GATE 2023 - Important Concepts, Short cuts, Complete Solutions, Examples and Practice Problems: GATE 2013

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GATE 2013 ECE Network Theory - Complete Video Solutions with Answers

2013

1. Consider a delta connection of resistors and its equivalent star connection as shown below.

If all elements of the delta connection are scaled by a factor k, k > 0, the elements of the corresponding star equivalent will be scaled by a factor of

a) k²

b) k

c) 1/k

d) √k

Solution: https://www.youtube.com/watch?v=DZotuMVh2vQ

2. The transfer function V₂(s)/V₁(s) of the circuit shown below is

Solution: https://www.youtube.com/watch?v=iVJ4qUlg8BE

3. A source V_s(t) = V cos100πt has an internal impedance of (4 + j3) Ω. If a purely resistive load connected to this source has to extract the maximum power out of the source, its value in Ω should be

a) 3

b) 4

c) 5

d) 7

Solution: https://www.youtube.com/watch?v=_a3PEIDOI08

4. In the circuit shown below, if the source voltage V_s = 100∟53.13^o volts then the thevenin's equivalent voltage in volts as seen by the load resistance R_L is

Solution: https://www.youtube.com/watch?v=XnD2y6tMyFM

5. The following arrangement consists of an ideal transformer and an attenuator which attenuates by a factor of 0.8. An ac voltage V_WX1 = 100 volts is applied across WX to get an open circuit voltage V_YZ1 across YZ. Next, an ac voltage V_YZ2 = 100 volts is applied across YZ to get an open circuit voltage V_WX2 across WX. Then V_YZ1/V_WX1, V_WX2/V_YZ2 are respectively

Solution: https://www.youtube.com/watch?v=IJX4fwiz-Fo

6. Two magnetically uncoupled inductive coils have Q factors q₁ and q₂ at the chosen operating frequency. Their respective resistances are R₁ and R₂. When connected in series, their effective Q factor at the same operating frequency is

a) q₁ + q₂

b) (1/q₁) + (1/q₂)

c) (q₁R₁ + q₂R₂) / (R₁ + R₂)

d) (q₁R₂ + q₂R₁) / (R₁ + R₂)

Solution: https://www.youtube.com/watch?v=v7q3ssCyLqw

7. Three capacitors C₁, C₂ and C₃ whose values are 10 µF, 5 µF and 2 µF respectively, have breakdown voltages of 10, 5 and 2 volts respectively.

For the interconnection shown below, the maximum safe voltage in volts that can be applied across the combination, and the corresponding total charge in µC stored in the effective capacitance across the terminals are respectively.

a) 2.8 and 3.6

b) 7 and 119

c) 2.8 and 36

d) 7 and 80

Solution: https://www.youtube.com/watch?v=9bRJQhA6s3A

Common Data for Questions 8 and 9:

consider the figure shown below

8. The current I_S in Amps in the voltage source, and the voltage V_S in volts across the current source respectively are

a) 13, - 20

b) 8, - 10

c) - 8, 20

d) - 13, 20

9. The current in the 1 Ω resistor in Amps is

a) 2

b) 3.33

c) 10

d) 12

Solution (7 & 8): https://www.youtube.com/watch?v=ABDbciYDFQY

GATE 2013 Control Systems - Complete Video Solutions

2013

1. The Bode plot of a transfer function G(s) is shown in the figure below.

The gain (20log|G(s)|) is 32 dB and – 8 dB at 1 rad/sec and 10 rad/sec respectively. The phase is negative for all ω. Then G(s) is

a) 39.8/s

b) 39.8/s²

c) 32/s

d) 32/s²

Answer:B

Solution : https://www.youtube.com/watch?v=YkPfY-Gufmg

2. Which one of the following is NOT TRUE for a continuous time causal and stable LTI system?

a) all the poles of the system must lie on the left side of the jω axis

b) zeros of the system can lie anywhere in the s-plane

c) all the poles must lie with in |s| = 1

d) all the roots of the characteristic equation must be located on the let side of the jω axis

Answer:C

Solution : https://www.youtube.com/watch?v=pKt_YzAm3z0

3. A polynomial f(x) = a₄x⁴+a₃x³+a₂x²+a₁x–a₀ with all coefficients positive has

a) no real roots

b) no negative real root

c) odd number of real roots

d) at least one positive and one negative real root

Answer:D

Solution :

4. Assuming zero initial conditions, the response y(t) of the system given below for a unit step input, u(t) is __________________

a) u(t)

b) t.u(t)

c) (1/2)t².u(t)

d) e^-t.u(t)

Answer:B

Solution : https://www.youtube.com/watch?v=haTwaJVl46E

5. The transfer function V₂(s)/V₁(s) of the circuit shown is

Answer:D

Solution : https://www.youtube.com/watch?v=iVJ4qUlg8BE

6. The open loop transfer function of a DC motor is given as ω(s)/V_a(s) = 10/(1+10s). when connected in feedback as shown below.

The approximate value of K_a that will reduce the time constant of the closed loop system by one hundred times as compared to that of the open loop system is

a) 1

b) 5

c) 10

d) 100

Answer:C

Solution : https://www.youtube.com/watch?v=594vhbYCvbs

7. A system is described by the differential equation d²y/dt²+5dy/dt+6y(t) = x(t). Let x(t) be a rectangular pulse given as x(t) = 1 for 0<t<2 and zero otherwise. Assuming that y(0) = 0 and dy/dt = 0 at t=0, then the Laplace transform of y(t) is

Answer:B

Solution : https://www.youtube.com/watch?v=Z6o8dcPFVgI

8. The signal flow graph for a system is given below.

The transfer function Y(s)/U(s) for this system is

Answer:A

Solution : https://www.youtube.com/watch?v=ndeVYkf7j6w

9. The state diagram of the system is shown below. A system is described by the state variable equations

a. State variable equations of the system shown in the above figure is

Answer:A

b. The state transition matrix e^At of the system shown in the figure above is

Answer:A

Solution (a & b) : https://www.youtube.com/watch?v=wnfqGfnPFcs

GATE 2013 ECE Video Solutions on Analog Circuits (Analog Electronics)

1. In the circuit shown below, what is the output voltage (V_out), if a silicon transistor Q and an ideal OP-AMP are used?

a. - 15 volts
b. - 0.7 volts
c. + 0.7 volts
d. + 15 volts

Solution: https://www.youtube.com/watch?v=vR9F9Cmapog

2. In a voltage – voltage feedback as shown below, which one of the following statements is TRUE, if the gain K is increased?

a. The input impedance increases and output impedance decreases
b. The input impedance increases and output impedance increases
c. The input impedance decreases and output impedance decreases
d. The input impedance decreases and output impedance increases

Solution: https://www.youtube.com/watch?v=3SI-KyaLnm8

3. The small signal resistance (ie. dV_B/dI_D) in KΩ offered by the n – channel MOSFET M shown in the figure below, at a bias point of V_B = 2 volts is (device data for M: device Transconductance parameter K_N = µ_NC_OX(W/L) = 40 µA/V², threshold voltage V_TN = 1 volt, and neglecting body effect and channel length modulation effects)

a. 12.5
b. 25
c. 50
d. 100

Solution: https://www.youtube.com/watch?v=78GP87ThDTg

4. The ac schematic of an NMOS common source stage is shown in the figure below, where part of the biasing circuit has been omitted for simplicity. For the n – channel MOSFET M, the Transconductance gm = 1 mA/V and body effect and channel length modulation effect are to be neglected. The lower cutoff frequency in Hz of the circuit approximately at

a. 8
b. 32
c. 50
d. 200

Solution: https://www.youtube.com/watch?v=2-LoL607LVE

5. In the circuit shown below, the OP-AMPs are ideal. Then V_out in volts is

a. 4
b. 6
c. 8
d. 10

Solution: https://www.youtube.com/watch?v=txQhRQhmZfE

6. A voltage 1000sinωt volts is applied across YZ. Assuming ideal diodes, the voltage measured across WX in volts is

a. Sinωt
b. (Sinωt + |Sinωt|) / 2
c. (Sinωt - |Sinωt|) / 2
d. 0 for all t

Solution: https://www.youtube.com/watch?v=gy9k16uKPDk

7. In the circuit shown below, the knee current of ideal zener diode is 10 mA. To maintain 5 volts across the load R_L, the minimum value of R_L in Ω’s and the minimum power rating of the zener diode in mW respectively are

a. 125 and 125
b. 125 and 250
c. 250 and 125
d. 250 and 250

Solution: https://www.youtube.com/watch?v=_QUM3VQQ78I

8. In the circuit shown below, the silicon NPN transistor Q has a very high value of β. The required value of R₂ in KΩ to produce I_C = 1 mA is

a. 20
b. 30
c. 40
d. 50

Solution: https://www.youtube.com/watch?v=seLmVm94TqY

GATE 2013 ECE Video Solution on Digital Circuits (Digital Electronics)

1. A bulb in a staircase has two switches, one switch being at the ground floor and the other one at the first floor. The bulb can be turned ON and also can be turned OFF by any one of the switches irrespective of the state of the other switch. The logic of switching of the bulb resembles
a. An AND gate
b. An OR gate
c. An XOR gate
d. A NAND gate

Solution : https://www.youtube.com/watch?v=74ShRriCyM0

2. For 8085 microprocessor, the following program is executed.
MVI A,05H
MVI B, 05H
PTR: ADD B
DCR B
JNZ PTR
ADI 03H
HLT
At the end of the program, accumulator contains
a. 17H
b. 20H
c. 23H
d. 05H

Solution : https://www.youtube.com/watch?v=9YjXsP1wh-Y

3. In the circuit shown below, Q₁ has negligible collector to emitter saturation voltage and the diode drops negligible voltage across it under forward bias. If V_CC is +5 volts, X and Y are digital signals with 0 volts as logic 0 and V_CC as logic 1, then the Boolean expression for Z is

Solution : https://www.youtube.com/watch?v=v85cfm1sDGs

4. There are four chips each of 1024 bytes connected to a 16 bit address bus as shown in the figure below. RAMs 1,2,3 and 4 respectively are mapped to addresses

Solution : https://www.youtube.com/watch?v=BenlPrppZYU

GATE 2013 ECE Video Solutions on EDC (Electronic Devices and Circuits)

1. In IC technology, Dry oxidation(using dry oxygen) as compared to Wet oxidation (using stream or water vapor) produces………..
a. Superior quality oxide with a higher growth rate
b. Inferior quality oxide with a higher growth rate
c. Inferior quality oxide with a lower growth rate
d. Superior quality oxide with a lower growth rate

Solution : https://www.youtube.com/watch?v=EEcf8aHius8

2. For a forward biased PN junction diode, the sequence of events that best describes the mechanism of current flow is
a. Injection and subsequent diffusion and recombination of minority carriers
b. Injection and subsequent drift and generation of minority carriers
c. Extraction and subsequent diffusion and generation of minority carriers
d. Extraction and subsequent drift and recombination of minority carriers

Solution : https://www.youtube.com/watch?v=uADJe1kw8ag

3. In MOSFET operating in saturation region, the channel length modulation effect causes
a. An increase in gate source capacitance
b. A decrease in Transconductance
c. A decrease in unity gain bandwidth product
d. A decrease in output resistance

Solution : https://www.youtube.com/watch?v=9QAOSh8OjSY

4. In the circuit shown below, the knee current of ideal zener diode is 10 mA. To maintain 5 volts across the load R_L, the minimum value of R_L in Ω’s and the minimum power rating of the zener diode in mW respectively are

a. 125 and 125
b. 125 and 250
c. 250 and 125
d. 250 and 250

Solution : https://www.youtube.com/watch?v=_QUM3VQQ78I

5. In the circuit shown below, the silicon NPN transistor Q has a very high value of β. The required value of R₂ in KΩ to produce I_C = 1 mA is

a. 20
b. 30
c. 40
d. 50

Solution : https://www.youtube.com/watch?v=seLmVm94TqY

GATE 2013 ECE Network Theory - Complete Video Solutions with Answers

GATE 2013 Control Systems - Complete Video Solutions

GATE 2013 ECE Video Solutions on Analog Circuits (Analog Electronics)

GATE 2013 ECE Video Solution on Digital Circuits (Digital Electronics)

GATE 2013 ECE Video Solutions on EDC (Electronic Devices and Circuits)

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