paper dec. 2014

ra
Sr. No.
18713
SUB'ECTCODE
BOOKTETCODE
2014'(ID
-
ENGINEERING SCIENCES
TEST BOOKLET
Time : 3:00 Hows
Maximun IrIarh:200
INSTRU.CTIONS
l.
This Test Booklet conains one hundred and fifteen (20 part .A'+ 25 paft .8, +
?0 part
'c') Multiph choice Questions (MCes). you arc required to answ€rarnrrirurn oits,
20
20 questions from part lAl ':B; and 'c' reipectivcry. If rnore tlun
rcquirod
number of qucsi'ons are answcred, onty first I5, 20 and zo qucstions hr parts iA' ,8,
'C' reryectively, will be takerr rp for araluation.
slpet has
Before pu shrt filling up 1,o.ur
particularq please ensure lecn-pryviC{gepararcly.
that he booklet containj requisite numbcr of pages and dr*
thesc are not bm or m'tilated. it so,
rfu qay request thc Invigihtddchanggthe
!f
bookla of trc same code. Likewnc,
check the oiliR answer $reet alt.
ror-rough
work have ben appended to rhc te* booklet.
your Roll
-rv.r No.,
-lvrr Name
rlstrv @
and ee'r
s€rhr Number
rtu*rusr of
ur ur:r
this Test
lc.5l D.^)ruc[
Booklct on urc
aliri0e
tlrc uorK
oMR
answer
'
4
-d
OYI-p""f
2.
!
3.
ih;
sheet in dre gace provided. Also put your signatures in ttre
ryace earmarkeo.
4.
5.
6-
Ercrr question in Pa{--:A' canics 2 marks, part ,B' 3.5 marks and parr ,c,
5 marks
respectively. Thcre will benegarivemrkng@2s%for each
each qyestirn in partiA', ,Br andicl four alternati"o or-r.ryo*es
ue given.
onli onc of these altcrnativcs is lbe'correct" option to the queJon vou traue to"nnd
for,cach quesiorq the corrcct or hcbe$ answer.
*l-*o.
Fp*
7.
'gandigbs
found,copying or.resorting to any unfair means :!re liable to
bc disqualified
from this and fuUne examinatirirs.
9an!iluc.struld not.rrritc alrything anlnrhere exc€pt on ansrcr
rougn worlc
Usc of scicntific calqtldlor without data connectivity is permittod.
9.
10.
II
nr"..6.
'
Candidates
ufu iit
ff tp entirc duration
&eir TeS bookl€t
or
sheets
for
of the exarn will only bc pcrnised to carry
!.3.?:.:...............
N** . hI$I.I\)!1.!R.9tn$R.$ft r r y
OMR Answer Sheet N"...6.1.1 3.?.J
t
2S/55
slreet
CSUI,HBE-1A
I
have verified alltre informaitn filled
in by fte candirlaR
r
.
NdzInvigib
Signa6eof the
3
4..
lildeFfu in different
L t tisogram. If the
integer, then
n(n+ t)(n+2)Q*3Xrd-4XrF 5)(n+6)
is divisible by
l.n
V
3.
4.
b *-
yadability during
ligwhich yearwasthe
the average of_
::Frf rilfttovs
t;lr-.c=s.
If n is a positive
l--\
{t\-/S:)
3butnotT
3and7
Tbutnot3
f,F
neither 3 nor 7
The area (in m2) of a niangular park
dirnencinno'(O m l?fl
a-J f 2n * :^
-
tr
!o
of
""b
9u
i-
lro
lu
l$0r
,1ro0rso
-so
5Ol
5q
2000
l.
3.
ttlow. He has a choice of )*.
'>
a VEG or a NON-VEG meal for hii
2iln
2002
2000
2002
lunch/dinner
2003
2, 2001
4. 2W3
3_
2.
4.
l:1.
l:3
days
(d) He
takes
meals
What is zr?
'
l.
3.
l:2
l:4
7. A
A long ribbon is wound
around a spool
up to a radius.R. Holding the tip of the
ribbon, a boy nns away from the spool
with a constant ryood maintaining tlrc
unwound portion ofthe ribbon
horizontal. In 4 mindes, tlre radius
the wormd portionbecomes*
further time, it wilt Uecome
y
min
2''[min
So
3Foo
v
h *nut
2.
1s'>
Z mtn \-
4.
4 min
a total
of
14 NON-VEG
2.
4.
18
20
bank offers
I
it9"
24
38
a scheme wherein
l(o
o
400_days would be Rs.
of
ih?
I
I
I
deposits m$e for 1600 days are
doubled in value, the interest being
compounded daily. The interest accrued
on a deposit of Rs.l000l- over the first
2s0
2.
4.
3. t48
@ What is the next
183
190
numbe.r
of
the
following sequence?
2, 3., 4, f,.Ll,.g, 15, 10 ...
.3.i*t,
l. f
)qz
F+t*
for ''
length and once around its breadth. The
ratio of volum* swept in the two cases
l.
3.
he
dinner
(a) tf he takes aNON-VEG lunch,
will bave only VEG for
(b) He takes NONT/EG dinner
exactly 9 days
(c) He takes VEG lunch for exactly 15
A rectangle of length d ud breadth d/2
is revolved once completely around its
ls
s
days is given
(rutr
l.
3.
$
-**
?,
2.
4.
t2
t7
13
t9
-/ tt
*Ltt
€
lr
9.
,b
9v
Two locomotives are running totilads
each othcr with spceds of 60 and 10
km/h. An object keeps on flying to d
fro llom the front tip of one loconotive
to the front tip of the other wi$ a ryeod
of 70 km/h. After 30 minutc, tlrc two
locomotives collide and the object is
crusherl. What distancc did the oUect
13. Find thqmissing letec
q'qn
^W
crQ vr s-i c
("iD
0
E.$K
U
(
\o
A
G'} I W
h
Y
cover beforc being cnrshcd?
l. 50km
3. 35km
s"
\a /n
€
$
!*'
C;il
' v
Weights (in kg)
below:
2.
4.
of
3Fo"
88, 90,
by
l.
3.
1
:
i
1r9"
2.
4.
Okg
1.6 kg
lkg
1.8
ks
least significant bit of an 8-bit
1:14./
'\-'l The
binary numtier is zero. A binary
number wlrose valrc is I times tlre
l.
2.
3.
4.
/
1.
3.
.1-i-
,Itl
w
O
2.
4.
Two solid iron spheres are heatod to
100"C and tlren allowed to cnol. One
has the sizc of a football; the other bas
the sizc of a pea. Which sp*rere will
attain thc room ternperature (constal$)
tlree zeros
four zeros
o
o
oe-^o,,o
three zeros
four zcroes
15. A person sells two objects at Rs.l035/each. On the first oQiect he suffers a loss
of fiYo while on the secord he gains
l5%. What is his net losvgain
letters followed by at most four identical
digiti. The code must have at least onc
lettcr and one digit. FIow many distirrct
l(oo
has
previous number
12 bits ending with
I I bits ending with
I I bits ending with
12 bits ending with
11. A codb consists of at most two identical
codes can be generated using latdn A
to Z and digits I to 9?
ll48
936
t872
2574
2.4
\j/ o
L
N
Two new persons having weiglrts lfl)
kg and 79'kg join the group. The
average weight of the group increases
l*900
1
13 perso$; are given
io, 72, 7 4, 7 6,7$, go, Bz, 94i86
92,94 .)e . )r ,roo
bpw
.
45km
lOkm
percentage?
l.
2.
3.
4.
16.
SYo
< l%
< l%
gain
loss
_o
58,7?, l0o
64,81, 100
43,47,53
55,89, ll3
so
.it
r\)
sa
9t"l'
no loss, no gain
Continue the sequence
2,.5,.10, 17,.28; 41,1, -,
l.
2.
3.
4.
.oos
gain
I
^1r
c*,1tt'
58
firut?
l.
2.
3.
The bigger spherc
Tlrc smaller sphere
Both sphcres will take the same
time
4
It will
depcnd
tempcrature
on the roorn
..5
A'
17. A ladder rests against a uall as slrown.
The top and tlrc bonom ends of the
ladder arc marked A ard B. The base B
slips. The central point C of the ladder
falls along
5
PART'B'
MATI{EMATICS
-2.
it
t.
\x
4.
21.
aparabola
A third order ordinary differential
with x, x lnx and r lnzx as
linearly indepcndent solutiorx is given by
equation
tbe arc of a circle
line
ahy'peftola
a straight
l. xty *2x2y"-xy *y=0
2. x3y"'*xy'_!=0
v
e
,uoooo
18.
of
3. xty"'+3x2y" -Zxy'+Zy 4. x3y'" * 4x2y' * xy' - I = 0
of a particular
course
getjobs rvithin one year of passing. 20lo
ofthcrcmaining strdents getjobs by the
16
end of second year of passing.
2U/o
students
If
.
22. The number of real solutions of the
strdents are still jobless, how many
shdentshad passed the course?
32
?5
100
3.
s
6
n
r9.
.arl
\)
Itr
{r
Zsinzx*10x2*r=Zcosx
is
1.0
3.2
(l +,rf = do *
apc+
a2f+.....+a;f ,
a6 d1,....., an are
n" I*t
constants
l.t
l5,,?t'
le
B
ir
rybcre is made up of very thin
corpentric shells of increasing radii
(leaving no gaps). The mass of an
arhituily chosen strell is
l. oqual to the mass ofthe preceding
.,^)
i
20. A
2.
3.
4.
a be a real number such that 0 < a < l.
of
lim n(ct+l + elln
nico \
*yn
4. *+n
rta
l.
4. rnore than 2
Then the nalue
depading on z. What is thc sum ao* at
! az+..-.+ an?
3. ,?
p
I
2.
ginomial theorem in algebra gives
whcre
15
equation
2.&
4.
l.
0
/\-t
u!
-
1)
is
2.-l
1.0
3. I
4.
cr
A solution of the first order differential
equation
sbell
y'cos(x+y)+ry=
proportional to its volume
proportional to its radius
to its surface aFea
et-cos(r+y)
ls
l. sin(x*
2.
3.
4.
l)-e'=
constant
e'tan (x + Y) = constant
x(cos(x + y) - e') + er = constant
x(sin(x + y) - e') + et = constant
I
:
25. l,et D be a rcgion in R2 arclosed by a
The rank of ttre
lo 1o z ol
le r B s rolis
lo z 3 1 o l
\o \ z t sl
f
| (2, + 3x2)dx+ (2r + 3y)dy
J
c
is
12 then the arca
2.6
3
26.
1.4
3.2
ofthe region D is
t.
t2
24
30.
I*t f (z) = 2 and g(z) = lzl2 for all
€ C. Then atz--0
l. /is analyic and g is NOT analytic
and B betwo 3x3 mafiices
such that A+ B,A2 = f ,Ag: BA and
Az + 2A +
0 where / is the identity
matrix. Let l4 denote the determinant
2.3
4.5
In a set of 4 dice, one is faulty with
number 6 unitten as 5. All dice are
thrown simultaneously. The probability
of obtaining a suri greaterthan 2l is
l.L
2. g is analytic and/isNOT analytic
3. f andgare analytic
4. neither/nor gis analytic
27. Iet A
matix
le 3 3 5 s\
simple smooth closed curve C. Suppose C
is oriented anticlochyise. If the value of
the line integral
3,
41
1
72
2.r
S,t
4. 81I
ENGINEERING APTMIJEE
I:
of any'matrix
L
Then
l. lAl+ 0 and [+
2. lA+Bl *
A1= g
0 and lAl = 0
3. lAl+0and[A+Bl+0
4. lAl :0
and
[
+ n1= g
Then the value ofthe surface integral
ff
+ 3r) -yz +sz.ldo
JJtfzt'
s
Ztr
8n
))'
In an ideal, 2-stage comprcssor with a
perfect intercoolo, air is compressed from
an inlet pres$re of 100 kPa (abs.) to a
final pressure of 8CI kPa The inlet
temperature of air is 300 K What should
be the pressure at the-exit of the l.t stage
compressor (in kPa) so that the total power
input to the compressor is minimum?
Assume air to behave as an ideal gas with
constant index
comfression.
(Atmosplreric pressure = l0l kPaf
a
f zs.l Let Sbe the unit sphere f1?+/ = t.
'\j
31.
2.
4t
4.
l}n
Lq**j-z)+ro\
l.
3.
of
282.8
425.6
2.
4.
300.0
551.0
32. Pure Fe is polymorphic. Wh would be
the approximate ratio of dolnic radius
of iron at 24oC (lafiicc parameter
0.287run) and iron at l00(Pc (latrice
parameter 0.352 nm)?
l. 0.8
t. l.l
2.
1.0
4.
1.2
-)
'i
wn"n of 6e foltowing statemenq
i'sl/
\J conceming airsandard
.
a ffion is 0.0U1. Ihe type as6
@ingconcentration of this matcrial are
cycle are TRIJE:
l.
-f3.
4-
(i) Foragivuroomphssion ratio and
inlet corditions, Otto cycle has
than Diesel cycle
higher efficiency
(ii) Fora givearnaximum cycle pressnrc
and tanpcrature and inlet conditions,
Diesel ryle fu higfuer efficiency
thanOfio cycle
Tcn
36.
l.
3.
with compression ratio
(iv)For a ghrcn compression ratio and
inlet conditions, the thermal el$iciency of piesel cycle increases
37.
with cut-offratio-
l. All oftrcabove
2. Only (i), Si) and (iii)
a
,
3. Only (ii) and (iii)
4. only(ii), fii) and (iv)
b"e and l0l3 cm'3
N-typeand 1.5 x 1016em'3
P-t)?o and 1.5 x 1016am'3
P-
cds
are required for a solar cell
H #;"f, l3'X4,i'
bc--:
(iii)-Ilne ttrcrmal efhciency of Otto cycle
irrcreases
N - type and l0r3 cm'3
o'
02n]
v{o.sr*
1.0 m2
2.0 m2
4.
et
ld
3e
er
1?
th
n.
.
_
\o
m
a
)';
In the circuit shown, a l0Vo-o sinusoidal
sigml at 60 Hz is appliecl as Vi,,.Asnrme
that, for the given load R, each diode
has an avenge conduction drop of 0.4V
od th€ cut-in voltages of the diodes are
rero. The average value of the output
voltageis
.
&
#,1i';
{b$
I
(i) Spccificenthalpy r
(ii) Specific volume " .,
(iii) Specific ohopy
(iv) Specifichcat
(v) Spocificintemal energy
ro
] tt"
1
Which ofthe following thermodynamic
properties canbe measured in a laboratorf
+
Vg
i
4ofiy0),
GD and
-
(v)
2. Only (ii) and (iv)
3. Otriy(ir)
4. only 0) (D and (iii)
\oS^o
"t
)e
o'i
At rmm tempcrature, for silicon, tlrc
band gap (EJ b l.l eV, the inuinsic
corrcentrdim(q) is
loro cms andth€nnal voltage
*r.
(tJ * ru
mV. The Fobability that an energy state
in the conduction band is occupied by
3'
- 0.79V
+a.79V
2.
4.
\"o
-2.38V
+2.38V
38. T*o naves of lGHz are travclling in
opcx*e dirtctions on a transmission
lbe. Ai x = 0 and t : 0, the amplitudc
andfrase of the fonrard wave is 3V and
ao, uihereas the amplitrade and phasc of
Ite bach^Erd wave is lV and rr13
reEcctively. The propagation constant
of 6cline at I Gllz is r-0.05 + jl2.
I
The.perJk voltage at x
= [ meter is
l. 0.95 volb
3. 4.95 volrs
2.
4.
41.
3.91 volts
5.05 volts
.
A
simply supported beam is loaded as
shown in the figrue. Find the magnitude
of bendkrg moment (BM) and shear force
(SF) at the mid-span.
39. The magnetic flru density in a region is
given by p = (zi+ 3l - +ft)s'zt
Wb/#. A squarc loop of 2 m side is
placed in ttrc regioq with its center at the
origin ad its sider along the co-ordinate
axes. The emf induced in'the lopp at t
:
I
sec is
l.
1.35 Volts
3. 4.33 Volts
2:.
4.
3.24 Volts
5.41 Volts
\'\
,4
l. vu=fr-ro=; 9)ry
40. Two positive point charges e are placed
-
\-,
\12
..\.
as shown in fte figrne a dijtance d away
from a grounded conarcting plane. The
2.
BM=
distance betwsr ttte point charges is 2d.
The. net force on the point charges
3.
BM=
located atthe point
(d
d)
ii
rA.
42.
,$*
\q,tiK i .e
#;sr:! :Y,W'
;;;; *w
PL
f,'; SF= P
'{ua-"j
3
ryZi"
Assume Fl and F2 are the buoyant forces
a
on rectangular iron block
(density 7000 kglmr) having dimension
Zcm x 4cm x 8cm, and
4-cm
cubical aluminum block (density 3500
kg/*t), rcspectively, both'of which are
immersed in thc same fluid. The relation
betrvoen Fr and Fz is
l. Fs=F2
2. F1=2F2
3. F; =4F2
4. Fr = 8Fz
acting
of
rffii
t
lzfi-t. zJ2+r.\
'''a;G'\Er-Et)
a
n
'#(i,-ii)
^
Q2
({z+t
.
JZ-r .t
"';mpi\F'-Tt)
43. For tre system shown, what is the natural
frequarcy
for small amplitudes
oscillations? The rod
mass m.
of
is uniform and has
45. Cmsidering the case of block
sliding over the block
I
only
4 find the smallest
rci$t of cYlinder D which will cause
tlte loss of static friction 655gme the
coefficient of friction betwwn block
I
dB
is 0.6 and betrn'een ttre block B and
the gouod (C) is 0:a. Also assume that
blocl,S docs not slide over surface C'
2Jffi
4.2
44. A horizontal water jet from a nozzle of
constant exit cross section impinges
normatly on a stationary vertical flat
to
flate. A certain force 'F' is rcquired
sbeam'
hold tbe plate against the water
If the water velocity is ripled, then the
rrcccsstry holding force will be
l.
3F
3. 9F
2.
4.
l. 64ks
2.
32kg
3. l2ks
4.
l6kg
6F
TzF
IFORROUGHWORN
PART 'C'
46.
What is mnted bv
nre following prograrn?
# ilgtyde (stato.it
void A
void B (void}
(void);
I
yoidC (void);
mtx= l;
intmain (void)
{ intr= j.
,ryrnf("Zdn,,x);
t lntr= 19 '
,
,
prinrffyd\n1r);
printf
(q/dhn,x);
AO;B(IcrT:-AO; B t);
ciii
pfintffydh",r).
:
return 0;
l
ygion (vo@
tntr=
(
15;
r+f,;
,J#Hl[Tfr"r}
]
( static.r = 50;
r^Fl;
printf
(,a/dh',r);
,
void C (void)
{
r* = l0; printf(yodn,,x)1.
1.5
l0
5
t6
5t
l0
t6
52
t00
5
2.5
t0
5
t6
50
t0
t6
50
l0
5
3.5
l0
5
t6
-5t
t0
l6
5l
l0
5
4.5
t0
5
l6
5I
l0
l6
52
t00
0
t1
The cost of minimum cost spanning
rcc ofhc graph strown below is
13
9
l.
79
2.
3.n
78
4.
76
(2?,H), Insert
Let H be a heap shown in Fig(a). After pcrforming Insert (45,H),-Insert
(10, H) and Ditetemin (tI), the-structure of the heap will be as-shown in Fig'(b)'-Irt
:1-VrZdcnote the values'in the nodes labeled by ttrem in Fig.(b)' The values of (X,
Y,Z)ae
l.
@Dl
(35,21,27)
<{rrt,lo,2t)
3.
(21,28,35)
4. (28,21,35)
may have.multiplc
Considcr tlrc creation of a Binary Scarch Trec for a set of keys that
di*inct
copies of sone kcys. \tr/c create-the tec by rcpeatod inscrtion. For.inserting
sircond and
values, the rsual insert procedure is followed. Honaver, while inscrting
s1@g€rrt copies of a kcr wc ahnays move to tre rigtrt child of the first copy- The
t
(23,10,10, 10, 23, 12,23,11,10'
1.9
z. s
50, 8, 10, 30, 5, E, 231 in that order is
4-
lt
,,\
6
= z1!'4Pi)
2\
12
The Statement
r.
-(p
c+ q) is equivalcntto
(fpn-dAlcn-p))
3. (tp A-e) v (q n-p)
n(q v-p))
4. (fp V-q) v (s n -p))
( 2.(<pv-q)
In the machine M, suppose that the insurrctiolts for floating point operations can be
enhanced to run l0 times faster. Assumc trat in a pograrn Pl, 85% of Instnrctions
arc floating point operations and in another progran Pl, Et% of its instructions are
floating point operations. Which of thc trio programs can be made at least 4 timcs
faster by enhancing
Only Pl
il?
2. Only
P2
3.lkitberPl norP2 4.
Both
Pl
and P2
What does the Boolean function
F
= (aeb)o(aob)CI(e@b)e (aob)
Evaluate to
if e stands for XOR and O stands forXi{OR
l. o.b+ a.b
53.
4. a*b
-)/o
2. a.b
a relation R(A,B,C),with the folhwing functional dependenciesi,lB -r
C;AC -+ B. A can take 20 distinct valucg I can ake l0 distinct values and C can
take 100 distinct values. What is the maximum possiblc*ize (in tuples) of the self
join offt on C.
Consider
t.
54.
operation?
2.
4000
4.
3. 4,m,000
200
Consider an instance of the relation Sailon
20000
sluiln below:
ir'.1: ,^\5r"f'O
srld
Nane
Rating
Age
t6
t'.tt")-\g-o/
iones
3
20.0
32
24
jonah
alwb
56.0
65
mbbv
4
7
6
qr$-',
43-0
.9)
a
r5s
What does the following query return?
SELECT S. Name
FROM Sailors S
WHERE S;rating>
Al{Y (SELECT Sl.
RdturgfROM Sailon
Sl WHERE St.
age<71)
l.
ahab
3. ahab,jonah
2. abab,indmoby
4, rnoby
13
cPU burst
considcr the following set of processes wiilr the anival timcs and the
times.given in milliseconds.
Proccss
Arrival Time
BuntTimc
5
P2
0
I
P3
2
3
P4
4
l
.Pl
3
pre-emptive shortest
What is the average waiting time for ttrese proccsscs with
reinaining time fust scheduling algonithm?
l.
2. 5.5 msec
2.5 msec
3.
l20mscc
4.
3.0 msec
ELECTRICAL SCIENCE
2MVA
3.3 kvr/O0v
2MVA
3.3 rv
r\'ryFg
o1,i-
$phate,
bdmc€d
gG*ve
load.
1-5
lr\rA
its own
A 2MVA, 3.3kV, three-phase generator has tfu following rcactance's on
basc:
:
+ve sequence reactance, x1 =j0-lOp.u
-ve sequence re8ctance' x2 :70. I 0p'u
:70-05p.u
zero sequence reactance, xs
reactance'from neutral to ground , xn:fl.05 p'q'
a 3-phase,
The generator supplies a 3-phase, 1.5 MVA balanced-passive load through
kVlqOOV, delta-star transformer with leakage reactance of 107o, as
Z.O rtVn,
tto*n in'tt" frgurr. A single-line-to-ground fault takes place at-the low voltage side
is
of tlre transformlr. The cuient flowing from thc fansformer to the fault
f.f
l.
-@.
:*
'*
:
:
5773.5A
2.
1237r.84
3.
14433.8A
4.
17320.5A
foi ahy
Which onc ofdre following dc to dcconverterican bcoperatcd at steady state
dutycycle, 6 in the r*g" o < 6 .< I without anploying a closcd loop feedbackcsrtrrol?
l.
3.
Buckconverter
Buckboost converter
V/
4.
goosconverter
C'uk converter
a< g<t
14
Currcnt distribution (dot o1 representing currcnt direction ort of the plane.of the
1
paperand cros (x) rcpr€senting currcnt direction into the plarrc ofthe paper;
absencc
of a dot or a cmss neans no currcnt is presart in drce conducrors)'in armature
of.a repnesentative 2-pole fully cunpcnsated dc motor rotating in
*nj55.
anticlochrise dircctiqr and operating under rcgencrativc mode ofbraking is
l/l
l.
x
t!
E.
utl
JU
tOr
$
ldfl hsslesg srngt phase dc to ac square wave inverterhaving
vac is feoding a purcly inductive
input dc voltagg
load as shown in thc Figure. switcrrei sr, sz o." 5N
and ss sr arc oFF forthe first half
arc OFF for the subsoquent
cyct
half cycle,
(r /zseconds) and s3, sr are oN and Sr, sz
(f/2
scconAs;.
?r
t
Tlrc wavcform ofthc output current, L oncc
cursiderable duraim of time is
fie inyertcr is in opcration for
15
-D<F - ->
rl2 v2
- -F-
rl2
,--F-->--->
rtz v2
il2
motor
A 400V, starconnected, 3-@, 50 H4 4 pole, 1440 rpm squ$l cage indirction
p.h?sc
pcr
..
The
0.5O
is having per phase rotor resistance refened to the stator, ri =
gana-stilf rotor rcactance, series stator impedurce and the effeot of the magnetizing
br"dt of thc machine can be neglected. This motor while bcing fed from a 400V, 3'
in
O, 50 Hz, ac $pply is coupled to a load wfiose torque, T1:20 Nm and is acting
dle same'diroetion as that of the direction of rotation of the motor load.sy$em as
losses, the
shown in ttre Figure. Neglecting friction, windage and odrer mechanical
'
stcady ote spced of the system, co in radians per second is
3.(,AQOY,
50Hr ac
tOAD
)rrroron
(0
r. (r -fi)+e1
,. (t + fu)sor
T!
2.
(r +f,.)so"
4.
(r+ft)so"
A drrcc phasc 50H4 Bdial transrnission line has a total saics impedance of (15+j
160F, and a{otal $unt adminancc of 0.8 x t0-3n{w. Ashgrt capcitor (C*) of
a&ni$ance 0. G x lf-3mlw is connectcd at thc receiving cnd of ttrc line for providing
rcactive porrer sryport. When the scnding end voltage is 4fi1 kV and there is no load
on thc line, Sc magintOes of the receiving end vottage and tre sending cnd current
arc respectirrcly
l. 476.13kV,475294
3. 427.34kY,330.934
2.
4.
476.13kV,616.124'
45A.42kY,475294.
16
@
jzn
j4rJ
m
lt
4
V= l0Z0'
; Z;
22=
j}{l;
For the circuit shown in the figure, a load impe/liltrce zlis connected across the
terminals a-D such that the power transfer to Ztismaximum. Thc value of ztis
t.
3.
n7\
gt
2. 2.236t263.435"
4. 7.2tllz$63l'
t.5so4/60.2s5'
2.69t/78.86"
A feedback.lnlr"l*vrlem as shown in the figurg has forward transfer G(s) =
and feedback transfer function H(s) =
fr. ru steady state eror for a unit
ramp input is
61fu5
'\
ri .?it
e4x: (,,o
I
t-l
S+\)
lt!Is*rXsJ\)
g
*
6c'-f
-*l
t*l
1.0
2- ll5
I
* -e_
I
4.
A
3-phase, 50H2, 200MvA, 33 kvtn(. kv, stardelta ransformer is protected for
inter-tum fault by a differential protection scherng. The possible pair of turns ratio for
the cunent transformers to be connected to the high volage and low voltage sidrb
respectively is
525:5 for h.v. side, 3500:5 for l.v. side
2. . 525:5 for h.v. sidc, 3500:
for l.v. side
l.
3.
4
5€
525:5 for h.v. side, 3500:
S/rE
forl.v. side
525:5/'lTforh.v. side, 3500: 5 for l.v. side
/6\ /
L6y A PDoqruoll€rbadded
passa thrurgh ttc
to tli6plant G(s) =
poi* -1 + i.
ffjru.tr
drat the resulting root locus
The-pgsition of dre PD zero is at
fi
1o--rs
r t*tt*t)
=
ffi
--E
q(e');':"--.
!-r9"' .
F'
l.
-0.5
2. - 0.75
3.
-L.25
''/
.q]i.o>t'
- t,s .-T g.'^ !v/
\+
JYF
MATERIATS SCIENCE
ffi.
..96t .i.
Two Pb-Sn alhys rmdergo equilibrium cooling from the liquid state; one with l0
rvPlo Sn ad balame Pb ard the other with 10 n'P/o Pb and balance Sn. The phase
diagram is shown in thc figure below. The volume'fractions ofthe pro-eutectic phases
at tlrese nvo conpositions are closest to:
()
L
!
I
t
E
wcllr *rxl(9r)
l. fs=SWo, fi,=S0flh&fg =ZAVo. ft= 8(P,6
2. fn = L$Wo,:fi. = 096 & fp = $AVo, fi, = 2@'6
3. fa = 250'6" fi" = 7596 & fp = 20o/s, ft = 8096
4. fs, = 20%, ft = 80Vo & fp = 20o{o, f1= 80%
6it .
A pondcr mixnne of t0 r+,tr26 Al and 2O vf/s Z,rOz is prepared in an auritor mill and
is wnpaod b r grcen density of 80o/o of theor€tical darsity. The densities of Al,
t,respectively.
AJzOr aa 7lrDzae2.?,3.96 and 5.6 dc
The atomic weights of Al,
O ad 7t arc2 n,16 and 91.22, respectively. The green body is oxidized prior to
sireiog.lf7.rof6e aluminum is oxidized, the finat compact will have:
l. *y
-gErcsila{H^
2. 2.7%porosity
3. 3.9ploporosity 4.
Z.7o/oswelling
1B
M
l'
a)
!
Assrnc carbon atoms sit in
the|,|,0
l.
0.31
abancr[ubfoE redius ofcarbon
Sal 4 = 0.77 A and radius of metal atom, r,tr = t?l l+bl rte disancg each of
tltc ncarcst metal atom be displaced to accommodat dtc crbo atorn?
.
3.
0.54
4.
LOA
ln silicon the Fenni level measurcd from tlrc intirsic Fcrmi leyel at 300 K is 0.358
eV. What is the approximate donor conccntiation in dre silicur? (Given: Intrinsic
caniiei density in si at 300 K is 9.6s x l}e lcms;Bolamann constant ks
= g.614 x
10-s eV /K)
*as'
_ix./
l.
70
0.zA
position in
-
Llslcmt
2.
LOtz1orrP
3. tor6lcaz
4.
lgzo l67nt
Tlrc Pilling-Bedworth ratio of alurninum and tantalum oxides are 1.28 and2.33,
respcctively. The characteristics of oxidation resistance and oxidation kinetics for
Alzor and Tazos can be dcscriH as:
l. Aluminium exhibits better oxidation resisance
than tantalum, and the kinetics of
oxidation for both the metals follorr the parabolic rate law.
2. Inferior oxidation resistrancc of tantalum is due to its porous oxide lryer, and it
follows the linear oxidation rate law unlike aluminum wtrich follows thi parabolic
oxidation rate law.
3.
4.
7l
.
-
-l0o/o
2.
-20%
3. -30%
4. 40%
'fhe bulk di{frnion cocflicients of maal A in B n" 1g-tz^zls
ud Lo-Lamz /s at
1300 K and 9{10 K, respectively. Thc Civ.qlion €ncrg}t for diffirsion of A drrough
grain boundarics of B considering its pagnittr{e to be 0.45 time dran fiat of bulk
diffirsion is [Givcn: Universal gas constant, R= B.3l J/mol-Kl:
'
73
oxidation ratc law.
Alurninum and tantalum shorv nearly equal oxidation resi$alrce, and the kinetics
of oxidation for both the mctals arc contnolled by fire loguithmic law.
In transmission electron microscopc, an operator changes thc normal operating
voltagc of l00keV to a high opcrating volhg; of200 keV. Ttrc perccntagc change in
spatial resolution due to such voltagc change will bc
l.
'17
Inferior oxidation resistance of tantalum is due to its cracked oxidc layer, and it
follows lincar oxidation ratc law unlike aluminum which follows the logarithmic
l.
.
,
?78.4wlnwl 2. zot.Lwtnxll 3. 100.6ulmol 4.50ikJ/mot
Tfrc sharpcs possiblc crack to causc brisle fractrre in a matcrial with Poisson's ratio
of 029 followftrg Griflith's eqrBim in plane shain condition slrouH possess crack
tig root radius as X timcs the intcr-atomic qpacing where X iseqrul to:
t.
I.00
2.
1.39
3.
2.78
4.
3.00
SrS5CSUt/t4#-Ai
:1e
I
74
.
20 mol% of NiO is added to FqOr to form nickel fcnitc (NiEoOr). The net spin
magretic moments (in Bohr rrgri-,1 for Fe2*, Fel* and Ni2* arc 4, 5 and 2,
resiecively. The . percentage charye in saturation qagnetization (which is
proportioryrl to the number of Bolu rmsrson per unit cell) will be closest to
l.
75.
2.
40%
3oo/o
3.
2Ao/a
4.
l0
0/:
An ideal plastic material cxhibits yidd Sess of 200 MPa anil catasrophic fihcture
oocurs from the peak stress valtr during tensile teg of a 25 mm gauge lengh
specimen, If dre tens-ile toughncss and tlr resilience of the flow c.urve are given as
50.4 and 0.+ irilmm3, respectively. Ttrc peromtage elongation of the material in the
pla$ic regime would be:
:
l. 25%
2.'
t2.50/o
3.
0.25%
4.
0.t25%
FLtnD MECHANICS
76
,
.
A fluid flows past a sphere with an upsbeam velocity of Yo = 40 m/s as shown in the
figure. It is found that the speed of ftefluid along the front part of the sphere is
V =2 Vosinl. The sfieamwise and rnrmal compinqrs ofacceleration in m/s2'at
if the radius of thg spherc is a:
0.20 m, - respectively are numaically
pint,\
V
closestto:
l.
3.
372A
rlndM30 2.
4430urd3720
4.
7440 and 886{l
8860 and
7440
$
il;
*!
fi
:l
I
!:
77.
The twodimensional velocity ficld for an incompressiblq Newtonian fluid is
descdbed us 7 = (l}ryz - 6xt)i+ (lSfy - +yt)i, wlrere i and i are the usrit
veclors along r and y directions rspcctivety. Hcre thc vclocity has units of m/s; r, y
being in meter. The stresses 67atcy,y,tay, I r = 0.5 m,I = 1.0 m, are given by (if
's
F*surc at this point is 6 kPa, and fluid visccity 1.5 Pa . s ).
= -5.98 kPa, o," : 45 PU to = -6.02 kPa
2. orx= -5.98kPa, oO= -6.021<Pa,Trr=45Pa
.i
t
{
t
ri
.I
l.
(Ixx
3.
4.
oxz
= 45Pa, or,
= -6.02 kP4 r,n = -5.98 kPa
6xx = -6.A2kPa, 6yy: -5.98lr}a., tt, = 45 Pa
20
78.
A cylindricalErn container has rolume V and bo6on arca e. Thc containcr is fillcd
with glycerin(dcnsrty p.) and rcsts on the lloor of ar elcvdor. The clwator has an
uprvard accclcration of a. What is the resultant force $d fre container errerts on the
floor of the elevatorduring this acceleration? Neglect fte weight of fte container.
l, pv
79
.
2. p(a- dv
3.
p(a+
g)v
4.
p(S
- a)v
A platc ofwood with specific gravity 0.4 is anchored to the bottom of a lake as shown
in the following figure. The dimensions of the platc arc 5 cm x 10 cm x 3 m, and
ttrc dcpdr of the lake is 1 m at this location.
Assrmc that the l0 cm dimension is
perpendicular to the plue of the figurc and
the density of the lake watcr is 1000 kg/m3.
The angle 0'at which tlrc plate
rvill fhat
is
numerically closest to:
l.
80
.
2.
150
.
600
4.
90"
A piezometer and a Pitot tube are tapped into a horizonat water pipc as shown in the
following figure, to measrc static and stagnation pressures. Assume the flow as
steady, incompressible and irrotational.
Negiecl cnergy losses. For the indicated
watcr column heightg the velocity of
wder at the centre rif pipe, taking
g = 1om/s2, is
l. tm/s
3. 3m/s
Sl
3.
300
2. 2m/s
4. 4mls
A &in fla plate of dimcnsions of 100 cm x 200cm is complecly immersed in an
oil streanr widr vetocity 6 m/s. The dcnsity and dylranric yisccity of oil may bc
taken as 890 kg/m'gd 0.29 kg/m.s respcctivcly. Asermc a dr4 cocfficicnt gvcn by
: Ce = 1.328 Relos, whcrc.Rel
the Rcynotds nrnrbcr bccd m thc plarc hnglh.
Thc total frictional fqcc,'if the fluid stream is almg dre long sirb of thc pla€, is
nsnerically closcst to
is
r.
4.435
N
2.
4435 N
3.
4435N
4.
4435N
21
'g2.
noT-g$ty pd to objcct shown in the
(-o s r S a) is
fisurc.n, niJ"cro.;t il;sth. 1i,[^it r dwing *catlrrc
crvftGof the front of the
drna to bc Y=yo(1*9), where a is thc ra{irnof
An incompcssible fluid with density p
uprilt velocity' If drs utrrcm ryYIfowis P6' obtain thc
l*
-o S x-3 -o,assrming iwisckl
objoct and lts is thc
p(r) for
AitniU,t
ffi*
P=Polx+o
,,
dividingsrcamline
p
.
= Po- pavts -
#)
p=po-pavfQ+4)
2.
p
= Po+ povte -
;)
4.
p
= Ps+ rrrvtfi -
#)
oonccnhic
A Couettc.viscomder consists of fluid nn€d befwcen tvo
shown in thc rigure.
rt"-ii""*viino"r
6aa.iusp) rotatos
:rl..lj:: :
t$l,:ljtl-:It:1tj'
"t
o, whilcthcotrterone isrcstraid lt^ msans
""rttity
torque acting on thc ottcr
to.S-al sprini. The
-deflcction
#il;;ilfi;*gurrr
t
;/ird; it toiut u by means. of spring g*ry
isuming' dre flow to bi steady, laminar, luryly
of
.OinO"rttd*t of Z direction, cxpression for thc dynanic
;',"";i,y in tenns of thc measured torque (T)' angular
are'
velocity (ar) and ofirer geometric paramctes
T1
ffiv
tft=2r'
arrilfi
t (rl+ri)
^J. ffiE
4.
r
('i-ri)
1n?'L
riri
thc rate (constanl) at
A rocket has an initial mass of mo (rockct + fuet) ard riL is
is given
whictr d1e mass
ii
ut"
r""fir
;t;dk.
1f the dragforce of air on the rocket
dren dre diffcsilial equation go1erni1g
io, (u6se r"f'ut tr rp..a oirtr" Io"\"0,
the rockct mdion ir
gi""i iitassu.ing
ttte orpcltcd mass to exit from the rocket at a
con$ant velocity u relativc to the rocke$
l.
-m'O fr+ t u' = theu- (mo - m"t)g
2. (no- m$fi+kv2 =(mo- thrt)(v+u)-(mo-m"t)9
(mo
kvz = fr"u- (mo - mrt)g
3. (no - n
"q*4. (mo- *r0**kvz = (mo -lhet)(v -u)-(no-th"t)g
22
85.
water (density =10fi) kg/m3) at 0.1 m?s and
alcohol (specifrc gravity = 0.8) at 0.3 m'A
are mixed in a T-junction as shown in the
figurc. Assrmring all the flows to bc steady
and incompresible, average density of thc
mixturc of alcohol and water, in kg/m', is
l.
340
2.
3.
4.
560
680
8v)
SOLID MECTIAMCS
86.
from the ceiling as strown in
. the figue. The crosssection of AB : 500 mm2, and
drat of BC = 200 mmz. Assuming that the density of
A
stepped bar is hung
to 7500 kglmt,
find the axial force at a section a-a'just above B.
Take g = I0 nt?. t downward forcs of 20 Ar is
both the rods are the same and equal
acting at
l.
87.
I
and a force
32.5 N
6{fimm
g'
B
20N
of 5 N at C is acting upwards.
5{Mmm
2. 22j N
3.
90 i\I
4.
l00N
A long ttrin walld closed ended cylindrical vessel of fiickness'l' is subjected to an
internal pres$rc 'p' as shown. Find the sbain energy stord in dre cental part of the
cylindcrof lengb 'f,' due to pressure'p'.
l.
Inpzd3t
t6Et
2.
zrpzd3t
srpzd3L
3.
16Et
4.
srpz ri3 L
32Et
23
tft
tb. thc average
load P.
Which one
as
shon'n.
a:ris,
0
to.ttre
an
angle
shear sfiess acting on a plane oricnted at
A baf of cross-soctional araA is zubjected to an axial
of the choices bclow conesponds to the variation of r with
e (0
respect to
< O<rfD.
e'
0
1.
3.
t,
0
0
0
t
nl4
nl2
P
P
u
0
P
;i
A
0
0
t
0
0
0
P
2.
nlz
rl4
e
4.
I
rl4
nlz
P
P
4A
2A
rl4
El2
P
LT
0
"A
A non-uniform loading on ttre bar causes a normal shain which can be expresged as
€r = &r2, wttere k is aconstant. Determine the displacement of thc end B of thc bar-
"lry
l.
KL3
xr]
3
3
3.
KLz
Vz r*
2
Determinc thc equivalent state of stress on an element oriented 45o counter-clockwise
from dre eleinent shov.,n
1(X) MPa
24
fmMPr
ilnMPr
91.
100
Mh
A solid shaft of diameter d resting on two journal bearings h sr$jecled to a hansverse
load.P, at the center and an axial load
as shown. Detcnnine the atial strcs, o,
that is developod at point ,{ shown. Ttre joufital bcdng may be assumed to srpport
only vertioal loads.
4
l.
/lf=-
BPL
tcd3
4F
rcdz
2.
(f=
4.
'1l=-
(8P-4F)
3.
92.
at =l--
ttd2
The fiber AB has length L afi orientatior 0.If
ic ends A and B undergo small displaccmens
u;and up ts shown, dctcrmhrc drc strain in the
fiber.
l.
LL+ stnl
-cos? %
9
z. -cosl | + ti"e "]
3. sinl %LL- cas? 2
4. -sinCI YLL-
cosl "2
lPL 8F
rcds td2
-$PL 1F
rrdt rdz
.G,.'
6
radius R and negligible mass is nllfo3
without slipping on a surftce as shown in thc Figtlc'
m is attached to dre disk at $c
A heavy p'oint
toptoti point. The center of the disk is anached to
til.t*" side walls by mcans of springs of *iffrress
qntcnt
as shown. Derivc the natural frcquency of $c
A disk of
t.tt
t
for srnall amplitude oscillations
?n
-gmR
2J*4
f"s
3' .J;-t
4J=
mernber is givcn
Thc stress state at a location in an aircrAft sfiuctural
by
/100 0 -30\
I o o o luPa
\-go o $ol
matcrial sudr drat the factor
Choose the closest valuc of the yicld sgrenglh ofthj
yield'
safety is about 2? Use Tresca criterion for
l.
25 MPa
2.
48 MPa
3.
4.
70 MPa
A rigid bar which is con$raind to move in
'thc vertical direction is suppofted by a
column,AB and rigid bar asscmbly CDE as
strown in thc Figure. Thc joint D is attachcd
to thc wall bY a sPring of stiftess L
Calorlate the diameter d of the column AB
sothatboth AB and asscmblyCDE havethe
same ftrctor of safety against buckling' Thc
elastic modulus of ttrp column AB is E'
The moment of inertia of .AB is
, o=(#)"n
3.
o=($"n
L Usc htlcr's formula forbuckling'
z.
o=r(fl
4. d=2
ffiI^
15 MPa
of
26
THERMOD\NAMICS
In a steady flow compressor a gas is comEessed from 100 kpa GaF) ud2.7 m%1o
proccss to be
a final stal of 300 fi'r tg.gOhd 1.5 m?s. Assuming dre compression
to:
reversible and polyUopiidt po*.t.input to the compressor (in kW) is close
(Afinospheric pressurc = l.0l bar)
96.
l.
A housq
97.
2.
59
that is losing heat at a rate
4.
3. 387
24t
of
395
54,000 kJ/h when the o$sidc tcnperature
drops to 4t, is to d n*tbO by electric resistance. heaters. If the house is to be
maintained aiZfCat all times, the second law effrciency of the heating proccss is
1.
93%
2.
3.
560/o
4.
14%
7%
Liquid water enters a 25 kW pump at l0{) kPa pressure 1a rate of 5 kg/s. The kiratic
and potential arergt changes o-f water during the pumping proce-ss may be neglected'
Oensity of water ii tmO [gmt tnhich may be assumed to remain constant during the
p*es!. The higlrest pressurr (in kPa) the liquid water can have at the exit of the
pump ls
i
r. '5100
9.
2.
The foltowing saturation properly data is available for the refrigerant CFC-I I
(molecular muss = I3?.4 lgnsnol): Using the data given and applying Clausiusdhyp.ron Equation, estimatc thc latent heat of vaporization of CFC-Il at 25oC. The
rs equal to 8.314
universal gas consqnt is
kJtmol.K
Sat. oressure (kPa)
l.
100
'
4.- 5l
105
510
l0:
.
50.9
Sat. tempera$rc
103.8
24.5
t07.4
25.5
2. 101.8
3.
183.2
104
fC)
4.
2032
In a steam boiler, 100 kg/s of liquid water at 40 bar and a0"C (enfralpy = 16l kl/rg
and entropy = 0.57 kJ/kg.K) is heated to a final tempemture and pressne of 6.?3 K
and 40 Uar lentnapy =-3Zil kJftg and enropy = 6.77 kJ/kg.K) uing ffrrc'g;ases
available at ?50 K. l.legtec'ting kinetic and potential inagy drangcs, thc ailropy
generation in the process (in kWK) is close to:
l.
7r4
2.
406
3. 620
4.
l(n6
105
101 .
The heat tansfcr ftir the rcversiblc
processT-Z-l (as shown in the figure),
in kJlkg, is
r(qc)
120
100
0.02
2.
t. 88
3.
170
1.0
4.
341
s (kJlkg.K)
682
refrigelation cycle and uses
i- +Lo irlaal wcnmrA heat pump operates on the idcal vapour<omprgssion
operates at- 1200 kPa while the
refrigerant l34a as il;;tLi"tfluid. Thc-condlnser
enthalpy of thg f^{iserant at the exit of
svaporator operates ;rsO F{ i[" ,e*inr
is 249'72kJke;
2E0
tPa
the compressor is zso kJ/kg. Refriggqt nron"n*il
;t"t it0'0 kPa is
l.
ttl -ll wile'
' 2. 3.36
2.36
\,*
The CoP (heating) of the system is
3.
436
4. 5.36
gas is now
gas atJ40 kPa and ?7cr.The
A pistbn+ylinder device contains l'kg of a
following pV l'3- = constant till the
compressed slowly in a polytropic.process
constantfor tire gas is 0'3 kJ/kgK and the
volume,is reduced Uyiuff fitt tiq!9.8f
unir. The entropy chinge of the gas during the
,p"rii"'i*iit6.z
consrant volume
pro@ss (in kJ/K) is
2.
1.0.3515
0.a625
3- -0.0625
4. -
0.3535
g i93t
fluid air mrybe asslmed t" F
an air-standard otto cycle, the working
begins ut g.l MPa and 35"C. The
gas. The compression ,uiio is ?. compression
0'287
ln
Also-given {r.RrgRerties: &i'=
maximum t"rp"rtur";il;t';y;i"-it iioo"c.
ouQut (in kJftg) of the cycle will be
kJ/kgK and C-p3i;=l.oos'ii[gr. The net work
l.
2.
131.4
231.4
3.
272.7
4.
5A4.2
Inasteampowerplantbasedonideal,simplel*fucyclltheturbinedevelopsa
fiquid yr91at pump inlet (density =
power oqput of tZ MW. Assuming otu*ied
punp?
condensate
gg3 kg/mr), what percentage of turbine o,tlpnt is required for thc
at condenser pressufc ate 2573 kJltrg
The enthalpy and ent'opy of satur*cd ]aPour
of steam at rcquirod
and 827 kJ/kg.K, respectively. The otlrer ,"1""** Prop€rties
state points are given in the table'
l.
0.036
,
2.0.36
3.
1.36
4.2.4
lt
luhicLcof drefollowin;".ffi;rri"rt*rtr*rH*,rht*.ogcSm giyqr as (A" B and C are Boolean variatiles):
te +
2. AB+C
A+B
107.
'
aXfFE)+i1a+c;
It
3. A+B+C 4.
B+AC
For thc circuit $rowq the cut-in
vblage of the diode is 0.6 V. What
wilt be the morimum reverse-bias
dr@ volAge ad drc fraction (in Vo) 24Sinnt
of trc cplc over which the diode
conducts?
t. 24Vand 67.60/o
3. 12Vand 67.6%
2. 36V ud 12.4%
4.
24V
afi
5A%
lt
s.*o)
10t
.
ag.9'
For the circuit stroum, the output voltage
5Kl
too
5f,l
e'
i
v,eolz-
\?
A JK flipllop has propagation delay (tp6) of 13 ns. wrat is drc largcst MoD ripple
oomtcr that can bc con$nrctcd using such flipflops ard can be ofratcd upo ib
MHz?
l.
M}D
-32 2. MoD - 64 ly'*or- 1zB 4.
MoD
-
zs6
vr
gr+
1o*toc
e"''iJ"rvY
h
7:n97.r
Fatlrc ciroril shown" the expression for
Fis
x
Y
l. XY +xv +z
2. XF +Z
3./^ x_f
+z
v. z+xY+xY
z
+_Y_x
f9
'fi
Vq
--\**1
o'u*{
l+x
-\
n"'a'-,
*-o'
t
44t
lt
29:!
.
tft-;, If u(k) and SG) rcpresant 0rc unit step rnd unit impulsc
j
"
-:
the inversc Z-ransform of F(z) =
*f*
(-l)ru(t)
ll2.
For ttrc nctwork $os'q
. quiescent values
of
Vce
d€terminc
rcspclhfit
k > 0 is given by
2.
4.
(-l)ed(ft)
functions,
d(t()
u(t()
14.6
.
ll{ .
;#
qrubflh
rL rfinm-clffffiJ
1tlat
transmitted simultaneously, the maximum bit duration is
: -l. 3.125 ps
2. 6.25 p
3. 25 ps
A PCM multiplexing qlstem is fuignod using a 256 tevels
of three signals each of which is band limitcd ro 5 kllz, lO
r'espectively. Assuming
eacfr signal is.wrpleA at its Nyqdr
transform
oftrc fimction
r(t), trcrl ft
A
l. ;tl?Xt"l, ifall poles ofx(s) tiein fic right tutfoffip e1h"
2. ;tjlXC"l; ifall potes ofX(s) tie in ilre teft hatf ofrhc athG.
3. .S sX(s), if all poles of sX(s) lie in dreright hatf of0r fii.
4. fj[ sX(s), if all potes ofsX(s) tie in fie tcft half of thc a1h.
,ll5
.
t*,
.,iit&,s
function is
by
An angle-modularod signal is given
s(t) = cosar{2 x 105t * 30sin(150r) f
maximum frequencyard fln*dcvhtions ofs(t)
10.5 k*zand 140 r
6 kHzand
(ry
3.
1.5b
x
fte
V and 8.?3 mA
If X(s) is the Laplace
-1'
dr'
ad IE The
2. 10.5 V and 3.85 mA
3. 16.43 V nd7.?ZmA
4. ll.68Vand 4.16mA
ll3
-
eF/
- (-1)k
- (-1)k
following Eansistor parametcrs ar€ assumed:
F = 90, Vse1gD = 0.7 V.
l.
fr*
.,,ltl+i
q@
40cos(150t)}.
.*i,,;
arc
radim 2.
Ir*
,Fif-t
l0.Skilzandlfilrradiar 4- 7-Skilzaaffr---