5/-J grm Cs a^)lsUSN

2a.

Third Semester B.E. Degree Examination, June / July 2Ol4Engineering Mathematics - lllNote: Answer FIYEfull questions, selecting

at least TWO questions from each part.

O6MAT31

Max. Marks:100Time: 3 hrs.

a.,,,,"''".obtain the Fourier Series of

PART _ A

**C! in

(06 Marks)

(07 Marks)

(07 Marks)

zero for x)a.(06 Marks)

function from

(07 Marks)

au

--ua

0z

Ay

c.

c.)oo(d

a(!

(B

o0)

6e

x,-5<i;r'-oo ll

cca.=N(g<H50goo=-< 9"1eE

oBEca=

ciodoO't,60E.8lg!E>e26€-

E(gz.A6ragtro.oj

grE,oia (EEErol=t>\ (kbootrooO=o. iBtr>Xo)oLF(c. <(

....:::r t\l

c):Z(6Poo.

i"'i"""/1 ,:: ,,r:'r 1 1 1Tt.lll-: I --+---+

b. Show tfi*t',r1[re half range sine series

c. Obtain the constani term and the co-efficient of the firs{,pqsine and sine terms in the FourierYdl I'

for the function f(x).3, *x2 in 0<x</ isu, ,.\,,...t\.*

I ,,,,'(07 Marks)

ffiy:lelt8l2al28l26l7al, ft forkt<t

Find the Fourier transform of, f(x): {O a, i,.i, ,

Find the Fourier transform of, f(x): tO a, i,.i,

- 'rsin s - .."L,# |Hence evaluate I --- - ds

Jq0'

.'::::::_ @ _-..

Find the Fourier sine transform of .-l*l . H"n e evaluate [x stn-+dx

.

6' l+x'Find the cosine tranq of a function of x which iS,. ity for O<x<a and

| .,,r"""

What is the funetioafuhose transform i, tt ut ?

ri. 'u S

3a. Form theu';#artial differential equation by

for which.-it ;1

=-2siny when x: 0 and z = Oif ,y. is an odd

.d*\,,

,," r.fie liminat ing' ='; arbitrary

_;.,-.,;

.d'r'' ,#11:f'11':

b. ;Solve -

= sin xsin y..,,*;|"' axay

^TEmulttple ot :.zc. Solve (y - z)p + (z- x)q = (x - y) .

a. Derive the one dimensional heat equation in the standard form.

b. Solve the wave equation # = c' #; given that u(0,1) : 0, u(/, t) : 0,

and u(x, O): ro.ir[Il)\/i

'u,!1""

@f-l'u'(06 Ma&$

,n,.,,,,,,,::, ..,

(07 Marks)

when t: 0

c. Obtain the various possible solutions of the Laplace's equation uxx + uyy

of separation of variables.I of2

(07 Marks)

= 0 by the method

(06 Marks)

nsion of v fromx: 0 1 2 J 4;n :5

v: 9 l8 24 28 26 .?u,

z=y.rr(+*roev).

5a.

b.

c.

ar"(irr,

6a.

O6MAT31PART _ B

Find the real root of the equation coS X = 3x - I coffect to three decimals using regula falsi(07 Marks)

Solve the system of equations by Gauss-Jordan method. x+y+z=9, x-2y+32=8,2x+y -z=3 (07 Marks)

Using Rayleigh's power method find numerically the largest eigen value and thecorresponding eigen vector ofthe matrtx. ..

lzs r 21e=l r 3 o l. (o6Marks)

, L2o-4)''-'"'t'*' - )]*

C".rtstt"r.t the interpolation polynomial for the data given below using:$e&ton's general

b.

int 0 ion formula for divided dix: )"" $A 5 6 8 10

V: 10 9g '196 350 868 t746A rod is rota@.in a plane. The follorod ras turned for $.drious values of the time tt 0 0.2 0.4= m.6 0.8 1.0 1.2

0: 0 0.r2 0.49 'lf,-4 2.02 3.20 4.67

Calculate the angular velbdiffi;and angular acce

fferences. i,:,,,* ' (07 Marks)M l'rt"

l .; "'... .:

\-$ ,f .,r

wing table gives the argle'O"radians through which thesecond. ',

&r,,, "'=

j,h .,r1"*'- 0.3, .lc. Use Simpson', ] rule to oUtainthe approximate value of J(r-t*')ra* Uy considering

3 equal intervals. , l* (06 Marks)

7 a. Prove that catenary is the crqVc,,4fuhich whd$ated about a line generates a surface ofminimumarea. qs

*h (07Marks)b. Find the geodesics on a su$#Ce given that the arc-ldngth on the surface is,

x'

-

S = ft*(f + y'21dx (07 Marks)

i =r,..j#"' Ld;""':-

c. Solve the varjatidral problem: ti;;, ""

ol(-.p.;:$ dx=o '{l;:lo .. {......rq,''

+:""""".,,,,,,.',"'

.,,,,..

Undef'the conditions y(0): 1 and y(l):2. (06 Marks)1,i..

8 a.fl-\ffiind the z-transforms, (i) (n+2)2 (ii) sinh 0 'q;."''i 407 Marks)

)w ,nn z,l L.] = .j . Hence rrna z,l L-] *a ,,1-' -l (07 Marks)o b' Shr"' "'o' orli]l - " ' rrerrvr ,,"* -r[1n + l)!] -'' -rL(,

+ 2Xl , _,*

'"'h -1' ^ 322 +22 ,{rl|l'\"'1q. -li''.,,1'' c. Compute the inverse z-transform of -- (06 Mark6;:.';,;:'

(52-l)(52+2)

| #'..leratiUh of the rod when t : 0.6 second.

2 of2

MATDIP3OlUSN

Third Semester B.E. Degree Examination, June/July 2Ol4Advanced Mathematies - I

4,, Time: 3 hrs. Max. Marks:100-. ,":::: ,:"' l\Tnla. luo.,,o* nn* P|L/F ftrll atroalinm< ':

-=t1".1"':n ",:' j,:,,,:,, Note: Answer any FIWfull questions ilils,

. ,";=,* Find the mo{ylus and amplitude of '',,,.ai ,1, ..;i 5 + 3i.9 . "... J 1 Jt

,,,,,,r',,. 't-,, (06 MafkS)E ".:::',:d ,,,,.',,,,,., 4-2i . '"'",,,,,,l,L-s ' ,,::::(g-

E o. Provethat (l+i)'+(l-i)" =2i, cosn7r (07Marks)r4o ,t,' t'.,.,.Eg /coso+isino)o d ' "'

_g c. prove that I :"]- '.."..l I = cos80 + isin 80 (07 Marks)

= \sinO+icos0/O;n ., fh , . .\.....'..; n 2v? 2 a. Obtain the nth derivatfup;of eu* sin(bx + c) (06 Marks)oa "{

-"+a{ L x1-Jt b. Find the n

h derivatir. of -=.-|L (07 Marks)B, (r:ffi + 2)- ;r.

E c. Ify: a cos(log x) + b sin(log x;, tffiovb* at x2yn+z+ (2n+ 1)x5+r + (n2 + 1)y. : 0B "- _ *. (07 Marks)E .:"d-"-9 ,*"i" -

E 3 a. Find the angle of intersection of.th&dLrves F:..$in 0 * cos 0, r:2 sin 0. (06 Marks)oO , ,. *1,,,,,,,"

&a

q()60do.

.51

ct,obI)

d0!C)

od)

aoLod

o50

gEhro

o.

(-)

c)

od

oo

oo.

o

o)

ozCd

Loo.

E- J a. Fmcl the angle of mtersectlon otr,thsd.rves F:.sln u + cos u, f : z sm u. (06 Marks)oo_5 b. Find the pedal equation of theieurve r': a" cos -' (07 Marks)

E c. Using Maclaurin's series-..$hnd log(1 + sin x) qi{'the term containing xa. (07 Marks)L

S qli /i,,""r,;l(BrE 2 z / ^ ^ \2 / n *\

E 4 a. tr z=!'*v',*iensrrowthat (?-*\' =*(r-?-Sl (0zMarks).Y x+y \dx dy) \ dx oy)E ^r{:$ \"^ "r./ \ ",. "r/,'f '."o r ,t ^O..l\^4

= 16 o( *' + y' l, tn., prove that x9. rP = tanu. . ' , (06 Marks)

d -^i b. It u =sua 'l----------:- l, thenprove that x ^ +Y ^ = tanuF . * .r;J,,,'.iJ+y'

E c. lfu:x+3f -23,y:4xzyz, w:222 -Xy,evaluate at(1,-1,0). (07Marks)F ,,,'."''', "' o(x,Y,z) I n*'-.,,:

'

o""oo;E 5 a. Obtain the reduction formula for0)> r,r ,rr ., ,, nl2

* 1, = fsin n x dx (06 Marks)

,.(l 1 o '.r,,,,,,,".,'

E6i r 4sino

b. Evaluate J J r'drde (07 Marks)0 2sin 0

lz x+z

c. Evaluate JI I(. +y+z)dxdydz (07Marks)

-l 0 x-z

I of2

MATDIP3Ol

6 a. With usual notations, prove that

*#* ^?,- n,)"{e Showthat 'i'1mt oer^'iS =i"j:'

;:r\ o o rr Sin 0{. - ....,,,...

f;c. 'ffi.rre.that 9(m, %) - 22^- ' 0(*, nr)

"t*w

7 a. Solve + y+ t)" if y(0) : 1.dx l*

8 a. Solve: (o'+ Dz + 4D + 4)y:; %-:b. Solve: (D' -5D + l)y: 1 + *1,"'#)fl&'=D. )OlVe: (U - >U -r I)Y: I 1- x

. - t1*.= ,t' ,:,sf

c. Solve: g - z! *5y = er. si, * sl

f\

= t1#- **t<*{'

.,i'1, :,

w'\.wryft-

, is, i

,5-""*,\*f

:::,,

,,,., $t'-'

(06 Mart $

*s F\1,@-ZMarks)

(07 Marks)

(06 Marks)

(07 Marks)

(07 Marks)

(06 Marks)

(07 Marks)

(07 Marks)

r,,._ ..

:: :,,,,,,

,,.,-.."''' ,:.ll

2 of2

10cs32USN

Third Semester B.E. Degree Examination, June/July 2OL4 #+,i...,,,,.. Etectronic Gircuits .-,qii

q

i',t:.,i,,,r, '::::t'1 "rlri "

rl"'-,,,l, ,r1 ':,.;,.'.-

t'Time, 3 hrs. Max. Marks:100""1"',r' .,.q LT-1-- t /----.- rltt/r7 e--r, ^--^-t:^--^ ^^t^^1:-^

t' ,, ;'"-;1,''" Note: l. Answer any FIVEfull questions, selecting:.:

ci .*.':.E h"ko#** 2. Any missing data may be assumed suitably.o dn\+s! *,/ d-rE PART_A -Ji"E ;r'*- - . {.=. !H A..** .rAI(l - A

-. &.-

-n f a. Draw a@gias circuit using BJT and derive the expressions futop6rating point. Mention

E its advantd$i$ disadvantage. ,*,1 l-' (08 Marks)!G'ii b. For the circuit *a,,1"" in Fig.Q.l(b), determine the opgi.@irg point. Given B : 100,

SS Vse: 0.7V. n (04 Marks)

3E f Vc< =tsvi4? I

=_-fE ^ f fq.-oo lr Ro t t+rg AC ourrur.= f lq11l L--{€-=4 Sr&r'rAL

E$ Acrd^rr _,, I fll 'o

+ E srqNnL 2, \,6= |-#frE; € Fig.e.l(bI = .. r:'E ?r=' Fig'Q:l(u)

3 * . Explain the construction and operating pri@iq,*of uni junction transistor (UJT) with

E i v'

relevant sketches. { (08 Marks){.

bPtr

: E 2 a. Explain the constructiort, working and characteristics of N-channel E-MOSFET with neat

E E sketches. ,' (lo Marks)

E f b. Give a.o*pprlsion between JFETs and MOSFETs (any four). ' " (04 Marks)

; : c. Briefly dirq,h ihe basic operation of CMOS inverter with a nWil'iagram. Mention any two

a.e advantagupu'" ,r"j (o6Marks)tr O. ,r s/

5 d *\d/

H € 3 a. With a neat diagram, explain the working of a photo conductor. Showtc$ resistance varies

; € with illuminance. Draw any two application circuits. (10 Marks)

E E b. What is an optocoupler? Explain the parameters of optocoupler. (06 Marks)

3,E c.'"A photodiode has a noise current of 1 x 10-rsA, responsivity of 0.5 A./W, actide,area of.E" $ 1mm2 and rise time of 3.5ns. Determine its i) NEP; ii) Detectivity; iii) D*; iv) Quarrtumg; ":.to ' efficienc.y at 850nm. (04 rffia#)

-"d

6 3t'\,-;! e 4 a. Obtain the expression for current gain, input impedance, voltage gain and output admittanCdr!ry

: : of a transistor amplifier using complete h-parameter model. (12 Marks)

ij b. Fig.Q.a@) shows a Darlington amplifier. The two transistors Qr and Qz are identical and the

2 h-parameters for both the transistors are h;" : 1Kf), hre : 100 and tro, : 40 x 10-6 mhos. The

E .rral,.r.s of voltages V". : 15V, Vssl : 0.7V and Vsez : 0.7V. Determine the following:tsI i) Input impedance; ii) Output impedance; iii) Voltage gain; iv) Current gain. (08 Marks)

I of2

10cs32

* ' Fie'Q'a1u) : ;-" {r= &.

{!u

5 a. Derive thed$pression for voltage gain, input resistance and qpff resistance in a voltager -. t

series feedbaffis.lopology. \- (10 Marks)

b. List the advantag{S{nd disadvantages of negative feedbacft;'.- "" (06 Marks)

c. Derive u, .*p..rrf"&#r gain of an amplifier with #eeAUict< in terms of gain withoutfeedback. (04 Marks)*so

_..:.:

6 a. Explain the operation of moqgqable multivibpto4with a neat diagram. (08 Marks)b. Explain RC low pass circuit &.disguss t[Bffii6viour of this circuit towards step and pulse

c. Write a note on Barkhausen criteriffid*J, (04 Marks)

f*.,:,...".r;.7 a. Explain the operation of buck rffih*dr with.aaeat diagram. (10 Marks)

b. Design a power transformer qith% multi-otlt@l.secondary and the following input/outputspecifications: . ;'

L Primary voltage: Z]trffiCI0H2. "% !. \II. Secondary voltagd#12-0-l2Y at 100mA and iiJSV at lA.

Assume B : 60,0[q$rcs per square inch and an efficiency af 910%. (06 Marks)c. Define load reffin and line regulation of regulated po*er supply (04 Marks)

8 a. List and q@n the performance parameters of operational amplitieB. (08 Marks)b. Explairqt$e.working of comparator as zero crossing detectors. d (06 Marks)c. For*",@*relaxation oscillator circuit shown in Fig.Q.8(c), determdq",$h. heat to heat

agrplii:uae and frequency of the square wave output given that saturation oulput voltage of

.=u.t= 'onamp is +t2.sY at power r"rrry:m '.

m5lu Marks)

o.o,u,{ J/-T"' ''"p),,l:l'*;t IIIl_t I

Fig.Q.8(c)

*rf{.r1.*

2 of2

" i *'-1

r_-7"i

Fig.Q.a@)

10cs33USN

Third Semester B.E. Degree Examination, June/July 2Ol4

Logic Design

,!^ Ma*',"ffP'

:,- *,'O .lf1 ,::r.: - (,

P q*:*- .ry"i,'='E E*, so n * PART-A .'r--d 'lui{'.JEq

E 1 a. rjffiu"-ri." time, fall time in u digtffiu-r.ro.*. what is the value orurifu,auty cycle (dutyE . *tr'*:'.^ . -' i rr :rtr:r^rrr-^ --^^:L:--^ .^--r^^cyclbffithe frequency of a digital waveform is 5 MHz and the wiflttsof the positive pulse

i^ A A< ,{g,{.ff*r -

.,,,,,,.1'" }tq

/o.d l\rrqrlzs\E is 0.05 ir$? .I.,, ** (04 Marks)

U b. Realize the basic gates using only NAND gates. , r, ; 11"" (06 Marks)

$" -B c. What is positive and negative logic? List the equivalences igpos,iiive and negative logic.g.= {" ;r,_ :'_j" (04 Marks)

E 5 d. Write a verilog ffffLj,eqde using structural model for h& input AND gate and prepare test-

E"'11 bench to simulate the eiqppit. Draw the timing diagrargr generated by simulating the verilogA T bench to simulate the eifo;rit. Draw the timing diagraqr generated by simulating the verilog

= f code. Assume 20 ns hol@time of each input combffiation. (06 Marks)

cg* la

t H 2 a. Simplify the Boolean function F($ B, Q, D) : I*(1, 3, 5, 7, 8, 10, 12, l4) by using

: E Karnaugh map method and realize#,bgidr{rcuit using only NAND gates. (06 Marks):.Y:..D:- - -- "----D -"'J '

7 =

b. Draw Karnaugh map of Y: F(A, B i. ) : fIM(0, 1,2,4,5, 10) ' d(8, 9, lI,12,13, 15)

6l

'E + d*t:'r oo

: : 2 a. Simplify the Boolean functionfl,-{, B, G-;" = ,

E z u- jtaw N<ull4uEill rrl(lP \rr r - r \^, Dt:.yt.:.1. - rrrYr\w, L, L) a) J) rv) u\u, /, L L) L2, LJ, LJ)

E .H and get the simplified POS form ff=K;' . (04 Marks)

3 * c. GetsimplifiedexpressionofY B,CiD};Im(2,3,7,g,11,13)+d(1, 10, 15)using

i : Quine-McClusky method. ,u&*=' fui;:,.== (10 Marks)6 0 \-' - -- -'- Jt< flt*H!\O.d '\ a rItO - ._l

€ I 3 a. What is a multiplexer?ffign a A-to-l multipleibr using logi€ 5 3 a. What is a multiplexer?ffign a A-to-l multipleibr using logic gates, write the truth table

E E and explain its worki4.rgp?inciple. (06 Marks)€ E L r\^^^-:L^ rL^.-,^-l-:-^ --:-^:-l^ ^f 2,a i^^^,{^- n^.;^- ^ l*";&.,,;+ tl".ot taolizao fha fnllnrrrinc3T b. Describe the wolkln"g principle of 3:8 decoder. Design affiuit that realizes the following

E s functions usinqh3.i 8 decoder and multi-input OR gates. Y-. r _

AE Fr(A, B, c) : ia(r ,3,7); Fz(A, B, c): rm(2, 3, 5) (06 Marks)F d ^ rrrr , | ',. ;:,:1 r ,-------r---o n--:--- ^-- ^ t-:L ^^----^^-^L^- ^--J ----:i^ LL^ +^-tL +^Lt^ .l^^l^iE Fr(A, B, c) : im(l ,3,7); Fz(A, B, c): Im(2, 3, 5) (06 Marks)

E q c. What is rn{$nitude comparator? Design one bit comparator and write.the truth table, logic

g E d. HorfrmHdes Prosrammable Loeic Arrays (PLA) differ from a Progradrupmble Array LogicH E d. Hoffies Programmable Logic Arrays (PLA) differ from a Prografiryffible Array Logic

F E E@z *P.._ (02 Markstr o 1"\aO '= '%\ {,

$E 4 pl hitt !!re help ofreatdiagram, explain the working of edge triggered JK flip-ffiY":l!" ln:g ; 4 ?. wl[n tne nerp oI neat oragram, sxprilrlr lfltr wurl(luB ur truBs urBBErEu Jr\ rrrP-rrulfi Yvr]re rue

E € t state diagram and excitation table. (06$4a.rt O

!, fr ". . b. What is switch contact bounce? Explain the working principle of a simple RS*,1atgh

: ; ' debounce circuit. (04 Mr$ltsi".r:; > oeDounce crcult.?.f, c. Write the state table and state diagram for the circuit shown in Fig.Q4(c).J8.i x;ozH -.:"rf II :*ff. tI Gt'Gz-+ANDgateE q{rTt | "-fru I cr,G+_+oRgate

Fig.Qa(c)I of2

tr

(10 Marks)

10cs33

PART _ B5 a. What is a shift register? Draw the logic diagram of a 4 bit serial in serial out (SISO) shift

register using negative edge triggered JK or D flip-flops and explain its operation with thewaveform to shift the binary number 1010 into the register. (08 Marks)

_.,"€ " b. Explain with logic diagram the use of S-bit SISO shift register in serial addition of two 8-$[sq#d* numbers. (0S M&*i'.*"';r,13+ g Write verilog HDL code for 4-bit SIPO shift register when all the flip-flop outpuQ are- ' ';..,* available externally. -..,.,'.@-?Iarks)

ai' ;a......,

4 Y stlsulv v^!vr.s,J ' 'i .\-:',,,: i

!,6 a:.'fo}.9t are asynchronous and synchronous counters? With a neat block .,SQeI. h, outgut

\@-6form and truth table, explain a 3-bit binary ripple counter constru@d.Iising negative

&h" (10 Marks)

b. ;Hffiffii.ff 3;'J:l',,i,g JK nip-nops having the reaturee#ir u,, u,,,)..;;;;.upp.urrl$d.-g*ter will reset to 000 at the next clock pulse. (10 Marks)

';,."-1q r" $ F'appcars, tq€-."{9}-}ulltgl wul l(is(i[ LU uvu .il. Lrls rrs^L ulrrrerl. Purss. (rv lvrarrs,

*tt {,t"

7 a. With neat blcick,.diagrams compare Mealy model and ,.IWhft" model of sequential logicq"system. ;" ;, tu (04 Marks)*r=..* ;. ;\ %"

art fop the Mealy machine shown m F&-Q7(b).\*=.,, f\olo "($b. Draw the ASM chatffi'tfre Mealy machine shown m F&Q7(b) (08 Marks)

Aolo i', !{' "

system. --f - i.n"^-r %' (04 Marks)

ft+,olo

,lo

c. Using row eliminatjo&iriethod reduce the state d/*lo

t;

Fig.Q7(b)the state diagramihown in Fig.Q7(c).

::

t* ""'i;

8

,lt

Fig.Q7(c).

'';::::'

"r i}f r"

LJ

%_(08 Markbp-,F=_

a.

b.

c.

What is the binary ladder? Explain the binary ladder with a digital input of 1000. (06 Marks)Define Accuracy and Resolution with respect to DAC. (04 Marks)With a neat circuit diagram, explain parallel ADC. (10 Marks)

!f***(*

2 of2

USN

3a.

.",,,t

,- t =

PART _ A

10cs34

Max. MaSs:100Note: Answer FIVEfull questions, selecting *1..,,\.

at least TWO questions from each part. ,.,'=,:* *".

(07 Marks)of a conditional with truth table. Write down

Third Semester B.E. Degree Examination, June/July 2O14

Discrete Mathematical Structures

ri"fliure:3 hrs.

,-1. _.

I l. - .:-.:

ai(,)

o(6L

tC)

()

E9

J)

:h

oo llEca.= c.Ia$i 6I)YOo<tc)

oBEn

3EOU

OEaoc.e(BEb>P-66-

!6aB5.E

o. 6-

o-,n.2o=<(Jia tEEEL()

=Eo.->9tr ot)

o=gotr>Xo5Lc}qJ<

- e-l

o

zd.o'o

I a. For any,ftee setsA, B, C,prove: An (B u C):(An B) u (An C)..,.,= (06Marks)b. Among@,fntegers from I to 200, find the number of integers that are;

i) not divist le by 5 d uq

ii) divisible by 2 or 5 or 9 di

iii) not divisible F,S? o.5 or 9. x (07 Marks)c. A problem is giveilto four students A, B, C, D whose W$r,€s of solving it are ll2,Il3,l14,

1/5 respectively. Find the probability that the problem,'is $6lved. (07 Marks)

2 a. Define a tautology and contradfotion. Prove thai, for any propositions p, Q, r, the compound

proposition t(p - q) n (q + r)l .+.(p -+ 0 i.; tautotogy. (06 Marks)b. Define the dual of logical statemeni. _Vcfr$, the principle of duality for the following logical

equivalence: [--(p ^ q) + --'p v (---p

c. Define converse, inverse and contra(-P v 0.

the contra-positive of [p + (qne sorura-poslrlve or [p -f (q -+:.r]!l wrm: r. ;D only one occumence of th*'connective -+ ;" '

ii) no occurrence of the csdiective -+.

Il,,i

Negate and simpliff'eaCh of the following:

(07 Marks)

(06 Marks)

4a.

Vx, [{-p(x) nq(x)}-+ r(x)l.'. Vx, [--r(x) -+ p(x)]

Prove that every even integer n with 2perfect squares.

...:,:,1,;

Let ao : l, a,t:2, d2:3 and &n: &n- I -l- an -z* an-l for n > 3. Prove that a, S 3n for a[I,,

.,=

'qp? lVlarks)( n ( 26 can be written as a sum of atnd''sfthree

(07 4vtrrks)

positive integers n. (06 Marks)

b. Find an explicit definition of the sequence defined recursively by ar : 7, a,n: 2an- r + 1 forn> 2. (07 Marks)

c. The Lucas numbers are defined recursively by Lo :2,Lr: 1 and Lr: Ln- r * Ln- zfor n) 2.Evaluate Lz to Lro.

I of2

(07 Marks)

10cs34

PART _ B5 a. Suppose A, B, C

=ZXZwithA: {(x, y)ly: 5x - 1}; L_1[,y)ly:6rIC: {(x,y)l3x- y: -7).Find: (i)An B, (ii) B n C, (iii) AuC, (iv) BuC. (06Marks)

b. Define stirling number of second kind. Find the number of ways of distributing four distinct

,,'*.*". objects among three identical containers with some containers possibly empty. (02 ru,1f{s}-$,;*

,: If f : A +B, g : B + C, and h : C -+ D are three functions then prove ttrat (h'S)'f

l$"$P_.,_j'

6'""a,r,*{.et A: {1,2,3,4}, B : {w.*. y. z} and C : {5, 6,7\. Also, let Rr be a relafloir,fiom A to"*,ffi*defined by Rr : {(1, x), (2, x), (3, y), (3, z)} and Rz and R: be relationS fiom B to C,

dEffi by Rz : {(w, 5), (x, 6)}, & : {(w, 5), (w, 6)}. Find Rr' &. (06 Marlis)

b. Findhb number of equivalence relations that can be defined on a finrJ{pgt A with l# = 6..:e. jdq ..,o."""'t,,. (07 Marks);m (07 Marks)

c. For A: {*ffi,d, e), the Hasse or"p- for the poset (A, Y?ffwn

below:

A. f *,-'=*'x,lrdP' -t; bJ \. "'F

l) LrglErllllllE LllE lgl4Llu[ rll(flll^. rt ra'I\;'

ii) Construct the diagraph for R ; ' , :::...:"

::, (07 Marks)

7 a. Definesubgroupofagroup,ffitGbeagroupWOl.tJ: { x e G lxy:yxforally e G}.Prove that J is a subgroup pf€. (06 Marks)

b. State and prove LagrargQt iheorem. , -.i,,,: (07.Marks)c. The word c : 101Sffi is sent through a binary sjimmetric channel. If p : 0.02 is the

probability of jryg#;;t _receipt of a signal, find tt " p.oU^pility that c is received as

r : 101111L Btffidne the error pattern. " "E (07 Marks)

a. fhe pal ck matrix for an encoding function E:z) -+ z! is givenby

r: \ [r 0l 1 0 0l *-**

.,u'*'l:.^^:^l,.;'"-

tr=[l : ; ; : :l

.fl."' [, o l o o l]= =,.,,.,

"'"*'t i) Determine the associated generator matrix. '"1 ' ,q,,1ff'r, ii) Does this code correct all single enors in transmission? 1oo'*rarxp;

#dn""-;'

c. Show that z6 is not an integral domain. (07 Marks)

2 of2

10cs35USN

I of2

6a.b.

*%'w# ;,1 j

7 *'$.-

10cs35

What is binary search tree? Write a recursive search routine for a binary search tree.

Explain selection trees, with suitable example. :

What is a forest? With a suitable example illustrate how you transformtree.

,+L

Define priority queue. List the single - ended and double-ended priority q"..1:mp}.ajio:t:::1; : '' I (06 Marks)

b. the following:ist trees

(08 Marks)(06 Marks)

a forest into a b.inacy

:oq:'qffi't

i) tnsertiori@p binomial heap d\\ q,

;lixJiiil:*lwapsand ffi*rt* (,8Marks)

I Write short notes on: ' *";T dq

^ r\-;:*^l L:-^*, -^^-^L *-^^.I llru * ' * "

iii) Wfiff&d leftist trees.

What is bffiffial heap? E:

i) Insertionffip binornii) Melding tw6 @pmia,

a. Optimal binary search trees d#,-- *"iI.* '

c. Red - black trees * . "

d. Splaytrees. ,ffi=

(2oMarks)

iii) Wffiffipd leftist trees. ") -. . (06Marks)

What is bffiffial heap? Explain the following associated with.@ftial heap :

i) Insertion%ffim binomial heap **\ M

ftist trees and i'-*,.t" iS"

2 of2

'l

USN 06cs36

(08 Marks)(06 Marks)

Third Semester B.E. Degree Examination, June/July 2014UNIX and Shel! Programming

,,,' Time:3 hrs. Max. Marks:leQ

'1-'' -. otez AnswerrFrvE *:Jf,x::fr'#':::;"!:,r, ,1i,",,*"

- -".. --i.t'"

,.'-, PART - A

'"$, '-

I a. EiplaLrr the salient features of UNIX operating system. {ii",.,,,' (06 Marks)

b. What,i arent - child relationship? With the help neat diagram expl?in,"UNr, *]::fT*tree. .,,'.. ", (06Marks)

c. Explain the"S.Howing, with examples : ''.1i:.. ,,,

i) Absolute,,and'relative pathnamesii) lntemal and extomal commands. . , 'r ;;;; (08 Marks)

)

6'l1r'

-;L{','il

":,

8

oC)

oEq(€

a

o(g()!

E9oo-

Ertoo ll

trop.= c.n(!+Hboya)otr,q !l

o3Eqgsbddob0c(!d

,H64'od5', 0)

5v:qn'H6<€ojo!toatE=urD3P>\ (HooocbO'o=!f9xoo-,

\J<-'.f.tooz(€

oo

Give the significanc. ffiu.r.n attributes of the Is - l qqmmana. (07 Marks)

Explain the differenl6idi!,..616peration in a vi editor witfr a suitable diagram. (07 Marks)

Explain two commands to c ,g.,g

the ownershffia file or directory, with example.(06 Marks)

What are environment variables? E different environment variables available in UNIXoperating system. :::,

"ry,d|ry,1, (08 Marks)

Explain concept of escaping an(qu&ffig'qmith suitable examples. (06 Marks)

Explain mechanism ofprocessucreation. (06 Marks)

Explain the sort command,l{}fiefly discuss the important sort options. (08 Marks)Explarn the sort command,u:l3ffletly drscuss the tmpO&Ant sort opflons.Explain the following commands with examples : i) umask ii) touch.Brieflv exolain the sip&,ificance of read. write and execule rermissionBriefly explain the.q'i1p,ificance of read, write and execG.Fpermission for a directory.

'ti"-.I ' ,,.-*-,, (06 Marks)

.-e+" *eq*'*6

- =,,,,,

t' -' pART - B \,*-.. ,,,

:

--a_. U ll' .,,

Withsd&fule examples, explain the grep command and its various - t hatS.Withsdl{dble examples, explain the grep command and its various -"6n46+S. (08 Marks)

ExpMUriefly extended regular.*pi.tiiot (ERE) and egrep. !! t (06 Marks)

, Explain line addressing and context addressing in sed with examples.

, * _,u (ou Marks)

: Explain the use of test and [ ] to evaluate expressions in shell. (o8 Marks)Explain the shell features of "while" and "fot'' with syntax. (06 Marks)Explain set and shift commands, with examples. 106Ma1k$

."ri ,,,'

r':!'

What is AWK? Discuss any 3 built- in functions available in awk. (08 Mart<i;,',,

Explain built- in variables used by awk. (06 Marks)Explain awk supports Looping with for. (06 Marks)

Discuss how lists and arrays are used in PERL with examples. (08 Marks)Explain the following string handling functions of PERL, with example.i) Length ii) Substr iii) Reverse. (06 Marks)

c. Using command line arguments, write a PERL program to find whether a given year is leapyear. (06 Marks)

10cs36USN

Third Semester B.E. Degree Examination, June/July 2Ol4

Object Oriented Programming with G++

,.,," Time: 3 hrs. Max. Marks:10,0' ;'u

,.. ,,:

Notez 'a"'wer ruunfilffifff,):;::;';:fr ,,.,i*

t ","'"" PART-A , -';,-

E I a. "'' €ompare object oriented programming with procedure oriented programminq. (06 Marks)!€ b. D6drp.function overloading. Write a C++ program to define overloaded functions to find

! "of"rne of cube, volume of cylinder and volume of cuboid. .,, (08 Marks)

n c. With afii;eqample, explain when the set of overloaded functiorp.'eafl 'be combined into aE

E single funotiFsdefinition by using default arguments. .:, (06 Marks)

E9S= 2 a. Define the terrlx glp$s and object. Write a C++ program to define a class called distanceg 1 with feet and inchos as data members and get( ), put( h hnd add( ) as members to read,EOf f display and add two d'i$tance objects. ":' (10 Marks)

T + b. With an example, illust@"",t!,re characteristics of a co'iBtiuctor. (05 Marks)

E S c. Write a short note on destructors. (05 Marks)

ETC g 3 a. With an example, explain the use,,o'f ftiend ffitions in C++. (06 Marks)

E 'E b. With an example, explain when_io,r{s&g-rernber function and when to use friend function as

fr g an operator function for overloading,,binar,,,y,operators. (08 Marks)

; ; c. Write a C++ program to arrange set of integer and floating point values in ascending ordera5E * by using a function template. ,,,,,. t,"" r , (06 Marks)

-Li(EO

fli 4 a. With the help of syntax for,,,cfedting the derived dFXp explain the visibility of the base class

# i members, for the access specifiers private, protect&]bnd public. (08 Marks)

f E b. With an example, ex.p.Uu.'*'multiple inheritance. . -_ . (06 Marks)

:T c. Explain the necessity of protected data members, with an example. (06 Marks)LA

EE5a.ExplaintheuSeofvirtualou.".,u,,.ffidshapedinheritarrce.(08Marks)8 c b. Explain the order of invocation of constructors and destructors in rhfth{lgvel inheritance.;o6 E (08 Marks)

A € c. Write a short note on use of scope resolution operator in inheritance. $r\ .' (04 Marks)=€a g 6 a. p"nr" virtual function. Explain the need of a virtual function with an example. (06 Marks)

$ B b. Write a C++ program to illustrate the virtual functions in hierarchical inheritance*l S-,Marks)E * c. Define abstract class. Write a C++ program to illustrate abstract elass. ft0ri4Vlarks)

g I 7 a. Explain the following output manipulators:5 i i) setrrr( ) ii) setprecision( ) iii) setfill( ) t06 Marke)-'j 6i b. Briefly explain the facilities available in fstream class for file operations. (06 Marks)

€ c. Write a C++ program to read a binary file, which contains the details of 5 students such as

7 Name, rollno, age and grade obtained by the student. Display the above read details on the

E screen. (08 Marks)oo.

'E 8 a. What is exception handling? Write a C++ program to demonstrate the '\y",'throw", and"catch" keywords for implementing exception handling. (10 Marks)

b. List and explain five member functions from vectors and lists classes in STL. (10 Marks)

*{<{<{<tl<