Relations and F...

If $$f : R \rightarrow R$$ satisfies $$f(x + y) = f(x) + f(y)$$, $$\forall x, y\, \in\, R$$ and $$f(1) = 7$$, then $$\sum_{r\, =\, 1}^{n}{f(r)}$$ is 

If $$A$$ and $$B$$ have $$n$$ elements in common, then the number of elements common to $$A\times B$$ and $$B\times A$$ is

Let $$f(x)=2-|x-3|, 1 \le x \le 5$$ and for rest of the values $$f(x)$$ can be obtained by using the relation $$f(5x)=\alpha\, f(x)\forall\, x \in R$$.
The value of $$f(2007)$$ taking $$\alpha = 5$$, is: 

Find the correct statement pertaining to the functions $$\displaystyle f\left( x \right) ={ \left( x-3 \right)  }^{ 2 }+2$$ and $$\displaystyle g\left( x \right) =\frac { 1 }{ 2 } x+1$$ graphed above

Let $$R$$ and $$S$$ be two non-void relations on a set $$A$$. Which of the following statements is false?

Let $$F_n (\theta) = \displaystyle \sum_{k = 0}^n  \frac{1}{4^K}  \sin^4 (2^{k} \theta)$$, then which of the following is true

Range of the function $$f(x)=\dfrac{sec^2\,x-tanx}{sec^2\,x+tanx}-\dfrac{\pi}{2}<x<\dfrac{\pi}{2}$$, is 

Let $$f:R \to R - \left\{ 3 \right\}$$ be a function such that for some p>0, $$\displaystyle f\left( {x + p} \right) = {{f\left( x \right) - 5} \over {f\left( x \right) - 3}}$$ for all $$x \in R$$. Then, period of $$f$$ is 

For a function F, F(0) = 2, F(1) = 3, F(x + 2) = 2 F(x) - F(x + 1) for x $$\geq$$ 0, then F(5) is equal to

If $$f\left( x \right)$$ satisfying the relation $$f\left( x \right) +f\left( x+4 \right) =f\left( x+2 \right) +f\left( x+6 \right) \ \forall x$$, then the period is