GATE 2023 - Important Concepts, Short cuts, Complete Solutions, Examples and Practice Problems: GATE 2005

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GATE 2005 ECE Network Theory - Complete Video Solutions with Answers

2005

1. The condition on R, L and C such that the step response y(t) in figure has no oscillations, is

Solution: https://www.youtube.com/watch?v=JfYzFU9Oc-0

2. The ABCD parameters of an ideal n:1 transformer shown in figure are given below. The value of 'x' will be

a) n
b) 1/n
c) n²
d) 1/n²

Solution: https://www.youtube.com/watch?v=wjvAb6BEi9o

3. In a series RLC circuit, R = 2 kΩ, L = 1 H, and C = 1/400 µF. The resonant frequency is
a) 2 x 10⁴ Hz
b) (1/π) x 10⁴ Hz
c) 10⁴ Hz
d) 2π x 10⁴ Hz

Solution: https://www.youtube.com/watch?v=B9Uk_uA0JbA

4. The maximum power that can be transferred to the load resistor R_L form the voltage source in figure is

a) 1 W
b) 10 W
c) 0.25 W
d) 0.5 W

Solution: https://www.youtube.com/watch?v=IW9o-PZYI6E

5. The first and Last critical frequency of an RC driving point impedance function must respectively be
a) a zero and a pole
b) a zero and a zero
c) a pole and a pole
d) a pole and a zero

Solution: https://www.youtube.com/watch?v=noq2x3cDycY

6. For the circuit in figure, the instantaneous current i₁(t) is

Solution: https://www.youtube.com/watch?v=BcmlFVwT5C4

7. Impedance Z as shown in figure is

a) j29 Ω
b) j9 Ω
c) j19 Ω
d) j39 Ω

Solution: https://www.youtube.com/watch?v=tPOeNM7EELI

8. For the circuit shown in figure, Thevenin's voltage and Thevenin's equivalent resistance at terminals a-b is

a) 5 V and 2 Ω
b) 7.5 V and 2.5 Ω
c) 4 V and 2 Ω
d) 3 V and 2.5 Ω

Solution: https://www.youtube.com/watch?v=wlcChf7gBWE

9. If R₁ = R₂ = R₄ = R and R₃ = 1.1R in the bridge circuit shown in figure, then the reading in the ideal voltmeter connected between a and b is

a) 0.238 V
b) 0.138 V
c) - 0.238 V
d) 1 V

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

10. The h-parameters of the circuit shown in figure are

Solution: https://www.youtube.com/watch?v=lI92Vfd0F1o

11. A square pulse of 3 volts amplitude is applied to RC circuit shown in figure. The capacitor is initially uncharged. The output voltage V_o at time t = 2 sec is

a) 3 V
b) -3 V
c) 4 V
d) -4 V

Solution: https://www.youtube.com/watch?v=lCb51w-rL_g

GATE 2005 ECE Control Systems - Complete Video Solutions with Answers

GATE 2005

1. A linear system is equivalently represented by two sets of state equations

Ẋ = AX + BU and Ẇ = CW + DU.

The eigen values of the representations are also computed as |λ| and |μ|. Which one of the following statements is TRUE?

Answer :

Solution :

2. Which one of the following polar diagrams corresponds to a lag network?

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

3. Despite the percentage of negative feedback, control systems still have problems of Instability because the

a) components used have non-linearity

b) dynamic equations of the sub-systems are not know exactly

c) mathematical analysis involves approximations

d) system has large negative phase angle at high frequencies

Solution : https://www.youtube.com/watch?v=1FtNWWBjrSU

4. The polar diagram of a conditionally stable system for open loop gain K = 1 is shown in figure. The open loop transfer function of the system is known to be stable. The closed loop system is stable for

Solution : https://www.youtube.com/watch?v=1mBpd1vOX78

5. In the derivation of expression for peak percent overshoot, which one of the following conditions is NOT required?

a) system is linear and time invariant

b) system transfer function has a pair of complex conjugate poles and no zeros

c) there is no transportation delay in the system

d) the system has zero initial conditions

Solution : https://www.youtube.com/watch?v=CCM2Ygcsj1s

6. A ramp input applied to an unity feedback system results in 5% steady state error. The Type number and zero frequency gain of the system are respectively

a) 1 and 20

b) 0 and 20

c) 0 and 1/20

d) 1 and 1/20

Solution : https://www.youtube.com/watch?v=cmSIdjxqW-s

7. A double integrator plant, G(s) = K/S², H(s) = 1 is to be compensated to achieve the damping ratio ξ = 0.5, and an undamped natural frequency ω_n = 5 rad/sec. Which one of the following compensator G_c(s) will be suitable?

Solution : https://www.youtube.com/watch?v=5FCT5oDsBf0

8. A unity feedback system is given as G(s) = k(1 – s) / [s(s + 3)]. Indicate the correct root locus diagram.

Solution : https://www.youtube.com/watch?v=cCAfe9ydiU8

Statement for Linked Answer Questions 9 & 10:

The open loop transfer function of a unity feedback is given by G(s) = 3e^–2s/ [s(s + 2)].

9. The Gain and Phase cross over frequencies in rad/sec are, respectively

a) 0.932 and 1.26

b) 0.632 and 0.485

c) 0.485 and 0.632

d) 1.26 and 0.632

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

10. based on the above results, the Gain and Phase Margins of the system will be

a) –7.09 dB and 87.5^o

b) 7.09 dB and 87.5^o

c) 7.09 dB and –87.5^o

d) –7.09 dB and –87.5^o

Solution : https://www.youtube.com/watch?v=aHVPuRMM0q8

GATE 2005 ECE Video Solutions on Analog Circuits (Analog Electronics)

1. The effect of current shunt feedback in an amplifier is to
a. Increase the input resistance and decrease the output resistance.
b. Increase both input and output resistances
c. Decrease both input and output resistances
d. Decreases the input resistance and increase the output resistance

Solution: https://www.youtube.com/watch?v=ZZ6rItV_wj8

2. The input resistance R_i of the amplifier shown in figure is

a. 30/4 KΩ
b. 10 KΩ
c. 40 KΩ
d. Infinite

Solution: https://www.youtube.com/watch?v=N7D9lXz25dU

3. The cascode amplifier is a multistage configuration of
a. CC – CB
b. CE – CB
c. CB – CC
d. CE – CC

Solution: https://www.youtube.com/watch?v=srt3MdOny5g

4. A square pulse of 3 volts amplitude is applied to RC circuit shown in figure. The capacitor is initially uncharged. The output voltage V_o at time t = 2 sec is

a. 3 volts
b.– 3 volts
c. 4 volts
d. – 4 volts

Solution:

5. For an NPN transistor connected as shown in figure, V_BE = 0.7 volts. Given that reverse saturation current of the junction at room temperature 300^oK is 10^-13 amp, the emitter current is

a. 30 mA
b. 39 mA
c. 49 mA
d. 20 mA

Solution: https://www.youtube.com/watch?v=3HVbE9qCcH8

6. The voltage e_o indicated in figure has been measured by an ideal voltmeter, which of the following can be calculated?

a. Bias current of the inverting input only
b. Bias current of the inverting and non-inverting inputs only
c. Input offset current only
d. Both the bias currents and the input offset current.

Solution: https://www.youtube.com/watch?v=OuIncy3Iz-w

7. The OP-AMP circuit shown in figure is a filter. The type of filter and its cut-off frequency are respectively.

a. High pass, 1000 rad/sec
b. Low pass, 1000 rad/sec
c. High pass, 10000 rad/sec
d. Low pass, 10000 rad/sec

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

8. In the differential amplifier shown in figure, a large value of R_E

a. Increases both the differential and common mode gains
b. Increases the common mode gain only
c. Decreases the differential mode gain only
d. Decreases the common mode gain only

Solution: https://www.youtube.com/watch?v=YH9E2xVqdv0

9. The circuit using a BJT with β = 50 and V_BE = 0.7 volts is shown in figure. The base current I_B and the collector voltage V_C are respectively.

a. 43 µA and 11.4 volts
b. 40 µA and 16 volts
c. 45 µA and 11 volts
d. 50 µA and 10 volts

Solution: https://www.youtube.com/watch?v=W8VHHTLp6Kg

10. Given the ideal operational amplifier circuit shown in figure indicate the correct transfer characteristics assuming ideal diodes with zero cut-in voltage.

Solution: https://www.youtube.com/watch?v=q_6bzIBuW7A

Common Data Questions for 11, 12 and 13:
Given r_d = 20 KΩ, I_DSS = 10 mA, V_P = - 8 volts.

11. Z_i and Z_o of the circuit are respectively
a. 2 MΩ and 2 KΩ
b. 2 MΩ and 20/11 KΩ
c. Infinity and 2 KΩ
d. Infinity and 20/11 KΩ

12. I_D and V_DS under DC conditions are respectively
a. 5.625 mA and 8.75 Volts
b. 7.50 mA and 5.0 Volts
c. 4.50 mA and 11.0 Volts
d. 6.25 mA and 7.5 Volts

13. Transconductance in milli-siemens (mS) and the voltage gain of the amplifier are
a. 1.875 mS and 3.41
b. 1.875 mS and – 3.41
c. 3.30 mS and – 6
d. 3.30 mS and 6

Solution(11, 12, 13): https://www.youtube.com/watch?v=3EaSdIyGqME

GATE 2005 ECE Video Solution on Digital Circuits (Digital Electronics)

1. Decimal 43 in Hexadecimal and BCD number system is respectively
a. B2, 0100 0011
b. 2B, 0100 0011
c. 2B, 0011 0100
d. B2, 0100 0100

Solution : https://www.youtube.com/watch?v=5-6JKj9bNzI

2. The Boolean function f implemented in the figure using two input multiplexers is

Solution : https://www.youtube.com/watch?v=gWh-fumZFRI

3. The Boolean expression for the truth table shown is

Solution : https://www.youtube.com/watch?v=xCS-TTQvhp8

4. The present output Q_n of an edge triggered JK flip-flop is logic ‘0’. If j = 1, then Q_n+1 is
a. Cannot be determined
b. Will be logic ‘0’
c. Will be logic ‘1’
d. Will race around

Solution : https://www.youtube.com/watch?v=3Txg02Wb8N0

5. The given figure shows a ripple counter using positive edge triggered flip-flops. If the present state of the counter is Q₂Q₁Q₀ = 011, then its next state Q₂Q₁Q₀ will be

a. 010
b. 100
c. 111
d. 101

Solution : https://www.youtube.com/watch?v=iZWdwF2lfmw

6. What memory address range is NOT represented by chip #1 and chip #2 in the figure. A0 to A15 in this figure are the address lines and CS means chip select.

a. 0100 – 02FF
b. 1500 – 16FF
c. F900 – FAFF
d. F800 – F9FF

Solution : https://www.youtube.com/watch?v=bv_jlwR4ivs

Statement for linked Answer Questions 7 & 8 :
Consider an 8085 microprocessor system.
7. The following program starts at location 0100H.
LXI SP, 00FF
LXI H, 0701
MVI A, 20H
SUB M
THE Contents of accumulator when the program counter reaches 0109H is
a. 20H
b. 02H
c. 00H
d. FFH
Answer:

8. If in addition, following code exists from 0109H onwards.
ORI 40H
ADD M
What will be the result in the accumulator after executing the last instruction?
a. 40H
b. 20H
c. 60H
d. 42H
Answer:

Solution (7 & 8):

GATE 2005 ECE Video Solutions on EDC (Electronic Devices and Circuits)

1. The band gap of silicon at room temperature is
a. 1.3 eV
b. 0.7 eV
c. 1.1 eV
d. 1.4 eV

Solution : https://www.youtube.com/watch?v=Z_suI3Hvt6I

2. A silicon PN junction at a temperature of 20^oC has a reverse saturation current of 10 pA. The reverse saturation current at 40^oC for the same bias is approximately
a. 30 pA
b. 40 pA
c. 50 pA
d. 60 pA

Solution : https://www.youtube.com/watch?v=is4Hb5QGpHg

3. The primary reason for the widespread use of silicon in semiconductor device technology is
a. Abundance of silicon on the surface of the earth
b. Larger band gap of silicon in comparison to germanium
c. Favorable properties of silicon – dioxide (S_iO₂)
d. Lower melting point

Solution : https://www.youtube.com/watch?v=6742WDMV-3U

4. A silicon sample A is doped with 10¹⁸ atoms/cm³ of boron. Another sample B of identical dimensions is doped with 10¹⁸ atoms/cm³ of phosphorous. The ratio of electron to hole mobility is 3. The ratio of conductivity of the sample A to B is
a. 3
b. 1/3
c. 2/3
d. 3/2

Solution : https://www.youtube.com/watch?v=4GDAybGas6c

5. A silicon PN junction diode under reverse bias has depletion region of width of 10 µm. The relative permittivity of silicon (Ԑ_r) is 11.7 and the permittivity of free space (Ԑ_o) is 8.85 x 10^-12 F/m. The depletion capacitance of the diode per square meter is
a. 100 µF
b. 10 µF
c. 1 µF
d. 20 µF

Solution : https://www.youtube.com/watch?v=rxp_jLO9dz0

6. For NPN transistor connected as shown in figure, V_BE = 0.7 volts. Given that the reverse saturation current of the junction at room temperature is 10^-13 Amp, then the emitter current is

Solution : https://www.youtube.com/watch?v=3HVbE9qCcH8

7. An N-channel MOSFET and its transfer curve is shown in figure, then the threshold voltage is

Solution : https://www.youtube.com/watch?v=UYrsnu-QIlU

8. The zener diode in the regulator circuit shown has a zener voltage of 5.8 volts and a zener knee current of 0.5 mA. The maximum load current drawn from this circuit ensuring proper functioning over the input voltage range between 20 and 30 volts is

Solution : https://www.youtube.com/watch?v=QxmLyMhJs6g

9. Both transistors T₁ and T₂ in figure have a threshold voltage of 1 volt. The device parameters K₁ and K₂ of T₁ and T₂ are 36 µA/v² and 9 µA/v² respectively. The output voltage V_o is

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

10. A MOS capacitor made using P type substrate is in the accumulation mode. The dominant charge is due to the presence of
a. Holes
b. Electrons
c. Positively charged ions
d. Negatively charged ions

Solution : https://www.youtube.com/watch?v=jlQ_ny0L4C0

GATE 2005 ECE Network Theory - Complete Video Solutions with Answers

GATE 2005 ECE Control Systems - Complete Video Solutions with Answers

GATE 2005 ECE Video Solutions on Analog Circuits (Analog Electronics)

GATE 2005 ECE Video Solution on Digital Circuits (Digital Electronics)

GATE 2005 ECE Video Solutions on EDC (Electronic Devices and Circuits)

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