stf ser-t-{ I ur^ I Erc - ELtrL- E-rF-x I , *f-r+-

nn-Etq lorl*r+

5uil l-Q.P. Code: 11837

[Time: Three Hours]

Pleasecheckwhetheryouhavegottherightquestionpaper.N,B: 1' Question.No'1 is compulsory'

?. Attempt any three from the remaining'

Q.1.a) Find the extremalot [?a',., l.

b) ls 10,;.-+ ta linear combination of " = t1'2'2)' 1" = 13'4'61

2x a>0,b>0b) Evaluate

JJ 1,'.rlr\t'i*

b) Find the sum ofthe resldues at singular points at 1 121 =:{z - l)( z - 2)

c) RedUcethe quadrati6form x' - 2y' + 10 st - l1,xl + 4x: - 27 to canonical fOrm and

hence, f:rnd:its:rank, indei and s.iSlltqre and'value class'

: . ' . ,.,, ,..1. ... -,,. . .11-2,t.i- ,i1,:

Oie.:il.Varit dviqv'Hd#lfo*tiieA-tt :1Si.,n :to I and hencefind x-' & ro

''' " ': "

' " 'tl '"'

' ' o" ^t,'

,, , .','utrsin!,n9ii6*r_-i.5EJ.rix.,e..y'11d$ i.717aL where C is lzl=4.

. .. l: . '.t-.. '",

lz llc)'Find the singular value decomposition of i i-':" [o z]

: i ' , : ') L" -l

l-- r +lQ.4. a) tt,r = i i , prove that 3tanA=Atan3

tL2 t-]

z-4

I Mar.ks:80]

{s}

(s)

{s}

ts)

(6)

{6}

(6)

A67 7 OF 26CF 24F,87 7 F;6B95 8 C4E 1 DFSD 1 3

c) Check whether

[r z

o -1., 1,, _ 1 -

[: 4

(6)

t8l

{6}

(8)

(5)

G9

+ jr, ,0) , and

= (0.1,2) are linearly independent '

(6)

(8)

leJ

0

' . -.,1'.' :':, ''

" .:: ' :-j1

';;.'1- j:_.'J,1':

j .,..:ij't ,::' ii'i:.' i::'.

'

A677OF26CF 24E877868958C4E 1 DF8D 1 3

t(x,,0I - (A:r r,0) is a vector space'

Q.5. a) Find the extremum of !(Lxv - v"')dx '

b) Construct an orthonorrnal basis of 'R 3 using Gram

S = {{3,0,4),(-1,0,7),(2,9, 11)}

c) Find all possible Laurent's expansions of _;

Express vo

,

N.B:

Please check whether you have got the right questiq4 prpu1....",

2. Attempt any three out of remaining fivequtistions;3. Assumptions made should be clearly s@:t€djr : -.'; ,,-; ,.

::'";.r

TII24 /T1046 THEORETICAL COMPUTER SCIENCE

[Time: Three Hours]

a)

b)c)d)

4. Figures to the right indicate full marks,5. Assume suitable data whenever required but justify that.

r'.''.

Explain Chomsky HierarchyExplain Rice's Theorem

Q.2 a)

b)

Q.1

a)Q.3

Q.s

Explain Pumping Lemma for CFG

b)

aJ Construct NFA for Given Regular expressions:

x

iJ [a+b)xab,ii) aa(a+b)*b,iiiJ aba[a+b)*,iv) (ablbaJ*/laa/bb)*

b) Construct PDA accepting the language L- {aznfun I nr0].

a] Design minimized DFA for accepting strings ending with 100 over alphabet (0,L).b) Design Turing machine to recognize wellformedness of parenthesis.

Write short note on (any four)a) Greibach Normal formb) Deterministic PDA and Multistack pDA

c) Variants of Turing Machined) Halting Probleme) Church-TuringThesis

1010

10

10

L0Q.4

Q.6

10

1010

20

F978F8CF49 4 AE2E1 8F 297DC3 427ED665

mrO )

f * w^:'t''TII24 IT1O47 COMPUTER GRAPHICS

.: .'1. ;l1. (a) Compare Raster and Random Scan Techniqries ' ::, ".).i' .::' '.;;

,":v.' ..: ; ,1":.! i. ,.';,'"..;.'',i"i" ... ., [os]

,

.r- ' . .r,' , :. ..'.. :.:,' .i.':::--i.r : .::.. ,.",

,:': :!": ,,"t .,:,'"-...-"'1' ,.'-1. r-, .. _i

t'').'n..:

Duration: 3 Hours Total Nlarks assigned: 80

N.B.: (l) Question No. 1 is compulsory ,j

(2) Attempt any three of remaining five questions.(3) Assume any suitable data if necessary and justify the same.

:.i

\4/, \,\Jlrrp4rs r\4)Lsl 4tlu l\iltluullt Juatt I trulurlLlugs , , lurl(b) What are the disadvantages of DDA algorithm? t05l(c) Derive the matrix for 2D rotation about an arbitrary point. [05J(d) Write a boundary fill procedure to fill 8-connected region.. I05l

..! .-::.-:;:

2,(a)ExplainBresenham,sCirc]edrawingalgorithmindetail.,,.. :] :;." [10]

(b) Derive the transforrnaffi:a.Irtri4.,t.o:m4g fv.:,,:.i,h , ngt iih've*ibes tl0]

[10]

[10]

4. (a) Define window, viewport and derive window to viewport transformation.

(b) Differentiate between parallel and perspective projection. Explain with the

[10]

u0l

[10]

Il0I

120)

s. (a)

(b)

6.

help of examples.

Explain Back Surface Detbction method in detailwith an example.

Discuss Halftoning and Dithering techniques.

Write a short note on any two of the following

B-Spline curves.

3-D rotation

Fractals.

(a)

(b)

(c)

9780C43F3 C 299 t2F C2827 BC3 t7 3 A8 I 47

3. (a) Explain

example.

(b) Explainits working

sel se^El r sas I ,u*pln*f - rtftoA

t 1l*- 1 ,>o tt

I Marksi80]

.MuB.r-v%

q.1a)

b)

ci

lli

q,/

n?

Answer any fourVrli-ite an aigoritiim foi'finciirrg nraximum and minirlurn number from given set.

VJriie the algorithm and derir,eci tlre conrplexity of Binary Search algorithrn.

Explain masters methoci with exarnpie

V,'ritc. a notc on {lc.w shop :il,edulin;Ccn-,pai-e diviCe alC con.luti. cyncinic p:ofrir',rr,,::,g ani E;cllirac[.ing ai:i-'loac'nc usco foi'

rlgoi-i'.hr;r design.

Vrlnie and exp!ail-i sii'irg malchir'ig rviih finitc au':ct-.r:ia '.'.'iih an erample

Explain how bi"anch anci hcur',d-<lrategyrcan be useo in 15 puzzle pyoblem.

V,/hai is 0/J. knaps;cli ai-rd fra;'iicr:al knapsacli ;.,i'cLie ;-li.

Q.P. Code :tl]Jq

[Time: Three Hours]

Please check v,,hether you have got the right question'paper.N.B: Subject AOA CSC 402 CBSGS R-12 SE comp SElv'l lV CBSGS

1.. Q.1 is compulsory.2. Solve any three from Remaining

Scl.,e {cilc".,ing usirg 0,i 1 !- ck rnethccil-ri rne

Itern.(i) 'Value ivi) Vi eieht(u;i)1 18

2 25 rJ

3 27 4

4 10 3

5 15 6

1

,4.6770F26CF24F,8',/ 78 6ts9 58C48 I E I 92 1 8

20

a)

b)

d)

L0

IU

l-tJ

10

10

10

10

10

(P.r.oI

Knapsack capacity=12.

binary search tree

? Find LCS for following string X = ACB AED

and (dr d: d, dr) (2,1,2,11find feasible solution.

6

u.b Vy'rite short noies (any threei:-a) Problem ot muiiiplyir-rg Long lniegei'si:) 5trassen's nrati'ix r:ruitipiicationcJ l(nuih lr4orris Prait's Pattsrn matchingd) Muiii stagc Gr apirr

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

Q.P. Code itgL7$

20

2

A6770F26Cr'z4EEi'1 E 6ts9 58C48 I E I 92 I 8

.l

gE sErn g carnp CB AJ TN AL'I LOI T

T\124 I T1044 CO]VIPUTER ORG,,\NIZA'f]ON AND ARCTIILCTUi{E

Q.F. Code:13085

ifimer Three Hoursl

Please check whether you have got the right question paper.N.B: i. Question no I js colilpullur\.

2. Atternpt any threc questions tilir rrntaining fir,e questitins.3 Assume suitable data ilrequrred4. f)rau, ueat diagran-r lvherevet' ltclessiiiy.

Solve any four out of flve.

A. Erpiain Virtual Mcmory.

B. What is lO buffering?

C. \lrite a note on scanner.

D. S'liat is Segmentation'/

Il. What is TLII1

A. I) Draw the tlow chart fbr Restore Div:ision Algoiithn:.

II) Divide using restore divrsion method 7/3.

B. Describe hai'd-wire control unit and specify its advantages.A. Multipiy i-5) and'(Z),using Boorh's Algorithm,

..'i ,,, 1,,' ,,'.. ' ' : ,.ti_ ,l:,',

B. A bloclli:Set,assodiative caehe consiits.,of 64.blocks dividedcontain6,4096;blocfs,riab! 12g,"uofds. of,1,5bit length.

-'' -'

,.t..-.,;i.--j',-'., - rr, _.... ,,'l

, .Ill{ow-many bils.dre lhere.in rnain memory address?

'\,:! ,...i, .] '\1.: l.;- :j.

:2) rlow manybigs are there in cache memory adcircss (rag. sei, and word fields)?Dj,ffeientiate befween L RISC and CISC processor.

IUQ.1

Q.2

Q.3

in 4 block sets. The niain rneinorv

as/n rf vat4

IMarks;80]

04

05

10

10

10

L0

L0

10

10

10

10

a.4

Q.s

B. Explairr F ilnn's classificatiorr.A. Discuss the firnctions of 808{i I,'O processor.

ts. Shovr IEEE 1'54 standards tbr BinaryFloatins: l'.:int I{i:prcsr:nlation iirr 32 bit single ibrrnat and 64brt douhlc fonrrarA. Explain diflbrent pipelining hazards.

7879AB9 8488CA7,1B2098 I 5:l B50C4C_ss2

Sr.ltEmfrlC"*f lcyhr FtpsTpwenry t*l-tvr11z4 ir1a45 s.E.(coMpurER. ENGGXSEM rv) (cBSGS) DATABASE MANAGEMEuisvsfnxag , ' . '

Q. P. Cod€:18323 '

N.B, : (1)Question Number 3" rs compulsory

(2) Solve any three question from the remaining questions

(3) Make suitabie assumptions if needed

1. (a) Construct an ER diagram for a hospital with a set of patients and a set of 10

medical doctors. Associated with each patient a log,of various'tests,and

(b) Explain lossless join decompositionand dependency preserving 5

Time:3 Hours

decomposition

(c) List four sigrtiflrcant ditferences betrveen file processing system and

2. (a) What is a deadlock? How is it detectbd? DiS,

prevention scheme.

(b) Write SQL queries flor the given datau'ase

Emp ioyee( ei d.en arne, street,city)

:tpes of.ile4dloek

5

t0

10

-'!" ,;', .,rl

,,,. -,' ..'(!ii): Fihd,all emF-loy.ee'id..,,who live,in same cities as the company for

,-t-.ir . :;:',1' ,,; U*r*,they.'WOikl ' r'i :r

,,

,,, 1,t1*i,,,::, - :{,iV)i,:give, to.ti{'nurnbgr of employees

-t;:. . , :.,., :

.,'' ,:.. ,-", ,.:- .{v)' ,'F'ind'the higliest,p'aid-employee

;, :3;i,:., :([)..-, 141'6u, is,.an atffibute? Explain.dif,.ferent types of attributes with examples. 10

;.) ii:' ,.' rieompanies, manufaoture ranges of products which are purchased by 10";'.:':,'ll

'' ,,,' ciiqfoiners. The lelation schema for this operation is given as :-'r.-'.' t. U$+lulllgl D. L rlg I ElfiLtull JUltgIltA lul LlllD UyprCllurr rD tsrvUrI OS .-

, ' .,Company(compan,.r- code,company_name,director#,director name,{product

. ri 'narne;,'eost, {cust#, customer_name, address}i) r,vhere i } represents a- , .repeatl.gg, groups and company_code, dirctor# and cust# contains unique- , .repeatl,gg,..groupg and company_code, dirctor# and cust# contains unique

" -,values. Norilalize this relation to third normal fonn.

O92EF8E 1 7?DD96EBE279CF D3C57 2'7 5? A

TURN OVER

Works(ei

raise in salary

Ttr24 tT104s S.E.(COMPUTER ENGGXSEM IV) (CBSGS) DATABASE MAN

4. (a)

(i)

(ii)

(iii)

(io)

set intersection

Generalized proj ection

liatural Join

Aggregation operator

(b)

(a)

(b)

(a)

(b)

10

10.'.,'.

. '.,;j'

' :. :rl.

092EF8 E I 77DD9 6EBE27 I CFD3 C57 27 57 A

Expiain tresied loop loin and block nested l

processmg.

Explain Hash join

4

5

o