Consider the following determinant $$$\Delta = \left| {\matrix{ 1 & a & {bc} \cr 1 & a & {ca} \cr 1 & a & {ab} \cr } } \right|$$$

Which of the following is a factor of $$\Delta $$ ?

Find the points of local maxima and minima if any of the following function defined in $$0 \le x \le 6,$$ $$\,\,\,\,f\left( x \right) = {x^3} - 6{x^2} + 9x + 15.$$

Which of the following is an example of spooled device?

Consider $$n$$ processes sharing the $$CPU$$ in a round-robin fashion. Assuming that each process switch takes $$s$$ seconds, what must be the quantum size $$q$$ such that the overhead resulting from process switching is minimized but, at the same time each process is guaranteed to get its turn at the $$CPU$$ at least every $$t$$ seconds?