1.1 When the plate area of a parallel plate capacitor is increased keeping the capacitor voltage
constant, the force between the plates
(a) increase
(b) decreases
(c) remains constant
(d) may increase or decrease depending on the metal making up the plates
1.2 Two parallel wires separated by a distance d are carrying a current I in the same direction.
The magnetic field along a line running parallel to these wires and midway between them
(a) depends upon I
(b) is zero
(c) depends upon d
(d) depends upon the permeability of medium between the wires
1.3 An electromagnetic field is radiated from
(a) a stationary point charge
(b) a capacitor with a DC voltage
(c) a conductor carrying a DC current
(d) an oscillating dipole
1.4 The mobility of an electron in a conductor is expressed in terms of
(a)
cm2/V—s
(b)
cm/V—s
(C)
cm2/V
(d)cm2/s
1.5 An enhancement type n-channel MOSFET is represented by the symbol
(a) .— I
(b) .__ I
(c)
(d)
1.6 As the temperature is increased, the voltage across a diode carrying a diode
carrying a constant current
(a) increases
(b) decreases
(c) remains constant
(d) may increase or decrease depending upon the doping levels in the junction
1.7 A single channel digital storage oscilloscope uses a 10 bit, i07 samples per second Analog-
to-Digital Converter. For a 100 KHz sine wave input, the number of samples taken per cycle of
the input will be
(a) i07
(b) i04
(c) i03
(d) 102
1.8 Higher synchronous reactance is preferred in the present day alternators,
because one can have
(a) reduced sub-transient currents
(b) reduced harmonic currents
(c) reduced transient currents
(d) higher voltage regulation with load
1.9 The RMS value of a half-wave rectified symmetrical square wave current of 2A is:
(a) 1OV
(b)
JA
(c) 200V
(d) 1A
1.10 Electodynamic type wattmeters have large errors while measuring power in ac circuits at
low power factor conditions, since the voltage across and the current through the
2Oc .ø—200
v—+
ioov (. 200V
5OHz I
(a) current coil are not in phase
(c) pressures coil are not in phase
(d) pressure coil are not in quadrature
1.11 The current in the circuit shown in Fig.1.12 is:
(a) 5A
(b) 1OA
(c) iSA
(d) 25A
1.12 For the circuit shown and Y will be
in Fig.below, the capacitance measured between terminals B
(a)
(b)
C+--
(c)
(c+3c)
(d)
3C+2C
An overhead line having a surge impedance of 400c is connected in series with an
underground cable having a surge impedance of iooc. If a surge of 50 kV travels from the line
end towards the line-cable junctions, the value of the transmitted voltage wave at the junction
is:
(a) 30 kV
(b) 20 kV
(c) 80 kV
(d) -30 kV
1.14 The load carrying capability of a long AC transmission line is:
(a) always limited by the conductor size
(b) limited by stability considerations
(c) reduced at a low ambient temperatures
(d) decreased by the use of bundled conductors of single conductors
1.15 Corona losses are minimized when
(a) conductor size is reduced
(b) smooth conductor is reduced
(c) sharp points are provided in the line hardware
(d) current density in conductors is reduced
1.16 In a DC transmission line
(a) it is necessary for the sending end and receiving end to be operated in synchronism.
(b) the effects of inductive and capacitive reactances are greater than in an AC transmission
line of the same rating.
(c) there are not effects due to inductive and capacitive reactances
(d) power transfer capability is limited by stability considerations.
1.18 Steady state stability of a power system is the ability of the power system to (a)
maintain voltage at the rated voltage level
(b) maintain frequency exactly at 50 Hz
(c) maintain a spinning reserve margin at all times
(d) maintain synchronism between machines and on external tie lines
1.17. A 4-pole lap-wound DC generator has a developed power of P watts and voltage of E
volts. Two adjacent brushes of he machine are removed as they are worn out. If the machine
operates with the remaining brushes, the developed voltage and power that can be obtained
from the machine are
EP p p
(a) E, P
(b) --,-
(c) E,
(d) E,
1.18. Starting torque can be obtained in the case of a single phase induction motor with
identical main and auxiliary windings by connecting
(a) a capacitor across the mains
(b) a capacitor in series with the machine
(c) a capacitor in series with the auxiliary winding
(d) the main and the auxiliary windings in series
1.19. The windings of a QkVA, •—volt, three-phase, Delta connected, core type
transformer are reconnected to work as a single phase transformer. The maximum voltage
and the power ratings of the new configuration are,
(a) -,3Q
(b) J-r- E
(c) ,2Q
(d)
1.20. Resonant converters are basically used to
(a) generate large peaky voltage
(b) reduce the switching losses
(c) eliminate harmonics
(d) convert a square wave into a sine wave
1.21. A PWM switching scheme is used with a three phase inverter to
(a) reduce the total harmonic distortion with modest filtering
(b) minimize the load on the DC side
(c) increase the life of the batteries
(d) reduce low order harmonics and increase high order harmonics
1.22 The following starting method for an induction motor is inferior view of the poor starting
torque per ampere of the line current drawn:
(a) Direct line starting
(b) Auto transformer method of starting
(c) Series inductor method of starting
(d) Star-Delta method of starting
2. This question consists of 25 (TWENTTY FIVE) sub-questions. Each sub-question carries TWO
marks. The answers to these sub-questions MUST be written only in the appropriate boxes
corresponding to the questions in the first page of the answer book.
2.1 The color code of a 1 kc resistance is:
(a) black, brown, red
(b) red, brown, brown
(c) brown, black, red
(d) black, black, red
2.2. A rectangular voltage pulse of magnitude V and duration T is applied to a series
combination of resistance R and capacitance C. The maximum voltage developed across the
capacitor is:
(a) V[1_exP
(c) V (d) Vexpj
2.3. When a periodic triangular voltage peak amplitude 1 V and frequency 0.5 Hz is applied to
a parallel combination of ic resistance and 1 F capacitance, the current through the voltage
source has wave-form.
(a) (b) //1
(c) h h (d)
2.4. For a flip-flop formed from two NAND X Q gates as shown in Fig below , the unusable
state corresponds to
2.5. The logic function
f
=
(x.)
+ is the same as
(a) f=(x+y)(x+y)
A
dB /6dBper
— —
I
octive
(b)
f=(x+y)+(x+y)
0dB
(c)
f
=
(x.y).(x.y)
(d) None of (a), (b) (c).
2.6. For a single phase overhead line having solid copper conductors of diameter 1 cm, spaced
60 cm between centers, the inductance in mH/km is:
(a) 0.05+0.21n60
(b) 0.21n60
(c) 0.05+0.2ln
(d) 0.2ln2
2.7. An industrial consumer has a daily load pattern of 2000 kW, 0.8 lag for 12 hours, and
1000 kW UPF for 12 hours. The load factor is:
(a) 0.5
(b) 0.75
(c) 0.6
(d) 2.0
2.8. A 220 kV, 20 km long, 3-phase transmission line has the following A, B, C, D constants. A
= D = 0.96 L3°, B = 55Z65°cVphase, C = 0.5E - 04Z80°S/phase. Its charging current per
phase is:
(a)
(b) hA
(c) 220A
(d)
2.9. A 3-phase, 11 kV, 50 Hz, 200 kW load has a power factor of 0.8 lag. A delta connected 3-
phase capacitor is used to improve the power factor to unity. The capacitance power phase of
the capacitor in microfarads is
(a) 3.948
(b) 1.316
(c) 0.439
(d) 11.844
2.10. A 10 kVA, 400 V/200V single-phase transformers with
10°h
impedance draws a steady
short circuit line current of
(a) 50 A
(b) 150 A
(c) 250 A
(d) 350 A
2.11. The percentage resistance and percentage reactance of a 10 kVA, 400 V/200 V,
3-phase transformer are 2% and lO% respectively. If the constant losses in the machine are
l%, the maximum possible percentage efficiency of the transformer is:
(a) 98.32
(b) 97.25
(c) 96.85
(d) 96.12
2.12. A 400V/100V, 10 kVA two-winding transformer is reconnected as an auto- transformer
across a suitable voltage source. The maximum rating of such an arrangement could be
(a) 50 kVA
(b) 15 kVA
(c) 12.5 kVA
(d) 8.75 kVA
2.13. A DC shunt motor is running t I200 rmp, when excited with 220 V DC. Neglecting the
losses and saturation, the speed of the motor when connected to a 175 V DC supply is:
(a) 750 RPM
(b) 900 RPM
(c) 1050 RPM
(d) 1200 RPM
2.14. A three phase alternator is wound with a 60 degree phase-spread armature windings
and develops 300 kVA. If the armature is reconnected utilizing all the coils for single phase
operation with a phase spread of 180 degrees, the new rating of the machine is
(a) 100 kVA
(b) 200 kVA
(c) 250 kVA
(d) 300 kVA
2.15. A 10 kVA, 400 V/200 V, single phase transformer with a percentage resistance of 3%
and percentage reactance of 6% is supplying a current of 50 A to a resistive load. The value of
the load voltage is:
(a) 194 V
(b) 390 V
(c) 192 V
(d) 196 V
2.16. For a dual ADC type 3-digit DVM, the reference voltage is 100 mV and the first
integration time is set to 300 ms. For some input voltage, the “deintegration” period is 370.2
ms. The DVM will indicate
(a) 123.4
(b) 199.9
(c) 100.0
(d) 1.141
2.17. When a resistor R is connected to a current source, it consumes a power of 18 W. when
the same R is connected to a voltage source having the same magnitude as
the current source, the power absorbed by R is 4.5 W. The magnitude of the
current source and the value of R are
(a)
-JfäA
and ic
(b) 3A and
(c) 1A and 18
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aq="" are:="" are="" armature="" as="" assume="" at="" attempted="" augmented="" average="" b:="" b="" bars="" base.="" based="" be="" being="" below="" between="" blocked="" boa.="" breaker="" bridge="" brush="" burden="" bus.="" bus="" by="" c-m="" c.="" c="" cable="" calculate:="" calculate="" can="" cap-pin="" capacitance="" capacitive="" capacitor.="" capacitor="" cb="" center="" charge="" choose="" circuit.="" circuit="" circuited="" class="" closed="" cm="" coil="" combination="" commercial="" common="" components="" condition="" conditions="" conducted="" conductor="" connected="" consider="" considered.="" consists="" constant="" construct="" control="" core="" cos="" critical="" current.="" current="" currents="" cv="" d="" data:="" dc="" delivered="" delta="" determine="" developed="" diagram="" diameter:="" diameter="" dielectric="" differential="" diode="" distance="" distributed="" does="" draw="" drawn="" driving="" drop="" e="" each.="" each="" effective="" electric="" 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star="" state="" stator="" straight="" stress="" string="" supply.="" supply="" supported="" suspension="" symmetrical="" synchronized="" synchronous="" system="" t-equivaient="" t="" taken="" tar="" terminals="" test="" that="" the="" their="" them="" then="" thermocouple="" these="" they="" this="" three="" throughout="" to="" together="" torque="" tower="" transfer="" transformer:="" transformer="" transformers="" transmission="" true:="" turns="" twenty="" two="" type.="" type="" u="" under="" uniformly="" unit.="" unit="" units="" unity="" unknown="" unscored="" upf="" used="" using="" v.="" v0.="" v0="" v11="" v1="" v1in="" v="" va="" value="" values="" vand="" var="" variable="" varied="" vdc="" vector="" very="" voltage.="" voltage="" voltages="" voltmeter.="" voltmeters="" volume="" w.="" w="" wattmeter.="" wattmeter="" wave="" waveforms="" well="" what="" when="" which="" whose="" will="" winding="" wire="" wires="" with="" within="" would="" x-axis="" x0="" x0e3="" x0e_3t="" x0et="" x1="" x:="" x="" xe="" xm.="" y="" yes="" z="" zero.="" zero="">> >> X
(b) X1 < (c) X1 = >>
X
(d) X1 =
X < 11. 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 (b) Star - Delta (c) Delta - Delta (d) Delta - Zigzag 12. For an induction motor, operating at a slip s, the ratio of gross power output to air gap power is equal to: (a) (1—s)2 (b) (1—s) (c) q(1_s) (d) (i_4) 13. 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 (a) 4, 0.4 (b) 100, 10 (c) 4, 10 (d) 100, 0.4 14. An 800 kV transmission line has a maximum power transfer capacity on the operated at 400 kV with the series reactance unchanged, the new maximum power transfer capacity is approximately 15. The insulation strength of an EHV transmission line is mainly governed by (A) load power factor (B) switching over-voltages (C) harmonics (D) corona 16. High Voltage DC (HVDC) transmission is mainly used for (a) bulk power transmission over very long distances (b) inter-connecting two systems with the same nominal frequency (c) eliminating reactive power requirement in the operation (d) minimizing harmonics at the converter stations 17. Q-meter works on the principle of (a) mutual inductance (b) self inductance (c) series resonance (d) parallel resonance 18. A PMMC voltmeter is connected across a series combination of a DC voltage source V1 = 2Vand an AC voltage source v2 (t) = 3sin(4t) V. The meter reads (c) [2+4V (d) [çv 19. Assume that D1 and D2 in Fig.Q below are ideal diodes. The value of current I is: (a) 0 mA (b) 0.5 mA 2kc (c) 1 mA lmA1 (d) 2 mA 2kc 20. The 8085 assembly language instruction registers into the memory locations 2050H that stores the contents of H and L and 2051H’ respectively, is: (a) SPHL 2050H (b) SPHL 2051H (c) SHLD 2050H (d) STAX 2050H 21. Assume that the N-channel MOSFET shown in Fig. below is ideal, and that its threshold voltage is +1.OV. The voltage Vab between nodes a and b is: (a) 5V (b) 2V (c) 1V (d) CV 22. The digital circuit shown in Fig. below works as a (a) JKflip-flop (b) Clocked RS flip-flop (c) Tflip-flop (d) Ring counter 23. A digital-to-analog converter with a full-scale output voltage of 3.5V has a resolution close to 14 mV. Its bit size is: (a) 4 (b) 8 (c) 16 (d) 32 24. The conduction loss versus device current characteristic of a power MOSFET is best approximated by (a) a parabola (b) a straight line (c) a rectangular hyperbola (d) an exponentially decaying function 25. A three-phase diode bridge rectifier is fed from a 400V RMS, 50 Hz, three-phase AC source. If the load is purely resistive, the peak instantaneous output voltage is equal to 400 (c) 4OOj V (d) -7=-V 26. The output voltage waveform of a three-phase square-wave inverter contains (a) only even harmonics (b) both odd and even harmonics (c) only odd harmonics (d) only triplen harmonics Q.31 — Q.80 carry two marks each 31. The RL circuit of Fig.Q31 is fed from a constant magnitude, variable frequency sinusoidal voltage source VIN. At 100 Hz, the R and L elements each have a voltage drop URMS. If the frequency of the source is changed to 50 Hz, the new voltage drop across R is: (a) JURMS (b) J1URMS (c) JURMS (d) 4JURMS 32. The circuit shown in Fig. below 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 = equals (a) 0 A (b) 0.5A (c) 1A (d) 2 A 33. For the three-phase circuit shown in Fig. below, the ratio of the current : I>,
:
18
is
(a) i:i:J
(b) 1:1:2
(c) 1:1:0
(d) i:i:J
34. For the triangular waveform shown in Fig. below, the RMS value of the voltage is equal to
(a)
T
T
2
(b)
2T t
2
1
(c). (d)
1 DV
t=o
35. The charge distribution in a metal-dielectric-semiconductor specimen is shown in Fig.
below. The negative charge density decreases linearly in the semiconductor as shown. The
electric field distribution is as shown in
(c)
(d) Dielectric
36. In Fig. below, the Thevenin’s equivalent pair (voltage, terminals P-Q, is given by
(a) (2V, 512)
(b) (2V, 7.512)
(c) (4V, 512)
(d) (4V, 7.512)
37. A unity feedback system, having an open loop gain
K(1-s)
G(s)H(s)
= ,becomes stable when
(1+s)
Metal
Semiconductor
(a) K>1
(b) K >1
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closed="" coil="" coils="" coin="" common="" compensated="" condition="" conduct="" connected="" connection="" consider="" considered="" constant="" constants="" control="" core="" correct="" correctness="" cos2x="" cost="" coulomb="" crossover="" current="" cylindrical="" d="" damper="" dc="" decrease="" decreases="" defined="" delivered="" designer="" determine="" developed="" developing="" device="" direct-axis="" direct-on-line="" direction="" display.="" dissipated="" does="" double-circuit="" draw="" drawn="" driven="" driving="" during="" duty="" e3="" e="" e_3t="" e_t="" e_t_e_3t="" each="" earth="" economic="" efficiency="" eigen="" either="" electric="" electronic="" emf="" emitter="" energy="" equal="" equation="" equidistant="" equivalent="" error="" evaluate="" exactly="" excitation="" extended="" f2="a+bP2+2cP" f="" factor.="" factor="" fair="" false="" fan="" fault="" field="" fig.="" fig.below="" fig.q62.="" fig.q63.="" fig.q66="" figure-of-s="" first="" flux="" following="" follows:="" for="" four="" fourier="" frequency="" friction="" from="" fuel="" full="" function="" functions="" g1="" g2="" g="" gain="" generating="" generation="" generator="" getting="" gh="" given="" giving="" goes="" gradient="" greater="" ground="" group.="" h="" half="" has="" have="" having="" head="" heads="" help="" high="" horizontal="" hour="" i.="" i.oc="" i="" ideal="" identify="" if="" ii="" impulse="" in="" increases="" induced="" inductance="" induction="" industrial="" inertia="" infinite="" infinity="" initial="" input="" inputs="" installed="" instant="" insulation="" integers="" inverse="" inverting="" is:="" is="" it="" its="" j0="" k12="" k="" keeping="" kg="" khz="" km="" kv="" kva="" kw="" lag="" lagging.="" laplace="" large="" leads="" let="" level="" limit="" line-to-line="" line="" linked="" loa="" load="" loaded="" long="" loop="" lost="" low="" m12="" m2.="" m2="" ma="" machines="" magnetic="" magnitude="" maintain="" maintained="" margin="" marks="" matrix="" maximum="" measure="" measured="" measurement="" meet="" meter="" minimum="" modulo="" moment="" mosfet="" most="" motor="" moved="" ms="" multiplication="" multiplications="" must="" mutual="" mva.="" mva="" mvar="" mw="" n-channel="" needed="" negative="" neglect="" neglecting="" negligible="" networks="" nm2="" nm="" no="" not="" notations="" number="" nyquist="" o="" obtained.="" obtained="" oc="" occurs="" of="" off="" on="" one="" only="" oo="" open="" operation="" operational="" or="" ordered="" oscilloscope="" otherwise="" out="" output="" over="" overhead="" p.u.="" p1="" p2.="" p2="" p="" pa="" pairs="" pandr="" parameters="" passes="" peak-peak="" percentage="" phase="" plane="" plates="" plausible="" plot="" point="" polarity="" pole="" poles="" polynomial="" pon="" position="" positive="" possible="" power="" powers="" practically="" probability="" produce="" produces="" q85b="" q="" qsin="" quadrature-axis="" questions:="" questions="" quick="" r.="" r1="" r="" rad="" range.="" range="" rated="" ratio="" reactance="" read="" readings="" reads="" real="" realize="" reason:="" reason="" reasons.="" reduced="" regarding="" region.="" relation="" remain="" remains="" represents="" required="" requires="" resistance:="" resistance="" resistances="" respective="" respectively.="" respectively="" resulting="" revolve="" rf="" ripple="" rotor="" row="" rs="" s2="" s="" salient="" scalar="" sec2="" sec="" seen="" self-start="" self="" semiconductor="" sequence="" series="" service="" set-up="" set="" sets="" shaft.="" short="" should="" shown.="" shown="" shows="" shunt="" sides="" signal="" signals="" simultaneous="" sin2="" sin2x="" sin="" single-line="" single="" sinx="" size="" sizes="" slip="" small-="" solution="" source.="" source="" speed.="" speed="" stability="" star="" start="" started="" starting="" starts="" state="" statement="" statements="" stationary="" stations="" stator="" steady="" step-down="" step-up="" step="" stored="" sub-="" sub-station="" subsets="" substation="" succession.="" supplies="" supply="" supplying="" susceptances="" switch="" switched="" switching="" synchronous="" system="" systems="" t1="" t2="" t31="" t="" taken="" terminal="" than="" that="" the="" their="" them="" then="" there="" thermal="" this="" three-="" three-phase="" three="" threshold="" through="" ti="" time="" times="" to:="" to="" top="" torque="" toss="" tossed="" tosses="" total="" transfer="" transform="" transformer="" transition.="" transition="" transmission="" transposed="" trblock="" tripped="" true="" turn="" two="" u="" under="" unit="" unity="" unstable="" upper="" used="" using="" usual="" v-curve="" v="" value="" values="" variable="" variation="" vector="" vertical="" very="" vi="" viscous="" voltage.="" voltage="" voltages="" voltmeter="" w.="" w="XxY" wattmeters="" what="" when="" where="" which="" while="" wide="" will="" wishes="" with="" x.x2="" x0="" x1.x2="" x1="" x1and="" x2="" x2e="" x="" xis:="" xm="0.1c/km" y="" z2="" z2xy="" z="" zero="" ztransform="" zx2="">
v.
Then R is:
(A) Neither a Partial Order nor an Equivalence Relation
(B) A Partial Order but not a Total Order
(C) A Total Order
(D) An Equivalence Relation
5. For which one of the following reasons does Internet Protocol (IP) use the time-
to-live (TTL) field in the IP datagram header?
(A) Ensure packets reach destination within that time
(B) Discard packets that reach later than that time
(C) Prevent packets from looping indefinitely
(D) Limit the time for which a packet gets queued in intermediate routers.
6. Consider three CPU-intensive processes, which require 10, 20 and 30 time units and arrive
at times 0, 2 and 6, respectively. How many context switches are needed if the operating
system implements a shortest remaining time first scheduling algorithm? Do not count the
context switches at time zero and at the end.
(A) 1
(B) 2
(C) 3
(D) 4
7. Consider the following grammar.
Consider the following LR(0) items corresponding to the grammar above.
Given the items above, which two of them will appear in the same set in the canonical sets-of-
items for the grammar?
(A) (i) and (ii)
(B) (ii) and (iii)
(C) (i) and (iii)
(D) None of the above
8. You are given a free running clock with a duty cycle of 50% and a digital waveform f which
changes only at the negative edge of the clock. Which one of the following circuits (using
clocked D flip-flops) will delay the phase of f by 1800?
9. A CPU has 24-bit instructions. A program starts at address 300 (in decimal). Which one of
the following is a legal program counter (all values in decimal)?
(A) 400
(B) 500
(C) 600
(D) 700
10. In a binary max heap containing
n
numbers, the smallest element can be found in time
(A)
0(n)
(B)
O(logn)
(C) 0(loglogn)
(D)
0(1)
11. Consider a weighted complete graph Gon the vertex set
{v1,v2
,v} such that the weight of
the edge
(v,,v)
is
2i-j.
The weight of a minimum spanning tree of G is:
(A)
n—i
(B)
2n—2
(C)
(D) 2
12. To implement Dijkstra’s shortest path algorithm on unweighted graphs so that it runs in
linear time, the data structure to be used is:
(A) Queue
(B) Stack
(C) Heap
(D) B-Tree
13. A scheme for storing binary trees in an array X is as follows. Indexing of X starts at 1
instead of 0. the root is stored at X[1]. For a node stored at X[i], the left child, if any, is stored
in X[2i] and the right child, if any, in X[2i+1]. To be able to store any binary tree on nvertices
the minimum size of X should be
(A) log2
n
(B)
n
(C)
2n+1
(D) 2—1
14. Which one of the following in place sorting algorithms needs the minimum number of
swaps?
(A) Quick sort
(B) Insertion sort
(C) Selection sort
(D) Heap sort
15. Consider the following C-program fragment in which
i,j
and nare integer variables.
for (i = n,j = 0; i >0; i
1=
2,j +=i);
Let val(j)denote the value stored in the variable jafter termination of the
for
loop. Which one
of the following is true?
(A)
val(j)
=
8(logn)
(B)
vaI(j)=8(fi)
(C)
val(j)=8(n)
(D)
val(j)= 8(nlogn)
16. Let S be an NP-complete problem and Q and R be two other problems not known to be in
NP. Q is polynomial time reducible to S and S is polynomial-time reducible to R. Which one of
the following statements is true?
(A) R is NP-complete
(B) R is NP-hard
(C) Q is NP-complete
(D) Q is NP-hard
17. An element in an array X is called a leader if it is greater than all elements to the right of
it in X. The best algorithm to find all leaders in an array
(A) Solves it in linear time using a left to right pass of the array
(B) Solves it in linear time using a right to left pass of the array
(C) Solves it using divide and conquer in time
8(nlogn)
(D) Solves it in time
8(n2)
18. We are given a set X {x1
x}
where x, = 2’. A sample S c Xis drawn by selecting each
x,independently with probability p, =-.The expected value of the smallest number in sample S
is:
(A)
(B) 2
(C)
(D)
n
19. Let
L1 {OnminOmnm>O1L {Onmin+mOmnm>O}
and
i
= {jt
n rnjn mflm
01. Which of these languages are NOT context free?
(A)
L1
only
(B)
L3
only
(C)
L1
and
L2
(D)
L2
and
L3
20. Consider the following log sequence of two transactions on a bank account, with initial
balance 12000, that transfer 2000 to a mortgage payment and then apply a 5% interest.
1. T1 start
2. T1 B old= 1200 new= 10000
3. T1 M old=0 new=2000
4. T1 commit
5. T2start
6. T2 B old= 10000 new= 10500
7. T2 commit
Suppose the database system crashes just before log record 7 is written. When
the system is restarted, which one statement is true of the recovery procedure?
(A) We must redo log record 6 to set B to 10500
(B) We must undo log record 6 to set B to 10000 and then redo log records 2 and 3
(C) We need not redo log records 2 and 3 because transaction Ti has committed
(D) We can apply redo and undo operations in arbitrary order because they are idempotent.
Q.21 — Q.75 Carry Two Marks Each
21. For each element in a set of size
2n,an
unbiased coin is tossed. The 2ncoin tosses are
independent. An element is chosen if the corresponding coin toss were head. The probability
that exactly
n
elements are chosen is:
(A) 2n
22. Let E, F and G be finite sets.
Let
X=(EflF)-(FflG)
and
Y=(E_(EflG))_(E_F).
Which one of the following is true?
(A)
XcY
(B)
XDY
(C)
X=Y
(D)
X-Y ØandY-X Ø
23. F is an nxn real matrix. b is an nxi real vector. Suppose there are two nxivectors,
u
and
vsuch that
u
v,and
Fu
=
b,Fv
=
b.
Which one of the following statements is false?
(A) Determinant of
F
is zero
(B) There are an infinite number of solutions to
Fx
=
b
(C) There is an x Osuch that
Fx
= 0
(D)
F
must have two identical rows
24.
integers S, and ,r(S) is the set of integers obtained by applying permutation rto each
element of S?
(A)
(n-AUBAHB
(B)
(A2
+B2)n2
(C)
n!
(D)
A
fl B2/[A U
B
25. Let S = {1,2,3
,m},m>3.
Let X1 X be subsets of S each of size 3.
Define a function ffrom Sto the set of natural numbers as,
f(i)is
the number of sets Xthat
contain the element
I.
That is
f (I)={jIE
x7[.
Then
f(i)is:
(A) 3m
(B)
3n
(C) 2m+1
(D) 2n+1
26. Which one of the first order predicate calculus statements given below correctly expresses
the following English statement?
Tigers and lions attack if they are hungry or threatened.
(A) vx[(tiger(x) A lion(x)) — {(hungry(x) v threatened(x)) — attacks(x))1
(B) Vx [(tiger (x) v lion (x)) — {(hungry (x) v threatened (x)) A attacks (x)j
(C) Vx[(tiger(x) v lion(x)) — {attacks(x) — (hungry(x) v threatened(x)))1
(D) vx[(tiger(x) v lion(x)) — {(hungry(x) v threatened(x)) — attacks(x))1
27. Consider the following propositional statements:
Pl:((AAB)C))((AC)A(BC))
P2:((AvB)C))((A—C)v(B_C))
Which one of the following is true?
(A) P1 is a tautology, but not P2
(B) P2 is a tautology, but not P1
(C) P1 and P2 are both tautologies
(D) Both P1 and P2 are not tautologies
28. A logical binary relation
a,
is defined as follows:
Let be the unary negation (NOT) operator, with higher precedence then o. Which one of the
following is equivalent to
A
A
B?
(A)
(‘-‘.‘AOB)
(B)
-‘.‘(AO’-..’B)
(C)
“.‘(“.‘Ao”.’B)
(D)
AOB)
29. If
s
is a string over (0 + 1)* then let
n0 (s)
denote the number of 0’s in
s
and
n1
(s)the number of l’s in
s.
Which one of the following languages is not
regular?
(A)
L
=
{s
(0 + 1)*n0
(s)
is a 3-digit prime
(B)
L
=
{s
E (0 + 1)* for every prefix
s’
of
s, fl0 (s’)
—
n1 (s’)
2}
(C)
L={sE(0+1)*n0(s)_n1(s)4}
(D)
L
=
{s
E (0 + 1) j
n0 (s)
mod 7 =
n1 (s)
mod 5 = 0)
30. For SE (0+1)*let d(s)denote the decimal value of
s(e.g.d(101)=
5). Let
L
=
{s
E (0 + 1) j
d (s)
mod 5 = 2 and
d (s)
mod 7 = 4)
Which one of the following statements is true?
(A) L is recursively enumerable, but not recursive
(B) L is recursive, but not context-free
(C) L is context-free, but not regular
(D) L is regular
31. Let SHAM3 be the problem of finding a Hamiltonian cycle in a graph G
=(V,E)with
V
divisible by 3 and DHAM3 be the problem of determining if a Hamiltonian cycle exists in such
graphs. Which one of the following is true?
A B
AoB
True True True
True Fals
e True
Fals
e True False
Fals
Fals
e
e True
(A) Both DHAM3 and SHAM3 are NP-hard
(B) SHAM3 is NP-hard, but DHAM3 is not
(C) DHAM3 is NP-hard, but SHAM3 is not
(D) Neither DHAM3 nor SHAM3 is NP-hard
32. Consider the following statements about the context free grammar G = {S -
SS,
S -
ab, S
-
ba, S
-}
I. G is ambiguous
II. G produces all strings with equal number of a’s and b’s
III. G can be accepted by a
deterministic PDA.
Which combination below expresses all the true statements about G?
(A) I only
(B) I and III only
(C) II and III only
(D) I, II and III
33. Let
L1
be a regular language,
L2
be a deterministic context-free language and
L3
a
recursively enumerable, but not recursive, language. Which one of the following statements is
false?
(A)
L1
fl
L
is a deterministic CFL
(B)
L3
fl
L
is recursive
(C)
L1
U
L2
is context free
(D)
L1
fl
L fl L3
is recursively enumerable
34. Consider the regular language
L
=(111+11111)*. The minimum number of
states in any DFA accepting this languages is:
(A) 3
(B) 5
(C) 8
(D) 9
Consider the circuit above. Which one of the following options correctly represents
f(x,y,z)?
(A)
xz+xy+yz
(B)
xz+xy+yz
(C)
xz+xy+yz
(D)
xz+xy+yz
36. Given two three bit numbers a2a1a0 and
b2b1b0
and
c,
the carry in, the function that
represents the
carry
generate function when these two numbers are added is:
(A)
a2b2
+
a2a1b1
+
a2a1a0b0
+
a2a0b1b0
+
a1b2b1
+
a1a0b2b0
+
a0b2b1b0
(B)
a2b2
+
a2b1b0
+
a2a1b1b0
+
a1a0b2b1
+
a1a0b2
+
a1a0b2b0
+
a2a0b1b0
(C) a2
+b2 +(a2 $b2)(a1 +b1 +(a1 $b1) (a0 +b0))
(D)
a2b2
+
a2a1b1
+
a2 a1a0b0
+
a2 a0 b1b0
+
a1 b2 b1
+
a1a0 b2b0
+
a0 b2b1b0
37. Consider the circuit in the diagram. The $ operator represents Ex-OR. The D flip- flops are
initialized to zeroes (cleared).
The following data: 100110000 is supplied to the “data” terminal in nine clock
cycles. After that the values of q2q1q0 are:
(A) 000
(B) 001
(C) 010
(D) 101
38. Consider a Boolean function
f (w,x,y,z).
suppose that exactly one of its inputs is allowed to
change at a time. If the function happens to be true for two input vectors
i
=
(w1,x1,y1,z1)
and ‘2
(w2,x2,y2,z2),
we would like the function to
remain true as the input changes from
i
to ‘2 (‘ and ‘2 differ in exactly one bit position),without becoming false
momentarily. Let
f (w,x,y,z)
= (5,7,11,12,13,15). Which of the following cube covers of f will
ensure that the required property is satisfied?
(A)
wxz, wxy, xyz, xyz, wyz
(B)
wxy,wxz,wyz
(C)
wxyz,xz,wxyz
(D)
wzy, wyz, wxz, wxz, xyz, xyz
39. We consider the addition of two 2’s complement numbers
b 1b
2
.b0
and a 1a 2....a0. A
binary adder for adding unsigned binary numbers is used to add the two numbers. The sum is
denoted by
c 1c 2....c0
and the carry-out by
cQLJ.
Which one of the following options correctly
identifies the overflow condition?
(A)
c0(a1sb1)
(B) a
1b
1c+a
1b
1C
(C)
cQLJ
1
(D)
a1$b1$c1
40. Consider numbers represented in 4-bit gray code. Let
h3h2h1h0
be the gray code
representation of a number nand let
g3g2g1g0be
the gray code of (n+1) (modulo 16) value of
the number. Which one of the following functions is correct?
(A)
g0(h3h2h1h0)=(1,2,3,6,1O,13,14,15)
(B)
g1(h3h2h1h0)=
(4,9,10,11,12,13,14,15)
(C)
g2(h3h2h1h0)=(2,4,5,6,7,12,13,15)
(D)
g3(h3h2h1h0)=(0,1,6,7,10,11,12,13)
41. A CPU has a cache with block size 64 bytes. The main memory has kbanks, each bank
being cbytes wide. Consecutive c—byte chunks are mapped on consecutive banks with wrap-
around. All the kbanks can be accessed in parallel, but two accesses to the same bank must
be serialized. A cache block access may involve multiple iterations of parallel bank accesses
depending on the amount of data obtained by accessing all the kbanks in parallel. Each
iteration requires decoding the bank numbers to be accessed in parallel and this takes
--ns.
The latency of one bank access is 80 ns. If
c
= 2 and
k
= 24, the latency of retrieving a cache
block starting at address zero from main memory is:
(A) 92 ns
(B) 104 ns
(C) 172 ns
(D) 184 ns
42. A CPU has a five-stage pipeline and runs at 1 GHz frequency. Instruction fetch happens in
the first stage of the pipeline. A conditional branch instruction computes the target address
and evaluates the condition in the third stage of the pipeline. The processor stops fetching
new instructions following a conditional branch until the branch outcome is known. A program
executes io instructions out of which 20% are conditional branches. If each instruction takes
one cycle to complete on average, the total execution time of the program is:
(A) 1.0 second
(B) 1.2 seconds
(C) 1.4 seconds
(D) 1.6 seconds
43. Consider a new instruction named branch-on-bit-set (mnemonic bbs). The instruction
“bbs
reg, pos, label”
jumps to label if bit in position
pos
of register operand
reg
is one. A register is
32 bits wide and the bits are numbered 0 to 31, bit in position 0 being the least significant.
Consider the following emulation of this instruction on a processor that does not have
bbs
implemented.
temp
—
reg & mask
Branch to
label
if temp is non-zero.
The variable
temp
is a temporary register. For correct emulation, the variable mask must be
generated by
(A)
mask —0x1< (B) mask f— 0 x rrrrrrrr >>
pos
(C)
mask—pos
(D)
mask —0xf
44. Station A uses 32 byte packets to transmit messages to Station B using a sliding window
protocol. The round trip delay between A and B is 80 milliseconds and the bottleneck
bandwidth on the path between A and B is 128 kbps. What is the optimal window size that A
should use?
(A) 20
(B) 40
(C) 160
(D) 320
45. Two computers Cl and C2 are configured as follows. Cl has IP address
203.197.2.53 and netmask 255.255.128.0. C2 has IP address 203.197.75.201 and netmask
255.255.192.0. which one of the following statements is true?
(A) Cl and C2 both assume they are on the same network
(B) C2 assumes Cl is on same network, but Cl assumes C2 is on a different network
(C) Cl assumes C2 is on same network, but C2 assumes Cl is on a different network
(D) Cl and C2 both assume they are on different networks.
46. Station A needs to send a message consisting of 9 packets to Station B using a sliding
window (window size 3) and go-back-n error control strategy. All packets are ready and
immediately available for transmission. If every 5th packet that A transmits gets lost (but no
acks from B ever get lost), then what is the number of packets that A will transmit for sending
the message to B?
(A) 12
(B) 14
(C) 16
(D) 18
47. Consider the following graph:
Which one of the following cannot be the sequence of edges added, in that
order, to a minimum spanning tree using Kruskal’s algorithm?
(A)
(a—b),(d—f),(b—f),(d—c),(d—e)
(B)
(a—b),(d—f),(d—c),(b—f),(d—e)
(C)
(d—f),(a—b),(d—c),(b—f),(d—e)
(D)
(d—f),(a—b),(b—f),(d—e),(d—c)
48. Let
T
be a depth first search tree in an undirected graph G. Vertices
u
and
v
are leaves of
this tree
T.
The degrees of both
u
and
v
in G are at least 2. which one of the following
statements is true?
(A) There must exist a vertex
w
adjacent to both
u
and
v
in G
(B) There must exist a vertex
w
whose removal disconnects
u
and
v
in G
(C) There must exist a cycle in G containing
u
and
v
(D) There must exist a cycle in G containing uand all its neighbours in G.
49. An implementation of a queue Q, using two stacks Si and S2, is given below:
void insert (Q, x)
push (Si, x);
void delete (Q)
if (stack—empty(52)) then
if
(stack—empty(Si)) then
print(”Q is empty”);
return;
else while (! (stack—empty (Si)))
x=pop (Si);
push(52,x)
x=pop (S2);
Let
flinsert
and
m(
n)delete operations be performed in an arbitrary order on an empty queue
Q. Let x and y be the number of
push
and pop operations performed respectively in the
process. Which one of the following is true for all
m
and
n?
(A)
n+m x<2n -2="" -="" ...="" 0="" 1="" 2="" 2m="" 2n="" 3="" 4="" 50.="" 51.="" 52.="" 53.="" 54.="" 55.="" 56.="" 57.="" 58.="" 59.="" 5="" 60.="" 61.="" 8="" a1="" a="" about="" access="" accessible="" add="" address="" after="" algorithm="" all="" allocate="" allowing="" always="" amp="" an="" and="" another="" any="" applied="" are="" arguments="" array.="" array="" arrays="" as="" at="" atomic="" ay="" b1="" b="" be="" binary="" binary_semaphore="" boolean="" both="" but="" by="" c-function="" c="" call="" can="" cell="" code.="" code="" common="" compared="" comparison="" compilation="" compiler="" complexity="" computation="" compute="" computed="" condition="" consider="" contains="" correct:="" correct="" correctly="" corresponding="" cpu="" dead="" depending="" e="" each="" effect="" either="" elements="" elimination="" else="" end="" entries="" er="" error="" even="" exactly="" execution="" f="" false="" fastest="" fault="" fetch-and-set="" fetches="" find="" five="" fl="" following="" follows:="" for="" form="" fortran="" found="" fr="" functions="" generate="" get="" given="" grammar:="" grammar="" hashing="" have="" here="" hold="" i.e.="" i.e="" i1="" i1a="" i3="" i="" ia="" ib="" id.value="" id="" idl="" if="" ifj="m" ifx="" ii="" implementation="" implements="" improve="" in="" initialize="" input="" instruction="" int="" integer="" integers="" intervening="" invariant="" is:="" is="" it="" ix="iy" iy="it" j="" k.="" k="" key="" l2:="" l2="" language="" largest="" li:="" li="" like="" line="" location="" locations="" loglogn="" logn="" loop="" m="" may="" median="" memory="" mibe="" mlare="" model="" mt="" n25="" n2="" n3="" n:="" n="" nameless="" neither="" nl="" nlogn="" nor="" not="" nt="" number="" numbers="" o="" of="" old="" on="" one="" only="" or="" otherwise="" output="" p="" parser="" pass-by-reference="" pass="" passed="" performance="" permitted="" pivot="" pointers.="" pointers="" predictive="" print="" prints="" procedure="" process="" program="" px="" py="" q="" quick="" r="" recurrence:="" reduce="" reduction="" referring="" report="" represented="" represents="" respectively.="" return="" runtime="" rz8="" s.="" s2:="" s2="" s3:="" s3="" s4:="" s4="" s5:="" s5="" s="" same="" scheme.="" scheme="" scope="" segment.="" segmentation="" selected="" semaphore="" set="" sets="" si:="" si="" size="" sj="" some="" sort="" sorted="" space="" span="" state="" statement="" statements:="" statements="" stored="" strength="" sub-expression="" subroutine="" subtract="" such="" sum="" swap="" t2="" t="" table="" takes="" temporary="" termination="" that="" the="" them.="" there="" these="" this="" ti="a[j]" time.="" time="" to="" token="" transformation="" transformations="" translation="" true="" two="" unconditionally="" unsigned="" v="" valid="" value.="" value="" void="" where="" which="" while="" will="" without="" work2="" worki="" workl="" written="" x-y="" x.="" x="" xfly="" xyz="" y="" z="" zzz="">value);
do
fetch—and—set x, y;
while (y)
void V (binary_semaphore *s)
S—>value = 0;
Which one of the following is true?
(A) The implementation may not work if context switching is disabled in P
(B) Instead of using
fetch-and —set,
a pair of normal load/store can be used
(C) The implementation of V is wrong
(D) The code does not implement a binary semaphore
62. A CPU generates 32-bit virtual addresses. The page size is 4 KB. The processor has a
translation look-aside buffer (TLB) which can hold a total of 128 page table entries and is 4-
way set associative. The minimum size of the TLB tag is:
(A) 11 bits
(B) 13 bits
(C) 15 bits
(D) 20 bits
63. A computer system supports 32-bit virtual addresses as well as 32-bit physical addresses.
Since the virtual address space is of the same size as the physical address space, the
operating system designers decide to get rid of the virtual memory entirely. Which one of the
following is true?
(A) Efficient implementation of multi-user support is no longer possible
(B) The processor cache organization can be made more efficient now
(C) Hardware support for memory management is no longer needed
(D) CPU scheduling can be made more efficient now
64. Consider three processes (process id 0, 1, 2 respectively) with compute time bursts 2, 4
and 8 time units. All processes arrive at time zero. Consider the longest remaining time first
(LRTF) scheduling algorithm. In LRTF ties are broken by giving priority to the process with the
lowest process id. The average turn around time is:
(A) 13 units
(B) 14 units
(C) 15 units
(D) 16 units
65. Consider three processes, all arriving at time zero, with total execution time of
10, 20 and 30 units, respectively. Each process spends the first 20% of execution time doing
I/O, the next
70°h
of time doing computation, and the last 10°h of time doing I/O again. The
operating system uses a shortest remaining compute time first scheduling algorithm and
schedules a new process either when the running process gets blocked on I/O or when the
running process finishes its compute burst. Assume that all I/O operations can be overlapped
as much as possible. For what percentage of time does the CPU remain idle?
(A) 0%
(B)
1O.6°h
(C)
30.O°h
(D)
89.4°h
66. Consider the following snapshot of a system running n processes. Process
i
is holding
x,instances of a resource R,
1 n.
currently, all instances of R are occupied. Further, for all
I,
process
i
has placed a request for an additional y, instances while holding the x, instances it
already has. There are exactly two processes p and q such that =
Yq
= 0. Which one of the
following can serve as a necessary condition to guarantee that the system is not approaching
a deadlock?
(A)
min(xp,xq)
< max Yk (B) X + Xq mink pq Yk (C) max(xp,xq)>1
(D)
min(xp,xq)>1
67. Consider the relation account (customer, balance) where customer is a primary key and
there are no null values. We would like to rank customers according to decreasing balance.
The customer with the largest balance gets rank 1. ties are
not broke but ranks are skipped: if exactly two customers have the largest balance they each
get rank 1 and rank 2 is not assigned.
select A.customer, count(B.customer)
Queryl: from account A, account B
where A.balance <=B.balance group by A.customer select A.customer, 1+count(B.customer) Query2: from account A, account B where A.balance < B.balance group by A.customer Consider these statements about Queryl and Query2. 1. Queryl will produce the same row set as Query2 for some but not all databases. 2. Both Queryl and Query2 are correct implementation of the specification 3. Queryl is a correct implementation of the specification but Query2 is not 4. Neither Queryl nor Query2 is a correct implementation of the specification 5. Assigning rank with a pure relational query takes less time than scanning in decreasing balance order assigning ranks using ODBC. Which two of the above statements are correct? (A) 2 and 5 (B) 1 and 3 (C) 1 and 4 (D) 3 and 5 68. Consider the relation enrolled (student, course) in which (student, course) is the primary key, and the relation paid (student, amount) where student is the primary key. Assume no null values and no foreign keys or integrity constraints. Given the following four queries: Queryl:select student from enrolled where student in (select student from paid) Query2:select student from paid where student in (select student from enrolled) Query3:select E.student from enrolled E, paid P where E.student = P.student Query4:select student from paid where exists (select * from enrolled where enrolled.student = paid.student) Which one of the following statements is correct? (A) All queries return identical row sets for any database (B) Query2 and Query4 return identical row sets for all databases but there exist databases for which Queryl and Query2 return different row sets. (C) There exist databases for which Query3 returns strictly fewer rows than Query2 (D) There exist databases for which Query4 will encounter an integrity violation at runtime. 69. Consider the relation enrolled (student, course) in which (student, course) is the primary key, and the relation paid (student, amount) where student is the primary key. Assume no null values and no foreign keys or integrity constraints. Assume that amounts 6000, 7000, 8000, 9000 and 10000 were each paid by 20% of the students. Consider these query plans (Plan 1 on left, Plan 2 on right) to “list all courses taken by students who have paid more than x” enrolled paid enrolled paid 1’ 1’ Probe index Sequential on student scan, select amount > x
A disk seek takes 4ms, disk data transfer bandwidth is 300 MB/s and checking a tuple to see if
amount is greater than x takes lOps. Which of the following statements is correct?
(A) Plan 1 and Plan 2 will not output identical row sets for all databases
(B) A course may be listed more than once in the output of Plan 1 for some data bases
(C) For x = 5000, Plan 1 executes faster than Plan 2 for all databases
(D) For x = 9000, Plan I executes slower than Plan 2 for all databases.
70. The following functional dependencies are given:
AB
-*
CD,AF
-*
D,DE
-*
F,C
-*
G,F
-*
E,G
-*
A.
Which one of the following options is false?
(A)
{CF} ={ACDEFG}
(B)
{BG}
=
{ABCDG}
(C)
{AF} ={ACDEFG}
(D)
{AB} ={ABCDFG}
Common Data Questions:
Common Data for Questions 71, 72, 73:
The 2 vertices of a graph G corresponds to all subsets of a set of size n, for
n < 6. Two vertices of G are adjacent if and only if the corresponding sets intersect in exactly two elements. 71. The number of vertices of degree zero in G is: (A) 1 (B) n (C) n+1 (D)2 72. The maximum degree of a vertex in G is: (A) 2J (B) 2 2 (C) 23x3 (D) 2 1 73. The number of connected components in G is: (A) n (B) n+2 (C) 2/2 (D) Common Data for Questions 74, 75: Consider two cache organizations: The first one is 32 KB 2-way set associative with 32- byte block size. The second one is of the same size but direct mapped. The size of an address is 32 bits in both cases. A 2-to-i multiplexer has a latency of 0.6 ns while a kbit comparator has a latency of k/lO ns. The hit latency of the set associative organization is h1while that of the direct mapped one is h2. 74. The value of h1is: (A) 2.4 ns (B) 2.3 ns (C) 1.8 ns (D) 1.7 ns 75. The value of h2 is: (A) 2.4 ns (B) 2.3 ns (C) 1.8 ns (D) 1.7 ns Linked Answer Questions: Q.76 to Q85 Carry Two Marks Each Statement for Linked Answer Questions 76 & 77: A 3-ary max heap is like a binary max heap, but instead of 2 children, nodes have 3 children. A 3-ary heap can be represented by an array as follows: The root is stored in the first location, a[0], nodes in the next level, from left to right, is stored from a[1] to a[3]. The nodes from the second level of the tree from left to right are stored from a[4] location onward. An item x can be inserted into a 3-ary heap containing n items by placing x in the location a[n] and pushing it up the tree to satisfy the heap property. 76. Which one of the following is a valid sequence of elements in an array representing 3-ary max heap? (A) 1, 3, 5, 6, 8, 9 (B) 9, 6, 3, 1, 8, 5 (C) 9, 3, 6, 8, 5, 1 (D) 9, 5, 6, 8, 3, 1 77. Suppose the elements 7, 2, 10 and 4 are inserted, in that order, into the valid 3- ary max heap found in the above question, Q.76. Which one of the following is the sequence of items in the array representing the resultant heap? (A) 10, 7, 9, 8, 3, 1, 5, 2, 6, 4 (B) 10, 9, 8, 7, 6, 5, 4, 3, 2, 1 (C) 10, 9, 4, 5, 7, 6, 8, 2, 1, 3 (D) 10, 8, 6, 9, 7, 2, 3, 4, 1, 5 Statement for Linked Answer Questions 78 & 79: Barrier is a synchronization construct where a set of processes synchronizes globally i.e. each process in the set arrives at the barrier and waits for all others to arrive and then all processes leave the barrier. Let the number of processes in the set be three and S be a binary semaphore with the usual P and V functions. Consider the following C implementation of a barrier with line numbers shown on left. void barrier (void) 1: P(S); 2: process_arrived++; 3. V(S); 4: while (process_arrived !=3); 5: P(S); 6: process_left++; 7: if (process_left==3) 8: process_arrived = 0; 9: process_left = 0; 10: 11: V(S); The variables process_arrived and process_left are shared among all processes and are initialized to zero. In a concurrent program all the three processes call the barrier function when they need to synchronize globally. 78. The above implementation of barrier is incorrect. Which one of the following is true? (A) The barrier implementation is wrong due to the use of binary semaphore S (B) The barrier implementation may lead to a deadlock if two barrier in invocations are used in immediate succession. (C) Lines 6 to 10 need not be inside a critical section (D) The barrier implementation is correct if there are only two processes instead of three. 79. Which one of the following rectifies the problem in the implementation? (A) Lines 6 to 10 are simply replaced by process_arrived-- (B) At the beginning of the barrier the first process to enter the barrier waits until process_arrived becomes zero before proceeding to execute P(S). (C) Context switch is disabled at the beginning of the barrier and re-enabled at the end. (D) The variable process_left is made private instead of shared Statement for Linked Answer Questions 80 & 81: A CPU has a 32 KB direct mapped cache with 128-byte block size. Suppose A is a two- dimensional array of size 512x512 with elements that occupy 8-bytes each. Consider the following two C code segments, P1 and P2. P1: for (i=0; i<512 -5v="" -="" -e="" -ee="" -eu="" -lv="" 0.5x="" 0="" 1.10="" 1.11="" 1.12="" 1.13="" 1.14="" 1.15="" 1.16="" 1.17="" 1.18="" 1.19="" 1.1="" 1.20="" 1.21="" 1.22="" 1.23="" 1.24="" 1.25="" 1.2="" 1.3="" 1.4="" 1.5="" 1.6="" 1.7="" 1.8="" 1.9="" 1.="" 100="" 12="" 12t2="" 12t3="" 12t="" 142.="" 16384="" 16="" 1="" 1c="" 1h="" 1k="" 2.="" 2048="" 20="" 24t="" 25="" 262144="" 28="" 2="" 2cc="" 2x="" 3-phase="" 3-step="" 3.="" 36="" 3="" 4-phase="" 4-pole="" 4.="" 40="" 4="" 4x="" 5.="" 50="" 5="" 5q="" 6.="" 7.="" 7="" 8.="" 80.="" 80="" 81.="" 82.="" 82="" 83.="" 83:="" 84.="" 84="" 85.="" 85:="" 8="" 8c="" 8cc="" 9.="" 9="" ________="" a.="" a="" ab="" above="" ac="" acbab="" acbe="" acbh="" accb="" achieved="" across="" advantages="" all="" alternator="" always="" amp="" amplifier="" an="" analogue="" and="" answer.="" answer="" answered.="" answers="" any="" applied="" appropriate="" arbitrary="" are="" arid="" armature="" array="" as="" assbab="" assumes="" at="" attempted="" average="" averaging="" avoid="" avoiding="" b.="" b2="" b3="" b4="" b5="" b="" back="" base="" based="" bases="" be="" because="" beginning="" being="" below.="" below="" between="" bi="" bjt="" bm="" book.="" book="" both="" boxes="" bridge.="" bridge="" bridges.="" bridges="" broadcast="" broken="" brushes.="" built="" but="" by="" c="" cache="" cage="" capacitor="" carefully:="" carries="" carry="" certain="" changes="" choice="" choices="" circuit="" circuits="" class="" clearly="" closest="" coming="" commutating="" commutation="" commutator="" compensating="" compensation="" component="" conflicts="" connected="" connection="" connections="" consider="" considerations="" considered="" consists="" constant="" constitute="" control="" controlled="" converter="" corona="" correct="" correctly="" corresponding="" credit.="" crossover="" ction="" current.="" current="" d="" damping="" data="" dc="" definite="" delay="" depth="" derivation="" design="" diagram="" direct="" direction="" distance="" distortion="" doubled="" draws="" drop="" due="" e="" each.="" each="" economizer="" effect="" electric="" electromagnetic="" electron="" electronic="" element="" else="" emf="" enable="" equal="" equally="" error="" errors="" evaluated="" excited="" executed="" exhibits="" experienced="" extends="" factor="" fault="" favour="" feature="" feed="" feedback="" feeds="" field="" fifteen="" fig.1.3="" fig.="" first="" five="" flashover="" flue="" following="" follows:="" for="" force="" forward-path="" forward="" forwarding="" found="" frames="" frequency="" fresh="" from="" fully="" function="" fundamental="" furnace="" g="" gases="" generate="" generates="" get="" given="" gives="" grammar="" grammars="" graph="" greater="" h.p.="" h12="" h1="" h1o="" h2="" h3="" h4="" h5="" h6="" h7="" h8="" h9="" harmonic="" has="" have="" heat="" heated="" hi="" high="" hil="" hio="" host="" hosts="" hvdc="" i="" ideal="" identified="" identifies="" if="" ii="" iii="" impedance="" important="" improper="" improving="" in="" ind="" independently="" index="" induction="" inductor="" inherent="" initial="" initially="" input="" insensitive="" inspite="" instances="" instantaneous="" instructions="" instrument="" interconnection="" interrupt="" into="" intr="" introduce="" introduces="" inverse="" inverter="" is:="" is="" it="" its="" iv="" j="" keeping="" known="" l.p.="" l="{a’" lan5="" lan="" language="" lans="" least="" legibly="" length="" less="" let="" level="" limitation="" line.="" line="" linear="" linked="" listed="" load="" located="" loop="" looping="" low="" lower="" lowest="" m1="" m="" machine="" magnetic="" magnitude="" mark.="" mark="" marking.="" marks="" max="" may="" measurement="" measurements.="" measures="" mechanical="" meter="" minimum="" misses="" mixed="" more="" motor="" multiple-choice="" multiple="" must="" namely="" negative="" next="" no="" non-zero="" none="" normal="" not="" number.="" number="" numbers="" o="" of="" off="" on="" one="" only="" opamp="" open="" operation="" options="" or="" order="" organize="" out="" output="" over-current="" p1="" p2:="" p2="" packet.="" packets="" page="" paper="" papers="" parameter="" parameters="" partial="" path="" paths="" peak="" per="" phase="" phases="" ping="" placed="" plant="" pole="" poles="" port="" possibility="" power="" preference="" preferred.="" previous="" primarily="" primary="" problems="" proper="" protection="" provided="" pwm="" question.="" question="" questions.="" questions="" questsof="" r="" ramp="" ratio="" reach="" reactance="" reaction="" reactive="" read="" registers.="" related="" relay="" remains="" represents="" required="" requirement="" resistance="" resolved="" responds="" response="" rest="" reverse="" reversed="" reversing="" rms="" root="" rotation="" rotor="" rst3="" rst7.5="" s-accb="" s="" same="" saturation="" score="" second="" secondary="" section="" sections:="" semi-converter="" send="" sends="" sensitive="" separately="" sequence="" serial="" servomotor="" setting="" sheets="" shoes="" short="" shortest="" should="" shown="" side="" signal="" slots.="" slots="" slowly="" source="" spanning="" sparking="" square-root="" square="" squirrel="" stability="" starring="" started="" state="" statement="" stator.="" stator="" steady-state="" steady="" steam="" step="" stepper="" steps="" strictly.="" string="" sub-question="" sub-questions.="" sub-questions="" subjected="" substantial="" such="" supplies.="" supplying="" surface="" system="" systems="" t3="" t5v="" t="" table="" tapped="" te_t="" teeth="" terminals="" than="" that="" the="" them="" themselves="" then="" there="" thermal="" these="" third="" this="" three-phase="" three="" through="" thyristorised="" ties="" time-invariant="" time.="" time="" to="" torque.="" total="" transfer="" transformer="" transformers="" transmission="" transparent="" trap="" traversal="" tree.="" tree="" triangular="" twenty-="" twenty-five="" twenty="" two-phase="" two="" type.="" type="" typically="" u="" unit-step="" unit="" units="" unity="" unscored="" up="" uses="" using="" uxb="" uxe="" v0="" v="" value.="" value="" vectored="" velocity="" very="" volt-ampere="" volt-amperes="" voltage="" voltages="" water="" waveform="" what="" when="" where="" which="" whose="" will="" winding="" windings="" with="" without="" working="" write="" written="" x.="" x="" y="" your="" zero.="" zero="" zones=""> 0. The transfer function of the system is:
(a) 1 2
(b) 1 2
(c) S 2
(d) 1
2. This question consists of 25 (TWENTTY FIVE) sub-questions. Each sub-question carries TWO
marks. The answers to these sub-questions MUST be written only in the appropriate boxes
corresponding to the questions in the first page of the answer book.
2.1 A two-port device is defined by the following pair of equations:
i
= 2v +
v2
and ‘2 =
V1 + V2
Its impedance parameters
(z111z121z211z22)are
given by
(a) (2,1,1,1)
(b) (1,-1,-1,2)
(c) (1,1,1,2)
(d) (2,-1,-1,1)
2.2. The circuit shown in Fig.2.2 is equivalent to a load of
(a) (0.54+jO.313) ohms
(b) (4 — j2) ohms
(c) (4.54 — jl.69) ohms
(d) (4 + j2) ohms
2.3. The minimal product of sums function described by the K-map given in Fig. below
01 1 0 0
100 0
2.4. A diode whose terminal characteristics are related as ‘D =Is[-where Isis the
reverse saturation current and
VTi5
the thermal voltage (=25mV), is biased at =
2mA.
Its
dynamic resistance is:
(a) 25 ohms
(b) 12.5 ohms
(c) 50 ohms
(d) 100 ohms
2.5. In the circuit of Fig. below, the value of the base current I8will be
(a) 0.0 micro amperes
(b) 18.2 micro amperes
(c) 26.7 micro amperes
(d) 40.0 micro amperes
2.6. A dual slope analog-to-digital converters uses an N-bit counter. when the input signal
Va
is being integrated, the counter is allowed to count up to a value
(a) equal to
2N
—2
(b) equal to
2N
—1
(c) proportional to
Va
(d) inversely proportional to
Va
2.7. A 3-phase delta/star transformer is supplied at 6000 V on the delta-connected side. The
terminal voltage on the secondary side when supplying full load as 0.8 lagging power-factor is
415 V: The equivalent resistance and reactance drops for the transformer are la/c and Se/c
respectively. The turn’s ratio of the transformer is:
(a) 14
(b) 24
(c) 42
(d) 20
2.8. A 240 V dc series motor takes 40A when giving its rated output at 1500 rpm. Its
resistance is 0.3 ohms. The value of resistance which must be added to obtain rated torque at
1000 rpm is:
(a) 6 ohms
(b) 5.7 ohms
(c) 2.2 ohms
(d) 1.9 ohms
2.9. The power input to a 415V, 50 Hz, 6 pole, 3-phase induction motor running at
975 rpm is 40 kW. The stator losses are 1kW and friction and windage losses total 2 kW. The
efficiency of the motor is
(a)
92.5°h
(b)
90°h
(c)
91°h
(d) 88°h
2.10. A single-phase, 2000V alternator has armature resistance and reactance of 0.8 ohms
and 4.94 ohms respectively. The voltage regulation of the alternator at 100A load at 0.8
leading power-factor is:
(a)
7°h
(b)
-8.9°h
(c) 14°h
(d)
0°h
2.11. A permanent magnet dc commutator motor has a no load speed of 6000 rpm when
connected to a 120V dc supply. The armature resistance is 2.5 ohms and other losses may be
neglected. The speed of the motor with supply voltage of 60V developing a torque 0.5 Nm, is:
(a) 3000 rpm
(b) 2673 rpm
(c) 2836 rpm
(d) 5346 rpm
2.12. A transmission line has equal voltages at the two ends, maintained constant by two
sources. A third source is to be provided to maintain constant voltage (equal to end voltages)
at either the midpoint of the line or at 755 of the distance from the sending end. Then the
maximum power transfer capabilities of the line in the original case and the other two cases
respectively will be in the following ratios.
(a) 1:1:1
(b) 1:2:1
(c) 1:2:4
(d)1:4:16
2.13. The plug setting of a negative sequence relay is 0.2A. The current transformer ratio is
5:1. The minimum value of line-to-line fault current for the operation of the relay is
(a) 1A
(b) 1
A
(c) 1.732A
(d) 0.2
A
2.14. The incremental cost chaçaceristlIf two generators delivering 200 MW are as follows
= 2.0 + 0.01P1,.- = 1.6 + 0.21’2
dP1 dP2
For economic operation, the generations P1 and
P2
should be
(a)
P1
=
P2
= 100MW
(b)
P1
=
8OMW,P2
= 120MW
(c)
P1
= 200MW,
P2
=
0MW
(d)
P1
=
120MW, P2
=
80MW
2.15. The corona loss on a particular system at 50 Hz is 1kW/km per phase. The
corona loss at 60 Hz would be
(a) 1kW/km per phase
(b) 0.83kW/km per phase
(c) 1.2kW/km per phase
(d) 1.13kW/km per phase
2.16. The severity of line-to-ground and three phase faults at the terminals of an unloaded
synchronous generator is to be same. If the terminal voltage is 1.0 p.u. and
z1 =z2
=jO.lp.u.,z0 =jO.05p.u.for
the alternator, then the required inductive reactance for neutral
grounding is:
(a) 0.0166 p.u.
(b) 0.05 p.u.
(c) 0.1 p.u.
(d) 0.15 p.u.
2.17. A three phase voltage source inverter supplies a purely inductive three phase load. Upon
Fourier analysis, the output voltage waveform is found to have an hth order harmonic of
magnitude ahtimes that of the fundamental frequency component
(ah < 1). The load current would then have an h-th order harmonic of magnitude (a) zero (b) ah times the fundamental frequency component (c) hahtimes the fundamental frequency component (d) ah lh times the fundamental frequency component 2.18. A step down chopper operates from a dc voltage source 4,and feeds a dc motor armature with a back emf Eb. From oscilloscope traces, it is found that the current increases for time tr,falls to zero over time t1,and remains zero for time t0, in every chopping cycle. Then the average dc voltage across the freewheeling diode is: (A) Vstr (Vstr +Ebtf) (B)(tr + tf + t0) (tr + tf + t0) (C) (Vstr +Ebto) Vstr +Eb (tf +t0) (D)(tr+tf+tO) - •. (t,+t+to) 2.19. A three phase, wound rotor induction motor is to be operated with slip energy recovery in the constant torque mode, when it delivers an output power F at slop s. then theoretically, the maximum power that is available for recovery at the rotor terminals, is equal to p0 p0.s (a) F (b) P0. (c) 1s (d) 1s 2.20. The two wattmeter method is used to measure active power on a three phase, three wire system. If the phase voltage is unbalanced, then the power reading is: (a) affected by both negative sequence and zero sequence voltages (b) affected by negative sequence voltages but not by zero sequence voltages (c) affected by zero sequence voltages but not by negative sequence voltages (d) not affected by negative or zero sequence voltages 2.21. If an ac voltage wave is corrupted with an arbitrary number of harmonics, then the overall voltage waveform differs from its fundamental frequency component in terms of (a) only the peak values (b) only the rms values (c) only the average values (d) all the three measures (peak, rms and average values) 2.22. The characteristic equation of a feedback control system is: 2s4 + s3 + 3s2 + 5s + 10 = 0 The number of roots in the right half of s-plane are: (a) zero (b) 1 (c) 2 (d) 3 2.23. A unity feedback system has open-loop transfer function G(s) = 25 The peak overshoot in the step-input response of the system is approximately equal to: (a) 5°h (b) 1O°h (c) 15°h (d) 20°h 2.24. Maximum phase-lead of the compensator D(s) = ,is (a) 52 deg at 4 rad/sec (b) 52 deg at 10 rad/sec (c) 55 deg at 12 rad/sec (d) None of the answers is correct SECTION - B This section consists of TWENTY qJtknof FIVE marks each. ANY FIFTEEN out of them have to be answered. If more number of quetions are attempted, score off the answers not be evaluated, else, only the first fifteen unscored answers will be considered. 3. Predict the current I in Fig. below in response to a voltage of 20Z0°V. The impedance values are given in ohms. Use the thevenin’s theorem. 4. (a) Show via the construction of a suitable Gaussian surface, that the capacitance of a spherical capacitor consisting of two concentric shells of radii a and b is given by ab C = 4,rs0 (b — a) where s0 is the free space permittivity. (b) A current 1 in the short conducting element shown in Fig.4 produces a flux density B at point 1. Determine the magnitude and the direction of the flux density vector at point 2. 5. A current amplifier has an input resistance of 1012, an output resistance of 10k12 and a current gain of 1000. It is feed by a current source having a source resistance of 10k12 and its output is connected to a i012 load resistance. Find the voltage gain and the power gain. 6. An active filter consisting of an op-amp, resistors R1,R2,R3 and two capacitors of value C each, has a transfer function 1 —s (R1 C) T(s)_ + 1 whereR=R111R2. ‘-7 RC) (RR3c2) If R1 = 2k12, R2 = .-k12, R3=200k12 and C = 0.1 pF, determine the centre frequency ak, gain A0 and the Q of the filter. 7. The counter shown in Fig. below is initially in state Q2 = 0,Q1 = 1,Q0 = 0.With reference to the CLK input, draw waveforms for Q2,Q1,Q0and P for the next three CLK cycles. 8. In a single-phase, three-winding transformer, the turns ratio for primary: secondary: tertiary windings is 20:4:1. With the lagging currents of 50A at a power factor of 0.6 in the tertiary winding, find the primary current and power- factor. 9. A belt driven dc shunt generator runs at 1500 rpm delivering 10k2, at 220V bus bars. The belt breaks, following which the machine operates as a motor drawing 2kW power. What will be its speed as a motor? The armature and field resistances are 0.25 ohms and 55 ohms respectively. Ignore armature reaction and assume the contact drop at each brush to be lv. 10. A 230V, 20 hp, 60 Hz, 6-pole, 3-phase induction motor driving a constant torque load at rated frequency, rated voltage and rated horse-power, has a speed of 1175 rpm and an efficiency of 92.1°h. Determine the new operating speed if a system disturbance causes 10°h drop in voltage and 6°h drop in frequency. Assume that friction, windage and stray power losses remain constant. 11. A 2300 V, 3-phase synchronous motor driving a pump is provided with a line ammeter and a field rheostat. When the rheostat is adjusted such that the ac line current is minimum. The ammeter reads 8.8A. What is the power being delivered to the pump, neglecting losses? How should the rheostat be adjusted so that the motor operates at 0.8 leading power factor? How many kVARs is the motor supplying to the system at this new power factor? 12. A 275 kV, 3-phase, 50 Hz, 400 km lossless line has following parameters: x=0.05 ohms/km, line charging susceptance y=3.0 micro-Siemens/km. (a) Calculate the receiving end voltage on open circuit using justifiable assumptions. (b) What load at the receiving end will result in a flat voltage profile on the line? (c) If the flat voltage profile is to be achieved at 1.2 times the loading in (b), what will be the nature and quantum of uniformly distributed compensation required? 13. In a 3-bus system, Gauss load flow method is to be used for finding the switched capacitor compensation required to maintain the voltage at bus 2 equal to 1.0 p.u. the data for the system is as follows: Line data: Z12 =Z13 =Z31 =jO.1 p.u.Neglect line charging. Bus data: Bus No. Bus Type Specifications 1 Slack V1 (1+jO)p.u. Load:P2 +jQ2 =(0.4+jO.2)p.u. 2 PV V2 (magnitude) = 1.Op.u. 3 PQ Load: P3 +jQ3 = (0.3+jO.15)p.u. All data are on common base values. With the help of one iteration of load flow, explain how you will achieve the stated objective. 14. For the configuration shown in Fig.14, the breaker connecting a large system to bus 2 is initially open. The system 3-phase fault level at bus 3 under this condition is not known. After closing the system breaker, the 3-phase fault level at bus 1 was found to be 5.0 p.u. What will be the new 3-phase fault level at system bus 3 after the interconnection? All per unit values are on common bases. Perfault load currents are neglected and prefault voltages are assumed to be 1.0 p.u. at all buses. IDle en System Eg = 1.0 pU. XT= 0.2 D.U. XLine = 0.3 pU. Xd 0.2 D.U. 15. A synchronous generator, having a reactance of 0.15 p.u., is connected to an infinite bus through two identical parallel transmission lines having reactance of 0.3 p.u. each. In steady state, the generator is delivering 1 p.u. Power to the infinite bus. For a three-phase fault at the receiving end of one line, calculate the rotor angle at the end of first time step of 0.05 seconds. Assume the voltage behind transient reactance for the generator as 1.1 p.u. and infinite bus voltage as 1.0 p.u. Also indicate how the accelerating powers will be evaluated for the next time step if the breaker clears the fault (a) at the end of an interval (b) at the middle of an interval 16. 16. A single phase voltage source of magnitude 4and frequency o (rad/s) is connected to an inductance L through an antiparallel back-to-back pair of thyristors. The forward and reverse conducting thyristors are fired at an angle of a from the positive going and negative going zero crossings of the supply voltage respectively, in each cycle. Obtain an expression for the inductor current in each cycle for a given value of x. The voltage drop across the thyristors, when either of them is in conclusion, may be assumed to be negligible. 17. A dc motor with armature resistance Ra5 fed from a step down chopper in the continuous mode, and operates at some known speed and known excitation current. The motor current rises from .tmin to .tmax in the ON period 7,of the chopper; and drops from Imax to .tmin in the OFF period T of the same circuit. Both the rise and fall of the current may be assumed to be approximately linear. What is the average power loss in the machine armature? 18. For perfectly balanced operation a certain three phase ac power electronic circuit generates odd harmonic currents of order five and seven in the three phases of the ac mains. Identify which of these harmonics form a positive-sequence system, and which form a negative-sequence system. 19. A three-phase load operates with balanced voltages applied to its terminals, and draws balanced currents. The potential coil of a moving coil wattmeter is connected from R to Y terminals of the load. The current coil of the meter is connected in series with phase B. by appropriate derivation, show that the quantity indicated by this wattmeter is proportional to the reactive power drawn by the load. 20. Open-loop transfer function of a unity-feedback system is: G(s) = G1(s).e = ___________ s(s+1)(s+2) Given: G1 (ja = 1 when a = 0.466. (a) Determine the phase margin when VD = 0. (b) Comment in one sentence on the effect of dead time on the stability of the system. (c) Determine the maximum value of dead time VD for the closed-loop system to be stable. 21. A unity feedback system has open-loop transfer function K(s+5) G(s)= ;K=0 s(s+2) (a) Draw a rough sketch of the root locus plot; given that the complex roots of the characteristic equation move along a circle. (b) As K increases, does the system become less stable? Justify your answer. (c) Find the value of K (if it exists) so that the damping of the complex closed loop poles i
constant, the force between the plates
(a) increase
(b) decreases
(c) remains constant
(d) may increase or decrease depending on the metal making up the plates
1.2 Two parallel wires separated by a distance d are carrying a current I in the same direction.
The magnetic field along a line running parallel to these wires and midway between them
(a) depends upon I
(b) is zero
(c) depends upon d
(d) depends upon the permeability of medium between the wires
1.3 An electromagnetic field is radiated from
(a) a stationary point charge
(b) a capacitor with a DC voltage
(c) a conductor carrying a DC current
(d) an oscillating dipole
1.4 The mobility of an electron in a conductor is expressed in terms of
(a)
cm2/V—s
(b)
cm/V—s
(C)
cm2/V
(d)cm2/s
1.5 An enhancement type n-channel MOSFET is represented by the symbol
(a) .— I
(b) .__ I
(c)
(d)
1.6 As the temperature is increased, the voltage across a diode carrying a diode
carrying a constant current
(a) increases
(b) decreases
(c) remains constant
(d) may increase or decrease depending upon the doping levels in the junction
1.7 A single channel digital storage oscilloscope uses a 10 bit, i07 samples per second Analog-
to-Digital Converter. For a 100 KHz sine wave input, the number of samples taken per cycle of
the input will be
(a) i07
(b) i04
(c) i03
(d) 102
1.8 Higher synchronous reactance is preferred in the present day alternators,
because one can have
(a) reduced sub-transient currents
(b) reduced harmonic currents
(c) reduced transient currents
(d) higher voltage regulation with load
1.9 The RMS value of a half-wave rectified symmetrical square wave current of 2A is:
(a) 1OV
(b)
JA
(c) 200V
(d) 1A
1.10 Electodynamic type wattmeters have large errors while measuring power in ac circuits at
low power factor conditions, since the voltage across and the current through the
2Oc .ø—200
v—+
ioov (. 200V
5OHz I
(a) current coil are not in phase
(c) pressures coil are not in phase
(d) pressure coil are not in quadrature
1.11 The current in the circuit shown in Fig.1.12 is:
(a) 5A
(b) 1OA
(c) iSA
(d) 25A
1.12 For the circuit shown and Y will be
in Fig.below, the capacitance measured between terminals B
(a)
(b)
C+--
(c)
(c+3c)
(d)
3C+2C
An overhead line having a surge impedance of 400c is connected in series with an
underground cable having a surge impedance of iooc. If a surge of 50 kV travels from the line
end towards the line-cable junctions, the value of the transmitted voltage wave at the junction
is:
(a) 30 kV
(b) 20 kV
(c) 80 kV
(d) -30 kV
1.14 The load carrying capability of a long AC transmission line is:
(a) always limited by the conductor size
(b) limited by stability considerations
(c) reduced at a low ambient temperatures
(d) decreased by the use of bundled conductors of single conductors
1.15 Corona losses are minimized when
(a) conductor size is reduced
(b) smooth conductor is reduced
(c) sharp points are provided in the line hardware
(d) current density in conductors is reduced
1.16 In a DC transmission line
(a) it is necessary for the sending end and receiving end to be operated in synchronism.
(b) the effects of inductive and capacitive reactances are greater than in an AC transmission
line of the same rating.
(c) there are not effects due to inductive and capacitive reactances
(d) power transfer capability is limited by stability considerations.
1.18 Steady state stability of a power system is the ability of the power system to (a)
maintain voltage at the rated voltage level
(b) maintain frequency exactly at 50 Hz
(c) maintain a spinning reserve margin at all times
(d) maintain synchronism between machines and on external tie lines
1.17. A 4-pole lap-wound DC generator has a developed power of P watts and voltage of E
volts. Two adjacent brushes of he machine are removed as they are worn out. If the machine
operates with the remaining brushes, the developed voltage and power that can be obtained
from the machine are
EP p p
(a) E, P
(b) --,-
(c) E,
(d) E,
1.18. Starting torque can be obtained in the case of a single phase induction motor with
identical main and auxiliary windings by connecting
(a) a capacitor across the mains
(b) a capacitor in series with the machine
(c) a capacitor in series with the auxiliary winding
(d) the main and the auxiliary windings in series
1.19. The windings of a QkVA, •—volt, three-phase, Delta connected, core type
transformer are reconnected to work as a single phase transformer. The maximum voltage
and the power ratings of the new configuration are,
(a) -,3Q
(b) J-r- E
(c) ,2Q
(d)
1.20. Resonant converters are basically used to
(a) generate large peaky voltage
(b) reduce the switching losses
(c) eliminate harmonics
(d) convert a square wave into a sine wave
1.21. A PWM switching scheme is used with a three phase inverter to
(a) reduce the total harmonic distortion with modest filtering
(b) minimize the load on the DC side
(c) increase the life of the batteries
(d) reduce low order harmonics and increase high order harmonics
1.22 The following starting method for an induction motor is inferior view of the poor starting
torque per ampere of the line current drawn:
(a) Direct line starting
(b) Auto transformer method of starting
(c) Series inductor method of starting
(d) Star-Delta method of starting
2. This question consists of 25 (TWENTTY FIVE) sub-questions. Each sub-question carries TWO
marks. The answers to these sub-questions MUST be written only in the appropriate boxes
corresponding to the questions in the first page of the answer book.
2.1 The color code of a 1 kc resistance is:
(a) black, brown, red
(b) red, brown, brown
(c) brown, black, red
(d) black, black, red
2.2. A rectangular voltage pulse of magnitude V and duration T is applied to a series
combination of resistance R and capacitance C. The maximum voltage developed across the
capacitor is:
(a) V[1_exP
(c) V (d) Vexpj
2.3. When a periodic triangular voltage peak amplitude 1 V and frequency 0.5 Hz is applied to
a parallel combination of ic resistance and 1 F capacitance, the current through the voltage
source has wave-form.
(a) (b) //1
(c) h h (d)
2.4. For a flip-flop formed from two NAND X Q gates as shown in Fig below , the unusable
state corresponds to
2.5. The logic function
f
=
(x.)
+ is the same as
(a) f=(x+y)(x+y)
A
dB /6dBper
— —
I
octive
(b)
f=(x+y)+(x+y)
0dB
(c)
f
=
(x.y).(x.y)
(d) None of (a), (b) (c).
2.6. For a single phase overhead line having solid copper conductors of diameter 1 cm, spaced
60 cm between centers, the inductance in mH/km is:
(a) 0.05+0.21n60
(b) 0.21n60
(c) 0.05+0.2ln
(d) 0.2ln2
2.7. An industrial consumer has a daily load pattern of 2000 kW, 0.8 lag for 12 hours, and
1000 kW UPF for 12 hours. The load factor is:
(a) 0.5
(b) 0.75
(c) 0.6
(d) 2.0
2.8. A 220 kV, 20 km long, 3-phase transmission line has the following A, B, C, D constants. A
= D = 0.96 L3°, B = 55Z65°cVphase, C = 0.5E - 04Z80°S/phase. Its charging current per
phase is:
(a)
(b) hA
(c) 220A
(d)
2.9. A 3-phase, 11 kV, 50 Hz, 200 kW load has a power factor of 0.8 lag. A delta connected 3-
phase capacitor is used to improve the power factor to unity. The capacitance power phase of
the capacitor in microfarads is
(a) 3.948
(b) 1.316
(c) 0.439
(d) 11.844
2.10. A 10 kVA, 400 V/200V single-phase transformers with
10°h
impedance draws a steady
short circuit line current of
(a) 50 A
(b) 150 A
(c) 250 A
(d) 350 A
2.11. The percentage resistance and percentage reactance of a 10 kVA, 400 V/200 V,
3-phase transformer are 2% and lO% respectively. If the constant losses in the machine are
l%, the maximum possible percentage efficiency of the transformer is:
(a) 98.32
(b) 97.25
(c) 96.85
(d) 96.12
2.12. A 400V/100V, 10 kVA two-winding transformer is reconnected as an auto- transformer
across a suitable voltage source. The maximum rating of such an arrangement could be
(a) 50 kVA
(b) 15 kVA
(c) 12.5 kVA
(d) 8.75 kVA
2.13. A DC shunt motor is running t I200 rmp, when excited with 220 V DC. Neglecting the
losses and saturation, the speed of the motor when connected to a 175 V DC supply is:
(a) 750 RPM
(b) 900 RPM
(c) 1050 RPM
(d) 1200 RPM
2.14. A three phase alternator is wound with a 60 degree phase-spread armature windings
and develops 300 kVA. If the armature is reconnected utilizing all the coils for single phase
operation with a phase spread of 180 degrees, the new rating of the machine is
(a) 100 kVA
(b) 200 kVA
(c) 250 kVA
(d) 300 kVA
2.15. A 10 kVA, 400 V/200 V, single phase transformer with a percentage resistance of 3%
and percentage reactance of 6% is supplying a current of 50 A to a resistive load. The value of
the load voltage is:
(a) 194 V
(b) 390 V
(c) 192 V
(d) 196 V
2.16. For a dual ADC type 3-digit DVM, the reference voltage is 100 mV and the first
integration time is set to 300 ms. For some input voltage, the “deintegration” period is 370.2
ms. The DVM will indicate
(a) 123.4
(b) 199.9
(c) 100.0
(d) 1.141
2.17. When a resistor R is connected to a current source, it consumes a power of 18 W. when
the same R is connected to a voltage source having the same magnitude as
the current source, the power absorbed by R is 4.5 W. The magnitude of the
current source and the value of R are
(a)
-JfäA
and ic
(b) 3A and
(c) 1A and 18
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aq="" are:="" are="" armature="" as="" assume="" at="" attempted="" augmented="" average="" b:="" b="" bars="" base.="" based="" be="" being="" below="" between="" blocked="" boa.="" breaker="" bridge="" brush="" burden="" bus.="" bus="" by="" c-m="" c.="" c="" cable="" calculate:="" calculate="" can="" cap-pin="" capacitance="" capacitive="" capacitor.="" capacitor="" cb="" center="" charge="" choose="" circuit.="" circuit="" circuited="" class="" closed="" cm="" coil="" combination="" commercial="" common="" components="" condition="" conditions="" conducted="" conductor="" connected="" consider="" considered.="" consists="" constant="" construct="" control="" core="" cos="" critical="" current.="" current="" currents="" cv="" d="" data:="" dc="" delivered="" delta="" determine="" developed="" diagram="" diameter:="" diameter="" dielectric="" differential="" diode="" distance="" distributed="" does="" draw="" drawn="" driving="" drop="" e="" each.="" each="" effective="" electric="" electrodyna="" elements="" else="" emf="" employed="" end.="" end="" entering="" equal.="" equal="" equation="" equivalent="" er.="" error="" estimate="" evaluate="" evaluated="" events="" excited="" exclusive="" existence="" expression="" expressions="" f="" factor="" fan="" fault="" feedback="" feeder="" feeding="" field="" fifteen="" fifth="" fig.14.="" fig.="" fig.below="" figure="" figures="" first="" fitted="" five="" fixed="" following="" for="" found="" frequency="" from="" full-scale="" full="" function="" g="" gain="" gauss="" given="" grid="" guard="" h="" has="" have="" hz="" i.="" i012="" i04="" i2.="" i="—6sin(at)mA" ideal="" if="" impedance.="" impedance="" implies="" in="" inclined="" independence="" independent="" indicate="" indicating="" induced="" inductance.="" inductance="" induction="" inductive="" inductor="" infinite="" infinity="" initial="" input="" inputs.="" inputs="" insulation="" insulator="" insulators.="" intensity="" internal="" io.oc="" ioj="" iron="" is:="" is="" j1812.="" j="" jo.0112="" jo.0212="" jo.08="" jo.2="" junction="" k="" khz="" km.="" km="" kv.="" kv="" kva="" kw="" l4cos="" l4sin="" l="" lag="" lagging.="" large="" law="" lc-r="" lead-sheathed="" leakage="" least="" length:4="" level="" lie="" line-end="" line="" load:="" load="" locos="" locus="" logic="" long="" loop="" loopa="" loss="" losses.="" ma="" machine="" made="" magnetizing="" magnitude="" magnitudes="" mains.="" margin="" marked="" marks="" matrix="" maximum="" measured="" mechanical="" meet="" merit.="" merit="" mesh="" meter.="" meter="" meters="" method="" mh="" mometer="" more="" motor="" moving="" multiplexer="" must="" mutually="" mva="" n-m.="" n="" nearest="" necessary="" neglect="" negligible="" neutral="" no.="" node.="" node="" nominal="" non-zero="" not="" null="" number="" o="" occurs="" of="" off="" ohms="" on="" one-="" one="" only="" oo="" oov="" open="" operating="" operation="" operational="" or="" order="" out="" output="" over="" overhead="" p.u.="" p="" parallel="" parameter.="" parameters:="" peak="" per="" percentage="" permittivity="" pf="" phase.="" phase="" phasor="" pmmc="" point="" power="" powers="" probability="" proportional="" provide="" px="q," q="" questions="" r-l="" r.="" r="" radius="" random="" range="" ranges="" rank="" rated="" rating="" ratio="" reach="" reactance.="" reactance="" reactive="" reading="" readings="" realize="" realized="" receiving="" rectified="" rectifier="" relative="" required.="" required="" resistance="" resistances="" resistivity="" resistors="" respectively.="" response="" ring="" rms="" rotor="" rpm.="" rpm="" s2="" s="" same="" satisfy="" scale="" score="" secondary="" section="" semi-circle="" sending="" sensitivities="" separately="" series="" share="" sheath="" short="" shown="" shunt="" sin="" sine="" single-phase="" single="" singular="" sinusoidal="" sketch.="" sketch="" so="" solution="" solve="" source.="" source="" speed.="" speed="" sphere="" square="" star="" state="" stator="" straight="" stress="" string="" supply.="" supply="" supported="" suspension="" symmetrical="" synchronized="" synchronous="" system="" t-equivaient="" t="" taken="" tar="" terminals="" test="" that="" the="" their="" them="" then="" thermocouple="" these="" they="" this="" three="" throughout="" to="" together="" torque="" tower="" transfer="" transformer:="" transformer="" transformers="" transmission="" true:="" turns="" twenty="" two="" type.="" type="" u="" under="" uniformly="" unit.="" unit="" units="" unity="" unknown="" unscored="" upf="" used="" using="" v.="" v0.="" v0="" v11="" v1="" v1in="" v="" va="" value="" values="" vand="" var="" variable="" varied="" vdc="" vector="" very="" voltage.="" voltage="" voltages="" voltmeter.="" voltmeters="" volume="" w.="" w="" wattmeter.="" wattmeter="" wave="" waveforms="" well="" what="" when="" which="" whose="" will="" winding="" wire="" wires="" with="" within="" would="" x-axis="" x0="" x0e3="" x0e_3t="" x0et="" x1="" x:="" x="" xe="" xm.="" y="" yes="" z="" zero.="" zero="">> >> X
(b) X1 < (c) X1 = >>
X
(d) X1 =
X < 11. 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 (b) Star - Delta (c) Delta - Delta (d) Delta - Zigzag 12. For an induction motor, operating at a slip s, the ratio of gross power output to air gap power is equal to: (a) (1—s)2 (b) (1—s) (c) q(1_s) (d) (i_4) 13. 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 (a) 4, 0.4 (b) 100, 10 (c) 4, 10 (d) 100, 0.4 14. An 800 kV transmission line has a maximum power transfer capacity on the operated at 400 kV with the series reactance unchanged, the new maximum power transfer capacity is approximately 15. The insulation strength of an EHV transmission line is mainly governed by (A) load power factor (B) switching over-voltages (C) harmonics (D) corona 16. High Voltage DC (HVDC) transmission is mainly used for (a) bulk power transmission over very long distances (b) inter-connecting two systems with the same nominal frequency (c) eliminating reactive power requirement in the operation (d) minimizing harmonics at the converter stations 17. Q-meter works on the principle of (a) mutual inductance (b) self inductance (c) series resonance (d) parallel resonance 18. A PMMC voltmeter is connected across a series combination of a DC voltage source V1 = 2Vand an AC voltage source v2 (t) = 3sin(4t) V. The meter reads (c) [2+4V (d) [çv 19. Assume that D1 and D2 in Fig.Q below are ideal diodes. The value of current I is: (a) 0 mA (b) 0.5 mA 2kc (c) 1 mA lmA1 (d) 2 mA 2kc 20. The 8085 assembly language instruction registers into the memory locations 2050H that stores the contents of H and L and 2051H’ respectively, is: (a) SPHL 2050H (b) SPHL 2051H (c) SHLD 2050H (d) STAX 2050H 21. Assume that the N-channel MOSFET shown in Fig. below is ideal, and that its threshold voltage is +1.OV. The voltage Vab between nodes a and b is: (a) 5V (b) 2V (c) 1V (d) CV 22. The digital circuit shown in Fig. below works as a (a) JKflip-flop (b) Clocked RS flip-flop (c) Tflip-flop (d) Ring counter 23. A digital-to-analog converter with a full-scale output voltage of 3.5V has a resolution close to 14 mV. Its bit size is: (a) 4 (b) 8 (c) 16 (d) 32 24. The conduction loss versus device current characteristic of a power MOSFET is best approximated by (a) a parabola (b) a straight line (c) a rectangular hyperbola (d) an exponentially decaying function 25. A three-phase diode bridge rectifier is fed from a 400V RMS, 50 Hz, three-phase AC source. If the load is purely resistive, the peak instantaneous output voltage is equal to 400 (c) 4OOj V (d) -7=-V 26. The output voltage waveform of a three-phase square-wave inverter contains (a) only even harmonics (b) both odd and even harmonics (c) only odd harmonics (d) only triplen harmonics Q.31 — Q.80 carry two marks each 31. The RL circuit of Fig.Q31 is fed from a constant magnitude, variable frequency sinusoidal voltage source VIN. At 100 Hz, the R and L elements each have a voltage drop URMS. If the frequency of the source is changed to 50 Hz, the new voltage drop across R is: (a) JURMS (b) J1URMS (c) JURMS (d) 4JURMS 32. The circuit shown in Fig. below 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 = equals (a) 0 A (b) 0.5A (c) 1A (d) 2 A 33. For the three-phase circuit shown in Fig. below, the ratio of the current : I>,
:
18
is
(a) i:i:J
(b) 1:1:2
(c) 1:1:0
(d) i:i:J
34. For the triangular waveform shown in Fig. below, the RMS value of the voltage is equal to
(a)
T
T
2
(b)
2T t
2
1
(c). (d)
1 DV
t=o
35. The charge distribution in a metal-dielectric-semiconductor specimen is shown in Fig.
below. The negative charge density decreases linearly in the semiconductor as shown. The
electric field distribution is as shown in
(c)
(d) Dielectric
36. In Fig. below, the Thevenin’s equivalent pair (voltage, terminals P-Q, is given by
(a) (2V, 512)
(b) (2V, 7.512)
(c) (4V, 512)
(d) (4V, 7.512)
37. A unity feedback system, having an open loop gain
K(1-s)
G(s)H(s)
= ,becomes stable when
(1+s)
Metal
Semiconductor
(a) K>1
(b) K >1
(c) K<1 ---1="" ---="" -1="" -7.5="" -="" .="" 0.01.112="" 0.01012="" 0.0112="" 0.02512="" 0.10="" 0.112="" 0.125="" 0.12="" 0.15="" 0.24="" 0.25="" 0.2="" 0.334="" 0.366="" 0.3="" 0.50="" 0.52="" 0.5="" 0.5a="" 0.684="" 0.6="" 0.732="" 0.75="" 0.80="" 0.85="" 0.90="" 0.97="" 001="" 0="" 1-core="" 1.00="" 1.0="" 1.366="" 1.44="" 1.5="" 1.="" 10.5="" 1000="" 100="" 100v="" 10="" 10z30="" 112="" 12.1c="" 12.5="" 120v="" 125="" 13.0="" 13.9="" 150="" 15="" 16v="" 175="" 18.1812="" 18.3="" 1="" 1oa="" 1sov="" 2.25="" 2.2c="" 2.35="" 2.40="" 2.738="" 2.="" 200012="" 200="" 20="" 20c="" 22.7212="" 220="" 232="" 24.6="" 24v="" 25="" 2="" 2a="" 2xyz="" 3-phase="" 3.125p.u.="" 3.="" 300="" 30="" 31t="" 33.0="" 39.="" 3="" 3k="" 4.033c="" 4.5="" 4.71="" 4.84="" 4.="" 40.="" 4000="" 4012="" 40="" 40i2="" 40z="" 41.="" 42.="" 43.="" 44.="" 45.="" 46.="" 47.="" 48.="" 49.="" 4="" 5.0="" 5.5="" 5.5c="" 50.="" 5000="" 500a="" 50="" 51.="" 52.="" 53.="" 54.="" 55.="" 56.="" 57.="" 58.="" 59.="" 5="" 5s2="" 6.00="" 6.25="" 6.6="" 60.="" 600="" 6012="" 61.="" 62.="" 63.="" 64.="" 65.="" 66.="" 67.="" 68.="" 69.="" 6="" 7.2="" 70.="" 71.="" 72.="" 73.="" 74.="" 75="" 7="" 8.0="" 81a="" 81b:="" 82.="" 82a="" 82b:="" 83.="" 83a="" 83b:="" 84.="" 84a="" 84b:="" 85a="" 85b:="" 8="" 8v="" 9.6="" 9012.="" 95="" 9="" _="" _______="" a0="" a1="" a1x="" a2x2="" a3x2="" a="" acceleration="" achieve="" across="" after="" all="" almost="" also="" ammeter="" amp="" amplifier="" an="" and="" andy="" angle="" answer="" any="" application="" applied="" approaches="" approximate="" approximately="" are="" armature="" around="" as:="" as="" assertion:="" assertion="" assume="" at="" ati="" axis="" b="" balanced="" bars="" bas="" base="" be="" becomes="" been="" below.="" below="" between="" biased="" boa.="" both="" bus="" but="" by="" c1="" c2.="" c2="" c="" cable.="" cables="" cage="" capacitor="" carry="" carrying="" cascade="" centre="" change="" characteristics="" chopper="" circuit="" close="" closed="" coil="" coils="" coin="" common="" compensated="" condition="" conduct="" connected="" connection="" consider="" considered="" constant="" constants="" control="" core="" correct="" correctness="" cos2x="" cost="" coulomb="" crossover="" current="" cylindrical="" d="" damper="" dc="" decrease="" decreases="" defined="" delivered="" designer="" determine="" developed="" developing="" device="" direct-axis="" direct-on-line="" direction="" display.="" dissipated="" does="" double-circuit="" draw="" drawn="" driven="" driving="" during="" duty="" e3="" e="" e_3t="" e_t="" e_t_e_3t="" each="" earth="" economic="" efficiency="" eigen="" either="" electric="" electronic="" emf="" emitter="" energy="" equal="" equation="" equidistant="" equivalent="" error="" evaluate="" exactly="" excitation="" extended="" f2="a+bP2+2cP" f="" factor.="" factor="" fair="" false="" fan="" fault="" field="" fig.="" fig.below="" fig.q62.="" fig.q63.="" fig.q66="" figure-of-s="" first="" flux="" following="" follows:="" for="" four="" fourier="" frequency="" friction="" from="" fuel="" full="" function="" functions="" g1="" g2="" g="" gain="" generating="" generation="" generator="" getting="" gh="" given="" giving="" goes="" gradient="" greater="" ground="" group.="" h="" half="" has="" have="" having="" head="" heads="" help="" high="" horizontal="" hour="" i.="" i.oc="" i="" ideal="" identify="" if="" ii="" impulse="" in="" increases="" induced="" inductance="" induction="" industrial="" inertia="" infinite="" infinity="" initial="" input="" inputs="" installed="" instant="" insulation="" integers="" inverse="" inverting="" is:="" is="" it="" its="" j0="" k12="" k="" keeping="" kg="" khz="" km="" kv="" kva="" kw="" lag="" lagging.="" laplace="" large="" leads="" let="" level="" limit="" line-to-line="" line="" linked="" loa="" load="" loaded="" long="" loop="" lost="" low="" m12="" m2.="" m2="" ma="" machines="" magnetic="" magnitude="" maintain="" maintained="" margin="" marks="" matrix="" maximum="" measure="" measured="" measurement="" meet="" meter="" minimum="" modulo="" moment="" mosfet="" most="" motor="" moved="" ms="" multiplication="" multiplications="" must="" mutual="" mva.="" mva="" mvar="" mw="" n-channel="" needed="" negative="" neglect="" neglecting="" negligible="" networks="" nm2="" nm="" no="" not="" notations="" number="" nyquist="" o="" obtained.="" obtained="" oc="" occurs="" of="" off="" on="" one="" only="" oo="" open="" operation="" operational="" or="" ordered="" oscilloscope="" otherwise="" out="" output="" over="" overhead="" p.u.="" p1="" p2.="" p2="" p="" pa="" pairs="" pandr="" parameters="" passes="" peak-peak="" percentage="" phase="" plane="" plates="" plausible="" plot="" point="" polarity="" pole="" poles="" polynomial="" pon="" position="" positive="" possible="" power="" powers="" practically="" probability="" produce="" produces="" q85b="" q="" qsin="" quadrature-axis="" questions:="" questions="" quick="" r.="" r1="" r="" rad="" range.="" range="" rated="" ratio="" reactance="" read="" readings="" reads="" real="" realize="" reason:="" reason="" reasons.="" reduced="" regarding="" region.="" relation="" remain="" remains="" represents="" required="" requires="" resistance:="" resistance="" resistances="" respective="" respectively.="" respectively="" resulting="" revolve="" rf="" ripple="" rotor="" row="" rs="" s2="" s="" salient="" scalar="" sec2="" sec="" seen="" self-start="" self="" semiconductor="" sequence="" series="" service="" set-up="" set="" sets="" shaft.="" short="" should="" shown.="" shown="" shows="" shunt="" sides="" signal="" signals="" simultaneous="" sin2="" sin2x="" sin="" single-line="" single="" sinx="" size="" sizes="" slip="" small-="" solution="" source.="" source="" speed.="" speed="" stability="" star="" start="" started="" starting="" starts="" state="" statement="" statements="" stationary="" stations="" stator="" steady="" step-down="" step-up="" step="" stored="" sub-="" sub-station="" subsets="" substation="" succession.="" supplies="" supply="" supplying="" susceptances="" switch="" switched="" switching="" synchronous="" system="" systems="" t1="" t2="" t31="" t="" taken="" terminal="" than="" that="" the="" their="" them="" then="" there="" thermal="" this="" three-="" three-phase="" three="" threshold="" through="" ti="" time="" times="" to:="" to="" top="" torque="" toss="" tossed="" tosses="" total="" transfer="" transform="" transformer="" transition.="" transition="" transmission="" transposed="" trblock="" tripped="" true="" turn="" two="" u="" under="" unit="" unity="" unstable="" upper="" used="" using="" usual="" v-curve="" v="" value="" values="" variable="" variation="" vector="" vertical="" very="" vi="" viscous="" voltage.="" voltage="" voltages="" voltmeter="" w.="" w="XxY" wattmeters="" what="" when="" where="" which="" while="" wide="" will="" wishes="" with="" x.x2="" x0="" x1.x2="" x1="" x1and="" x2="" x2e="" x="" xis:="" xm="0.1c/km" y="" z2="" z2xy="" z="" zero="" ztransform="" zx2="">
v.
Then R is:
(A) Neither a Partial Order nor an Equivalence Relation
(B) A Partial Order but not a Total Order
(C) A Total Order
(D) An Equivalence Relation
5. For which one of the following reasons does Internet Protocol (IP) use the time-
to-live (TTL) field in the IP datagram header?
(A) Ensure packets reach destination within that time
(B) Discard packets that reach later than that time
(C) Prevent packets from looping indefinitely
(D) Limit the time for which a packet gets queued in intermediate routers.
6. Consider three CPU-intensive processes, which require 10, 20 and 30 time units and arrive
at times 0, 2 and 6, respectively. How many context switches are needed if the operating
system implements a shortest remaining time first scheduling algorithm? Do not count the
context switches at time zero and at the end.
(A) 1
(B) 2
(C) 3
(D) 4
7. Consider the following grammar.
Consider the following LR(0) items corresponding to the grammar above.
Given the items above, which two of them will appear in the same set in the canonical sets-of-
items for the grammar?
(A) (i) and (ii)
(B) (ii) and (iii)
(C) (i) and (iii)
(D) None of the above
8. You are given a free running clock with a duty cycle of 50% and a digital waveform f which
changes only at the negative edge of the clock. Which one of the following circuits (using
clocked D flip-flops) will delay the phase of f by 1800?
9. A CPU has 24-bit instructions. A program starts at address 300 (in decimal). Which one of
the following is a legal program counter (all values in decimal)?
(A) 400
(B) 500
(C) 600
(D) 700
10. In a binary max heap containing
n
numbers, the smallest element can be found in time
(A)
0(n)
(B)
O(logn)
(C) 0(loglogn)
(D)
0(1)
11. Consider a weighted complete graph Gon the vertex set
{v1,v2
,v} such that the weight of
the edge
(v,,v)
is
2i-j.
The weight of a minimum spanning tree of G is:
(A)
n—i
(B)
2n—2
(C)
(D) 2
12. To implement Dijkstra’s shortest path algorithm on unweighted graphs so that it runs in
linear time, the data structure to be used is:
(A) Queue
(B) Stack
(C) Heap
(D) B-Tree
13. A scheme for storing binary trees in an array X is as follows. Indexing of X starts at 1
instead of 0. the root is stored at X[1]. For a node stored at X[i], the left child, if any, is stored
in X[2i] and the right child, if any, in X[2i+1]. To be able to store any binary tree on nvertices
the minimum size of X should be
(A) log2
n
(B)
n
(C)
2n+1
(D) 2—1
14. Which one of the following in place sorting algorithms needs the minimum number of
swaps?
(A) Quick sort
(B) Insertion sort
(C) Selection sort
(D) Heap sort
15. Consider the following C-program fragment in which
i,j
and nare integer variables.
for (i = n,j = 0; i >0; i
1=
2,j +=i);
Let val(j)denote the value stored in the variable jafter termination of the
for
loop. Which one
of the following is true?
(A)
val(j)
=
8(logn)
(B)
vaI(j)=8(fi)
(C)
val(j)=8(n)
(D)
val(j)= 8(nlogn)
16. Let S be an NP-complete problem and Q and R be two other problems not known to be in
NP. Q is polynomial time reducible to S and S is polynomial-time reducible to R. Which one of
the following statements is true?
(A) R is NP-complete
(B) R is NP-hard
(C) Q is NP-complete
(D) Q is NP-hard
17. An element in an array X is called a leader if it is greater than all elements to the right of
it in X. The best algorithm to find all leaders in an array
(A) Solves it in linear time using a left to right pass of the array
(B) Solves it in linear time using a right to left pass of the array
(C) Solves it using divide and conquer in time
8(nlogn)
(D) Solves it in time
8(n2)
18. We are given a set X {x1
x}
where x, = 2’. A sample S c Xis drawn by selecting each
x,independently with probability p, =-.The expected value of the smallest number in sample S
is:
(A)
(B) 2
(C)
(D)
n
19. Let
L1 {OnminOmnm>O1L {Onmin+mOmnm>O}
and
i
= {jt
n rnjn mflm
01. Which of these languages are NOT context free?
(A)
L1
only
(B)
L3
only
(C)
L1
and
L2
(D)
L2
and
L3
20. Consider the following log sequence of two transactions on a bank account, with initial
balance 12000, that transfer 2000 to a mortgage payment and then apply a 5% interest.
1. T1 start
2. T1 B old= 1200 new= 10000
3. T1 M old=0 new=2000
4. T1 commit
5. T2start
6. T2 B old= 10000 new= 10500
7. T2 commit
Suppose the database system crashes just before log record 7 is written. When
the system is restarted, which one statement is true of the recovery procedure?
(A) We must redo log record 6 to set B to 10500
(B) We must undo log record 6 to set B to 10000 and then redo log records 2 and 3
(C) We need not redo log records 2 and 3 because transaction Ti has committed
(D) We can apply redo and undo operations in arbitrary order because they are idempotent.
Q.21 — Q.75 Carry Two Marks Each
21. For each element in a set of size
2n,an
unbiased coin is tossed. The 2ncoin tosses are
independent. An element is chosen if the corresponding coin toss were head. The probability
that exactly
n
elements are chosen is:
(A) 2n
22. Let E, F and G be finite sets.
Let
X=(EflF)-(FflG)
and
Y=(E_(EflG))_(E_F).
Which one of the following is true?
(A)
XcY
(B)
XDY
(C)
X=Y
(D)
X-Y ØandY-X Ø
23. F is an nxn real matrix. b is an nxi real vector. Suppose there are two nxivectors,
u
and
vsuch that
u
v,and
Fu
=
b,Fv
=
b.
Which one of the following statements is false?
(A) Determinant of
F
is zero
(B) There are an infinite number of solutions to
Fx
=
b
(C) There is an x Osuch that
Fx
= 0
(D)
F
must have two identical rows
24.
integers S, and ,r(S) is the set of integers obtained by applying permutation rto each
element of S?
(A)
(n-AUBAHB
(B)
(A2
+B2)n2
(C)
n!
(D)
A
fl B2/[A U
B
25. Let S = {1,2,3
,m},m>3.
Let X1 X be subsets of S each of size 3.
Define a function ffrom Sto the set of natural numbers as,
f(i)is
the number of sets Xthat
contain the element
I.
That is
f (I)={jIE
x7[.
Then
f(i)is:
(A) 3m
(B)
3n
(C) 2m+1
(D) 2n+1
26. Which one of the first order predicate calculus statements given below correctly expresses
the following English statement?
Tigers and lions attack if they are hungry or threatened.
(A) vx[(tiger(x) A lion(x)) — {(hungry(x) v threatened(x)) — attacks(x))1
(B) Vx [(tiger (x) v lion (x)) — {(hungry (x) v threatened (x)) A attacks (x)j
(C) Vx[(tiger(x) v lion(x)) — {attacks(x) — (hungry(x) v threatened(x)))1
(D) vx[(tiger(x) v lion(x)) — {(hungry(x) v threatened(x)) — attacks(x))1
27. Consider the following propositional statements:
Pl:((AAB)C))((AC)A(BC))
P2:((AvB)C))((A—C)v(B_C))
Which one of the following is true?
(A) P1 is a tautology, but not P2
(B) P2 is a tautology, but not P1
(C) P1 and P2 are both tautologies
(D) Both P1 and P2 are not tautologies
28. A logical binary relation
a,
is defined as follows:
Let be the unary negation (NOT) operator, with higher precedence then o. Which one of the
following is equivalent to
A
A
B?
(A)
(‘-‘.‘AOB)
(B)
-‘.‘(AO’-..’B)
(C)
“.‘(“.‘Ao”.’B)
(D)
AOB)
29. If
s
is a string over (0 + 1)* then let
n0 (s)
denote the number of 0’s in
s
and
n1
(s)the number of l’s in
s.
Which one of the following languages is not
regular?
(A)
L
=
{s
(0 + 1)*n0
(s)
is a 3-digit prime
(B)
L
=
{s
E (0 + 1)* for every prefix
s’
of
s, fl0 (s’)
—
n1 (s’)
2}
(C)
L={sE(0+1)*n0(s)_n1(s)4}
(D)
L
=
{s
E (0 + 1) j
n0 (s)
mod 7 =
n1 (s)
mod 5 = 0)
30. For SE (0+1)*let d(s)denote the decimal value of
s(e.g.d(101)=
5). Let
L
=
{s
E (0 + 1) j
d (s)
mod 5 = 2 and
d (s)
mod 7 = 4)
Which one of the following statements is true?
(A) L is recursively enumerable, but not recursive
(B) L is recursive, but not context-free
(C) L is context-free, but not regular
(D) L is regular
31. Let SHAM3 be the problem of finding a Hamiltonian cycle in a graph G
=(V,E)with
V
divisible by 3 and DHAM3 be the problem of determining if a Hamiltonian cycle exists in such
graphs. Which one of the following is true?
A B
AoB
True True True
True Fals
e True
Fals
e True False
Fals
Fals
e
e True
(A) Both DHAM3 and SHAM3 are NP-hard
(B) SHAM3 is NP-hard, but DHAM3 is not
(C) DHAM3 is NP-hard, but SHAM3 is not
(D) Neither DHAM3 nor SHAM3 is NP-hard
32. Consider the following statements about the context free grammar G = {S -
SS,
S -
ab, S
-
ba, S
-}
I. G is ambiguous
II. G produces all strings with equal number of a’s and b’s
III. G can be accepted by a
deterministic PDA.
Which combination below expresses all the true statements about G?
(A) I only
(B) I and III only
(C) II and III only
(D) I, II and III
33. Let
L1
be a regular language,
L2
be a deterministic context-free language and
L3
a
recursively enumerable, but not recursive, language. Which one of the following statements is
false?
(A)
L1
fl
L
is a deterministic CFL
(B)
L3
fl
L
is recursive
(C)
L1
U
L2
is context free
(D)
L1
fl
L fl L3
is recursively enumerable
34. Consider the regular language
L
=(111+11111)*. The minimum number of
states in any DFA accepting this languages is:
(A) 3
(B) 5
(C) 8
(D) 9
Consider the circuit above. Which one of the following options correctly represents
f(x,y,z)?
(A)
xz+xy+yz
(B)
xz+xy+yz
(C)
xz+xy+yz
(D)
xz+xy+yz
36. Given two three bit numbers a2a1a0 and
b2b1b0
and
c,
the carry in, the function that
represents the
carry
generate function when these two numbers are added is:
(A)
a2b2
+
a2a1b1
+
a2a1a0b0
+
a2a0b1b0
+
a1b2b1
+
a1a0b2b0
+
a0b2b1b0
(B)
a2b2
+
a2b1b0
+
a2a1b1b0
+
a1a0b2b1
+
a1a0b2
+
a1a0b2b0
+
a2a0b1b0
(C) a2
+b2 +(a2 $b2)(a1 +b1 +(a1 $b1) (a0 +b0))
(D)
a2b2
+
a2a1b1
+
a2 a1a0b0
+
a2 a0 b1b0
+
a1 b2 b1
+
a1a0 b2b0
+
a0 b2b1b0
37. Consider the circuit in the diagram. The $ operator represents Ex-OR. The D flip- flops are
initialized to zeroes (cleared).
The following data: 100110000 is supplied to the “data” terminal in nine clock
cycles. After that the values of q2q1q0 are:
(A) 000
(B) 001
(C) 010
(D) 101
38. Consider a Boolean function
f (w,x,y,z).
suppose that exactly one of its inputs is allowed to
change at a time. If the function happens to be true for two input vectors
i
=
(w1,x1,y1,z1)
and ‘2
(w2,x2,y2,z2),
we would like the function to
remain true as the input changes from
i
to ‘2 (‘ and ‘2 differ in exactly one bit position),without becoming false
momentarily. Let
f (w,x,y,z)
= (5,7,11,12,13,15). Which of the following cube covers of f will
ensure that the required property is satisfied?
(A)
wxz, wxy, xyz, xyz, wyz
(B)
wxy,wxz,wyz
(C)
wxyz,xz,wxyz
(D)
wzy, wyz, wxz, wxz, xyz, xyz
39. We consider the addition of two 2’s complement numbers
b 1b
2
.b0
and a 1a 2....a0. A
binary adder for adding unsigned binary numbers is used to add the two numbers. The sum is
denoted by
c 1c 2....c0
and the carry-out by
cQLJ.
Which one of the following options correctly
identifies the overflow condition?
(A)
c0(a1sb1)
(B) a
1b
1c+a
1b
1C
(C)
cQLJ
1
(D)
a1$b1$c1
40. Consider numbers represented in 4-bit gray code. Let
h3h2h1h0
be the gray code
representation of a number nand let
g3g2g1g0be
the gray code of (n+1) (modulo 16) value of
the number. Which one of the following functions is correct?
(A)
g0(h3h2h1h0)=(1,2,3,6,1O,13,14,15)
(B)
g1(h3h2h1h0)=
(4,9,10,11,12,13,14,15)
(C)
g2(h3h2h1h0)=(2,4,5,6,7,12,13,15)
(D)
g3(h3h2h1h0)=(0,1,6,7,10,11,12,13)
41. A CPU has a cache with block size 64 bytes. The main memory has kbanks, each bank
being cbytes wide. Consecutive c—byte chunks are mapped on consecutive banks with wrap-
around. All the kbanks can be accessed in parallel, but two accesses to the same bank must
be serialized. A cache block access may involve multiple iterations of parallel bank accesses
depending on the amount of data obtained by accessing all the kbanks in parallel. Each
iteration requires decoding the bank numbers to be accessed in parallel and this takes
--ns.
The latency of one bank access is 80 ns. If
c
= 2 and
k
= 24, the latency of retrieving a cache
block starting at address zero from main memory is:
(A) 92 ns
(B) 104 ns
(C) 172 ns
(D) 184 ns
42. A CPU has a five-stage pipeline and runs at 1 GHz frequency. Instruction fetch happens in
the first stage of the pipeline. A conditional branch instruction computes the target address
and evaluates the condition in the third stage of the pipeline. The processor stops fetching
new instructions following a conditional branch until the branch outcome is known. A program
executes io instructions out of which 20% are conditional branches. If each instruction takes
one cycle to complete on average, the total execution time of the program is:
(A) 1.0 second
(B) 1.2 seconds
(C) 1.4 seconds
(D) 1.6 seconds
43. Consider a new instruction named branch-on-bit-set (mnemonic bbs). The instruction
“bbs
reg, pos, label”
jumps to label if bit in position
pos
of register operand
reg
is one. A register is
32 bits wide and the bits are numbered 0 to 31, bit in position 0 being the least significant.
Consider the following emulation of this instruction on a processor that does not have
bbs
implemented.
temp
—
reg & mask
Branch to
label
if temp is non-zero.
The variable
temp
is a temporary register. For correct emulation, the variable mask must be
generated by
(A)
mask —0x1< (B) mask f— 0 x rrrrrrrr >>
pos
(C)
mask—pos
(D)
mask —0xf
44. Station A uses 32 byte packets to transmit messages to Station B using a sliding window
protocol. The round trip delay between A and B is 80 milliseconds and the bottleneck
bandwidth on the path between A and B is 128 kbps. What is the optimal window size that A
should use?
(A) 20
(B) 40
(C) 160
(D) 320
45. Two computers Cl and C2 are configured as follows. Cl has IP address
203.197.2.53 and netmask 255.255.128.0. C2 has IP address 203.197.75.201 and netmask
255.255.192.0. which one of the following statements is true?
(A) Cl and C2 both assume they are on the same network
(B) C2 assumes Cl is on same network, but Cl assumes C2 is on a different network
(C) Cl assumes C2 is on same network, but C2 assumes Cl is on a different network
(D) Cl and C2 both assume they are on different networks.
46. Station A needs to send a message consisting of 9 packets to Station B using a sliding
window (window size 3) and go-back-n error control strategy. All packets are ready and
immediately available for transmission. If every 5th packet that A transmits gets lost (but no
acks from B ever get lost), then what is the number of packets that A will transmit for sending
the message to B?
(A) 12
(B) 14
(C) 16
(D) 18
47. Consider the following graph:
Which one of the following cannot be the sequence of edges added, in that
order, to a minimum spanning tree using Kruskal’s algorithm?
(A)
(a—b),(d—f),(b—f),(d—c),(d—e)
(B)
(a—b),(d—f),(d—c),(b—f),(d—e)
(C)
(d—f),(a—b),(d—c),(b—f),(d—e)
(D)
(d—f),(a—b),(b—f),(d—e),(d—c)
48. Let
T
be a depth first search tree in an undirected graph G. Vertices
u
and
v
are leaves of
this tree
T.
The degrees of both
u
and
v
in G are at least 2. which one of the following
statements is true?
(A) There must exist a vertex
w
adjacent to both
u
and
v
in G
(B) There must exist a vertex
w
whose removal disconnects
u
and
v
in G
(C) There must exist a cycle in G containing
u
and
v
(D) There must exist a cycle in G containing uand all its neighbours in G.
49. An implementation of a queue Q, using two stacks Si and S2, is given below:
void insert (Q, x)
push (Si, x);
void delete (Q)
if (stack—empty(52)) then
if
(stack—empty(Si)) then
print(”Q is empty”);
return;
else while (! (stack—empty (Si)))
x=pop (Si);
push(52,x)
x=pop (S2);
Let
flinsert
and
m(
n)delete operations be performed in an arbitrary order on an empty queue
Q. Let x and y be the number of
push
and pop operations performed respectively in the
process. Which one of the following is true for all
m
and
n?
(A)
n+m x<2n -2="" -="" ...="" 0="" 1="" 2="" 2m="" 2n="" 3="" 4="" 50.="" 51.="" 52.="" 53.="" 54.="" 55.="" 56.="" 57.="" 58.="" 59.="" 5="" 60.="" 61.="" 8="" a1="" a="" about="" access="" accessible="" add="" address="" after="" algorithm="" all="" allocate="" allowing="" always="" amp="" an="" and="" another="" any="" applied="" are="" arguments="" array.="" array="" arrays="" as="" at="" atomic="" ay="" b1="" b="" be="" binary="" binary_semaphore="" boolean="" both="" but="" by="" c-function="" c="" call="" can="" cell="" code.="" code="" common="" compared="" comparison="" compilation="" compiler="" complexity="" computation="" compute="" computed="" condition="" consider="" contains="" correct:="" correct="" correctly="" corresponding="" cpu="" dead="" depending="" e="" each="" effect="" either="" elements="" elimination="" else="" end="" entries="" er="" error="" even="" exactly="" execution="" f="" false="" fastest="" fault="" fetch-and-set="" fetches="" find="" five="" fl="" following="" follows:="" for="" form="" fortran="" found="" fr="" functions="" generate="" get="" given="" grammar:="" grammar="" hashing="" have="" here="" hold="" i.e.="" i.e="" i1="" i1a="" i3="" i="" ia="" ib="" id.value="" id="" idl="" if="" ifj="m" ifx="" ii="" implementation="" implements="" improve="" in="" initialize="" input="" instruction="" int="" integer="" integers="" intervening="" invariant="" is:="" is="" it="" ix="iy" iy="it" j="" k.="" k="" key="" l2:="" l2="" language="" largest="" li:="" li="" like="" line="" location="" locations="" loglogn="" logn="" loop="" m="" may="" median="" memory="" mibe="" mlare="" model="" mt="" n25="" n2="" n3="" n:="" n="" nameless="" neither="" nl="" nlogn="" nor="" not="" nt="" number="" numbers="" o="" of="" old="" on="" one="" only="" or="" otherwise="" output="" p="" parser="" pass-by-reference="" pass="" passed="" performance="" permitted="" pivot="" pointers.="" pointers="" predictive="" print="" prints="" procedure="" process="" program="" px="" py="" q="" quick="" r="" recurrence:="" reduce="" reduction="" referring="" report="" represented="" represents="" respectively.="" return="" runtime="" rz8="" s.="" s2:="" s2="" s3:="" s3="" s4:="" s4="" s5:="" s5="" s="" same="" scheme.="" scheme="" scope="" segment.="" segmentation="" selected="" semaphore="" set="" sets="" si:="" si="" size="" sj="" some="" sort="" sorted="" space="" span="" state="" statement="" statements:="" statements="" stored="" strength="" sub-expression="" subroutine="" subtract="" such="" sum="" swap="" t2="" t="" table="" takes="" temporary="" termination="" that="" the="" them.="" there="" these="" this="" ti="a[j]" time.="" time="" to="" token="" transformation="" transformations="" translation="" true="" two="" unconditionally="" unsigned="" v="" valid="" value.="" value="" void="" where="" which="" while="" will="" without="" work2="" worki="" workl="" written="" x-y="" x.="" x="" xfly="" xyz="" y="" z="" zzz="">value);
do
fetch—and—set x, y;
while (y)
void V (binary_semaphore *s)
S—>value = 0;
Which one of the following is true?
(A) The implementation may not work if context switching is disabled in P
(B) Instead of using
fetch-and —set,
a pair of normal load/store can be used
(C) The implementation of V is wrong
(D) The code does not implement a binary semaphore
62. A CPU generates 32-bit virtual addresses. The page size is 4 KB. The processor has a
translation look-aside buffer (TLB) which can hold a total of 128 page table entries and is 4-
way set associative. The minimum size of the TLB tag is:
(A) 11 bits
(B) 13 bits
(C) 15 bits
(D) 20 bits
63. A computer system supports 32-bit virtual addresses as well as 32-bit physical addresses.
Since the virtual address space is of the same size as the physical address space, the
operating system designers decide to get rid of the virtual memory entirely. Which one of the
following is true?
(A) Efficient implementation of multi-user support is no longer possible
(B) The processor cache organization can be made more efficient now
(C) Hardware support for memory management is no longer needed
(D) CPU scheduling can be made more efficient now
64. Consider three processes (process id 0, 1, 2 respectively) with compute time bursts 2, 4
and 8 time units. All processes arrive at time zero. Consider the longest remaining time first
(LRTF) scheduling algorithm. In LRTF ties are broken by giving priority to the process with the
lowest process id. The average turn around time is:
(A) 13 units
(B) 14 units
(C) 15 units
(D) 16 units
65. Consider three processes, all arriving at time zero, with total execution time of
10, 20 and 30 units, respectively. Each process spends the first 20% of execution time doing
I/O, the next
70°h
of time doing computation, and the last 10°h of time doing I/O again. The
operating system uses a shortest remaining compute time first scheduling algorithm and
schedules a new process either when the running process gets blocked on I/O or when the
running process finishes its compute burst. Assume that all I/O operations can be overlapped
as much as possible. For what percentage of time does the CPU remain idle?
(A) 0%
(B)
1O.6°h
(C)
30.O°h
(D)
89.4°h
66. Consider the following snapshot of a system running n processes. Process
i
is holding
x,instances of a resource R,
1 n.
currently, all instances of R are occupied. Further, for all
I,
process
i
has placed a request for an additional y, instances while holding the x, instances it
already has. There are exactly two processes p and q such that =
Yq
= 0. Which one of the
following can serve as a necessary condition to guarantee that the system is not approaching
a deadlock?
(A)
min(xp,xq)
< max Yk (B) X + Xq mink pq Yk (C) max(xp,xq)>1
(D)
min(xp,xq)>1
67. Consider the relation account (customer, balance) where customer is a primary key and
there are no null values. We would like to rank customers according to decreasing balance.
The customer with the largest balance gets rank 1. ties are
not broke but ranks are skipped: if exactly two customers have the largest balance they each
get rank 1 and rank 2 is not assigned.
select A.customer, count(B.customer)
Queryl: from account A, account B
where A.balance <=B.balance group by A.customer select A.customer, 1+count(B.customer) Query2: from account A, account B where A.balance < B.balance group by A.customer Consider these statements about Queryl and Query2. 1. Queryl will produce the same row set as Query2 for some but not all databases. 2. Both Queryl and Query2 are correct implementation of the specification 3. Queryl is a correct implementation of the specification but Query2 is not 4. Neither Queryl nor Query2 is a correct implementation of the specification 5. Assigning rank with a pure relational query takes less time than scanning in decreasing balance order assigning ranks using ODBC. Which two of the above statements are correct? (A) 2 and 5 (B) 1 and 3 (C) 1 and 4 (D) 3 and 5 68. Consider the relation enrolled (student, course) in which (student, course) is the primary key, and the relation paid (student, amount) where student is the primary key. Assume no null values and no foreign keys or integrity constraints. Given the following four queries: Queryl:select student from enrolled where student in (select student from paid) Query2:select student from paid where student in (select student from enrolled) Query3:select E.student from enrolled E, paid P where E.student = P.student Query4:select student from paid where exists (select * from enrolled where enrolled.student = paid.student) Which one of the following statements is correct? (A) All queries return identical row sets for any database (B) Query2 and Query4 return identical row sets for all databases but there exist databases for which Queryl and Query2 return different row sets. (C) There exist databases for which Query3 returns strictly fewer rows than Query2 (D) There exist databases for which Query4 will encounter an integrity violation at runtime. 69. Consider the relation enrolled (student, course) in which (student, course) is the primary key, and the relation paid (student, amount) where student is the primary key. Assume no null values and no foreign keys or integrity constraints. Assume that amounts 6000, 7000, 8000, 9000 and 10000 were each paid by 20% of the students. Consider these query plans (Plan 1 on left, Plan 2 on right) to “list all courses taken by students who have paid more than x” enrolled paid enrolled paid 1’ 1’ Probe index Sequential on student scan, select amount > x
A disk seek takes 4ms, disk data transfer bandwidth is 300 MB/s and checking a tuple to see if
amount is greater than x takes lOps. Which of the following statements is correct?
(A) Plan 1 and Plan 2 will not output identical row sets for all databases
(B) A course may be listed more than once in the output of Plan 1 for some data bases
(C) For x = 5000, Plan 1 executes faster than Plan 2 for all databases
(D) For x = 9000, Plan I executes slower than Plan 2 for all databases.
70. The following functional dependencies are given:
AB
-*
CD,AF
-*
D,DE
-*
F,C
-*
G,F
-*
E,G
-*
A.
Which one of the following options is false?
(A)
{CF} ={ACDEFG}
(B)
{BG}
=
{ABCDG}
(C)
{AF} ={ACDEFG}
(D)
{AB} ={ABCDFG}
Common Data Questions:
Common Data for Questions 71, 72, 73:
The 2 vertices of a graph G corresponds to all subsets of a set of size n, for
n < 6. Two vertices of G are adjacent if and only if the corresponding sets intersect in exactly two elements. 71. The number of vertices of degree zero in G is: (A) 1 (B) n (C) n+1 (D)2 72. The maximum degree of a vertex in G is: (A) 2J (B) 2 2 (C) 23x3 (D) 2 1 73. The number of connected components in G is: (A) n (B) n+2 (C) 2/2 (D) Common Data for Questions 74, 75: Consider two cache organizations: The first one is 32 KB 2-way set associative with 32- byte block size. The second one is of the same size but direct mapped. The size of an address is 32 bits in both cases. A 2-to-i multiplexer has a latency of 0.6 ns while a kbit comparator has a latency of k/lO ns. The hit latency of the set associative organization is h1while that of the direct mapped one is h2. 74. The value of h1is: (A) 2.4 ns (B) 2.3 ns (C) 1.8 ns (D) 1.7 ns 75. The value of h2 is: (A) 2.4 ns (B) 2.3 ns (C) 1.8 ns (D) 1.7 ns Linked Answer Questions: Q.76 to Q85 Carry Two Marks Each Statement for Linked Answer Questions 76 & 77: A 3-ary max heap is like a binary max heap, but instead of 2 children, nodes have 3 children. A 3-ary heap can be represented by an array as follows: The root is stored in the first location, a[0], nodes in the next level, from left to right, is stored from a[1] to a[3]. The nodes from the second level of the tree from left to right are stored from a[4] location onward. An item x can be inserted into a 3-ary heap containing n items by placing x in the location a[n] and pushing it up the tree to satisfy the heap property. 76. Which one of the following is a valid sequence of elements in an array representing 3-ary max heap? (A) 1, 3, 5, 6, 8, 9 (B) 9, 6, 3, 1, 8, 5 (C) 9, 3, 6, 8, 5, 1 (D) 9, 5, 6, 8, 3, 1 77. Suppose the elements 7, 2, 10 and 4 are inserted, in that order, into the valid 3- ary max heap found in the above question, Q.76. Which one of the following is the sequence of items in the array representing the resultant heap? (A) 10, 7, 9, 8, 3, 1, 5, 2, 6, 4 (B) 10, 9, 8, 7, 6, 5, 4, 3, 2, 1 (C) 10, 9, 4, 5, 7, 6, 8, 2, 1, 3 (D) 10, 8, 6, 9, 7, 2, 3, 4, 1, 5 Statement for Linked Answer Questions 78 & 79: Barrier is a synchronization construct where a set of processes synchronizes globally i.e. each process in the set arrives at the barrier and waits for all others to arrive and then all processes leave the barrier. Let the number of processes in the set be three and S be a binary semaphore with the usual P and V functions. Consider the following C implementation of a barrier with line numbers shown on left. void barrier (void) 1: P(S); 2: process_arrived++; 3. V(S); 4: while (process_arrived !=3); 5: P(S); 6: process_left++; 7: if (process_left==3) 8: process_arrived = 0; 9: process_left = 0; 10: 11: V(S); The variables process_arrived and process_left are shared among all processes and are initialized to zero. In a concurrent program all the three processes call the barrier function when they need to synchronize globally. 78. The above implementation of barrier is incorrect. Which one of the following is true? (A) The barrier implementation is wrong due to the use of binary semaphore S (B) The barrier implementation may lead to a deadlock if two barrier in invocations are used in immediate succession. (C) Lines 6 to 10 need not be inside a critical section (D) The barrier implementation is correct if there are only two processes instead of three. 79. Which one of the following rectifies the problem in the implementation? (A) Lines 6 to 10 are simply replaced by process_arrived-- (B) At the beginning of the barrier the first process to enter the barrier waits until process_arrived becomes zero before proceeding to execute P(S). (C) Context switch is disabled at the beginning of the barrier and re-enabled at the end. (D) The variable process_left is made private instead of shared Statement for Linked Answer Questions 80 & 81: A CPU has a 32 KB direct mapped cache with 128-byte block size. Suppose A is a two- dimensional array of size 512x512 with elements that occupy 8-bytes each. Consider the following two C code segments, P1 and P2. P1: for (i=0; i<512 -5v="" -="" -e="" -ee="" -eu="" -lv="" 0.5x="" 0="" 1.10="" 1.11="" 1.12="" 1.13="" 1.14="" 1.15="" 1.16="" 1.17="" 1.18="" 1.19="" 1.1="" 1.20="" 1.21="" 1.22="" 1.23="" 1.24="" 1.25="" 1.2="" 1.3="" 1.4="" 1.5="" 1.6="" 1.7="" 1.8="" 1.9="" 1.="" 100="" 12="" 12t2="" 12t3="" 12t="" 142.="" 16384="" 16="" 1="" 1c="" 1h="" 1k="" 2.="" 2048="" 20="" 24t="" 25="" 262144="" 28="" 2="" 2cc="" 2x="" 3-phase="" 3-step="" 3.="" 36="" 3="" 4-phase="" 4-pole="" 4.="" 40="" 4="" 4x="" 5.="" 50="" 5="" 5q="" 6.="" 7.="" 7="" 8.="" 80.="" 80="" 81.="" 82.="" 82="" 83.="" 83:="" 84.="" 84="" 85.="" 85:="" 8="" 8c="" 8cc="" 9.="" 9="" ________="" a.="" a="" ab="" above="" ac="" acbab="" acbe="" acbh="" accb="" achieved="" across="" advantages="" all="" alternator="" always="" amp="" amplifier="" an="" analogue="" and="" answer.="" answer="" answered.="" answers="" any="" applied="" appropriate="" arbitrary="" are="" arid="" armature="" array="" as="" assbab="" assumes="" at="" attempted="" average="" averaging="" avoid="" avoiding="" b.="" b2="" b3="" b4="" b5="" b="" back="" base="" based="" bases="" be="" because="" beginning="" being="" below.="" below="" between="" bi="" bjt="" bm="" book.="" book="" both="" boxes="" bridge.="" bridge="" bridges.="" bridges="" broadcast="" broken="" brushes.="" built="" but="" by="" c="" cache="" cage="" capacitor="" carefully:="" carries="" carry="" certain="" changes="" choice="" choices="" circuit="" circuits="" class="" clearly="" closest="" coming="" commutating="" commutation="" commutator="" compensating="" compensation="" component="" conflicts="" connected="" connection="" connections="" consider="" considerations="" considered="" consists="" constant="" constitute="" control="" controlled="" converter="" corona="" correct="" correctly="" corresponding="" credit.="" crossover="" ction="" current.="" current="" d="" damping="" data="" dc="" definite="" delay="" depth="" derivation="" design="" diagram="" direct="" direction="" distance="" distortion="" doubled="" draws="" drop="" due="" e="" each.="" each="" economizer="" effect="" electric="" electromagnetic="" electron="" electronic="" element="" else="" emf="" enable="" equal="" equally="" error="" errors="" evaluated="" excited="" executed="" exhibits="" experienced="" extends="" factor="" fault="" favour="" feature="" feed="" feedback="" feeds="" field="" fifteen="" fig.1.3="" fig.="" first="" five="" flashover="" flue="" following="" follows:="" for="" force="" forward-path="" forward="" forwarding="" found="" frames="" frequency="" fresh="" from="" fully="" function="" fundamental="" furnace="" g="" gases="" generate="" generates="" get="" given="" gives="" grammar="" grammars="" graph="" greater="" h.p.="" h12="" h1="" h1o="" h2="" h3="" h4="" h5="" h6="" h7="" h8="" h9="" harmonic="" has="" have="" heat="" heated="" hi="" high="" hil="" hio="" host="" hosts="" hvdc="" i="" ideal="" identified="" identifies="" if="" ii="" iii="" impedance="" important="" improper="" improving="" in="" ind="" independently="" index="" induction="" inductor="" inherent="" initial="" initially="" input="" insensitive="" inspite="" instances="" instantaneous="" instructions="" instrument="" interconnection="" interrupt="" into="" intr="" introduce="" introduces="" inverse="" inverter="" is:="" is="" it="" its="" iv="" j="" keeping="" known="" l.p.="" l="{a’" lan5="" lan="" language="" lans="" least="" legibly="" length="" less="" let="" level="" limitation="" line.="" line="" linear="" linked="" listed="" load="" located="" loop="" looping="" low="" lower="" lowest="" m1="" m="" machine="" magnetic="" magnitude="" mark.="" mark="" marking.="" marks="" max="" may="" measurement="" measurements.="" measures="" mechanical="" meter="" minimum="" misses="" mixed="" more="" motor="" multiple-choice="" multiple="" must="" namely="" negative="" next="" no="" non-zero="" none="" normal="" not="" number.="" number="" numbers="" o="" of="" off="" on="" one="" only="" opamp="" open="" operation="" options="" or="" order="" organize="" out="" output="" over-current="" p1="" p2:="" p2="" packet.="" packets="" page="" paper="" papers="" parameter="" parameters="" partial="" path="" paths="" peak="" per="" phase="" phases="" ping="" placed="" plant="" pole="" poles="" port="" possibility="" power="" preference="" preferred.="" previous="" primarily="" primary="" problems="" proper="" protection="" provided="" pwm="" question.="" question="" questions.="" questions="" questsof="" r="" ramp="" ratio="" reach="" reactance="" reaction="" reactive="" read="" registers.="" related="" relay="" remains="" represents="" required="" requirement="" resistance="" resolved="" responds="" response="" rest="" reverse="" reversed="" reversing="" rms="" root="" rotation="" rotor="" rst3="" rst7.5="" s-accb="" s="" same="" saturation="" score="" second="" secondary="" section="" sections:="" semi-converter="" send="" sends="" sensitive="" separately="" sequence="" serial="" servomotor="" setting="" sheets="" shoes="" short="" shortest="" should="" shown="" side="" signal="" slots.="" slots="" slowly="" source="" spanning="" sparking="" square-root="" square="" squirrel="" stability="" starring="" started="" state="" statement="" stator.="" stator="" steady-state="" steady="" steam="" step="" stepper="" steps="" strictly.="" string="" sub-question="" sub-questions.="" sub-questions="" subjected="" substantial="" such="" supplies.="" supplying="" surface="" system="" systems="" t3="" t5v="" t="" table="" tapped="" te_t="" teeth="" terminals="" than="" that="" the="" them="" themselves="" then="" there="" thermal="" these="" third="" this="" three-phase="" three="" through="" thyristorised="" ties="" time-invariant="" time.="" time="" to="" torque.="" total="" transfer="" transformer="" transformers="" transmission="" transparent="" trap="" traversal="" tree.="" tree="" triangular="" twenty-="" twenty-five="" twenty="" two-phase="" two="" type.="" type="" typically="" u="" unit-step="" unit="" units="" unity="" unscored="" up="" uses="" using="" uxb="" uxe="" v0="" v="" value.="" value="" vectored="" velocity="" very="" volt-ampere="" volt-amperes="" voltage="" voltages="" water="" waveform="" what="" when="" where="" which="" whose="" will="" winding="" windings="" with="" without="" working="" write="" written="" x.="" x="" y="" your="" zero.="" zero="" zones=""> 0. The transfer function of the system is:
(a) 1 2
(b) 1 2
(c) S 2
(d) 1
2. This question consists of 25 (TWENTTY FIVE) sub-questions. Each sub-question carries TWO
marks. The answers to these sub-questions MUST be written only in the appropriate boxes
corresponding to the questions in the first page of the answer book.
2.1 A two-port device is defined by the following pair of equations:
i
= 2v +
v2
and ‘2 =
V1 + V2
Its impedance parameters
(z111z121z211z22)are
given by
(a) (2,1,1,1)
(b) (1,-1,-1,2)
(c) (1,1,1,2)
(d) (2,-1,-1,1)
2.2. The circuit shown in Fig.2.2 is equivalent to a load of
(a) (0.54+jO.313) ohms
(b) (4 — j2) ohms
(c) (4.54 — jl.69) ohms
(d) (4 + j2) ohms
2.3. The minimal product of sums function described by the K-map given in Fig. below
01 1 0 0
100 0
2.4. A diode whose terminal characteristics are related as ‘D =Is[-where Isis the
reverse saturation current and
VTi5
the thermal voltage (=25mV), is biased at =
2mA.
Its
dynamic resistance is:
(a) 25 ohms
(b) 12.5 ohms
(c) 50 ohms
(d) 100 ohms
2.5. In the circuit of Fig. below, the value of the base current I8will be
(a) 0.0 micro amperes
(b) 18.2 micro amperes
(c) 26.7 micro amperes
(d) 40.0 micro amperes
2.6. A dual slope analog-to-digital converters uses an N-bit counter. when the input signal
Va
is being integrated, the counter is allowed to count up to a value
(a) equal to
2N
—2
(b) equal to
2N
—1
(c) proportional to
Va
(d) inversely proportional to
Va
2.7. A 3-phase delta/star transformer is supplied at 6000 V on the delta-connected side. The
terminal voltage on the secondary side when supplying full load as 0.8 lagging power-factor is
415 V: The equivalent resistance and reactance drops for the transformer are la/c and Se/c
respectively. The turn’s ratio of the transformer is:
(a) 14
(b) 24
(c) 42
(d) 20
2.8. A 240 V dc series motor takes 40A when giving its rated output at 1500 rpm. Its
resistance is 0.3 ohms. The value of resistance which must be added to obtain rated torque at
1000 rpm is:
(a) 6 ohms
(b) 5.7 ohms
(c) 2.2 ohms
(d) 1.9 ohms
2.9. The power input to a 415V, 50 Hz, 6 pole, 3-phase induction motor running at
975 rpm is 40 kW. The stator losses are 1kW and friction and windage losses total 2 kW. The
efficiency of the motor is
(a)
92.5°h
(b)
90°h
(c)
91°h
(d) 88°h
2.10. A single-phase, 2000V alternator has armature resistance and reactance of 0.8 ohms
and 4.94 ohms respectively. The voltage regulation of the alternator at 100A load at 0.8
leading power-factor is:
(a)
7°h
(b)
-8.9°h
(c) 14°h
(d)
0°h
2.11. A permanent magnet dc commutator motor has a no load speed of 6000 rpm when
connected to a 120V dc supply. The armature resistance is 2.5 ohms and other losses may be
neglected. The speed of the motor with supply voltage of 60V developing a torque 0.5 Nm, is:
(a) 3000 rpm
(b) 2673 rpm
(c) 2836 rpm
(d) 5346 rpm
2.12. A transmission line has equal voltages at the two ends, maintained constant by two
sources. A third source is to be provided to maintain constant voltage (equal to end voltages)
at either the midpoint of the line or at 755 of the distance from the sending end. Then the
maximum power transfer capabilities of the line in the original case and the other two cases
respectively will be in the following ratios.
(a) 1:1:1
(b) 1:2:1
(c) 1:2:4
(d)1:4:16
2.13. The plug setting of a negative sequence relay is 0.2A. The current transformer ratio is
5:1. The minimum value of line-to-line fault current for the operation of the relay is
(a) 1A
(b) 1
A
(c) 1.732A
(d) 0.2
A
2.14. The incremental cost chaçaceristlIf two generators delivering 200 MW are as follows
= 2.0 + 0.01P1,.- = 1.6 + 0.21’2
dP1 dP2
For economic operation, the generations P1 and
P2
should be
(a)
P1
=
P2
= 100MW
(b)
P1
=
8OMW,P2
= 120MW
(c)
P1
= 200MW,
P2
=
0MW
(d)
P1
=
120MW, P2
=
80MW
2.15. The corona loss on a particular system at 50 Hz is 1kW/km per phase. The
corona loss at 60 Hz would be
(a) 1kW/km per phase
(b) 0.83kW/km per phase
(c) 1.2kW/km per phase
(d) 1.13kW/km per phase
2.16. The severity of line-to-ground and three phase faults at the terminals of an unloaded
synchronous generator is to be same. If the terminal voltage is 1.0 p.u. and
z1 =z2
=jO.lp.u.,z0 =jO.05p.u.for
the alternator, then the required inductive reactance for neutral
grounding is:
(a) 0.0166 p.u.
(b) 0.05 p.u.
(c) 0.1 p.u.
(d) 0.15 p.u.
2.17. A three phase voltage source inverter supplies a purely inductive three phase load. Upon
Fourier analysis, the output voltage waveform is found to have an hth order harmonic of
magnitude ahtimes that of the fundamental frequency component
(ah < 1). The load current would then have an h-th order harmonic of magnitude (a) zero (b) ah times the fundamental frequency component (c) hahtimes the fundamental frequency component (d) ah lh times the fundamental frequency component 2.18. A step down chopper operates from a dc voltage source 4,and feeds a dc motor armature with a back emf Eb. From oscilloscope traces, it is found that the current increases for time tr,falls to zero over time t1,and remains zero for time t0, in every chopping cycle. Then the average dc voltage across the freewheeling diode is: (A) Vstr (Vstr +Ebtf) (B)(tr + tf + t0) (tr + tf + t0) (C) (Vstr +Ebto) Vstr +Eb (tf +t0) (D)(tr+tf+tO) - •. (t,+t+to) 2.19. A three phase, wound rotor induction motor is to be operated with slip energy recovery in the constant torque mode, when it delivers an output power F at slop s. then theoretically, the maximum power that is available for recovery at the rotor terminals, is equal to p0 p0.s (a) F (b) P0. (c) 1s (d) 1s 2.20. The two wattmeter method is used to measure active power on a three phase, three wire system. If the phase voltage is unbalanced, then the power reading is: (a) affected by both negative sequence and zero sequence voltages (b) affected by negative sequence voltages but not by zero sequence voltages (c) affected by zero sequence voltages but not by negative sequence voltages (d) not affected by negative or zero sequence voltages 2.21. If an ac voltage wave is corrupted with an arbitrary number of harmonics, then the overall voltage waveform differs from its fundamental frequency component in terms of (a) only the peak values (b) only the rms values (c) only the average values (d) all the three measures (peak, rms and average values) 2.22. The characteristic equation of a feedback control system is: 2s4 + s3 + 3s2 + 5s + 10 = 0 The number of roots in the right half of s-plane are: (a) zero (b) 1 (c) 2 (d) 3 2.23. A unity feedback system has open-loop transfer function G(s) = 25 The peak overshoot in the step-input response of the system is approximately equal to: (a) 5°h (b) 1O°h (c) 15°h (d) 20°h 2.24. Maximum phase-lead of the compensator D(s) = ,is (a) 52 deg at 4 rad/sec (b) 52 deg at 10 rad/sec (c) 55 deg at 12 rad/sec (d) None of the answers is correct SECTION - B This section consists of TWENTY qJtknof FIVE marks each. ANY FIFTEEN out of them have to be answered. If more number of quetions are attempted, score off the answers not be evaluated, else, only the first fifteen unscored answers will be considered. 3. Predict the current I in Fig. below in response to a voltage of 20Z0°V. The impedance values are given in ohms. Use the thevenin’s theorem. 4. (a) Show via the construction of a suitable Gaussian surface, that the capacitance of a spherical capacitor consisting of two concentric shells of radii a and b is given by ab C = 4,rs0 (b — a) where s0 is the free space permittivity. (b) A current 1 in the short conducting element shown in Fig.4 produces a flux density B at point 1. Determine the magnitude and the direction of the flux density vector at point 2. 5. A current amplifier has an input resistance of 1012, an output resistance of 10k12 and a current gain of 1000. It is feed by a current source having a source resistance of 10k12 and its output is connected to a i012 load resistance. Find the voltage gain and the power gain. 6. An active filter consisting of an op-amp, resistors R1,R2,R3 and two capacitors of value C each, has a transfer function 1 —s (R1 C) T(s)_ + 1 whereR=R111R2. ‘-7 RC) (RR3c2) If R1 = 2k12, R2 = .-k12, R3=200k12 and C = 0.1 pF, determine the centre frequency ak, gain A0 and the Q of the filter. 7. The counter shown in Fig. below is initially in state Q2 = 0,Q1 = 1,Q0 = 0.With reference to the CLK input, draw waveforms for Q2,Q1,Q0and P for the next three CLK cycles. 8. In a single-phase, three-winding transformer, the turns ratio for primary: secondary: tertiary windings is 20:4:1. With the lagging currents of 50A at a power factor of 0.6 in the tertiary winding, find the primary current and power- factor. 9. A belt driven dc shunt generator runs at 1500 rpm delivering 10k2, at 220V bus bars. The belt breaks, following which the machine operates as a motor drawing 2kW power. What will be its speed as a motor? The armature and field resistances are 0.25 ohms and 55 ohms respectively. Ignore armature reaction and assume the contact drop at each brush to be lv. 10. A 230V, 20 hp, 60 Hz, 6-pole, 3-phase induction motor driving a constant torque load at rated frequency, rated voltage and rated horse-power, has a speed of 1175 rpm and an efficiency of 92.1°h. Determine the new operating speed if a system disturbance causes 10°h drop in voltage and 6°h drop in frequency. Assume that friction, windage and stray power losses remain constant. 11. A 2300 V, 3-phase synchronous motor driving a pump is provided with a line ammeter and a field rheostat. When the rheostat is adjusted such that the ac line current is minimum. The ammeter reads 8.8A. What is the power being delivered to the pump, neglecting losses? How should the rheostat be adjusted so that the motor operates at 0.8 leading power factor? How many kVARs is the motor supplying to the system at this new power factor? 12. A 275 kV, 3-phase, 50 Hz, 400 km lossless line has following parameters: x=0.05 ohms/km, line charging susceptance y=3.0 micro-Siemens/km. (a) Calculate the receiving end voltage on open circuit using justifiable assumptions. (b) What load at the receiving end will result in a flat voltage profile on the line? (c) If the flat voltage profile is to be achieved at 1.2 times the loading in (b), what will be the nature and quantum of uniformly distributed compensation required? 13. In a 3-bus system, Gauss load flow method is to be used for finding the switched capacitor compensation required to maintain the voltage at bus 2 equal to 1.0 p.u. the data for the system is as follows: Line data: Z12 =Z13 =Z31 =jO.1 p.u.Neglect line charging. Bus data: Bus No. Bus Type Specifications 1 Slack V1 (1+jO)p.u. Load:P2 +jQ2 =(0.4+jO.2)p.u. 2 PV V2 (magnitude) = 1.Op.u. 3 PQ Load: P3 +jQ3 = (0.3+jO.15)p.u. All data are on common base values. With the help of one iteration of load flow, explain how you will achieve the stated objective. 14. For the configuration shown in Fig.14, the breaker connecting a large system to bus 2 is initially open. The system 3-phase fault level at bus 3 under this condition is not known. After closing the system breaker, the 3-phase fault level at bus 1 was found to be 5.0 p.u. What will be the new 3-phase fault level at system bus 3 after the interconnection? All per unit values are on common bases. Perfault load currents are neglected and prefault voltages are assumed to be 1.0 p.u. at all buses. IDle en System Eg = 1.0 pU. XT= 0.2 D.U. XLine = 0.3 pU. Xd 0.2 D.U. 15. A synchronous generator, having a reactance of 0.15 p.u., is connected to an infinite bus through two identical parallel transmission lines having reactance of 0.3 p.u. each. In steady state, the generator is delivering 1 p.u. Power to the infinite bus. For a three-phase fault at the receiving end of one line, calculate the rotor angle at the end of first time step of 0.05 seconds. Assume the voltage behind transient reactance for the generator as 1.1 p.u. and infinite bus voltage as 1.0 p.u. Also indicate how the accelerating powers will be evaluated for the next time step if the breaker clears the fault (a) at the end of an interval (b) at the middle of an interval 16. 16. A single phase voltage source of magnitude 4and frequency o (rad/s) is connected to an inductance L through an antiparallel back-to-back pair of thyristors. The forward and reverse conducting thyristors are fired at an angle of a from the positive going and negative going zero crossings of the supply voltage respectively, in each cycle. Obtain an expression for the inductor current in each cycle for a given value of x. The voltage drop across the thyristors, when either of them is in conclusion, may be assumed to be negligible. 17. A dc motor with armature resistance Ra5 fed from a step down chopper in the continuous mode, and operates at some known speed and known excitation current. The motor current rises from .tmin to .tmax in the ON period 7,of the chopper; and drops from Imax to .tmin in the OFF period T of the same circuit. Both the rise and fall of the current may be assumed to be approximately linear. What is the average power loss in the machine armature? 18. For perfectly balanced operation a certain three phase ac power electronic circuit generates odd harmonic currents of order five and seven in the three phases of the ac mains. Identify which of these harmonics form a positive-sequence system, and which form a negative-sequence system. 19. A three-phase load operates with balanced voltages applied to its terminals, and draws balanced currents. The potential coil of a moving coil wattmeter is connected from R to Y terminals of the load. The current coil of the meter is connected in series with phase B. by appropriate derivation, show that the quantity indicated by this wattmeter is proportional to the reactive power drawn by the load. 20. Open-loop transfer function of a unity-feedback system is: G(s) = G1(s).e = ___________ s(s+1)(s+2) Given: G1 (ja = 1 when a = 0.466. (a) Determine the phase margin when VD = 0. (b) Comment in one sentence on the effect of dead time on the stability of the system. (c) Determine the maximum value of dead time VD for the closed-loop system to be stable. 21. A unity feedback system has open-loop transfer function K(s+5) G(s)= ;K=0 s(s+2) (a) Draw a rough sketch of the root locus plot; given that the complex roots of the characteristic equation move along a circle. (b) As K increases, does the system become less stable? Justify your answer. (c) Find the value of K (if it exists) so that the damping of the complex closed loop poles i
