Consider a matrix $$A = u{v^T}$$ where $$u = \left( {\matrix{ 1 \cr 2 \cr } } \right),v = \left( {\matrix{ 1 \cr 1 \cr } } \right).$$ Note that $${v^T}$$ denotes the transpose of $$v.$$ The largest eigenvalue of $$A$$ is _____.

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?