If the sum of the slopes of the lines represented by $4x^{2}+2hxy-7y^{2}=0$ is equal to the product of their slopes, then h is equal to:

If $f(x)=log_{e}(x+\sqrt{1+x^{2}})$, then $f^{-1}(x)$ is equal to:

If $\alpha, \beta$ are roots of $x^{2}-ax+b=0$ and $v_{n}=\alpha^{n}+\beta^{n}$ then which of the following is correct?

The length of the common chord of the circles $(x-a)^{2}+y^{2}=c^{2}$ and $x^{2}+(y-b)^{2}=c^{2}$ is equal to :