Relations and F...

If $$ f: R->R$$ is defined by $$f(x) = |x|$$, then

If $$a \times b =2 a - 3b + ab$$, then $$3 \times 5+5\times 3$$ is equal to

If $$x \times y = x^{2}+y^{2}-xy$$ then the value of $$9 \times 11$$ is :

Let $$R$$ be the relation on $$Z$$ defined by $$R = \{(a, b): a, b \in z, a - b$$ is an integer$$\}$$. Find the domain and Range of $$R$$.

Let $$f(x)={x}^{3}-6{x}^{2}+15x+3$$. Then, 

Read the following information and answer the three items that follow :
Let $$f(x) = x^2 + 2x - 5 $$ and $$g(x) = 5x + 30$$
If $$h(x) = 5f(x) - xg (x)$$, then what is the derivative of $$h(x)$$ ?

The number of binary operation on {1, 2, 3... n} is..

Read the following information and answer the three items that follow :
Let $$f(x) = x^2 + 2x - 5 $$ and $$g(x) = 5x + 30$$
Consider the following statements:
1. $$f[g(x)]$$ is a polynomial of degree 3.
2. $$g[g(x)]$$ is a polynomial of degree 2.
Which of the above statements is/are correct ?

Let $$f(x)=\cfrac { 1 }{ 1-x } $$. Then $$\left\{ f\circ \left( f\circ f \right)  \right\} (x)$$

Read the following information and answer the three items that follow :
Let $$f(x) = x^2 + 2x - 5 $$ and $$g(x) = 5x + 30$$
What are the roots of the equation $$g[f(x)] = 0$$ ?