The positive values of “K” and “a” so that the system shown in the figure below oscillates at a frequency of 2 rad/sec respectively are

For the polynomial
P(s) = s⁵ + s⁴ + 2s³ + 2s² + 3s + 15 ,
the number of roots which lie in the right half of the s-plane is

The open-loop transfer function of a unity feedback system is $$$G\left(s\right)=\frac k{s\left(s^2+s+2\right)\left(s+3\right)}$$$ the range of 'k' for which the system is stable

The characteristic polynomial of a system is
q(s) = 2s⁵ + s⁴ + 4s³ + 2s² + 2s + 1. The system is