GATE EC 2011 Question Paper (13-Feb-2011) (Shift 2)

The system of equations

x + y + z = 6;

x + 4y + 6z = 20;

x + 4y + λz = μ

has NO solution for values of λ and μ given by

A fair dice is tossed two times. The probability that the second toss results in a value that is higher than the first toss is

The channel resistance of an N-channel JFET shown in the figure below is 600 Ω when the full channel thickness (t${}_{ch}$) of 10 μm is available for conduction. The built-in voltage of the gate P⁺ N junction (V${}_{bi}$) is – 1 V. When the gate to source voltage (V${}_{GS}$) is 0 V, the channel is depleted by 1 μm on each side due to the built-in voltage and hence the thickness available for conduction is only 8 μm.

The input-output transfer function of a plant $H\left(s\right)=\frac{100}{s{\left(s+10\right)}^2}.$ The plant is placed in a unity negative feedback configuration as shown in the figure below.



The gain margin of the system under closed loop unity negative feedback is

The input-output transfer of a plant $H\left(s\right)=\frac{100}{s{\left(s+10\right)}^2}.$ The plant is placed in a unity negative feedback configuration as shown in the figure below.



The signal flow graph that DOES NOT model the plant transfer function $H(s)=\frac{100}{s{\left(s+10\right)}^2}$ is:

1.



2.



3.



4.