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GATE EC 2020: Full Revision Test (App update required to attempt this test)

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Question 1

The open-loop transfer function of a feedback control system is given by

G(s) H(s)= K(s+2)/s(s+4)(s²+4s+8)

In the root locus diagram of the system, the asymptotes of the root loci for large value of k meet a point in the s-plane. The co-ordinates of that point are (-a,0)

Question 2

A silicon transistor with V_BE(sat) = 0.8V, β = 100, V_CE(sat) = 0.2V is used as shown in figure. Then the minimum value of R_C (in kΩ) for which transistor remains in the saturation region.

Question 3

Consider the cascaded structure shown below and find the function y(t) in terms of x(t)

Question 4

If the semi-circular contour D of radius 2 is as shown in the figure, then the value of the integral

ds is:

Question 5

A band limited low-pass signal

of bandwidth 5 kHz is sampled at a sampling rate

The signal

is reconstructed using the reconstruction filter

whose magnitude response is shown below:

The minimum sampling rate (in kHz) for perfect reconstruction of is _________.

Question 6

Consider two random variables ‘X’ and ‘Y’ having joint probability density function given by

= 0 elsewhere

The value of E [xy²] is __________ .

Question 7

A function is defined as shown in the table below

Find the value of integral using Trapezoidal rule method

Question 8

Select the correct statement for the given circuits

Question 9

A 16K

8 ROM IC is interfaced to 8085 microprocessor. What is the address space?

Question 10

An antenna in air radiates a total power of 100KW so that a maximum radiated electric field strength of 12 m V/m is measured 20 km from the antenna. What would be its maximum power gain if h_r = 98%

Question 11

The Transfer function of two cascaded systems H₁(z) & H₂(z) is known to be
H(z)=

It’s also known that the unit step response of first system is [2-(0.5)ⁿ]u(n).
Then find the value of H₁(z) & H₂(z) ?

Question 12

A message signal m(t) has been sent by imposing it on a carrier frequency c(t). There are two Modulations schemes under consideration, AM and FM. Peak Frequency deviation for FM is set to be 2 times that of bandwidth used in AM, whereas magnitude for spectral components at 10MHz ±4 kHz are same for both schemes. Given below are the signals. The modulations indices for AM and FM respectively under given constraints is

[Values of Bessel function if required: J₁(2)=0.577, J₁(4)=0.066, J₁(8)=0.235, J₁(16)=0.094]

Question 13

A unity feedback control system has a forward path transfer function

If the system is subjected to an input r(t)=1+t+(1/2)t², t > 0, the steady state error of the system will be :

Question 14

If a discrete random variable X has the following probability distribution, then the standard deviation is

Question 15

The transfer function of a lag compensator is given as, G(s)=k

If this lag compensator is designed by the RC circuit shown below, then the value of α will be

Question 16

Consider the signal

The Fourier transform of signal x(t) is

Question 17

Consider the given transition probability diagram of a binary symmetric channel as shown in figure. The input binary symbols 0 and 1 occur with probabilities respectively

Then probabilities of binary symbols 0 and 1 appearing at the channel output are.

Question 18

A 4 – bit shift register (right) is initialised to value 1000 for (Q₃, Q₂, Q₁, Q₀). The D input Is derived from Q₀, Q₂ and Q₃ through two XOR gates. The pattern 1000 will appear at

Question 19

Find the conductivity of germanium for both
(A) with donor impurity of 1 part in 10⁶
(B) with acceptor impurity of 1 part in 10⁷
Given that n_i for Ge at 300K is 2.5

10¹³ cm^-3, μ_n and μ_p for Ge are 3800 and 1800 cm²/Vs respectively and the no. of Ge atoms = 4.4

10²²

Question 20

Consider the circuit given below

The L_eq for the circuit is _______H.

Question 21

Consider a unity feedback system having an open loop transfer function.

If phase margin is 0°, then value of k is ____

Question 22

For the voltage regulator circuit shown, the input voltage (V_in) is 20V ±20% and the regulated output voltage (V_out) is 10V. Assume the opamp to be ideal. For a load R_L drawing 200 mA, the maximum power dissipation in Q₁ (in Watts) is_______.

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Question 23

The transistor in the amplifier circuit shown in figure below is biased at I_c = 1 mA. (Use V_T = kT/q = 26 mV, β₀ = 200, r_b = 0 and r₀ → ∞)

The small signal mid band voltage gain V₀/V_i is:

Question 24

Consider the two port network shown below

then C₂ is _______ F.

Question 25

In the circuit shown below, for the MOS transistors, μ_nC_ox= 100 μA/V^₂and the threshold voltage V_T = 1V. The voltage V_x (in Volt) at the source of the upper transistor is

Question 26

If a semiconductor has electron mobility = 1000 cm² / V-sec, hole mobility = 600 cm² / V-sec and intrinsic conductivity is 10^–6/Ω – cm find the minimum conductivity will be ________

Question 27

The Cross-section of a waveguide is shown in figure 1,

Its electrical discontinuity is shown in figure 2, if the guide operates at 8 GHz in the dominant mode , then the standing wave ratio is _______

Question 28

A 500 m lossless transmission line is terminated by a load that is located at P on the smith chart of given figure . If

How many voltage maxima exist on the line ?

Question 29

Consider the combinational circuit given below. For how many combinations of A & B does the LED glow?

Question 30

In the circuit shown in the figure, the angular frequency w (in rad/s), at which the Norton equivalent impedance as seen from terminals b-b' is purely resistive, is
__________________.

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