The range of values of $$k$$ for which the function $$\,\,f\left( x \right) = \left( {{k^2} - 4} \right){x^2} + 6{x^3} + 8{x^4}$$ has a local maxima at point $$x=0$$ is

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

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