Let  $a,b,c\; \in R.$ If $f\left( x \right) = a{x^2} + bx + c$ is such that $a + b + c = 3$ and $f\left( {x + y} \right) = f\left( x \right) + f\left( y \right) + xy,$ $\forall x,y \in R,$ then $\mathop \sum \limits_{n = 1}^{10} f\left( n \right)$ is equal to : 

Let $f\left( n \right) = \left[ {\frac{1}{3} + \frac{{3n}}{{100}}} \right]n$ , where $[n]$ denotes the greatest integer less than or equal to $n$. Then $\sum\limits_{n = 1}^{56} {f\left( n \right)} $ is equal to

If $a+\alpha=1, b+\beta=2$ and $\operatorname{af}(x)+\alpha f\left(\frac{1}{x}\right)=b x+\frac{\beta}{x}, x \neq 0,$ then the value of expression $\frac{ f ( x )+ f \left(\frac{1}{ x }\right)}{ x +\frac{1}{ x }}$ is ..... .

Let $A=\{(x, y): 2 x+3 y=23, x, y \in N\}$ and $B=\{x:(x, y) \in A\}$. Then the number of one-one functions from $\mathrm{A}$ to $\mathrm{B}$ is equal to ................

The graph of the function $y = f(x)$ is symmetrical about the line $x = 2$, then

Which pair $(s)$ of function $(s)$ is/are equal ?

where $\{x\}$ and $[x]$ denotes the fractional part $\&$ integral part functions.