Relations and F...

If $$f(t)=\dfrac{1+t}{1-t}, then f(-t)$$ is

If $$\left\{ \left( 7,11 \right) ,\left( 5,a \right)  \right\} $$ represents a constant function, then the value of '$$a$$' is :

Let $$f : N\rightarrow R$$ be such that $$f(1) = 1$$ and $$f(1) = 2f(2) + 3f(3) + .... + nf(n) = n(n + 1)f(n)$$, for all $$n\epsilon N, n\geq 2$$, where $$N$$ is the set of natural numbers and $$R$$ is the set of real numbers. Then the value of $$f(500)$$ is

Let the number of elements of the sets $$A$$ and $$B$$ be $$p$$ and $$q$$ respectively. Then the number of relations from the set $$A$$ to the set $$B$$ is

If a function $$f(x)=x+\dfrac{1}{x}$$ is shifted along $$y-axis$$ as $$g(x)=f(x)+2$$. Then calculate the number of solution for $$g(x)=3$$.

The function $$f$$ is a differentiable function and satisfies the functional equation $$f(x) + f(y) = f(x + y)-  xy-  1$$ for every pair $$x, y$$ of real numbers. If $$f(1) = 1$$, then the number of integers $$n\neq  1$$ for which $$f(n) = n$$ is

In $$[0, 1]$$ Lagranges Mean Value theorem is NOT applicable to

Let $$f(x) = x\left(\frac{1}{x-1}+\frac{1}{x}+\frac{1}{x+1}\right), x > 1$$ Then

The relation $$R$$ defined on set $$A = \left \{x :|x| < 3, x\epsilon I\right \}$$ by $$R = \left \{(x, y) : y = |x|\right \}$$ is

How many ordered pairs of (m, n) integers satisfy $$\displaystyle\frac{m}{12}=\frac{12}{n}$$?