The value of $$\int_0^{\pi /4} {x\cos \left( {{x^2}} \right)dx} $$ correct to three decimal places (assuming that $$\pi = 3.14$$ ) is ________.

Consider a system with $$3$$ processes that share $$4$$ instances of the same resource type. Each process can request a maximum of $$K$$ instances. Resource instances can be requested and released only one at a time. The largest value of $$K$$ that will always avoid deadlock is ____.

In a system, there are three types of resources: $$E, F$$ and $$G.$$ Four processes $${P_0},$$ $${P_1},$$ $${P_2}$$ and $${P_3}$$ execute concurrently. At the outset, the processes have declared their maximum resource requirements using a matrix named Max as given below. For example, Max$$\left[ {{P_{2,}}F} \right]$$ is the maximum number of instances of $$F$$ that $${{P_{2,}}}$$ would require. The number of instances of the resources allocated to the various processes at any given state is given by a matrix named Allocation.

Consider a state of the system with the Allocation matrix as shown below, and in which $$3$$ instances of $$E$$ and $$3$$ instances of $$F$$ are the only resources available.

Allocation
	E	F	G
P0	1	0	1
P1	1	1	2
P2	1	0	3
P3	2	0	0

Max
	E	F	G
P0	4	3	1
P1	2	1	4
P2	1	3	3
P3	5	4	1

From the perspective of deadlock avoidance, which one of the following is true?

Consider a storage disk with $$4$$ platters (numbered as $$0, 1, 2$$ and $$3$$), $$200$$ cylinders (numbered as $$0, 1,$$ … , $$199$$), and $$256$$ sectors per track (numbered as $$0, 1, … , 255$$). The following $$6$$ disk requests of the form [sector number, cylinder number, platter number] are received by the disk controller at the same time: $$[120, 72, 2] , [180, 134, 1] , [60, 20, 0] , [212, 86, 3] , [56, 116, 2] , [118, 16, 1]$$

Currently the head is positioned at sector number $$100$$ of cylinder $$80,$$ and is moving towards higher cylinder numbers. The average power dissipation in moving the head over $$100$$ cylinders is $$20$$ milliwatts and for reversing the direction of the head movement once is $$15$$ milliwatts. Power dissipation associated with rotational latency and switching of head between different platters is negligible.

The total power consumption in milliwatts to satisfy all of the above disk requests using the Shortest Seek Time First disk scheduling algorithm is _______.