Biotransformation of an organic compound having concentration $$(x)$$ can be modeled using an ordinary differential equation $$\,{{d\,x} \over {dt}} + k\,{x^2} = 0,$$ where $$k$$ is the reaction rate constant. If $$x=a$$ at $$t=0$$ then solution of the equation is

The eigen values of the matrix $$\left[ {\matrix{ 4 & { - 2} \cr { - 2} & 1 \cr } } \right]$$ are

Real matrices $$\,\,{\left[ A \right]_{3x1,}}$$ $$\,\,{\left[ B \right]_{3x3,}}$$ $$\,\,{\left[ C \right]_{3x5,}}$$ $$\,\,{\left[ D \right]_{5x3,}}$$ $$\,\,{\left[ E \right]_{5x5,}}$$ $$\,\,{\left[ F \right]_{5x1,}}$$ are given. Matrices $$\left[ B \right]$$ and $$\left[ E \right]$$ are symmetric. Following statements are made with respect to their matrices.
$$(I)$$ Matrix product $$\,\,{\left[ F \right]^T}\,\,$$ $$\,\,{\left[ C \right]^T}\,\,$$ $$\,\,\left[ B \right]\,\,$$ $$\,\,\left[ C \right]\,\,$$ $$\,\,\left[ F \right]\,\,$$ is a scalar.
$$(II)$$ Matrix product $$\,\,{\left[ D \right]^T}\,\,$$ $$\,\left[ F \right]\,\,$$ $$\,\left[ D \right]\,\,$$ is always symmetric.
With reference to above statements which of the following applies?

The value of the function, $$f\left( x \right) = \mathop {Lim}\limits_{x \to 0} {{{x^3} + {x^2}} \over {2{x^3} - 7{x^2}}}\,\,\,$$ is