GATE 2023 - Important Concepts, Short cuts, Complete Solutions, Examples and Practice Problems: GATE 2008

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GATE 2008 ECE Network Theory - Complete Video Solutions with Answers

2008

1. In the following graph, the number of trees (P) and the number of cut-sets (Q) are

a) P = 2, Q = 2
b) P = 2, Q = 6
c) P = 4, Q = 6
d) P = 4, Q = 10

2. In the following cirucit, the switch S is closed at t = 0. The rate of change of current di(0⁺)/dt is given by

Solution: https://www.youtube.com/watch?v=WiYzbTZyhi0

3. The Thevenin equivalent impedance Z_TH between the nodes P and Q in the following circuit is

Solution: https://www.youtube.com/watch?v=vl6exaG9eY0

4. The driving point impedance of the following network is given as shown. The component values are

Solution: https://www.youtube.com/watch?v=CI2Na_stYRg

Common Data Questions: 5 & 6
The following series RLC circuit with zero initial conditions is excited by a unit impulse function δ(t).

5. For t > 0, the output voltage V_c(t) is

Solution: https://www.youtube.com/watch?v=DB4jmdoaFIk

6. For t > 0, the voltage across the resistor is

Solution: https://www.youtube.com/watch?v=nn6PggFjKgA

Statement for Linked Answer Questions: 7 & 8
A two port network shown below is excited by external DC sources. The voltages and the currents are measured with voltmeters V₁, V₂ and ammeters A₁, A₂ (all assumed to be ideal), as indicated. Under following switch conditions, the readings obtained are:

7. The Z-parameter matrix for this network is

8. The h-parameter network for this network is

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

GATE 2008 ECE Control Systems - Complete Video Solutions with Answers

GATE 2008

1. The pole-zero plot given below corresponds to a

a) Low pass filter

b) High pass filter

c) band pass filter

d) Notch filter

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

2. Step response of a set of three second order under damped systems all have the same percentage overshoot. Which of the following diagrams represents the poles of the three systems?

Solution : https://www.youtube.com/watch?v=X0RUYGCL8P4

3. Group – I lists a set of four transfer functions. Group – II gives a list of possible step responses y(t). Match the step responses with the corresponding transfer functions.

a) P - 3, Q - 1, R - 4, S - 2

b) P - 3, Q - 2, R - 4, S - 1

c) P - 2, Q - 1, R - 4, S - 3

d) P - 3, Q - 4, R - 1, S – 2

Solution : https://www.youtube.com/watch?v=jXGZriqlb1c

4. A certain system has transfer function G(s) = (s + 8)/(s² + αs – 4 ), where α is a parameter. Consider the standard negative unity feedback configuration shown below.

Which of the following statements is true?

a) The closed loop system is never stable for any value of α

b) For some positive values of α, the closed loop system is stable, but not for all positive values

c) For all positive values of α, the closed loop system is stable

d) The closed loop system is stable for all values of α, both positive and negative

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

5. A signal flow graph of a system is given below.

The set of equations that correspond to this signal flow graph is

Solution : https://www.youtube.com/watch?v=cxlX8Rpj9cs

6. The number of open right half plane poles of G(s) = 10 / (s⁵ + 2s⁴ + 3s³ + 6s² + 5s + 3) is

a) 0

b) 1

c) 2

d) 3

Solution : https://www.youtube.com/watch?v=Seaj7dcM1yk

7. The magnitude of frequency response of an under damped second order system is 5 at 0 rad/sec and peaks to 10/√3 at 5√2 rad/sec. The transfer function of the system is

Solution : https://www.youtube.com/watch?v=3a4n-8XUFCg

8. Group – I gives two possible choices for the impedance Z in the diagram. The circuit elements in Z satisfy the condition R₂C₂>R₁C₁. The transfer function V_o/V₁ represents a kind of controller. Match the impedance's in Group – I with the types of controllers in Group – II.

a) Q – 1, R – 2

b) Q – 1, R – 3

c) Q – 2, R – 3

d) Q – 3, R – 2

Solution : https://www.youtube.com/watch?v=Q3O1G2CU5Xw

GATE 2008 ECE Video Solutions on Analog Circuits (Analog Electronics)

1. Consider the following circuit using an ideal OP-AMP. The I-V characteristic of the diode is described by the relation I = I_o(exp(V/V_T) - 1), where VT = 25 mV, I_o = 1 µA and V is the voltage across the diode(taken as positive for forward bias). For an input voltage V_i = - 1 volts, the output voltage V_o is

a. 0 volts
b. 0.1 volts
c. 0.7 volts
d. 1.1 volts

Solution: https://www.youtube.com/watch?v=Hm-AQGstHH0

2. The OP-AMP circuit shown below represents a

a. High pass filter
b. Low pass filter
c. Band pass filter
d. Band reject filter

Solution: https://www.youtube.com/watch?v=iNclgQhX8gs

3. Consider the schmitt trigger circuit shown below.

A triangular wave which goes from –12 volts to +12 volts is applied to the inverting input of OP-AMP. Assume that the output of the OP-AMP swings from +15 volts to –15 volts. The voltage at the non-inverting input switches between
a. – 12 volts and +12 volts
b. – 7.5 volts and +7.5 volts
c. – 5 volts and +5 volts
d. 0 volts and +5 volts

Solution: https://www.youtube.com/watch?v=U1PM8Q0IT0o

Statement for Linked Answer Question:
In the following transistor circuit, V_BE = 0.7 volts, r_e = 25 mV/I_E, β and all the capacitances are very large.

4. The value of DC current I_E is
a. 1 mA
b. 2 mA
c. 5 mA
d. 10 mA

5. The mid-band voltage gain of the amplifier is approximately
a. – 180
b. – 120
c. – 90
d. – 60

Solution(4 & 5): https://www.youtube.com/watch?v=eX0es1gFdW4

GATE 2008 ECE Video Solution on Digital Circuits (Digital Electronics)

1. An 8085 executes the following instructions
2710 LXI H, 30A0H
2713 DAD H
2714 PCHL
All addresses and constants are in Hexa decimal. Let PC be the contents of the program counter and HL be the contents of HL register pair just after executing PCHL.
Which of the following statements is correct?
a. PC = 2715H and HL = 30A0H
b. PC = 30A0H and HL = 2715H
c. PC = 6140H and HL = 6140H
d. PC = 6140H and HL = 2715H

Solution : https://www.youtube.com/watch?v=YS9fVY4bdn4

2. The logic function implemented by the following circuit at the terminal OUT is

a. P NOR Q
b. P NAND Q
c. P OR Q
d. P AND Q

Solution : https://www.youtube.com/watch?v=cH-YodnqAt4

3. The two numbers represented in signed 2’s compliment form are P = 11101101 and Q = 11100110. If Q is subtracted from P, the value obtained in signed 2’s compliment form is
a. 100000111
b. 00000111
c. 11111001
d. 111111001

Solution : https://www.youtube.com/watch?v=blIZILSmO8o

4. Which of the following Boolean expression correctly represents the relation between P, Q, R and M₁?

Solution : https://www.youtube.com/watch?v=toMIhaj1omc

5. For the circuit shown in the following figure, I₀ – I₃ are inputs to the 4:1 multiplexer, R(MSB) and S are control inputs. The output Z can be represented by

Solution : https://www.youtube.com/watch?v=WCRHS7QwqYM

6. For each of the positive edge triggered JK flip flop used in the following figure, the propagation delay is ΔT.

Which of the following waveforms correctly represents the output at Q₁?

Solution : https://www.youtube.com/watch?v=N7ZYplccPcA

7. For the circuit shown in the figure, D has a transition from 0 to 1 after CLK changes from 1 to 0. Assume gate delays to be negligible.

Which of the following statements is TRUE?
a. Q goes to 1 at the CLK transition and stays at 1
b. Q goes to 0 at the CLK transition and stays at 0
c. Q goes to 1 at the CLK transition and goes to 0 when D goes to 1
d. Q goes to 0 at the CLK transition and goes to 1 when D goes to 1

Solution : https://www.youtube.com/watch?v=FvPG9aLQcHg

Statement for Linked Answer Questions 8 and 9:
In the following circuit, the comparator output is logic ‘1’ if V₊ > V_- and is logic ‘0’
otherwise. The D/A conversion is done as per the relation.

The counter starts from the clear state.

8. The stable reading of the LED display is
a. 06
b. 07
c. 12
d. 13

9. The magnitude of the error between VDAC and Vin at steady state in volts is
a. 0.2
b. 0.3
c. 0.5
d. 1.0

Solution (8 & 9) : https://www.youtube.com/watch?v=8WEFmNeqxYI

GATE 2008 ECE Video Solutions on EDC (Electronic Devices and Circuits)

1. Which of the following is NOT associated with a PN junction?
a. Junction capacitance
b. Charge storage capacitance
c. Depletion capacitance
d. Channel length modulation

Solution : https://www.youtube.com/watch?v=7kYKPLc5ujM

2. Which of the following is TRUE?
a. A silicon wafer heavily doped with boron is a P⁺ substrate
b. A silicon wafer lightly doped with boron is a P⁺ substrate
c. A silicon wafer heavily doped with Arsenic is a P⁺ substrate
d. A silicon wafer lightly doped with Arsenic is a P⁺ substrate

Solution : https://www.youtube.com/watch?v=wWLqWJ5JX3U

3. In the following limiter circuit, an input voltage V_i = 10sin100πt applied. Assume that the diode drop is 0.7 volts when it is forward biased. The zener breakdown voltage is 6.8 volts.
The maximum and minimum values of the output voltage respectively are

a. 6.1 volts, -0.7 volts
b. 0.7 volts, -7.5 volts
c. 7.5 volts, -0.7 volts
d. 7.5 volts, -7.5 volts

Solution : https://www.youtube.com/watch?v=2LAYX1bdh5o

4. A silicon wafer has 100nm of oxide on it and is inserted in a furnace at a temperature above 1000^oC for further oxidation in dry oxygen. The oxidation rate
a. Is independent of current oxide thickness and temperature
b. Is independent of current oxide thickness but depends on temperature
c. Slows down as the oxide grows
d. Is zero as the existing oxide prevents further oxidation

Solution : https://www.youtube.com/watch?v=6yl7336P2kA

5. The drain current of a MOSFET in saturation is given by I_D = K(V_GS-V_T)², where K is a constant. The magnitude of the Transconductance g_m is

Solution : https://www.youtube.com/watch?v=pYDNlQanv2g

6. For the circuit shown in the following figure, transistors M1 and M2 are identical NMOS transistors. Assume that M2 is in saturation and the output is unloaded. The I_X is related to I_bias as

Solution : https://www.youtube.com/watch?v=CBXqcvlx97A

7. The measured Transconductance g_m of an NMOS transistor operating in the linear region is plotted against the gate voltage V_G at constant drain voltage V_D. Which of the following figures represents the expected dependence of g_m on V_G?

Solution : https://www.youtube.com/watch?v=KE_MLvt-M-4

8. Two identical NMOS transistors M1 and M2 are connected as shown below. V_bias is chosen so that both transistors are in saturation. The equivalent g_m of the pair is defined to be d_Iout / dV_i at constant V_out, is

a. The sum of individual g_m’s of the transistors
b. The product of individual g_m’s of the transistors
c. Nearly equal to the g_m of M1
d. Nearly equal to g_m1/g_m2 of M2

Solution : https://www.youtube.com/watch?v=oySwKD3Vtjg

9. Silicon is doped with boron to a concentration of 4x10¹⁷atoms/cm³. Assuming the intrinsic carrier concentration of silicon to be 1.5x10¹⁰ cm^-3 and the value of KT/q to be 25 mV at 300^oK. Compared to undoped silicon, the Fermi level of doped silicon
a. Goes down by 0.13 eV
b. Goes up by 0.13 eV
c. Goes down by 0.427 eV
d. Goes up by 0.427 eV

Solution : https://www.youtube.com/watch?v=B4keN9lEFS8

10. The cross section of a JFET is shown in the figure. Let V_G be -2 volts and V_P be the initial pinch off voltage. If the width W is doubled (with other geometric parameters and doping levels remaining the same), then the ratio between the mutual Transconductance of the initial and the modified JFET is

Solution : https://www.youtube.com/watch?v=i1HcEXiUqXA

11. Consider the following assertions.
S1: For zener effect to occur, a very abrupt junction is required
S2: For quantum tunneling to occur, a very narrow energy barrier is required.
Which of the following is correct?
a. Only S2 is true
b. Both are true but S2 is not a reason for S1
c. Both are true but S2 is a reason for S1
d. Both are false

Solution : https://www.youtube.com/watch?v=FMoJlAI1-84

GATE 2008 ECE Network Theory - Complete Video Solutions with Answers

GATE 2008 ECE Control Systems - Complete Video Solutions with Answers

GATE 2008 ECE Video Solutions on Analog Circuits (Analog Electronics)

GATE 2008 ECE Video Solution on Digital Circuits (Digital Electronics)

GATE 2008 ECE Video Solutions on EDC (Electronic Devices and Circuits)

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