GATE EE 1995
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GATE EE

1
The common mode voltage of a unity gain (voltage follower) op-amp buffer in terms of its output voltage $${V_0}$$ is __________.
2
The impulse response of an initially relaxed linear system is $${e^{ - 2t}}u\left( t \right).$$ To produce a response of $${te^{ - 2t}}u\left( t \right),$$ the input must be equal to
3
The Laplace transformation of $$f(t)$$ is $$F(s).$$ Given $$F\left( s \right) = {\omega \over {{s^2} + {\omega ^2}}},$$ the final value of $$f(t)$$ is
4
The steady state error due to a step input for type $$1$$ system is ______________.
5
The closed loop transfer function of a control system is given by $${{C\left( s \right)} \over {R\left( s \right)}}\, = \,\,{{2\left( {s - 1} \right)} \over {\left( {s + 2} \right)\left( {s + 1} \right)}}$$ for a unit step input the output is
6
Closed loop stability implies that $$\left[ {1 + G\left( s \right)H\left( s \right)} \right]$$ has only ____________ in the left half of the $$s$$-plane.
7
A system is described by the state equation $$\mathop X\limits^ \bullet = AX + BU$$ , The output is given by $$Y=CX$$ Where $$A = \left( {\matrix{ { - 4} & { - 1} \cr 3 & { - 1} \cr } } \right)\,\,B = \left( {\matrix{ 1 \cr 1 \cr } } \right)\,\,C = \left[ {10} \right]$$

Transfer function $$G(s)$$ of the system is

8
For a $$J$$-$$K$$ flip-flop its $$J$$ input is tied to its own $$Q$$ output and its $$K$$ input is connected to its own $$Q$$ output. If the flip-flop is fed with a clock of frequency $$1$$ $$MHz,$$ its $$Q$$ output frequency will be ______________
9
In an $$8085$$ microprocessor, after the execution of $$XRA$$ $$A$$ instruction
10
A series $$R-L-C$$ circuit has the following parameter values:
$$R = 10\Omega ,\,\,L = 0.01\,H,\,\,C = 100\,\,m\,\,F.$$
The $$Q$$ factor of the circuit at resonance is
11
In the circuit of Figure, Ammeter $${A_2}$$ reads $$12$$ $$A$$ and $${A_3}$$ reads $$9$$ $$A.$$ $${A_1}$$ will read ______ GATE EE 1995 Electric Circuits - Sinusoidal Steady State Analysis Question 35 English
12
A certain oscilloscope with 4 c.m by 4 c.m screen has its own sweep output fed to its input. If the x and y sensitivities are same, the oscilloscope will display a.
13
A $$3{1 \over 2}\,$$ digit, $$2$$ $$V$$ full scale slope $$ADC$$ has its integration time set to $$300$$ $$ms.$$ If the input to the $$ADC$$ is ($$1$$+$$1sin$$ $$314$$ $$t$$) V, then the ADC output will be
14
A Kelvin double bridge is best suited for the measurement of
15
Fringing in capacitive type transducer can be minimized by providing a _________
16
Four ammeters $$M1, M2, M3$$ and $$M4$$ with the following specifications are available. GATE EE 1995 Electrical and Electronics Measurement - Basic of Indicating Instruments Question 38 English

A current of $$1$$ $$A$$ is to be measured. To obtain minimum error in the reading, one should select meter

17
Two $$100V$$ full scale $$PMMC$$ type D.C voltmeter having figure of merits ($$FOM)$$ of $$10k\Omega /V$$ and $$20k\Omega /V$$ are connected in series. The series combination can be used to measure a maximum dc voltage of _______.
18
The distribution factor for a $$36$$ slot stator with three-phase, $$8$$-pole winding, having $${120^ \circ }$$ phase Spread, is _________
19
A differentially compounded d.c. motor with interpoles and with brushes on the neutral axis is to be driven as a generator in the same direction with the same polarity of the terminal voltage. It will then
20
The percentage impedance of a 100 kVA, 11 kV/400V, delta/wye, 50 Hz transformer is 4.5%. For the circulation of half the full load current during short circuit test, with low voltage terminals shorted, the applied voltage on the high voltage side will be __________.
21
Supply to one terminal of a $$\triangle$$ - Y connected three-phase core type transformer which is on no-load, fails. Assuming magnetic circuit symmetry, voltages on the secondary side will be:
22
An induction motor is fed from a balanced three phase supply at rated voltage and frequency through a bank of three single phase transformers connected in delta-delta. One unit of the bank develops fault and is removed. Then
23
A synchronous motor on load draws a current at a leading power factor angle $$\phi$$. If the internal power factor angle – which is the phase angle between the excitation e.m.f. and the current in the time phasor diagram is $$\psi$$, then the air gap excitation m.m.f lags the armature m.m.f by
24
A monochromatic plane electromagnetic wave travels in vacuum in the position $$x$$ direction ($$x, y, z$$ system of coordinates). The electric and magnetic fields can be expressed as
25
The Laplace transform of $$f(t)$$ is $$F(s).$$ Given $$F\left( s \right) = {\omega \over {{s^2} + {\omega ^2}}},$$ the final value of $$f(t)$$ is __________.
26
The inverse of the matrix $$S = \left[ {\matrix{ 1 & { - 1} & 0 \cr 1 & 1 & 1 \cr 0 & 0 & 1 \cr } } \right]$$ is
27
Given the matrix $$A = \left[ {\matrix{ 0 & 1 & 0 \cr 0 & 0 & 1 \cr { - 6} & { - 11} & { - 6} \cr } } \right].\,\,$$ Its eigen values are
28
The rank of the following $$(n+1)$$ $$x$$ $$(n+1)$$ matrix, where $$'a'$$ is a real number is $$$\left[ {\matrix{ 1 & a & {{a^2}} & . & . & . & {{a^n}} \cr 1 & a & {{a^2}} & . & . & . & {{a^n}} \cr . & {} & {} & {} & {} & {} & {} \cr . & {} & {} & {} & {} & {} & {} \cr 1 & a & {{a^2}} & . & . & . & {{a^n}} \cr } } \right]$$$
29
$$\mathop {Lim}\limits_{x \to \infty } \,x\sin {\raise0.5ex\hbox{$\scriptstyle 1$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle x$}} = \_\_\_\_\_.$$
30
If $$f(0)=2$$ and $$f'\left( x \right) = {1 \over {5 - {x^2}}},$$ then the lower and upper bounds of $$f(1)$$ estimated by the mean value theorem are ______.
31
If at every point of a certain curve , the slope of the tangent equals $${{ - 2x} \over y},$$ the curve is _______.
32
Consider the chopper circuit of figure. The chopper operates at $$400$$ $$Hz$$ and $$50$$% duty cycle. The load current remains almost ripple free at $$10A.$$ Assuming the input voltage to be $$200V$$ and the devices to be ideal, the turn-off time available to the thyristor $$Th$$ $$M$$ is____________ $$\mu s$$ GATE EE 1995 Power Electronics - Choppers and Commutation Techniques Question 42 English
33
Figure, show two thyristors each rated $$500A$$ (continuous) sharing a load current. Current through thyristor $$y$$ is $$120A.$$ The current through thyristor $$x$$ will be nearly __________ $$A.$$ GATE EE 1995 Power Electronics - Power Semiconductor Devices Question 33 English
34
A three phase $$ac$$-to-$$dc$$ diode bridge rectifier is supplied from a three-phase, $$440V$$ source. The rectifier supplies a purely resistive load. The average $$dc$$ voltage across the load will be ___________ $$V$$.
35
A single phase diode bridge rectifier supplies a highly inductive load. The load current can be assumed to be ripple free. The ac supply side current waveform will be:
36
A $$dc$$ to $$dc$$ transistor chopper supplied from a fixed voltage $$dc$$ source feeds a fixed resistive-inductive load and a free-wheeling diode. The chopper operates at $$1$$ $$kHz$$ and $$50$$% duty cycle. Without changing the value of the average $$dc$$ current through the load, if it is desired to reduce the ripple content of load current, the control action needed will be
37
A single phase Inverter with square wave output voltage will have in its output waveform a fifth harmonic component equal to ______ percentage of the fundamental
38
An inverter capable of supplying a balanced three - phase variable voltage variable frequency output is feeding a three - phase induction motor rated for $$50$$ $$Hz$$ and $$440V.$$ The stator winding resistances of the motor are negligible small. During starting, the current inrush can be avoided without sacrificing the starting torque by suitably applying.
39
Match the following GATE EE 1995 Power Electronics - Inverters Question 5 English 1 GATE EE 1995 Power Electronics - Inverters Question 5 English 2 GATE EE 1995 Power Electronics - Inverters Question 5 English 3

$$(P)$$ single phase fully controlled $$ac-dc$$ converter
$$(Q)$$ Voltage commutated $$dc-ac$$ chopper ($$E$$ = input $$dc$$ voltage)
$$(R)$$ Phase voltage of a star connected balanced three-phase load fed from a three-phase inverter with $${180^ \circ }$$ conduction (input $$dc$$ voltage=$$E$$)
$$(S)$$ Line voltage of a six stepped inverter with input dc voltage $$E$$
$$(T)$$ Three-phase diode bridge rectifier.

40
The insulation level of a $$400$$ kV, EHV overhead transmission line is decided on the basis of
41
The insulation resistance of a cable of length $$10$$ km is $$1$$ $$M\Omega $$. For a length of $$100$$ km of the same cable, the insulation resistance will be
42
The surge impedance of a $$400$$ km long overhead transmission line is $$400$$ $$\Omega $$. For a $$200$$ km length of the same line, the surge impedance will be
43
The rated load of an underground cable is always _______its natural load.
44
In order to have a lower cost of electrical energy generation,
45
The positive sequence component of the voltage at the point of fault in a power system is zero for a _________fault.
46
The inductance and capacitance of a power system network upto a circuit breaker location are $$1H$$ and $$0.01$$ $$\mu F$$ respectively, the value of the shunt resistor across the circuit breaker, required for critical damping of the restriking voltage is
47
The distance relay with inherent directional property is known as ________relay.
48

Type of Relay
$$A.$$ Buchholz Relay
$$B.$$ Translay relay
$$C.$$ Carrier current, phase comparison relay
$$D.$$ Directional over Current relay
$$E.$$ Negative sequence relay

Most suited for
$$P.$$ Feeder
$$Q.$$ Transformer
$$R.$$ Radial distributed
$$S.$$ Generator
$$T.$$ Ring main distributor
$$U.$$ Long over head transmission line

49
In load-flow analysis, a voltage-controlled bus is treated as a load bus in subsequent iteration for a _________limit is violated.
50
The $$rms$$ value of the periodic waveform $$e(t),$$ shown in figure is GATE EE 1995 Signals and Systems - Continuous Time Periodic Signal Fourier Series Question 13 English
51
The Laplace transformation of f(t) is F(s). Given F(s)=$$\frac\omega{s^2+\omega^2}$$, the final value of f(t) is
52
The convolution of the function $$f_1\left(t\right)=e^{-2t}\;u\left(t\right)$$ and $$f_2\left(t\right)=e^t\;u\left(t\right)$$ is equal to __________.
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