The first two rows in the Routh table for the characteristic equation of a certain closed-loop control system are given as The range of K for which the system is stable is

A second-order linear time-invariant system is described by the following state equations $$$\eqalign{& {d \over {dt}}{x_1}\left( t \right) + 2{x_1}\left( t \right) = 3u\left( t \right) \cr & {d \over {dt}}{x_2}\left( t \right) + {x_2}\left( t \right) = u\left( t \right) \cr} $$$

Where x₁(t), then the system is

Following is the k-map of a Boolean function of five variable P, Q, R, S and X. The minimum for the function is

For the circuit shown in the figure, the delays of NOR gates, multiplexers and inverters are 2 ns, 1.5 ns and 1 ns, respectively. If all the inputs P, Q, R, S and T are applied at the same time instant, the maximum propagation delay (in ns) of the circuit is ___________.