GATE EE 2006
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GATE EE

1
A relaxation oscillator is made using op-amp as shown in figure. The supply Voltage of the op-amp are $$ \pm 12$$ the voltage waveform at point $$'p'$$ will be GATE EE 2006 Analog Electronics - Operational Amplifier Question 30 English
2
Consider the circuit shown in figure. If the $$\beta $$ of the transistor is $$30$$ and $${{\rm I}_{CBO}}$$ is $$20$$ $$nA$$ and the input voltage is $$5V$$ then the transistor would be operating in GATE EE 2006 Analog Electronics - Bjt and Mosfet Biasing Question 3 English
3
For given sinusoidal input voltage, the voltage waveform at point $$P$$ of the clamper circuit shown in figure will be GATE EE 2006 Analog Electronics - Operational Amplifier Question 46 English 1 GATE EE 2006 Analog Electronics - Operational Amplifier Question 46 English 2
4
Assuming the diodes $${D_1}$$ and $${D_2}$$ of the circuit shown in the figure to be ideal ones, the transfer characteristics of the circuit will be GATE EE 2006 Analog Electronics - Diode Circuits and Applications Question 7 English
5
What are the states of the three ideal diodes of the circuit shown in figure? GATE EE 2006 Analog Electronics - Diode Circuits and Applications Question 11 English
6
For a system with the transfer function $$H\left( s \right) = {{3\left( {s - 2} \right)} \over {{s^3} + 4{s^2} - 2s + 1}},\,\,$$ the matrix $$A$$ in the state space form $$\mathop X\limits^ \bullet = AX + BU$$ is equal to
7
Consider the following Nyquist plots of loop transfer functions over $$\omega = 0$$ to $$\omega = \infty .$$ Which of these plots represents a stable closed loop system? GATE EE 2006 Control Systems - Polar Nyquist and Bode Plot Question 11 English 1 GATE EE 2006 Control Systems - Polar Nyquist and Bode Plot Question 11 English 2 GATE EE 2006 Control Systems - Polar Nyquist and Bode Plot Question 11 English 3 GATE EE 2006 Control Systems - Polar Nyquist and Bode Plot Question 11 English 4
8
The Bode magnitude plot of $$H\left( {j\omega } \right) = {{{{10}^4}\left( {1 + j\,\omega } \right)} \over {\left( {10 + j\,\omega } \right){{\left( {100 + j\omega } \right)}^2}}}$$ is
9
A closed loop system has the characteristic function $$\left( {{s^2} - 4} \right)\left( {s + 1} \right) + K\left( {s - 1} \right) = 0.$$
Its root locus plot against $$K$$ is
10
The algebraic equation
$$F\left( s \right) = {s^5} - 3{s^4} + 5{s^3} - 7{s^2} + 4s + 20$$
$$F\left( s \right) = 0$$ has
11
A software delay subroutine is written as given below: GATE EE 2006 Digital Electronics - Microprocessor Question 14 English

How many times $$DCR$$ $$L$$ instruction will be executed?

12
A student has made a-$$3$$ bit binary down counter and connected to the $$R$$-$$2R$$ ladder type $$DAC$$ [Gain $$=$$ $$\left( { - 1k\Omega /2R} \right)$$ as shown in figure to generate a staircase waveform.

The output achieved is different as shown in figure. What could be the possible cause of this error?

GATE EE 2006 Digital Electronics - Analog to Digital and Digital to Analog Converter Question 2 English 1 GATE EE 2006 Digital Electronics - Analog to Digital and Digital to Analog Converter Question 2 English 2
13
A TTL NOT gate circuit is shown in figure. Assuming $${V_{BE}} = 0.7\,v$$ of both the transistors, if $${V_i} = 3.0\,V,$$ then the states of the two transistors will be GATE EE 2006 Digital Electronics - Logic Families and Memories Question 1 English
14
A $$4 \times 1\,\,MUX$$ is used to implement a $$3$$- input Boolean function as shown in figure. The Boolean function $$F\left( {A,\,\,B,\,\,C} \right)$$ implemented is GATE EE 2006 Digital Electronics - Combinational Circuits Question 3 English
15
In the figure the current source is $$1\,\,\angle \,0\,A,$$ $$R = \,1\,\,\Omega ,$$ the impedances are $${Z_C} = - j\,\,\Omega ,$$ and $${Z_L} = 2\,j\,\,\Omega .$$ The Thevenin equivalent looking into the circuit across $$X-Y$$ is. GATE EE 2006 Electric Circuits - Network Theorems Question 13 English
16
The parameters of the circuit shown in the figure are
$${R_i} = 1\,\,M\,\Omega ,\,\,{R_0} = 10\,\Omega ,\,\,A = {10^6}\,\,V/V.$$ If $${V_i} = 1\,\,\mu V,\,\,$$ the output voltage, input impedance and output impedance respectively are GATE EE 2006 Electric Circuits - Two Port Networks Question 3 English
17
A $$400V$$, $$50$$ $$Hz,$$ three phase balanced source supplies power to a star connected load whose rating is $$12\,\,\angle 3\,\,kVA,$$ $$0.8$$ $$pf$$ (lag). The rating $$($$in $$kVAR)$$ of the delta connected (capacitive) reactive power bank necessary to bring the $$pf$$ to unity is
18
The circuit shown in the figure is energized by a sinusoidal voltage source $${V_1}$$ at a frequency which causes resonance with a current of $${\rm I}$$. GATE EE 2006 Electric Circuits - Sinusoidal Steady State Analysis Question 12 English

The phasor diagram which is applicable to this circuit is

19
An ideal capacitor is charged to a voltage $${V_0}$$ and connected at $$t=0$$ across an ideal inductor $$L.$$ (The circuit now consists of a capacitor and inductor alone). If we let $${\omega _0} = 1/\sqrt {LC} ,$$ the voltage across the capacitor at time $$t>0$$ is given by
20
A variable $$'w'$$ is related to three other variables $$x, y, z$$ as $$w=xy/z.$$ The variables are measured with meters of accuracy$$ \pm $$ $$0.5$$% reading, $$ \pm 1\% $$ of full scale value and $$ \pm 1.5\% $$ reading the actual readings of the three meters are $$80,20$$ and $$50$$ with $$100$$ being the full scale value for all three. The maximum uncertainty in the measurement of $$'w'$$ will be
21
A current of $$ - 8 + 6\sqrt 2 \left( {\sin \,\omega t + {{30}^0}} \right)\,\,A$$ is passed though three meters. They are a center zero $$PMMC$$ meter, true $$r.m.s$$ meter and moving $${\rm I}$$ron instrument. The respective reading (in $$A$$) will be
22
The time/div and voltage/div axes of an oscilloscope have been erased. A student connects a 1kHz, 5V p-p square wave calibration pulse to channel-1 of the scope and observes the screen to be as shown in the upper trace of the fig. An unknown signal is connected to channel -2 (lower trace ) of the scope. If the time/div and V/div on both channels are the same, the amplitude (p-p) and period of the unknown signal are respectively. GATE EE 2006 Electrical and Electronics Measurement - Cathode Ray Oscilloscope Question 4 English
23
A $$200/1$$ current transformer $$(CT)$$ is wound with $$200$$ turns on the secondary on a toroidal core. When it carries a current of $$160$$ $$A$$ on the primary, the ratio and phase errors of the $$CT$$ are found to be $$-$$ $$50$$% and $$30$$ minutes respectively. If the number of secondary turns is reduced by $$1$$ the new ratio error (%) and phase error (min) will be respectively.
24
An energy meter connected to an immersion heater (resistive) operating on an $$AC$$ $$230V,$$ $$50$$ $$Hz,$$ $$AC$$ single phase source reads $$2.3$$ units ($$kWh$$) in $$1$$ hour. The heater is removed from the supply and now connected to a $$4000$$ $$V$$ peak to peak square wave source of $$150$$ $$Hz.$$ The power in $$kW$$ dessipated by the heater will be
25
A sampling wattmeter (that computes power from simultaneously sampled values of voltage and current) is used to measure the average power of a load. The peak to peak voltage of the square wave is $$10V$$ and the current is triangular wave of $$5A$$ $$p$$-$$p$$ as shown in the figure. The period is $$20$$$$ms$$. The reading in $$W$$ will be GATE EE 2006 Electrical and Electronics Measurement - Measurement of Energy and Power Question 24 English
26
$${R_1}$$ and $${R_2}$$ are the opposite arms of $${R_3}$$ and $${R_4}$$ of a wheat stone bridge. The source voltage is applied across $${R_1}$$ and $${R_3}$$ under balanced conditions, which one of the following is true?
27
A $$3$$ phase, $$10$$ $$kW$$, $$400$$ $$V,$$ $$4$$ pole, $$50$$ $$Hz$$, star connected induction motor draws $$20$$ A on full load. Its no load and blocked rotor test data are given below.
No Load Test: $$400V$$ $$6A$$ $$1002W$$
Blocked Rotor Test: $$90V$$ $$15A$$ $$762W$$
Neglecting copper loss in No Load Test and core loss in Blocked Rotor Test, estimate motor's full load efficiency.
28
A $$4$$ pole, $$50$$ $$Hz,$$ synchronous generator has $$48$$ slots in which a double layer winding is house. Each coil has $$10$$ turns and is short pitched by an angle to $$36$$ degrees electrical. The fundamental flux per pole is $$0.025$$ $$Wb$$

The line to line induced $$emf$$, for a three phase star connection is approximately

29
A $$4$$ pole, $$50$$ $$Hz,$$ synchronous generator has $$48$$ slots in which a double layer winding is house. Each coil has $$10$$ turns and is short pitched by an angle to $$36$$ degrees electrical. The fundamental flux per pole is $$0.025$$ $$Wb$$

The line to line induced $$emf,$$ for two phase connection is

30
A $$3$$-phase $$4000$$ $$V,$$ $$5$$ $$kW,$$ star connected synchronous motor having an internal reactance of $$10$$ $$ohms$$ is operating at $$50\% $$ load, unity power factor. Now, the excitation is increased by $$1\% $$, what will be the new load in percent, if the power factor is to be kept same? Neglect all losses and consider linear magnetic circuit.
31
A synchronous generator is feeding a zero power factor (lagging) load at rated current the armature reaction is
32
The speed of a $$4$$-pole induction motor is controlled by varying the supply frequency while maintaining the ratio of supply voltage to supply frequency $$(V/f)$$ constant. At rated frequency of $$50$$ $$Hz$$ and rated voltage of $$400$$ $$V$$ its speed is $$1440$$ $$rpm$$. Find the speed at $$30$$ $$Hz,$$ if the load torque is constant
33
A $$3$$ phase, $$4$$ pole, $$400$$ $$V,$$ $$50$$ $$Hz,$$ star connected induction motor has following circuit parameters $${r_1} = 1.0\Omega ,\,{r_2} = 0.5\Omega ,$$ $${\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {x_1} = x{'_2} = 1.2\Omega ,{\mkern 1mu} {x_m} = 35\Omega $$
The starting torque when the motor is started direct-on-line is (use approximate equivalent circuit model)
34
A $$300$$ $$kVA$$ transformer has $$95\% $$ efficiency at full load $$0.8$$ $$pf$$ lagging and $$96\% $$ efficiency at half load, unity $$pf.$$

What is the maximum efficiency (in %) at unity $$pf$$ load?

35
Two transformers are to be operated in parallel such that they share load in proportion to their $$kVA$$ ratings. The rating of the first transformer is $$500$$ $$kVA$$ and its $$pu$$ leakage impedance is $$0.05$$ $$pu.$$ If the rating of second transformer is $$250$$ $$kVA,$$ its $$pu$$ leakage impedance is
36
A $$300$$ $$kVA$$ transformer has $$95\% $$ efficiency at full load $$0.8$$ $$pf$$ lagging and $$96\% $$ efficiency at half load, unity $$pf.$$

The iron loss $$\left( {{P_i}} \right)$$ in $$kW,$$ under full load operation are

37
In transformers, which of the following statements is valid?
38
A $$220V$$ $$DC$$ machine supplies $$20$$ $$A$$ at $$200V$$ as a generator. The armature resistance is $$0.2$$ ohm. If the machine is now operated as a motor at same terminal voltage and current but with the flux increased by $$10\% ,$$ the ratio of motor speed to generator speed is
39
In a $$DC$$ machine, which of the following statements is true?
40
Which of the following statements holds for the divergence of electric and magnetic flux densities?
41
Consider the following statements with reference to the equation $$\nabla.\overrightarrow J=-\frac{\partial\rho}{\partial t}$$

1. This is a point from the continuity equation
2. Divergence of current density is equal to the decrease of charge per unit volume per unit time at every point.
3. This is Maxwell's divergence equation
4. This represents the conservation of charge.

Select the correct answer.
42
The concept of an electrically short, medium, and long line is primarily based on the
43
The expression $$V = \int\limits_0^H {\pi {R^2}{{\left( {1 - {h \over H}} \right)}^2}dh\,\,\,} $$ for the volume of a cone is equal to _________.
44
A single - phase bridge converter is used to charge a battery of $$200$$ $$V$$ having an internal resistance of $$2\,\,\Omega $$ as shown in figure. The $$SCRs$$ are triggered by a constant $$dc$$ signal. If $$SCR$$ $$2$$ gets open circuited, what will be the average charging current? GATE EE 2006 Power Electronics - Single and Three Phase Rectifier Question 16 English
45
A single $$-$$ phase half wave uncontrolled converter circuit is shown in figure. A $$2$$ -winding transformer is used at the input for isolation. Assuming the load current to be constant and $${V_{in}} = {V_m}$$ $$\,\sin \omega t,$$ the current waveform through diode $${D_2}$$ will be GATE EE 2006 Power Electronics - Single and Three Phase Rectifier Question 17 English
46
A voltage commutation circuit is shown in figure. If the turn off time of the $$SCR$$$$s$$ is $$50$$ $$\mu \sec $$ and as safety margin of $$2$$ is considered, what will be the approximate minimum value of capacitor required for proper commutation? GATE EE 2006 Power Electronics - Choppers and Commutation Techniques Question 8 English
47
A voltage commutated chopper operating at $$1$$ $$kHz$$ is used to control the speed of $$dc$$ motor as shown in figure. The load current is assumed to be constant at $$10$$ $$A.$$ GATE EE 2006 Power Electronics - Choppers and Commutation Techniques Question 12 English

The average output voltage of the chopper will be

48
A voltage commutated chopper operating at $$1$$ $$kHz$$ is used to control the speed of $$dc$$ motor as shown in figure. The load current is assumed to be constant at $$10$$ $$A.$$ GATE EE 2006 Power Electronics - Choppers and Commutation Techniques Question 13 English

The minimum time in $$\mu $$ sec for which the $$SCR$$ $$M$$ should be ON is

49
An $$SCR$$ having a turn ON time of $$5\,\,\mu \,\,\sec $$, latching current of $$50$$ $$mA$$ and holding current of $$40$$ $$mA$$ is triggered by a short duration pulse and is used in the circuit shown in figure The minimum pulse width required To turn the $$SCR$$ ON will be GATE EE 2006 Power Electronics - Power Semiconductor Devices Question 5 English
50
A solar cell of $$350V$$ is feeding power to an $$ac$$ supply of $$440$$ $$V,$$ $$50$$ $$Hz$$ through a $$3$$- phase fully controlled briodge converter. A large inductance is connected in the $$dc$$ circuit to maintain the $$dc$$ current at $$20A.$$ If the solar cell resistance of $$0.5\Omega ,$$ then each thryristor will be reverse biased for a period of
51
A $$3$$ $$-$$ phase fully controlled bridge converter with free wheeling diode is fed from $$400$$ $$V$$, $$50$$ $$Hz$$ $$AC$$ source and is operating at a firing angle of $${60^ \circ }.$$ The load current is assumed constant at $$10A$$ due to high load inductance The input displacement factor $$(IDF)$$ and the input power factor $$(IPF)$$ of the converter will be
52
Three identical star connected resistors of $$1.0$$ $$p.u$$ are connected to an unbalanced $$3$$ phase supply. The load neutral is isolated. The symmetrical components of the line voltages in $$p.u.$$ calculations are with the respective base values, the phase to neutral sequence voltages are
53
A generator is connected through a $$20$$ MVA, $$13.8/138$$ kV step up transformer, to a transmission line. At the receiving end of the line a load is supplied through a step down transformer of $$10$$ MVA, $$138/69$$ kV rating. A $$0.72$$ p.u. load, evaluated, on load side transformer ratings as base values of $$10$$ MVA and $$69$$ kV in load circuit, the value of the load (in per unit) in generator circuit will be
54
An HVDC link consists of rectifier, inverter transmission line and other equipments. Which one of the following is true for this link?
55
For a power system the admittance and impedance matrices for the fault studies are as follows. $$$\eqalign{ & {Y_{bus}} = \left[ {\matrix{ { - j8.75} & {j1.25} & {j2.50} \cr {j1.25} & { - j6.25} & {j2.50} \cr {j2.50} & {j2.50} & { - j5.00} \cr } } \right] \cr & {Z_{bus}} = \left[ {\matrix{ {j0.16} & {j0.08} & {j0.12} \cr {j0.08} & {j0.24} & {j0.16} \cr {j0.12} & {j0.16} & {j0.34} \cr } } \right] \cr} $$$

The pre-fault voltages are $$1.0$$ $$p.u.$$ at all the buses. The system was unloaded prior to the fault. A solid $$3$$ phase fault takes place at bus $$2.$$

The per unit fault feeds from generators connected to buses $$1$$ and $$2$$ respectively are

56
For a power system the admittance and impedance matrices for the fault studies are as follows. $$$\eqalign{ & {Y_{bus}} = \left[ {\matrix{ { - j8.75} & {j1.25} & {j2.50} \cr {j1.25} & { - j6.25} & {j2.50} \cr {j2.50} & {j2.50} & { - j5.00} \cr } } \right] \cr & {Z_{bus}} = \left[ {\matrix{ {j0.16} & {j0.08} & {j0.12} \cr {j0.08} & {j0.24} & {j0.16} \cr {j0.12} & {j0.16} & {j0.34} \cr } } \right] \cr} $$$

The pre-fault voltages are $$1.0$$ $$p.u.$$ at all the buses. The system was unloaded prior to the fault. A solid $$3$$ phase fault takes place at bus $$2.$$

The post fault voltages at buses $$1$$ and $$3$$ in per unit respectively are

57
The Gauss Seidel load flow method has following disadvantages. Tick the incorrect student.
58
In a biased differential relay the bias is defined as a ratio of
59
Keeping in view the cost and overall effectiveness, the following circuit breaker is best suited for capacitor bank switching
60
A generator feeds power to an infinite bus through a double circuit transmission line. A 3 phase fault occurs at the middle point of one of the lines. The infinite bus voltage is 1 pu, the transient internal voltage of the generator is 1.1 pu and the equivalent transfer admittance during fault is 0.8 pu. The 100 MVA generator has an inertia constant of $$5$$ MJ/MVA and it was delivering 1.0 pu power prior of the fault with rotor power angle of $${30^ \circ }\,\,$$. The system frequency is 50Hz.

The initial accelerating power (in pu) will be

61
A generator feeds power to an infinite bus through a double circuit transmission line. A $$3$$ phase fault occurs at the middle point of one of the lines. The infinite bus voltage is $$1$$ pu, the transient internal voltage of the generator is $$1.1$$ pu and the equivalent transfer admittance during fault is $$0.8$$ pu. The 100 MVA generator has an inertia constant of $$5$$ MJ/MVA and it was delivering $$1.0$$ pu power prior of the fault with rotor power angle of $${30^ \circ }\,\,$$. The system frequency is 50Hz.

If the initial accelerating power is $$X$$ pu, the initial acceleration in elect deg/sec2, and the inertia constant in MJ-sec/elect deg respectively will be

62
The $$A, B, C, D$$ constant of a $$220$$ $$kV$$ line are:
$$A = D = 0.94\,\angle \,10,\,\,\,B = 130\,\angle \,730,\,\,\,C = 0.001\,\angle \,900.\,\,$$ If the sending end voltage of the line for a given load delivered at nominal voltage is $$240$$ $$kV$$, the % voltage regulation of the line is
63
A $$400$$ V, $$50$$ Hz, three phase balanced source supplies power to a star connected load whose rating is $$12\sqrt 3 $$ kVA, $$0.8$$ pf(lag). The rating (in kVAR) of the delta connected (capacitive) reactive power bank neccessary to bring the pf to unity is
64
The concept of an electricity short, medium and long line is primarily based on the
65
$$x\left[ n \right] = 0;\,n < - 1,\,n > 0,\,x\left[ { - 1} \right] = - 1,\,x\left[ 0 \right]$$
$$\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 2$$ is the input and
$$y\left[ n \right] = 0;\,n < - 1,\,n > 2,\,y\left[ { - 1} \right] = - 1,\, = y\left[ 1 \right],\,y\left[ 0 \right] = 3,\,y\left[ 2 \right]$$
$$\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, =- 2$$ is the output of a discrete-time $$LTI$$ system. The system impulse response $$h\left[ n \right]$$ will be
66
$$x(t)$$ is a real valued function of a real variable with period $$T.$$ Its trigonometric. Fourier Series expansion contains no terms of frequency
$$\omega = 2\pi \left( {2k} \right)/T;\,\,k = 1,2,........$$ Also, no sine terms are present. Then $$x(t)$$ satisfies the equation
67
A continuous-time system is described by $$y\left( t \right) = {e^{ - |x\left( t \right)|}},$$ where $$y(t)$$ is the output and $$x(t)$$ is the input. $$y(t)$$ is bounded
68
$$y\left[ n \right]$$ denotes the output and $$x\left[ n \right]$$ denotes the input of a discrete-time system given by the difference equation $$y\left[ n \right] - 0.8y\left[ {n - 1} \right] = x\left[ n \right] + 1.25\,x\left[ {n + 1} \right].$$ Its right-sided impulse response is
69
A discrete real all pass system has a pole at $$z = 2\angle {30^ \circ };\,$$ it, therefore,
70
The discrete-time signal $$$x\left[n\right]\leftrightarrow X\left(z\right)={\textstyle\sum_{n=0}^\infty}\frac{3^n}{2+n}z^{2n}$$$ where $$\leftrightarrow$$ denote a transform-pair relationship, is orthogonal to the signal
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