GATE 2023 - Important Concepts, Short cuts, Complete Solutions, Examples and Practice Problems: GATE 2009

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GATE 2009 ECE Network Theory - Complete Video Solutions with Answers

2009

1. A fully charged mobile phone with a 12 volts battery is good for a 10 min talk time.

Assume that, during the talk time, the battery delivers a constant current of 2 Amp and its voltage drops linearly from 12 volts to 10 volts as shown in the figure. How much energy does the battery deliver during this talk-time?
a) 220 J
b) 12 kJ
c) 13.2 kJ
d) 14.4 kJ

Solution: https://www.youtube.com/watch?v=GV1gFYMN_wc

2. In the interconnection of ideal sources shown in figure, it is known that the 60 volts source is absorbing power. Which of the following can be the value of the current source I?

a) 10 A
b) 13 A
c) 15 A
d) 18 A

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

3. An AC source of RMS voltage 20 volts with internal impedance Z_i = (1+2j) Ω feeds a load of impedance Z_L = (7+4j) Ω in the figure below. The reactive power consumed by the load is

a) 8 VAR
b) 16 VAR
c) 28 VAR
d) 32 VAR

Solution: https://www.youtube.com/watch?v=w36Rox8j0KA

4. The switch in the circuit shown was on position 'a' for a long time, and is moved to position 'b' at time t=0. The current i(t) for t > 0 is given by

Solution: https://www.youtube.com/watch?v=ptI9Yzy17OQ

5. In the circuit shown, what value of R_L maximizes the power delivered to R_L?

a) 2.4 Ω
b) 8/3 Ω
c) 4 Ω
d) 6 Ω

Solution: https://www.youtube.com/watch?v=yqt0czRs6_I

6. The time domain behaviour of an RL circuit is represented as shown below. For an initial current of i(0) = V_o/R, the steady state value of the current is given by

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

GATE 2009 ECE Control Systems - Complete Video Solutions with Answers

2009

1. The magnitude plot of a rational transfer function G(s) with real coefficients is shown below. Which of the following compensator has such a magnitude plot?

a) Lead compensator

b) Lag compensator

c) PID compensator

d) Lead – Lag compensator

Solution : https://www.youtube.com/watch?v=JVBUSrYEb7Q

2. If the transfer function of the following circuit is V_o(s)/V_i(s) = 1/(2+sCR), then the value of the load resistor R_L is

a) R/4

b) R/2

c) R

d) 2R

Solution : https://www.youtube.com/watch?v=0bJX_BCy6bc

3. consider the system,

where p and q are arbitrary real numbers, which one of the following statements about the controllability of the system is TRUE?

a) the system is completely state controllable for any non zero values of p and q

b) only p=0 and q=0 result in controllability

c) the system is uncontrollable for all values of p and q

d) we cannot conclude about controllability from the given data

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

4. the feedback configuration and the pole-zero locations of G(s) = (s² – 2s + 2)/(s² + 2s +2), are shown below.

The root locus for negative values of k, i.e. for –∞ < k < 0, has break away/break in points and angle of departure at pole P (w.r.t. the positive real axis) equal to

a) ± √2 and 0^o

b) ± √2 and 45^o

c) ± √3 and 0^o

d) ± √3 and 45^o

Solution : https://www.youtube.com/watch?v=uagcsFAoEB0

5. The unit step response of an under damped second order system has steady state value of – 2. Which of the following transfer functions has these properties?

Solution : https://www.youtube.com/watch?v=FVflQ49wsF8

Common Data Questions: (6 & 7)

The Nyquist plot of a stable transfer function G(s) is shown in the figure. We are interested in the stability of the closed loop system in the feedback configuration shown.

6. Which of the following statements is TRUE?

a) G(s) is an all pass filter

b) G(s) has a zero in the right half plane

c) G(s) is the impedance of a passive network

d) G(s) is marginally stable

Solution : https://www.youtube.com/watch?v=2t0EyW64kfI

7. The gain and phase margin of G(s) for closed loop stability are

a) 6 dB and 180^o

b) 3 dB and 180^o

c) 6 dB and 90^o

d) 3 dB and 90^o

Solution : https://www.youtube.com/watch?v=RlFKoEWXgw8

GATE 2009 ECE Video Solutions on Analog Circuits (Analog Electronics)

1. In the following Astable Multivibrator circuit, which properties of V_o(t) depend on R₂ ?

a. Only the frequency
b. Only the amplitude
c. Both the amplitude and the frequency
d. Neither the amplitude nor the frequency

Solution: https://www.youtube.com/watch?v=CNrhstw1lQI

2. In the circuit shown below, the OP-AMP is ideal, the transistor has V_BE = 0.6 volts and β = 150. Decide whether the feedback in the circuit is positive or negative and determine the voltage V at the output of the OP-AMP.

a. Positive feedback, V = 10 Volts
b. Positive feedback, V = 0 Volts
c. Negative feedback, V = 5 Volts
d. Negative feedback, V = 2 Volts

Solution: https://www.youtube.com/watch?v=H6FpEgr7ZYI

3. A small signal source Vi(t) = Acos20t + Bsin10⁶t is applied to a transistor amplifier as shown below. The transistor has β = 150 and h_ie = 3 KΩ. Which expression best approximate V_o(t).

a. V_o(t) = - 1500 (Acos20t + Bsin10⁶t)
b. V_o(t) = - 150 (Acos20t + Bsin10⁶t)
c. V_o(t) = - 1500 (Bsin10⁶t)
d. V_o(t) = - 150 (Bsin10⁶t)

Solution: https://www.youtube.com/watch?v=C-1mKYDJhY4

GATE 2009 ECE Video Solution on Digital Circuits (Digital Electronics)

1. In a microprocessor, the service routine for a certain interrupt starts from a fixed location of memory which cannot be externally set, but the interrupt can be delayed or rejected. Such an interrupt is
a. non-maskable and non-vectored
b. maskable and non-vectored
c. non-maskable and vectored
d. maskable and vectored

Solution : https://www.youtube.com/watch?v=pJ-6A_o5-LU

2. If X = 1 in the given logic equation, then

a. Y = Z
b. Y = Z’
c. Z = 1
d. Z = 0

Solution : https://www.youtube.com/watch?v=qHzk5M1H6DU

3. What are the minimum number of 2 to 1 multiplexers required to generated a 2 input AND gate and a 2 input EX-OR gate?
a. 1 and 2
b. 1 and 3
c. 1 and 1
d. 2 and 2

Solution : https://www.youtube.com/watch?v=wixmXaKDQ5Q

4. Refer to the NAND and NOR latches shown in the figure. The inputs (P₁, P₂) for both the latches are first made (0, 1) and then, after a few seconds, made (1, 1). The corresponding stable outputs (Q₁, Q₂) are

Solution : https://www.youtube.com/watch?v=CmdmJ9qQjdk

5. What are the counting stages (Q₁, Q₂) for the counter shown in the figure below?

a. 11, 10, 00, 11, 10….
b. 01, 10, 11, 00, 01….
c. 00, 11, 01, 10, 00…..
d. 01, 10, 00, 01, 10…..

Solution : https://www.youtube.com/watch?v=marTcMTzg0Y

Statement for linked answer questions: 6 & 7
Two products are sold from a vending machine, which has two push buttons P₁ and P₂. When a button is pressed, the price of the corresponding product is displayed in a 7-segment display.
If no buttons are pressed, ‘0’ is displayed, signifying ‘Rs. 0’.
If only P₁ is pressed, ‘2’ is displayed, signifying ‘Rs. 2’.
If only P₂ is pressed, ‘5’ is displayed, signifying ‘Rs. 5’.
If both P₁ and P₂ are pressed, ‘E’ is displayed, signifying ‘Error’.
The names of the segments in the 7-segment display, and the glow of the display for ‘0’, ‘2’, ‘5’ and ‘E’ are shown below.

Consider
(i) Push button pressed / not pressed is equivalent to logic 1 / 0 respectively
(ii) A segment glowing / not glowing in the display is equivalent to logic 1 / 0 respectively
6. If segments a to g are considered as functions of P₁ and P₂, then which of the following is correct?

7. What are the minimum numbers of NOT gates and 2-inout OR gates required to design the logic of the driver for this 7-segment display?
a. 3 NOT and 4 OR
b. 2 NOT and 4 OR
c. 1 NOT and 3 OR
d. 2 NOT and 3 OR

Solution (6 & 7) : https://www.youtube.com/watch?v=njEr-LoSbw4

GATE 2009 ECE Video Solutions on EDC (Electronic Devices and Circuits)

1. In an N type silicon crystal at room temperature, which of the following can have a concentration of 4x10¹⁹ cm^-3?
a. Silicon atoms
b. Holes
c. Dopant atoms
d. Valence electrons

Solution : https://www.youtube.com/watch?v=ck2TRWxTGGM

2. The full forms of the abbreviations TTL and CMOS in reference to logic families are
a. Triple Transistor Logic and Chip Metal Oxide semiconductor
b. Tristate Transistor Logic and Chip Metal Oxide semiconductor
c. Transistor Transistor Logic and Complementary Metal Oxide semiconductor
d. Tristate Transistor Logic and Complementary Metal Oxide semiconductor

Solution : https://www.youtube.com/watch?v=v-0BYB0NkMI

3. The ratio of the mobility to the diffusion coefficient in a semiconductor has the units
a. V^-1
b. cm. V^-1
c. V. cm^-1
d. V.sec

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

4. In the circuit below, the diode is ideal. The voltage V is given by

a. Min(V_i,1)
b. Max(V_i,1)
c. Min(-V_i,1)
d. Max(-V_i,1)

Solution : https://www.youtube.com/watch?v=yMHePwsPly0

5. Consider the following two statements about the internal conditions in an N channel MOSFET operating in the active region.
S1: the inversion charge decreases from source to drain
S2: the channel potential increases from source to drain
Which of the following is correct?
a. Both are TRUE
b. Both are FALSE
c. Both are TRUE, but S2 is not a reason for S1
d. Both are TRUE, and S2 is a reason for S1.

Solution : https://www.youtube.com/watch?v=qbq2JXNCe_Q

6. Common Data Question:
Consider a silicon PN junction at room temperature having the following parameters:
Doping on the N side = 1x10¹⁷ cm^-3
Depletion width on N side = 0.1 µm
Depletion width on the P side = 1 µm
Intrinsic carrier concentration = 1.4x10¹⁰ cm^-3
Thermal voltage = 26 mV
Permittivity of free space = 8.85x10^-14 F/cm
Dielectric constant of silicon = 12

i. The built in potential of the junction is
a. 0.70 volts
b. 0.76 volts
c. 0.82 volts
d. Cannot be estimated from given data

ii. The peak electric field in the device is
a. 0.15 Mvolts/cm, directed from P region to N region
b. 0.15 Mvolts/cm, directed from N region to P region
c. 1.80 Mvolts/cm, directed from P region to N region
d. 1.80 Mvolts/cm, directed from N region to P region

Solution : https://www.youtube.com/watch?v=ZbOv57yZfQg

7. Linked Questions:
Consider the CMOS circuit shown, where the gate voltage V_G of the N channel MOSFET is increased from zero, while the gate voltage of the P channel MOSFET is kept constant at 3 volts. Assume that, for both transistors, the magnitude of the threshold voltage is 1 volts and the product of the transconductance parameter and the (W/L) ratio i.e. the quantity µc_ox(W/L) is 1 mA/V².

i. For small increase in V_G beyond 1 volt, which of the following gives the correct description of the region of operation of each MOSFET?
a. Both are in saturation region
b. Both are in triode region
c. NMOS is in triode region and PMOS is in saturation region
d. NMOS is in saturation region and PMOS is in triode region

ii. Estimate the output voltage, V_o for V_G = 1.5 volts. (Hint: use the appropriate current voltage equation for each MOSFET, based on the answer to above question)

Solution : https://www.youtube.com/watch?v=_BU3wB8FoBA

GATE 2009 ECE Network Theory - Complete Video Solutions with Answers

GATE 2009 ECE Control Systems - Complete Video Solutions with Answers

GATE 2009 ECE Video Solutions on Analog Circuits (Analog Electronics)

GATE 2009 ECE Video Solution on Digital Circuits (Digital Electronics)

GATE 2009 ECE Video Solutions on EDC (Electronic Devices and Circuits)

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