GATE 2023 - Important Concepts, Short cuts, Complete Solutions, Examples and Practice Problems: GATE 2004

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GATE 2004 ECE Network Theory - Complete Video Solutions with Answers

2004
1. Consider the network graph shown in figure. Which one of the following is NOT a ‘tree’ of this group?

Solution: https://www.youtube.com/watch?v=xjHxZjJq8PI

2. The equivalent inductance measured between the terminals 1 and 2 for the circuit shown in figure, is

a) L₁ + L₂ + M
b) L₁ + L₂ - M
c) L₁ + L₂ + 2M
d) L₁ + L₂ - 2M

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

3. The circuit shown in figure, has R = 1/3 Ω, L = 1/4 H, C = 3 F has input voltage v(t) = sin2t. The resulting current i(t) is

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

4. For the circuit shown, the time constant RC = 1 ms. The input voltage is v_i(t) = √2 sin10³t. The output voltage v_o(t) is equal to

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

5. For the R-L circuit shown, the input voltage v_i(t) = u(t). The current i(t) is

Solution: https://www.youtube.com/watch?v=OFlCLWEvc2U

6. For the lattice circuit shown in figure, Z_a = j2Ω and Z_b = 2Ω. The values of the open circuit impedance parameters (Z-parameters) are

Solution: https://www.youtube.com/watch?v=Vn-O5Ll3CwU

7. The circuit shown in figure has initial current i_L(0^-) = 1 A through the inductor and an initial voltage V_c(0^-) = - 1 volt across the capacitor. For input v(t) = u(t), the Laplace transform of the current i(t) for t ≥ 0 is

Solution: https://www.youtube.com/watch?v=Xa5N6PQTPLs

8. Consider the following statements S1 and S2
S1: at the resonant frequency, the impedance of a series RLC circuit is zero.
S2: In a parallel G-L-C circuit, increasing the conductance G results in increase in its Q-factor.
Which one of the following is correct?
a) S1 is FALSE and S2 is TRUE
b) Both S1 and S2 are TRUE
c) S1 is TRUE and S2 is FALSE
d) Both S1 and S2 are FALSE

Solution: https://www.youtube.com/watch?v=s3hM-idhg2s

GATE 2004 ECE Control Systems - Complete Video Solutions with Answers

GATE 2004

1. The gain margin for the system with open loop transfer function G(s)H(s) = 2(1 + s)/s², is

a) ∞

b) 0

c) 1

d) - ∞

Solution : https://www.youtube.com/watch?v=L2Y_rS_Zc9M

2. Given G(s)H(s) = K /[s(s + 1)(s + 3)], the point of intersection of the asymptotes of the root loci with the real axis is

a) - 4

b) 1.33

c) - 1.33

d) 4

Solution : https://www.youtube.com/watch?v=1eQ1YNdEF_4

3. Consider the Bode magnitude plot shown in figure. The transfer function H(s) is

Solution : https://www.youtube.com/watch?v=0K0Ls-_nRDQ

4. The transfer function H(s) of an RLC circuit is given as 10⁶/[s²+20s+10⁶], then the Q – factor of this circuit is

a) 25

b) 50

c) 100

d) 5000

Solution : https://www.youtube.com/watch?v=uyZ1HtXU6Ow

5. For the circuit shown in figure, the initial conditions are zero. Its transfer function V_o(t)/V_i(t) is

Solution : https://www.youtube.com/watch?v=JKzEzWRjN4Q

6. A system has poles at 0.01 Hz, 1 Hz and 80 Hz; zeros at 5 Hz, 100 Hz and 200 Hz. The approximate phase of the system response at 20 Hz is

a) - 90^o

b) 0^o

c) 90^o

d) - 180^o

Solution : https://www.youtube.com/watch?v=8SWwr0wlV0E

7. Consider the signal flow graph shown in figure. The gain X₅/X₁ is

Solution : https://www.youtube.com/watch?v=e6XPNiFMSGo

8. The open loop transfer function of a unity feedback system is G(s) = K/[s(s²+ s + 2)(s + 3)]. The range of K for which the system is stable is

a) 21/44 > K > 0

b) 13 > K > 0

c) 21/4 < K < ∞

d) - 6 < K < ∞

Solution : https://www.youtube.com/watch?v=KmUOC_i7USs

9. for the polynomial R(s) = s⁵ + s⁴ + 2s³ + 2s² + 3s + 15, the number of roots which lie in the Right Half of the S-plane is

a) 4

b) 2

c) 3

d) 1

Solution : https://www.youtube.com/watch?v=P_CSEbYpX0s

10. The state variable equations of a system are:

ẋ₁ = -3x₁ -x₂ + u

ẋ₂ = 2x₁

y = x₁ + u

Then the system is

a) controllable but not observable

b) observable but not controllable

c) neither controllable nor observable

d) controllable and observable

Solution : https://www.youtube.com/watch?v=CVH0VsecVuQ

11. The state transition matrix e^At for the given matrix A, is

Solution : https://www.youtube.com/watch?v=w9zVGFsZ3Bw

GATE 2004 ECE Video Solutions on Analog Circuits (Analog Electronics)

1. An ideal OP-AMP is an ideal
a. Voltage Controlled Current Source
b. Voltage Controlled Voltage Source
c. Current Controlled Current Source
d. Current Controlled Voltage Source

Solution: https://www.youtube.com/watch?v=-3pE3zjlc-I

2. Voltage series feedback (also called series-shunt feedback) results in
a. Increase in both input and output impedances
b. Decrease in both input and output impedances
c. Increase in input impedance and decrease in output impedance
d. Decrease in input impedance and increase in output impedance

Solution: https://www.youtube.com/watch?v=W1PMTIiCpuU

3. The circuit in the figure is a

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

Solution: https://www.youtube.com/watch?v=hUwaNK0aINo

4. A bipolar transistor is operating in the active region with a collector current of 1 mA. Assuming that the β of the transistor is 100 and the thermal voltage (V_T) is 25 mV. The Transconductance (g_m) and the input resistance (r_π) of the transistor in the common emitter configuration are
a. g_m = 25 mA/V and r_π = 15.625 KΩ
b. g_m = 40 mA/V and r_π = 4.0 KΩ
c. g_m = 25 mA/V and r_π = 2.5 KΩ
d. g_m = 40 mA/V and r_π = 2.5 KΩ

Solution: https://www.youtube.com/watch?v=cK0KRkqCWVw

5. the value of capacitor C required for sinusoidal oscillations of frequency 1 kHz in the circuit of the figure is

Solution: https://www.youtube.com/watch?v=dcCpebp-_Cs

6. in the OP-AMP circuit given in the figure, the load current i_L is

a. – V_S / R₂
b. V_S / R₂
c. – V_S / R_L
d. V_S / R₁

Solution: https://www.youtube.com/watch?v=TxVYCU-8ejQ

7. In the full wave rectifier using two ideal diodes, V_dc and V_m are the dc and peak values of the voltage respectively across a resistive load. If PIV is the peak inverse voltage of the diode, then the appropriate relationships for this rectifier are

Solution: https://www.youtube.com/watch?v=bN5s61Q90RE

GATE 2004 ECE Video Solution on Digital Circuits (Digital Electronics)

1. A Master – Slave flip flop has the characteristic that
a. Change in the input immediately reflected in the output.
b. Change in the output occurs when the state of the master is affected
c. Change in the output occurs when the state of the slave is affected
d. Both the master and the slave states are affected at the same time.

Solution : https://www.youtube.com/watch?v=oViyDQttV2E

2. The range of signed decimal numbers that can be represented by 6 bit 1’s complement form is
a. -31 to +31
b. -63 to +64
c. -64 to +63
d. -32 to +31

Solution : https://www.youtube.com/watch?v=0mvda9-_j6Y

3. A digital system is required to amplify a binary encoded audio signal. The user should be able to control the gain of the amplifier from a minimum to a maximum in 100 increments. The minimum number of bits required to encode in straight binary is
a. 8
b. 6
c. 5
d. 7

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

4. Choose the correct one from among the alternatives A,B,C,D after matching an item from Group 1 with the most appropriate item in Group 2.

Group 1	Group 2
P: Shift Register	1: Frequency division
Q: Counter	2: Addressing in memory chips
R: Decoder	3: Serial to Parallel data conversion

a. P – 3, Q – 2, R – 1
b. P – 3, Q – 1, R – 2
c. P – 2, Q – 1, R – 3
d. P – 1, Q – 2, R – 2

Solution : https://www.youtube.com/watch?v=2d-9lEnp3x8

5. Figure given below shows the internal schematic of a TTL AND-OR-Invert (AOI) gate. For the inputs shown in the given figure, the output Y is

Solution : https://www.youtube.com/watch?v=Qh1KCgKrp0Q

6. The minimum number of 2 to 1 multiplexers required to realize a 4 to 1 multiplexer is
a. 1
b. 2
c. 3
d. 4

Solution : https://www.youtube.com/watch?v=vq8UAnVdqzA

7. The Boolean expression AC + BC’ is equivalent to

Solution : https://www.youtube.com/watch?v=ln-baJRcMlY

8. 11001, 1001 and 111001 correspond to the 2’s complement representation of which one of the following sets of number?
a. 25, 9 and 57 respectively
b. -6, -6 and -6 respectively
c. -7, -7 and -7 respectively
d. -25, -9 and -57 respectively

Solution : https://www.youtube.com/watch?v=prvoIVvnID4

9. The 8255 programmable peripheral interface is used as described below.
(i) An A/D converter is interfaced to a microprocessor through an 8255. The conversion is initiated by a signal from the 8255 on port C. A signal on port C. A signal on port C causes data to be strobed into port A.
(ii) Two computers exchange data using a pair of 8255s. Port A works as a bidirectional data port supported by appropriate handshaking signals.
The appropriate modes of operation of the 8255 for (i) and (ii) would be
a. Mode 0 for (i) and Mode 1 for (ii)
b. Mode 1 for (i) and Mode 0 for (ii)
c. Mode 2 for (i) and Mode 0 for (ii)
d. Mode 2 for (i) and Mode 1 for (ii)
Answer:
Solution :

10. The number of memory cycles required to execute the following 8085 instructions
(i) LDA 3000H
(ii) LXI D, F0F1H
Would be
a. 2 for (i) and 2 for (ii)
b. 4 for (i) and 3 for (ii)
c. 3 for (i) and 3 for (ii)
d. 3 for (i) and 4 for (ii)
Answer:
Solution :

11. In the modulo – 6 ripple counter shown in the given figure, the output of the 2 input gate is used to clear the JK flip flops.

The 2 input gate is
a. NAND gate
b. NOR gate
c. OR gate
d. AND gate

Solution : https://www.youtube.com/watch?v=2b1wBH220Oo

12. Consider the sequence of 8085 instructions given below.
LXI H, 9258H
MOV A, M
CMA
MOV M, A
Which one of the following is performed by this sequence of instructions?
a. Contents of location 9258 are moved to the accumulator
b. Contents of location 9258 are compared with the contents of the accumulator
c. Contents of location 9258 are complemented and stored in location 9258
d. Contents of location 5892 are complemented and stored in location 5892.

Solution : https://www.youtube.com/watch?v=Us-RGGYexA8

13. A Boolean function f of two variables x and y is defined as follows:
f(0,0) = f(0,1) = f(1,0) = 1; and f(1,0) = 0
Assuming complements of x and y are not available, a minimum cost solution for realizing f using only 2 input NOR gates and 2 input OR gates (each having unit cost) would have a total cost of
a. 1 unit
b. 4 units
c. 3 unit
d. 2 units

Solution : https://www.youtube.com/watch?v=iE50qMj8NR8

14. It is desired to multiply the numbers 0AH by 0BH and store the result in the accumulator. The numbers are available in registers B and C respectively. A part of the 8085 program for this purpose is given below:
MVI A, 00H
LOOP: ..............
..............
..............
HLT
END
The sequence of instructions to complete the program would be
a. JNZ LOOP, ADD B, DCR C
b. ADDB, JNZ LOOP, DCR C
c. DCR C, JNZ LOOP, ADD B
d. ADD B, DCR C, JNZ LOOP

Solution : https://www.youtube.com/watch?v=gdjv_EzqPB0

GATE 2004 ECE Video Solutions on EDC (Electronic Devices and Circuits)

1. The impurity commonly used for realizing the base region of a silicon NPN transistor is
a. Gallium
b. Indium
c. Boron
d. Phosphorous

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

2. If for a silicon NPN transistor, the base to emitter voltage (V_BE) is 0.7 volts and collector to base voltage (V_CB) is 0.2 volts, then the transistor is operating in the
a. Normal active mode
b. Saturation mode
c. Inverse active mode
d. Cutoff mode

Solution : https://www.youtube.com/watch?v=EWiTi5LriHE

3. Consider the following statements S₁ and S₂.
S₁: the β of a BJT reduces if the base width is increased
S₂: the β of a BJT increases if the doping concentration in the base is increased
Which of the following is correct?
a. S₁ is FALSE and S₂ is TRUE
b. Both S₁ and S₂ are TRUE
c. Both S₁ and S₂ are FALSE
d. S₁ is TRUE and S₂ is FALSE

Solution : https://www.youtube.com/watch?v=91xuzfdvnqk

4. Assuming V_CEsat = 0.2 volts and β = 50, the minimum base current (I_Bmin) required to drive the transistor in figure to saturation is

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

5. The given figure is the voltage transfer characteristic of

Solution : https://www.youtube.com/watch?v=lPY4XzAWeSg

6. In abrupt PN junction, the doping concentrations on the P side and N side are N_A = 9 x 10¹⁶ cm^-3 and N_D = 1 x 10¹⁶ cm^-3 respectively. The PN junction is reverse biased and the total depletion width is 3 µm. The depletion width on the P side is
a. 2.7 µm
b. 0.3 µm
c. 2.25 µm
d. 0.75 µm

Solution : https://www.youtube.com/watch?v=XyzrofQ1DsI

7. The resistivity of a uniformly doped N type silicon sample is 0.5 Ω-cm. If the electron mobility (µ_n) is 1250 cm²/V-sec and the charge of an electron is 1.6 x 10^-19 coulomb, then the donor impurity concentration (N_D) in the sample is
a. 2 x 10¹⁶ / cm³
b. 1 x 10¹⁶ / cm³
c. 2.5 x 10¹⁵ / cm³
d. 2 x 10¹⁵ / cm³

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

8. Consider an abrupt PN junction. Let V_bi be the built in potential of this junction and V_R be the applied reverse bias. If the junction capacitance (C_J) is 1 pF for V_bi + V_R = 1 volt, then for V_bi + V_R = 4 volts, the value of C_J will be
a. 4 pF
b. 2 pF
c. 0.25 pF
d. 0.75 pF

Solution : https://www.youtube.com/watch?v=3jTOs2F7oHA

9. Consider the following statements S₁ and S₂.
S₁: the threshold voltage (V_T) of a MOS capacitor decreases with increase in gate oxide thickness
S₂: the threshold voltage (V_T) of a MOS capacitor decreases with increase in substrate doping concentration.
Which of the following is correct?
a. S₁ is FALSE and S₂ is TRUE
b. Both S₁ and S₂ are TRUE
c. S₁ is TRUE and S₂ is FALSE
d. Both S₁ and S₂ are FALSE

Solution : https://www.youtube.com/watch?v=jmKFRCr0xa0

10. The drain of an N channel MOSFET is shorted to the gate so that V_GS = V_DS. The threshold voltage (V_T) of MOSFET is 1 volt. If the drain current (I_D) is 1 mA for V_GS = 2 volts, then for V_GS = 3 volts, I_D is
a. 2 mA
b. 3 mA
c. 9 mA
d. 4 mA

Solution : https://www.youtube.com/watch?v=F1cZOGLgZIA

11. The longest wavelength that can be absorbed by silicon, which has the band gap of 1.12 eV is 1.1 µm. If the longest wavelength that can be absorbed by another material is 0.87 µm, then the band gap of this material is
a. 1.416 eV
b. 0.886 eV
c. 0.854 eV
d. 0.706 eV

Solution : https://www.youtube.com/watch?v=wlIK6u3cSrE

12. The neutral base width of a bipolar transistor biased in the active region is 0.5 µm. The maximum electron concentration and the diffusion constant in the base are 10¹⁴ cm^-3 and D_n = 25 cm²/sec respectively. Assuming negligible recombination in the base, the collector current density is
a. 800 A/cm²
b. 8 A/cm²
c. 200 A/cm²
d. 2 A/cm²

Solution : https://www.youtube.com/watch?v=y5ivXtuocFU

13. Assuming that the β of the transistor is extremely large and V_BE = 0.7 volts, I_C and V_CE in the circuit shown are

Solution : https://www.youtube.com/watch?v=ETrg3InTVmY

14. In the voltage regulator shown, the load current can vary from 100 mA to 500 mA. Assuming that the zener diode is ideal (i.e. the zener knee current is negligibly small and zener resistance is zero in the breakdown region), the value of R is

Solution : https://www.youtube.com/watch?v=ow6gYqOD3_w

GATE 2004 ECE Network Theory - Complete Video Solutions with Answers

GATE 2004 ECE Control Systems - Complete Video Solutions with Answers

GATE 2004 ECE Video Solutions on Analog Circuits (Analog Electronics)

GATE 2004 ECE Video Solution on Digital Circuits (Digital Electronics)

GATE 2004 ECE Video Solutions on EDC (Electronic Devices and Circuits)

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