{ 2 } ,\quad \text{when n is odd} \\ -\cfrac { n }{ 2 } ,\quad \text{when n is even} \end{cases}$$  is

Let $$f:[2,\infty )\rightarrow X$$ be defined by $$f(x)=4x-{x}^{2}$$. Then, $$f$$ is invertible, if $$X=$$