A particle moves along a curve whose parametric equations are: $$\,x = {t^3} + 2t,\,y = - 3{e^{ - 2t}}\,\,$$ and $$z=2$$ $$sin$$ $$(5t),$$ where $$x, y$$ and $$z$$ show variations of the distance covered by the particle (in cm) with time $$t $$ (in $$s$$). The magnitude of the acceleration of the particle (in cm/s²) at $$t=0$$ is _______.

$$\,\,\mathop {Lim}\limits_{x \to \infty } \left( {{{x + \sin x} \over x}} \right)\,\,$$ equal to

Given the matrices $$J = \left[ {\matrix{ 3 & 2 & 1 \cr 2 & 4 & 2 \cr 1 & 2 & 6 \cr } } \right]$$ and $$K = \left[ {\matrix{ 1 \cr 2 \cr { - 1} \cr } } \right],\,\,$$ the product $${K^T}JK$$ is ______.

The sum of Eigen values of the matrix, $$\left[ M \right]$$
is where $$\left[ M \right] = \left[ {\matrix{ {215} & {650} & {795} \cr {655} & {150} & {835} \cr {485} & {355} & {550} \cr } } \right]$$