At $$x=0,$$ the function is $$f\left( x \right) = \left| {\sin {{2\pi x} \over L}} \right|\left( { - \infty < x < \infty ,L > 0} \right)$$

The eigen values of the matrix are $$\left[ {\matrix{ 0 & 1 \cr { - 1} & 0 \cr } } \right]$$

The number of solutions of the simultaneous algebraic equations $$y=3x+3$$ and $$y=3x+5$$ is

For the two functions
$$f\left( {x,y} \right) = {x^3} - 3x{y^2}\,\,$$ and $$\,\,g\left( {x,y} \right) = 3{x^2}y - {y^3}\,\,$$

Which one of the following options is correct?