GATE EE 2005
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GATE EE

1
Consider the inverting amplifier, using an ideal operational amplifier shown in figure. The designer wishes to realize the input resistance seen by the small signal source to be as large as possible, while keeping the voltage gain between $$–10$$ and $$–25.$$ the upper limit on $${R_F}$$ is $$1\,M\Omega .$$ The value of $${R_1}$$ should be GATE EE 2005 Analog Electronics - Operational Amplifier Question 32 English
2
Assume that the threshold voltage of the $$N$$-channel $$MOSFET$$ shown in figure is $$0.75$$ $$V.$$ The output characteristics of the $$MOSFET$$ are also shown GATE EE 2005 Analog Electronics - Bjt and Mosfet Biasing Question 5 English 1 GATE EE 2005 Analog Electronics - Bjt and Mosfet Biasing Question 5 English 2

The Transconductance of the $$MOSFET$$ is

3
Assume that the threshold voltage of the $$N$$-channel $$MOSFET$$ shown in figure is $$0.75$$ $$V.$$ The output characteristics of the $$MOSFET$$ are also shown GATE EE 2005 Analog Electronics - Bjt and Mosfet Biasing Question 4 English 1 GATE EE 2005 Analog Electronics - Bjt and Mosfet Biasing Question 4 English 2

The voltage gain of the amplifier is

4
The common emitter amplifier shown in the figure is biased using a $$1mA$$ ideal current source. The approximate base current value is_____. GATE EE 2005 Analog Electronics - Bjt and Mosfet Biasing Question 16 English
5
Assume that the $$N$$-channel $$MOSFET$$ shown in figure is ideal, and that its threshold voltage is The voltage $${\rm I}V,$$ the voltage $${{V_{ab}}}$$ between nodes $$'a'$$ and $$'b'$$ is GATE EE 2005 Analog Electronics - Bjt and Mosfet Biasing Question 29 English
6
The typical frequency response of a two-stage direct coupled voltage amplifier is as shown in figure
7
In the given figure, if the input is a sinusoidal signal, the output-will appear as shown GATE EE 2005 Analog Electronics - Operational Amplifier Question 31 English 1 GATE EE 2005 Analog Electronics - Operational Amplifier Question 31 English 2
8
Assume that $${D_1}$$ and $${D_2}$$ in figure are ideal diodes the value of current $${I_s}$$ is GATE EE 2005 Analog Electronics - Diode Circuits and Applications Question 27 English
9
In the $$GH(s)$$ plane, the Nyquist plot of the loop transfer function $$G\left( s \right)\,H\left( s \right) = {{\pi {e^{ - 0.25s}}} \over s}$$ passes through the negative real axis at the point
10
A state variable system
$$\mathop X\limits^ \bullet \left( t \right) = \left( {\matrix{ 0 & 1 \cr 0 & { - 3} \cr } } \right)X\left( t \right) + \left( {\matrix{ 1 \cr 0 \cr } } \right)u\left( t \right)$$ with the initial condition $$X\left( 0 \right) = {\left[ { - 1\,\,3} \right]^T}$$ and the unit step input $$u(t)$$ has

The state transition equation

11
A state variable system
$$\mathop X\limits^ \bullet \left( t \right) = \left( {\matrix{ 0 & 1 \cr 0 & { - 3} \cr } } \right)X\left( t \right) + \left( {\matrix{ 1 \cr 0 \cr } } \right)u\left( t \right)$$ with the initial condition $$X\left( 0 \right) = {\left[ { - 1\,\,3} \right]^T}$$ and the unit step input $$u(t)$$ has

The state transition matrix

12
If the compensated system shown in the figure has a phase margin of $${60^ \circ }$$ at the crossover frequency of $$1 rad/sec,$$ the value of the gain $$K$$ is GATE EE 2005 Control Systems - Polar Nyquist and Bode Plot Question 28 English
13
The gain margin of a unity feedback control system with the open loop transfer function $$G\left( s \right) = {{\left( {s + 1} \right)} \over {{s^2}}}$$ is
14
A system with zero initial conditions has the closed loop transfer function $$T\left( s \right) = {{{s^2} + 4} \over {\left( {s + 1} \right)\left( {s + 4} \right)}}.$$ The system output is zero at the frequency
15
When subjected to a unit step input, the closed loop control system shown in the figure will have a steady state error of GATE EE 2005 Control Systems - Time Response Analysis Question 7 English
16
Figure shows the root locus plot (location of poles not given) of a third order system whose open loop transfer function is GATE EE 2005 Control Systems - Root Locus Techniques Question 15 English
17
When subjected to a unit step input, the closed loop control system shown in the figure will have a steady state error of GATE EE 2005 Control Systems - Time Response Analysis Question 17 English
18
The $$8085$$ assembly language instruction that stores the content of $$H$$ and $$L$$ registers into the memory locations $$2050H$$ and $$2051H,$$ respectively, is
19
A digital-to-analog converter with a full -scale output voltage of $$3.5$$ $$V$$ has a resolution close to $$14$$ $$m$$ $$V.$$ Its bit size is
20
If $${X_1}$$ and $${X_2}$$ are the inputs to the circuit shown in the figure, the output $$Q$$ is GATE EE 2005 Digital Electronics - Logic Families and Memories Question 3 English
21
Select the circuit which will produce the given output $$Q$$ for the input signals $${X_1}$$ and $${X_2}$$ given in the figure. GATE EE 2005 Digital Electronics - Sequential Circuits Question 16 English
22
The digital circuit shown in the figure works as a GATE EE 2005 Digital Electronics - Sequential Circuits Question 17 English
23
In the figure, as long as $${X_1} = 1$$ and $${X_2} = 1,$$ the output $$Q$$ remains GATE EE 2005 Digital Electronics - Logic Gates Question 5 English
24
In the figure given below the value of $$R$$ is GATE EE 2005 Electric Circuits - Network Elements Question 29 English
25
Two networks are connected in cascade as shown in the Fig. With the usual notations the equivalent $$A,B,C$$ and $$D$$ constants are obtained. Given that, $$C$$ $$ = 0.025\angle {45^ \circ },$$ the value of $${Z_2}$$ is GATE EE 2005 Electric Circuits - Two Port Networks Question 4 English
26
For the two port network shown in the Fig. the $$Z$$ $$-$$ matrix is given by GATE EE 2005 Electric Circuits - Two Port Networks Question 10 English
27
The $$RL$$ circuit of the figure is fed from a constant magnitude, variable frequency sinusoidal voltage source $${V_{IN.}}$$ At $$100Hz,$$ the $$R$$ and $$L$$ elements each have a voltage drop $${u_{RMS}}.$$ If the frequency of the source is changed to $$50Hz,$$ then new voltage drop across $$R$$ is GATE EE 2005 Electric Circuits - Sinusoidal Steady State Analysis Question 14 English
28
A coil of inductance $$10$$ $$H$$ resistance $$40\,\,\Omega $$ is connected as shown in Fig. After the switch $$S$$ has been in connection with point $$1$$ for a very long time, it is moved to point $$2$$ at $$t = 0.$$

For the value of $$R$$ obtained in the above question, the time taken for $$95\% $$ of the stored energy to be dissipated is close to

29
The circuit shown in the Fig. is in steady state, when the switch is closed at $$t=0.$$ Assuming that the inductance is ideal, the current through the inductor at $$t = {0^ + }$$ equals GATE EE 2005 Electric Circuits - Transient Response Question 20 English
30
A coil of inductance $$10$$ $$H$$ resistance $$40\,\,\Omega $$ is connected as shown in Fig. After the switch $$S$$ has been in connection with point $$1$$ for a very long time, it is moved to point $$2$$ at $$t = 0.$$

If, at $$t = {0^ + }$$, the voltage across the coil is $$120$$ $$V,$$ the value of resistance $$R$$ is

GATE EE 2005 Electric Circuits - Transient Response Question 19 English
31
In the Fig. given below, the initial capacitor voltage is zero. The switch is closed at $$t = 0.$$ the final steady-state voltage across the capacitor is GATE EE 2005 Electric Circuits - Transient Response Question 26 English
32
In the given Fig. the Thevenin's equivalent pair (voltage, impedence), as seen at the terminals $$P-Q$$, is given by GATE EE 2005 Electric Circuits - Network Theorems Question 16 English
33
A digital-to-analog converter with a full scale output voltage of $$3.5V$$ has resolution close to $$14mV.$$ It's bit size is _____.
34
The simultaneous application of signals $$x(t)$$ and $$y(t)$$ to the horizontal and vertical plates, respectively, of an oscilloscope, produces a vertical figure-of-$$8$$ display. If $$P$$ and $$Q$$ are constants, and $$x(t)=P$$ $$sin(4t+30),$$ then $$y(t)$$ is equal to
35
A $$PMMC$$ voltmeter is connected across a series combination of a $$DC$$ voltage source $${V_1} = 2V$$ and $$AC$$ voltage source $${V_2}\left( t \right) = 3$$ $$sin(4t)$$ $$V.$$ The meter reads GATE EE 2005 Electrical and Electronics Measurement - Basic of Indicating Instruments Question 3 English
36
Two wattmeter's, which are connected to measure the total power on a three-phase system supplying a balanced load, read $$10.5$$ $$kW$$ and $$–2.5$$ $$kW$$ respectively. The total power and the power factor respectively are
37
A DC ammeter has a resistance of $$0.1$$$$\Omega $$ and its current range is $$0$$ – $$100A.$$ If the range is to be extended to $$0$$ –$$500A,$$ the meter requires the following shunt resistance
38
A $$1000$$ $$V$$ $$DC$$ supply has two $$1-core$$ cables as its positive and negative leads: their insulation resistances to earth are $$4\,\,M\Omega $$ and $$6\,\,M\Omega $$, respectively, as shown in figure. A voltmeter with resistance $$50\,\,k\Omega $$ is used to measure the insulation of the cable. When connected between the positive core and earth, the voltmeter reads GATE EE 2005 Electrical and Electronics Measurement - Basic of Indicating Instruments Question 15 English
39
The set-up in the figure is used to measure resistance $$R$$. The ammeter and voltmeter resistances are $$0.01$$$$\Omega $$ and $$2000$$$$\Omega $$, respectively. Their readings are $$2A$$ and $$180$$ $$V$$, respectively, giving a measured resistance of $$90$$ $$\Omega $$. The percentage error in the measurement is GATE EE 2005 Electrical and Electronics Measurement - Error Analysis and Measurement Question 3 English
40
A $$1000$$ $$kVA,$$ $$6.6$$ $$kV,$$ $$3$$-phase star connected cylindrical pole synchronous generator has a synchronous reactance of $$20\Omega .$$ Neglect the armature resistance and consider operation at full load and unity power factor.

The power angle is close to

41
A $$1000$$ $$kVA,$$ $$6.6$$ $$kV,$$ $$3$$-phase star connected cylindrical pole synchronous generator has a synchronous reactance of $$20\Omega .$$ Neglect the armature resistance and consider operation at full load and unity power factor.

The induced $$emf$$ is close to (line to line)

42
On the torque/speed curve of induction motor shown in Fig, four points of operation are market as W, X, Y and Z. Which one of them represents the operation at a slip greater than 1? GATE EE 2005 Electrical Machines - Induction Machines Question 67 English
43
In relation to the synchronous machines, which one of the following statements is false?
44
In a single phase induction motor driving a fan load, the reason for having a high resistance rotor is to achieve
45

Assertion [a]: Under V/f control of induction motor, the maximum value of the developed torque remains constant over a wide range of speed in the subsynchronous region.

Reason [r]: The magnetic flux is maintained almost constant at the rated value by keeping the ratio V/f constant over the considered speed range.

46
A three-phase cage induction motor is started by direct-on-line (DOL) switching at the rated voltage. If the starting current drawn is 6 times the full load current, and the full load slip is 4%, the ratio of the starting developed torque to the full load torque is approximately equal to
47
Under no load condition, if the applied voltage to an induction motor is reduced from the rated voltage to half the rated value,
48
For an induction motor, operating at a slip 's', the ratio of gross power output to air gap power is equal to:
49
Which three-phase connection can be used in a transformer to introduce a phase difference of 30° between its output and corresponding input line voltages
50
A 50 kW dc shunt motor is loaded to draw rated armature current at any given speed. When driven
(i) at half the rated speed by armature voltage control and
(ii) at 1.5 times the rated speed by field control, the respective output powers delivered by the motor are approximately
51
In relation to DC machines, match the following and choose the correct combination.

Group-I(Performance variables)
(P) Armature emf (E)
(Q) Developed torque (T)
(R) Developed power (P)

Group-II(Proportional to)
1.Flux ($$\phi$$), speed ($$\omega$$) and armature current ($$I_a$$)
2.$$\phi$$ and $$\omega$$ only
3.$$\phi$$ and $$I_a$$ only
4.$$I_a$$ and $$\omega$$ only
5.$$I_a$$ only

52
Two magnetic poles revolve around a stationary armature carrying two coils ($$c_1-c'_1$$ , $$c_2-c'_2$$ ) as shown in Figure. Consider the instant when the poles are in a position as shown. Identify the correct statement regarding the polarity of the induced emf at this instant in coil sides $$c_2$$ and $$c_1$$. GATE EE 2005 Electrical Machines - D.C Machines Question 60 English
53
If $$S = \int\limits_1^\infty {{x^{ - 3}}dx} $$ then $$S$$ has the value
54
For the function $$f\left( x \right) = {x^2}{e^{ - x}},$$ the maximum occurs when $$x$$ is equal to
55
If $$R = \left[ {\matrix{ 1 & 0 & { - 1} \cr 2 & 1 & { - 1} \cr 2 & 3 & 2 \cr } } \right]$$ then the top row of $${R^{ - 1}}$$ is
56
For the matrix $$P = \left[ {\matrix{ 3 & { - 2} & 2 \cr 0 & { - 2} & 1 \cr 0 & 0 & 1 \cr } } \right],$$ one of the eigen values is $$-2.$$ Which of the following is an eigen vector?
57
In the matrix equation $$PX=Q$$ which of the following is a necessary condition for the existence of atleast one solution for the unknown vector $$X.$$
58
for the scalar field $$u = {{{x^2}} \over 2} + {{{y^2}} \over 3},\,\,$$ the magnitude of the gradient at the point $$(1,3)$$ is
59
For the equation $$\,\,\mathop x\limits^{ \bullet \bullet } \left( t \right) + 3\mathop x\limits^ \bullet \left( t \right) + 2x\left( t \right) = 5,\,\,\,$$ the solution $$x(t)$$ approaches the following values as $$t \to \infty $$
60
The solution of the first order differential equation $$\mathop x\limits^ \bullet \left( t \right) = - 3\,x\left( t \right),\,x\left( 0 \right) = {x_0}\,\,\,\,$$ is
61
If $$P$$ and $$Q$$ are two random events, then which of the following is true?
62
A fair coin is tossed $$3$$ times in succession. If the first toss produces a head, then the probability of getting exactly two heads in three tosses is
63
The output voltage waveform of a three - phase square-wave inverter contains
64
The given figure shows a step $$-$$ down chopper switched at $$1$$ $$KHz$$ with a duty ratio $$D = 0.5.$$ The peak - peak ripple in the load current is close to GATE EE 2005 Power Electronics - Choppers and Commutation Techniques Question 30 English
65
Consider a phase $$-$$ controlled converter shown in figure The thyristor is fired at an angle $$\alpha $$ in every positive half cycle of the input voltage. If the peak value of the instantaneous output voltage equals $$230$$ $$V,$$ the firing angle $$\alpha $$ is close to GATE EE 2005 Power Electronics - Single and Three Phase Rectifier Question 37 English
66
A three - phase diode bridge rectifier is fed from a $$400$$ $$V$$ $$RMS$$. $$50$$ $$Hz$$, three $$-$$ phase $$AC$$ source. If the load is purely resistive, then peak instantaneous output voltage is equal to
67
An electronic switch $$S$$ is required to block voltages of either polarity during its OFF state as shown in figure (a). This switch is required to conduct in only one direction during its ON state as shown in the figure (b). GATE EE 2005 Power Electronics - Power Semiconductor Devices Question 11 English 1

Which of the following are valid realizations of the switch $$s$$?

GATE EE 2005 Power Electronics - Power Semiconductor Devices Question 11 English 2
68
The figure shows the voltage across a power semiconductor device and the current through the device during a switching transition. Is the transition a turn ON transition or a turn OFF transition? What is the energy lost during the transition? GATE EE 2005 Power Electronics - Power Semiconductor Devices Question 12 English
69
The conduction loss versus device current characteristic of a power $$MOSFET$$ is best approximated by
70
The parameters of transposed overhead transmission line are given as: self reactance $${X_s} = 0.4\,\,\Omega /km$$ and Mutual reactance $$\,{X_m} = 0.1\,\,\Omega /km.\,\,$$ The positive sequence reactance $${X_1}$$ and zero sequence reactance $${X_0}$$ respectively in $$\Omega /km$$ are
71
The p.u. parameters for a $$500$$ MVA machine on its own base are:
Inertia, M = $$20$$ p.u.; reactance X = $$2$$ p.u. The p.u. values of inertia and reactance on $$100$$ MVA common base, respectively are
72
High Voltage DC (HVDC) transmission is mainly used for
73
The network shown in the given figure has impedances in p.u. as indicated. The diagonal element $$Y22$$ of the bus admittance matrix $${Y_{BUS}}$$ of the network is GATE EE 2005 Power System Analysis - Load Flow Studies Question 17 English
74
At a $$220$$ kV substation of a power system, it is given that the three-phase fault level is $$4000$$ MVA and single-line to ground fault level is $$5000$$ MVA. Neglecting the resistance and the shunt susceptances of the system.

The zero sequence driving point reactance at the bus is

75
At a $$220$$ kV substation of a power system, it is given that the three-phase fault level is $$4000$$ MVA and single-line to ground fault level is $$5000$$ MVA. Neglecting the resistance and the shunt susceptances of the system.

The positive sequence driving point reactance at the bus is

76
A generator with constant 1.0 p.u. terminal voltage supplies power through a step-up transformer of 0.12 p.u. reactance and a double-circuit line to an infinite bus bar as shown in the figure. The infinite bus voltage is maintained at 1.0 p.u. Neglecting the resistances and susceptances of the system, the steady state stability power limit of the system is 6.25 p.u. If one of the double-circuit is tripped, the resulting steady state stability power limit in p.u. will be GATE EE 2005 Power System Analysis - Power System Stability Question 22 English
77
A load centre is at an equidistant from the two thermal generating stations $${G_1}$$ and $${G_2}$$ as shown in figure. The fuel cost characteristics of the generating stations are given by
$${F_1} = a + b{P_1} + cP_1^2\,Rs/hour$$
$${F_2} = a + b{P_2} + 2cP_2^2\,Rs/hour$$ GATE EE 2005 Power System Analysis - Power Generation Cost Question 12 English

Where $${P_1}$$ and $${P_2}$$ are the generations in $$MW$$ of $${G_1}$$and $${G_2}$$, respectively. For most economic generation to meet $$300MW$$ of load $${P_1}$$ and $${P_2},$$ respectively, are

78
At an industrial sub-station with a $$4$$ $$MW$$ load, a capacitor of $$2$$ MVAR is installed to maintain the load power factor at $$0.97$$ lagging. If the capacitor goes out of service, the load power factor becomes
79
The insulation strength of an EHV transmission line is mainly governed by
80
For the triangular waveform shown in the figure, the $$RMS$$ value of the voltage is equal to GATE EE 2005 Signals and Systems - Continuous Time Periodic Signal Fourier Series Question 7 English
81
If u(k) is the unit step and $$\delta\left(k\right)$$ is the unit impulse function, the inverse z-transform of $$F\left(z\right)=\frac1{z+1}$$ for k>0 is:
82
For the equation $$\ddot x\left(t\right)+3\dot x\left(t\right)+2x\left(t\right)=5$$, the solution x(t) approaches which of the following values as t$$\rightarrow\infty$$ ?
83
The Laplace transform of a function f(t) is F(s) = $$\frac{5s^2+23s+6}{s\left(s^2+2s+2\right)}$$. As $$t\rightarrow\infty$$, f(t) approaches
84
The Fourier series for the function f(x) = sin2 x is
85
The RMS value of the voltage v(t) = 3 + 4cos(3t) is
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