The eigen vector (s) of the matrix
$$\left[ {\matrix{ 0 & 0 & \alpha \cr 0 & 0 & 0 \cr 0 & 0 & 0 \cr } } \right],\alpha \ne 0$$ is (are)

The value of the double integral $$\int\limits_0^1 {\int\limits_x^{{1 \over x}} {{x \over {1 + {y^2}}}\,\,dx\,\,dy = \_\_\_\_\_.} } $$

The details of an interrupt cycle are shown in Figure
Given that an interrupt input arrives every $$1$$ $$msec,$$ what is the percentage of the total time that the $$CPU$$ devotes for the main program execution.

Assume that the following jobs are to be executed on a single processor system.

Job Id	CPU Burst Time
p	4
q	1
r	8
s	1
t	2

The jobs are assumed to have arrived at time $${0^ + }$$ and in the order $$p,q,r,s,t.$$ Calculate the departure time (completion time) for job $$p$$ if scheduling is round robin with time slice$$1.$$