06cHEt2t22

I a. Selecl lhe correcl aDswer:i) The rendency of knocking is more in ......... hydrocarbons K=

Time: 3 hrs- Max. Marks:100Notei I. Answer any FtVEfutl qaestions, choosing at least twofrom each parL

2. Answer all objective trye q eslions oilt! on OMR sheet page S of ihe answer booklet.3. Ansper to objecrive type questions on sheets other than O-MR ilt not be valued.

PART_A

a-!

E3

oi

z

E

b.

'c.d.

A) Aromaric B, SEaighl chain C) Olefins D) Cy"l,y'.ini-ii)

lat:lyjr us:dl fluidized-bed caralyic cracl,irg is- 'r7-rn"";L t,'ii) Catalyst used in fluidized-bed caralyic cracl,ing is ., fl' _-"otl, ',

A)Zrol+Ceo) B)Al2Or rFe2Or \:t tEr.,. ";r j /

C ) Fluidi,.ed At2O, andSiO2 DrAt2Oj CeOr :.\. "'" /iii) Petr_ol obtained liom petroleum oil is subjected 1c rcforming because \ti.f 7/

A) To remove impurities and water B) For structural modifrcationC) For degradation ofhigh mol. weight hydrocarbons D) To reduce weighr.

iv)...........jrmctionisusedintheconversio[ofsoiarenergyintoelectricalenergy.A)p-n-p B) -p-n C)p-n D) none ofthese. (04 Mark)

DeIine net and gross calorific value of a fuel. Describe how calorific value ofa solid sampleis determined- (07 Marks)

Explain the terms 'octane' and 'cetaae' numbe$. (05 Mark)

Calculate the gross calorifi-c ofa sample ofcoke frolr the following data:Mass ofcoke: 0.73x10-rkg Water equivalent ofthe calorimeter: 0.32g kgMass ofwater: 1.25 kg Specific heat of water: 4.187 kJ kg"LK1Rise in temperature: 1.9K. (0a Mark)

a. Select the corect answer:i) Glass electode can not be used in the presence of fluoride ions because

B) loss its attivityD) leads to as),rnmetric potential.

ii) The value of EMF is , if AG : -212.3 klll.rcI, T = 298 K andFaraday constart: 9.65 kJ,nr'lmol.A) 11.0 V B) r.r v c) 2.2 V D) 22.0 V

iii) EMF ofa cell mainly depends onA) Size ofthe cellC) Weight of the cell

B) it is compactD) it gives constant and reproducible potential.

(04 Marks)

l of 4

A) alkalile erorC) glass membnne dissolves

B) Quantity oithe electrolyteD) Difference between Ec,rn,a. and E*.a..

iv) Use of secondriry reference electrode is prefefied over primary reference electrodebecasue

A) it is light weightC) it is reversible with electrol]te

06cHEt2/22

2 b What are ion-selective electodes? Explain the principle, construction and working of a glasselecbode. (06 Mark!)-

c Derive the Nernst equation for a single elecrode. Wdte Nemst equation for the give! cell:

Cu(s) Cu (aql Ae (aq) lAg

d. Calculate E:",./2, , ifthe emfofzn I Zn"(a=l) | lNl*(a=l) Ni is 0.51 and

Ni I Nl.(a=r) I I sCE is 0.49 V. Given E:cu = 0.24v.

3 a. Select the collect aaswer:i) The electrolye used in Li-MnO2 battery is

A) l0% Hrso4 B) 6M KOHC) Li-halide a1ld organic solvents ' D) NLIqCI + ZnCI,

ii) Hot KOH solution should be used in H2O2 fuel cell

d.

1a.

(0s Mark)

(05 Mark)

(06 Mark)

(0s Mark)

(0s Marks)

(06 Mark)

(0s Marks)

A) to incrcase conductiviryC) for better reduction ofO2

B) to enhance the absorption ofhydrogen on anode

D) to avoid dilution ofKOH.

iii) In some batteries, graphite is used as an additive, becauseA) it reduces the total weight B) it absorbs the moistueC) it improves the conductivity D) to increase the sulface area ofthe electrode.

iv) Lithium metal is used as anodic mate al in Lithium batte es becauseA) it readily iooses the electrons B) its rcduction potential is very highC) its size is very small D) it rcadily reacts with ivater. (04 Marks)

b. What are the modern batteries? Explain the construction, reactions and applications of aNi-MH battery.

c. Explain the following chamcte stics ofa battery:i) Capacity ii) Cycle life.

ii) Cathodic coating isA) coating oftin on iron B) coatiag ofzinc on ironC) conversion of whole specimen into cathode D) immemion ilto ho1 ZnC12 soln.

iii) A bolt and a nut made ofthe same metal is p.efered in practice to avoidA) stress comosionC) differential metal cooosion

iv) The rcaclion at an anode during cotosion isA) Oxidation B) Reduction .

b. Define metallic colrosion. Discuss tbe following factoN which inlluence the rate ofcorosion: i) Natue ofcorrosion products ii) Hydrogen over-voltage

c. What is arodizing? Explain the anodizing ofaluminium.

d. Write a note on phosphating.

How is a fuel ceil, in which chemical energy is coltverted into electrical enetgyj moreadvantageous over the cotrventional batteries? Jusdry - "fuel air is only an energyconversion device and not an energy storage dcvice". (05 Marks)

Select the corect answer:i) Appropdate corosion control for a buried pipeline is

A) Painting B) Cathodic protection C) Calhodic coating D) Meta]lic coating

B) difGre[tiai aeration corosionD) caustic emb ttlement.

C) Redox D) Conversion. (04 Marks)

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06cHEt2t22

PART _ B5 a. Select the cofect answer:

i) 'Pickling'isA) alkali cleaning B) acid cleaning C) organic solvcnt cleaning D) water cleaning

. ii) As lemperature increases the elecbo-depositionA) decreases

C) no effectB) increasesD) first decreases and then increases

iii) The experimentally detemined discharge potentiai oi an electrode is 2.58V and itstheoretical discharge potential is 1.53V; theIl over-voltage isA) 3.345 V B) -r.0s v c) 4.11 V D) 1.05 V

iv) As over-voltage increases, electroplatingA) decreases B) increases C) no change

Explain the significance ofthe following electroplating:i) Polarization ii) Over-voltage. (08 Mark)

Differentiate between electroplating and electroless plating. (0,t Mark)

Explain the sudace propagation and electroplating olchromiurn on a steel material.(01Markj)

Select the corect answer:i) The molecular ordering in nematic phase is

A) No positional order and orientational orderB) Perfect positional alld orientational orderC) No positional but orientational orderD) Total loss in molecular ordering.

ii) The layered structure is found in ........,..... phase.A) nematic B) discotic C) meso

iii) ln porenriometric acid-base rilralion, the indicalor elecrrode isA) calomel B) Ag-AsCl C) Glass-electrode D) platinum

iv) Mathematical expression ofBeer-Lambert law isA)A:-logT=C/ B)A=1ogT=C/C) log (Io / [) = eC/ D)lo9(11116)= eC/

b- What are the liquid crystals? Discuss the classification, with examples.

Eraiain the liquid crystalline behaviour in PAA homologous series.

Explain the theory behind the conductometric titation. Draw aodconductometric titration curve for the following fitations:i) A strong acid and a strong base ii) A strong acid and a weak base.

Select the corect answer:i) A poll.rner of high optical clarity used in preparation of lelses is

A) Teflon B) Phenol-fonnaldehyde C) Neoprene D) PMMA

D) increases and decreases.(04 Mark)

d.

6a.

d.

(04 Mark)

(07 Mark)

(01 Mark)

explain the

(05 Mark)

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06cHEt2t22

7 a. ii) Tte glass transirion rempemture (TJ depends onA) t,?e ofmonomer used B) t)?e ofpol),rnerizarionC) chemical resistance D) molecular weight

iii) Monomer used in Teflon isA) fluorine B) bisphenol C) tetrafluoroethylene D) epicblotohydrin

iv) The moiecular weight of addition polymer is integral multiple of rhe motecuiar weighl ofmonomer used becauseA) it is a linear pollmerC) it involves a catalyst

B) no solvent in addedD) no elimination of byproducts

D) Ag2CrOa

D) reverse osmosis (04 Mark)

(04 Mrrks)

(0s Marks)b. Wlat is polymerization? Explain the solution polymerization.

c. Justiry rhe following :

(0s Mrrk)

d. What are lesins? Give the synthesis, properties and uses of phenol-formaldehyde. (06 Marls)

8 a. Select the correct ans\ er:r) tne puresl ioral oj t\dte[ Is

A) dver B) Borewell C) Rain D) Spring

ii) In chlbride analysis (Argentometric), the end point is bdck-red, due to

i) Crystalline pollmers possess higher streogdr tharl amorphous pol1mers,ii) Themal control is mther difficult in buik polymedzation.

A)AgCr2O7 B) AsNOI

iii) Complexing agent for spectophotometric analysis oftitrate isA) SPADNS B) Ammonia C) Phenol suiphonic acid D) phenol disuiphonic acid

C) AeCl

iv) The method removing temporary hardness isA) soda process B) boiling C) distillation

b.

c.

Define alkalinity. lf 'P' represents the phenolphthaiei! alkaiinity and .M, represents rhemethyl orange alkalinity, for a given sample of water, how do you pledict the rypes ofalkalinity, when (i) P = M (irP= %M (iiDp>%M (iv)p<%M? (osrrlarrsr

A river courses firsr *uough a tenain rich ir limesrone and througb a terrain rich rn gypsum.Identify the tlpe of hardness it accumulates in its path. Explain the need for maintaining aconstant pH ard the colour changes that occur, when the hardness of this water is beiflgdetermined by titmlion against EDTA, using Eriochrome black-T as the indicator. (05 Marks)

Gve an account o[the following:d.i) COD is higher lhan BOD.ii) IlgSOa and Ag2SOa are to be added during COD analysis.iiD Chlorine is a powerful disinfectant only at lower pH values.

4 of 4

(06 Marks)

USN

Time: 3 hrs.

First/Second Semester B,E. Degree Examination, Jr*ne/July 2011Engineering Ghemistry

06cHEt2t22

Max. Marks:l00

PART - A(04 Marks)

B) Oxygen cooteltD) Nituogen corterit

temperature required for fllidized bed catalltic

Clays and 55O9CZeolites aoil.3500C

Note,l.Akswef a ! FIWfu questions, choosing at least t ro from eorh part,2-4nswer all objeclhe 4)pe questions otul! in Otr IR sheel page S af.t*e Answer Booklet.3.Answer to objective 4)pe qaestions on sheets othel tht i OMn ffi ,rat be yalaed-

1. a.

i)Choose the corect answerIgnition point of fuel depends on

A) Hydroger contentC) Sulf,r contentMention the catalyst and workingcracking process.A) Clays and 3500CC) Zeolites and 55OoCReformation is a process of

A) Copper B) Tin C) Zirrc D) IronExplair the determination of c.il.sific value of solid fuel

i,

iii)

B)D)

A) Structulal rearangement of hydrocarbonB) Breaking of heavier hydrocarbon to lower hydrocarbonC) Stuchral rearangement without altering the number of qsfbqrD) None ofrhese

iv) Mentior the catalyst used to convert caxbon monoxide and,hldrogen at 1g0 _ 2500Cto form a mixture of aliphatic hydrocarbons

d.

2, a.

D

b. Defiae calorific value offuel.sample.

A) Fluoride ionsC) Chloride ions

B) Hydrogen iunsD) None

Define octalle number. Exptain the methods of improving octane fnmrber.Explain tie consrrucion and r.rorkirg ofphotovoliaic cell.

Choose the correct answerGalvanlc cells can convertA) Chemical energy into electical e[ergyB) Electrical energy into chemical energyC) Solar energy into chemical energy

(06 Marks)(05 Marks)(0s Marks)

(04 Mark)

D) None oftheseii) Electochemical reactiols axe spontaneous when change in froeenrlgy is... A) Positive B) Negative C1 Zero , t Non"iii) Cell porenlial ofa concenrrarion cell is positive only if.. 4) cr.c, B) Cr=Cr c) a2>cr .D) Noreiv) Glass electrode exchanges

b. Define single electrode potential. Derive Nemst equation for si+ile.6lectrode.

What are reference electrodes. Explain the constructionelectode.

I of 4

(06 Marl$)arfl iwoiking of coloured

(05ll{arl(!)

c.

L

06cEm2D2

d. For the cell, Fe,Ec'z.(O.OtStv0 llag*(0.t3M) / Bg, wdte the cell reaatior and calculate

the emf of the cell at STP, if standard electrode potentials of iron and silver arc -0.44vand 0.80V rcspectively. (05 Marb)

3. a. Choose the corect answer (04 Mrrks)i) Shelf life ofa dry cell is limited to 2 years because

A) Zinc rnetal always contacts rvith ammonium hydroxide.B) Zinc metal always contacts with ammonium chloride.C) Zinc metal always contacts with potassium ahlorideD) None oflhese,

ii) Mention the electrolyte used itr Nicad batteryA) Sodiumhy&oxide B) Sutfiuic acidC) Hydrochloric acid D) Potassium chlodde

iii) Which bau,ery has more power density?A) Zn - MnO2 B) Zr- Ag;.O C) Zn-HgO D) Zn-O2

iv) Which electrolyte is used in hydrogen - oxygen fue1 cellA) Potassium chloride B) Potassium nitateC) Potassim hydrodde D) Potassium sulfate

b. What are primary batteries? Explain the co[struction and working ofa dry cell.(06 Marks)

c. Explain the construction and working oflead - Acid batiery. (05 Marks)

d. What are fuel cells? Explain the construction and working of hydrogen - oxygen fuelcel[. (05 Marks)

4. a. Choose the corect answer (04 Marks)

i) Rate of corosion is more ifA) Cathodic area is larger than anodic areaB) Cathodic area is smaller than anodic areaC) Cathodic and anodic areas are equalD) None ofthese

ii) Water line conosion is an example ofA) Differenlial metal corosior B) Differential aeratio!! corosiotrC) Stress conosion D) None ofthese

iii) Caustic embdttlemetrt is a classical example ofA) Stress conosion B) Differential metal conosionC) Differential aeration conosion D) None ofthese.

iv) Galvanising is the process of coatitrg a base metal by :

A) Tin B) Copper C) Zirrc D) Nickelb. Define the term conosion. Explain the electrochemical theory of corosion with respect

to ircn, (06 Marks)c, What is cathodic protection? How a metal is cathodically Eotected by sacrificial anode

method. (06 Marks)d. Write a note otr Galvanisation. (04 Marks)

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06cH812t22

(04 Msrks)5, a.

i)

c.

d.

6, a.

,)

ii)

PART - BChoose the corect answetPoladzation effect will be minimum during metal finishing ifA) Rate ofanode reaction is equal to cathode reactioLB) Rate of anode reaction is smaller than that of cathode.C) Rate ofanode reaction is greater than that ofcathodeD) None ofthese.Which anode is used in chromium electroplating?ii)

b.

iii) When the metal structure to be plated is iregular, the process employed is :

A) Electroplating B) Electroless platingC) Electopolishing D) None oftheie

iv) Reduchg agent used in electroless plating ofcopper is :

A) Soluble chromium anodeC) Inert anodes

A) Sodiwr hnophosphireC) Sodium acetate

A) Calomel electrodeC) Platinum electrode

C) Ag - AgCl electrode

B) Insoluble anodesD) None ofthese

B) FormaldehydeD) Sodium Succinate

B) Glass electrodeD) None ofthese

D) None ofthese

Detrne the term metal finishing. Mention any four technological importa[ce of metalfrnishing. (06 Marks)Explain the process ofelectroplating ofgold. (04 Mark)What is electroless plating? Explain the process of electoless plating of nickil.

Choose the correct answerThe mesophases which are formed by heating and cooling are calledA) Lyotropic phases B) Thermotropic phasesC) Monotropic phases D) None oftheseMention thg electodes used in conductivitv cell

(06 M.rks)

(04 Marks)

A) Platinum elechode B) Glass eiectrodeC) Both are platinum electrodeD) Glass electode and platinum electode

iii) In the estimation of FAS by potediometry, the indicator electuode used is

iv) An ioll selective electrode used in the determination ofpH ofa solution isA) Calomel electrode B) Glass electrode

b.c.

d.

,Define thermotrophic and tyotrophic liquid crystal with suitable example. (06 Marks)

What axe homologous series? Explain the liquid crystalline behaviour in pAA series.

Explain the nature ofconductometdc gaph for the folJowing tihations : (05 Marks)

i) Saong acid with strong base ii) Strcng acid with w;ak base. (0s Marks)

Choose the correct answerTemporary hardness ofwater is caused due to the presence of dissol.,r"a ,ao(31*'*)A) ?lcium and magnesium carbonates B) Calcium and magnesium bicarbonatesC) Calcium and magnesium sulfate D) Calcium nitate

7. a.

r)

3of4

USN

b.c.

d.

2a.

Quna=f

O6MAT11

(06 Mark)

X'irst Semester B.E. Degree Examination, June/July 2011Engineering Mathematics - I

Time: 3 hrs. Max. Marks:100Note|l.Answer FIW full q estiohs choosihg at least t to from each part

. 2-4nswer all objectire q)pe questiohs only it OMR sheet pqge S olftheAnswer Baoklet.i.Anstter to objective tlpe queslions on sheets other than OMR i'ill t ot be talued-

^ d0 - I I I /dr\']tt taDo =_ t))_= f_t _l' dr p' r' r'[d0]

€

c,2

5.i

e!

9E

oi

z

E

I a. select the correct answer : PART-A

i) Ify: a" then y, is41m loga.amx 8)1m loga.1'.a^"

ii) The nr derivative ofsis(cx + b) is

A) a" sin(ax + b + I! )2

C)aosintax+b+Ir- 2'

Bt trnd = .!9'dr

C) loga.a'* D) (m loga)2.a'*

B)-a'sin(ax+b+ T)D) a' sin(a + bx + 11)

iii) If { be the angle betwe€n the radius vector and the tangent at any point of the curver = f(0) then,

A) cotq=!9

iv) The Pedal equatiol in polar coorditate system is

A) l0r - 0: l:-t B)r:(1 - cosO)

D) None of these.

Fi-od the n'hderivaLive ol ) e"'sin(bx r- c).lfy|a+y' r'm 2x. prove thar (xl ltyn,z, (2n+ l)xyn-r t(n2

Fin<l the angle between the cuwes . = , _** *O . = ;..,aO

Select the corect answer :

i) Ifu=x,, theD + is €quattodx.N

.. A) x*l(ylogx + 1) B)xv l(ylogx+ 1) i) xv-tlxlogx + 11ii) If u be a homogeneous function of degree n in a and y then

ar ^4+vff=n sr-$-r.fr -n, 6,1 *A-r4_n,iii)Ifu=x'z+2xy+f+x+y then ,@*y4 i. rqoul to

B)u c)zerc

y : r sino, then lG:I) is equal too(r,u)

(04 Marks)

. (04 Mark)- m')y, = 0 (06 Mrrk)

-1)

*. au AuD) x__ v_ = nrr&'ay

A) 2u

iv) Ifx=rcoso,

A)1 B)r C) llr

D) None ofthese.

D) Zerc (04 Mark)

IJ u - x) tan-r() /x) - y) tan r(x/)). show lf,a i" - *i -y'dxfo x2 +y2

I of 4

(04 Marks)

06cHEl2/22

The products that are fomed urder anaerobic oxidation in BOD experimeat are

iii) Role of oxidizing agent in detemination of COD of waste waterA) It helps to reduce wastes present in waterB) It helps to oxidize wastes preselt in waterC) Both A and BD) None ofthese

iv) Which indicator is used in determination of chloride ions present in water usiog silvernitate solution?

A) Carbon dioxide and waterC) Both A and B

A) Potassium dichromateC) Potassium sulfate

B) Ammonia and hydrogen sulfide' D) None ofthese

B) Potassium nitrateD) Potassium chomate

(06 Mark)

(05 Marks)

(01Marks)

D) Teflon

b. Explain the determination oftotal hardness ofwater sample.c.

d.What^is meant by desalination? Explain the process of reverse osmosis. (05 uark)25cm of seuage sample lorCOD is reacfed with I0cmrof K:CrzOr solurion and rheuneacted K2C.2O7 requires 8.5cm3 of0.025N FAS solution. Under similar conditioos,in blank titmtion 15cm3 ofsame FAS is used up. Calculate the COD ofthe sample.

8. a.

i)

ii)

iii.)

b.

Choose the correct answerPhenol - fomaldehyde resin is commercialiy called as

C) BakeliteHexamethylene diamine and adipic acid gives the following polymer.A) Nyton 66 B) PVCSulfur is used particularly inA) CompoundingofresinsC) Both A and B

C) Nylon

iv) Wl ch tlpes ofpol-vmer is used in smart window material.A) Teflon

A) PVC B) Nylon

B) PVC

D) None

B) Vulcanization of rubberD) None ofthese

C) Polyaniline D) Buna S

(06 Marks)

i) Pollmethyl methacrylate ii) Teflon (06 Marks)d. Define the te1m glass transition temperature of a polymer. Mention the factors which

affect the sarne. (04 Mark)

Explain the ftee radical mechanism of addition pollmerization.Explain the Feparation and mention the application ofthe following pollmers :

4 of4

c.

d.

lf u=x2 -1. v=2xy and x - r cos0, y = rsin0, frnd 4I*.d(r,0)

per 1000, find the approximate error in the gost.

3 a., Select the corect answer :

it lsinn xdx is eoual to

nrl n+l ^ D-1.A) "-l-11., B) r1,., C)

=- i"-,

nn... f. rhI lsln'xcos- x ox $eouallo,)

b.

4a.

A) ; Jr,do B) ; Ir'de

a;"dr.(fl)'

,n estimating the cost of a pile of bricks measued as 2mx15mx1.2E, the tape is stetched1% beyond the standard length. If the count is 450 bricks to 1 cu.m and bricks cost Rs.530

O6MAT11

(06 Marks)

(06 Mark!)

-1Dl -iI",

tr

A)l16

iii) The cuwe f(Za-x)=x1 is s,,rDmetrical about theA) y - axis B) x - axis C) x and y axis D) None ofthese.

iv) The asymptote for the cuwe r = a sin30 is equal toB)0=30 C)0=a D) No aslmptotes.

B)!32

A)0=a

Using the reduction formula, evaluate Jtanu

x ax .

" ------. (2n+I)l a" z

If n is a posirive inreger. show thal J*'Jz* - *' o*- a-,*o ? ,

Trace the Leminiscale if = * G -x')

Select the corect answer :

i) Area bounded by the curve r - f(0) and the mdii vectors 0 : o, 0 = p is

c)a D)I324

l," ,i,F*fl* ",'ilF.[tJ'l* ,,'1ffi*

c.

d.

(04 Marks)

(04 Mark)

(06 Mrrks)

(06 Marks)

ii) The length of the arc of the cuwe y - f(x) between the points where x = a and x = b is

10-cr -: lr'do.,J

C) J2Trxds

18-o1 : Jfdo

iii) The surface area of the solid generuted by the revolution about x-axis of tlle arc of the

cuIvey= l(x) lrom x. a to x=b is

D) I2?rdsA) f2rwds gr fzrvdx)'

.. d [0.-. ].rv)

-l ll(x,(I)dxl ls equal to

do Li l

,cr igrtx,qtdx s; iarl*,.,'t a* c)i1rt*.ota* D) t+r(x.o)dx (04 M,rk)iAq ;dx jd(t :oq

b. Find the entire length ofthe asteroid x"t + y'" = a'''. using tlrc value of fl = #.

2.,f4 (04 Marks)

c.

5 a. Selectthe colrect answer :

i) rte order orthe eo*,i", l,.rf+)''l =al*l' ,., L \dx/.1 \ax,/c)3

Find the volume of the sotid geoeiated by the revolution of the cardioidabout the initial line.

Evaluarc ljjdx. cr> 0.j log x

PART - B

O6MAT11

r=a(1 + cosO)(06 Marks)

(06 Marks)

A)1 B)2

B)P<1

D) None ofthese.ii) The standard form ofa linear differe*ial equalion ofthe fust order is

A) 9+v=p sl 9+Py=a cr 9-pv=p o) 9+av=a'-' dx ' 'd\ 'dx ' 'dx '"

iii) what is the value of dY, for the differenlial equation'tu

(t + zxycos x' - zxylx r (sin x' - x')ay = o

A) 2x cos x2 - 2x B) 2y cos x2 - 2x C.1 2x cos x2 - 2y D) -2x cos x2 - 2x

iv) The differcntial equation ofthe family l= 4a(x + a) ls

. dv( I dv)A) v' = --:1 x +-v--1 |

dx\ 2' dx )

cr ,, =zudYl**-!rdY l'dx[ 2' dx )Solve dy/dx = el"-'?Y + x'?s-'zv

solus !I -.1s;12y = yr 6632 y

Fid the orthogonal trajectories ofthe family ofconfocal conics "'*-y'-=1,*6"."1i"' a' b'+)"the parameter. (06 Marks)

Select the corect answer :

.111i) The series ,,

, ,, , ,., r........ converges ifA)P>0

,, ,, -rdy[** tudy)'dx( 2" dx)

o, u' = zr9[,.* u dY)

" dxt 'dx)b.

c.

(04 Msrks)

(04 Merks)

(06 Marks)

6a.

c)P>l D)P<1.-- Lim u - -u) Ir a posrhve term senes }un , lf a =

^ , then llre senes drverges lor

tl)@ un

A)1,>1 B)l<1 c)),=1 D)r<1.

iii)rhe nb termorthe *,i* [4-?] '*[4-1) '*f4, 4) *...-.-..."o i.[r' 1) \2' 2) (3" 3]

o,ftn rt)'_n+tl-' ".,ftn-r)""

*n+ll "

6lf rn-rr,,_n*r l' plf rn+t)"'_n+rl"L n"-' nl I n'" nl 1," "l 1"" nl

.2345iv) The series f -;ri-:. r......... is

A) Conditiomlly convergenl B) Absolutely coNergentC) Divergent D) None ofthe above.

3 of4(04 Marks)

b. Testtheconvergenceoftheseries 1 * 3 * 5 *.-..t.2.3 2.i.4 t.4.5

2n -l

c. Discuss rhe nanre ofthe series ' ,'^*l,t)'^,*l.1ix,,...-..o (x>0i2 j \ 4./ \5,/

d. Discuss the absolute convetgence 'and conditional convetgence of579tl---+--- +......-.-246I

7 a. Select the corect answet i

O6MAT11

+..-. co (04 Marks)n(n+lxr + 2)

i) If l, m, n be the dircction cosine of the nomal to the plare, then the normal form of theequation ofthe plare is

'A)ln+my+oz:0C)ln+my+IIz=p

ii) Sfnmetrical form ofthe equations ofthe straight line through the poirt A(xr, yr, zr) andhaving direction cosines l, m, n are

A\ x xr y-Yr z-z,., |

_ ,-n

_ ,

at x-xt y yt z zl'' l,. *y -;

B)ln+my-nz=pD) None of these.

Rl x+xr y+yr z+zllm

D)lx+my+nz=0.

(06 Mark)

the sedes

(06 Marks)

(04 Marks)(04 Marks)(06 Mark!)

plane2\-+}y+52+6=Oc. Show that flrc thes ]j=J:f z+3. x 8 v-4 -z 5

.445713common point and the equalion of the plane on which they lie. (06 Msrks)

(06 Marks)

8 a. Select the corect answer :

i) Tle velociry of rhemovingpaniclealongtfrecunex-rl .l.y t2.z 2r. 3 isA)(r'r lI'11 -(21 -l)k B)fl'- tli 2rj-(2r rl)kc)3lir 1j | (2r , l,k D)3l,ir2ri I ik

ii) The divergence of a continuously differentiable vector point function F is denoted bydivF and is dehned by

a,i9-;9F,r4 B,iT.ig-k9t c);!l i9l-pdF D) r.aF r idj+r.91d( .) cz dx 4 ,Jz a). -a) Az d\ "fu Aziii) div curl F is equal to

A)i+j+k B)1 C)0iv, Il F. x2 ' y2 - z2.lhen curl grad F is

A)-l B)0 c)lFind dir F. r.rhere F = grad {xr + y' zr - 3x1z)Prove that curl (g.ad O) = 0.

iii) The equation of any plane through the lt" :t = ? = ? *A) a(x xl) + b(y y1) + c(z - z1):0 where al+ bm + cn = 0B) a(x + xr) + b(y + yr) + c(z + zl) : 0 where al + bltr + cn = 0C) (x + xr) + (y + y, + (z + zr) = 0 where al+ bm + cn = 0 D) None ofthese.

x+l v-l zi\) A point on tle line :j--: - 1 - = -- is' 2 I -tA) (1, 6, 1) B) (-1, 6, -1) c) (1, -6, 1) D) (1, 6, -1) (04 Marks)

b. Find the equation of the plane which passes through the poiat (3, -3, 1) aod is parauel to the(04 Mrrks)

are coplanar. Find their

d. Find the magnitude and the equations ofthe shortest distance between the linesxyz.-Ax2y-tz+22 3t 3 5 2

D)2.

D)2.b.c.

d. Show thal roR is any irrotational vectot for any value of c. but is solenoidal if o + 3 : O

where R: xi + yj + zk and r is the magnitude ofR.*****

4 of 4

(06 Mark)

l

I

USNIt."

Time: 3 hrs.

2d.

Max. Marks:100

lOMATI1

(04 Marks)(06 Marks)

(05 Marks)(0s Marks)

First Semester B.E. Degree Examination, January 2011Engineering Mathematics - t

E

E

EO:

Etl

!e

bdEE.sd

tsE

E.

zE

E

Note'. l. Answer any FIYE full questions, choosing ot least twa from each palL2, Answer all objectite t)pe questions onb) on OMR sheei page S of the answer baokleL3. Answer to objectit'e Drpe questiot s on sheets other than OtrlIR ii not be ralued,

I a. 'Choose the correct answer :

i) Iff(x) is continuous in [a, b], differenriable in (A b) and f(a): f(b), then there exists

i,

C e(a, b) such that f(c):0.A) unique B) inlinite C) al least oneThe Maclaurin's series off(x) - k(constant) is,A)(x)=k B) f(x) = 0 C) does not exist

Choose ihe collect ans$er :

D) no such

D) f(x) = k!

D) None ofthese,

D) None ofthese.

ijil The nrh derivative of -L-

i.(x r 2)'

^. (-lf (n+2)l ^. I^., 7i* * 2f - o,

t* , ,r . c) zERo

iv) The 126 derivative of y -err r;"[, 1,

$@ary B) -4096y c) (32)y

b.c,

d.

Expand log(sec x) by using the Maclaudn's series expansioa

Ifx=tan(logy), prove that (l+x)y,1r +(2Ix(- 1)yn + n(Il l)ya r=0

i) Which stateme[t is true?

A) i ,3, .o - -, O*- are nor indererminale B) 00,

C) I - is not indelerminate D) None ofthese.ii) The angle between r = asinO and r = bcosg, is

A\ 1tl2 B ) ,t C) - n/2iii) The radius of a curvahre it the polar fo.m is,

o, [t' +,i']t"'-' 12 + 2r,, _rr,

Lim )r -1rx-+0 5'-6'

o,log(213)loc( 5/ 6)

1r,' + r2l3t2

tj + 2r' - fr)

IS,

B) tosl :-i I-13 6l

c, It'n l'1"'' r' + 2r1, -r.,

c) r"J4lLY6 ]

D) None ofthese.

D) None ofthese.

D) None of these.

(04 Marks)

(06 Marks)

B)

c,d.

Evaruare:i)::, '*+t l)::o [rll:{]'Derive an expression for the mdius ofcurvirrule in the pedal form. (05 Marks)Find the mdius ofcurvature of a2y =3,ar at the loint ;here the curve cuts x_axis.(05 Mark)

1of4

3 a. choose the conectaoswer: 10MAT11

i) Ifu= a* + bf + auxy, th". 0't ,^ .}

'aq tt

A) Zerc B) a + b + ab C) ab D) None ofthese.ii) The Talor's series of{x, y) = xy at (1, l) is

A)l+(x-1)+(y-1)lC)(x-lXv-1)

b.

c,

d.

respectively.

4 a. Choose the corlgct answer :

i) The gadient, divergence, cwl are respectivelyA) scalar, scalar, vectotC) scalar, vector, vector

PART _ B5 a. Choose the correct answer:

i) The value of Jsin5

xcos6 x dx is0

- 5x3xl'llx9x1

B) 1 + [(x - l) + (y- l)] + [(x- 1Xy - l)lD) None ofthese.

iii.; The Jacobian of transformalion from the Ca(esiaD to polar coordinate system is,. A)l B) lcosg C) lsin0 D)None ofrhese.iv) Ifu = f(x, y), x: O(t), y = iy(t), then du/dt is,

n; !I!I* d'$ et gl*9I c) to & * & dY D)None orrhese.'dxdt dy dt dt dt 'a(dr ay dt -'

1J.1, u =It. .6o*,t,u, *$*y$ =3ruoux+y ox dy

16u: II,, = Il .16 * = I1, 9,6, - 6(u,v,w) .z' x y' d(x,y,z)'

If the H.P. required by the steamer varies as the cube of the velocity aad the square of thelength, firrd the percentage change in H.P. fot 3Vo aurrd, 4yo increase ia velocity and length

(04 Mirks)

(06 Mrrks)

(05 Mrrks)

(0s Marks)

B) vector, scalar, vectorD) vector, vector, scalar

ii; V=y'zi+z'xj+x'y[ isA) constant vector B) solenoidal vector C) scalar

iii) Curl grad f is,A) gad curl f B) curl giad f+ $ad curl f C) zero D) does not exist.

iv) Ifthe curvilinear system is spherical polar coordinate system then the radius vector R isA) rsin gcos {i+ rsin gsinQj + rcos0[ B) rsin0i + rcos0j + dC) i+ j+k D) None ofthese. (0{ Marks)

A) J2ry dx z1 lzm dy c) Jzry as

2of4

D) None ofthese.

D) J2mds

b.

c.d.

Iti=x2+'f +* ana F-x'i+y'j+z'i,thenfiod gradQ, divF, crulF. (06 MsrLs)

Provethat div Curl F = V.Vx F:0. (05 Ma.ks)Prove that the cylindrical coordinate system is orthogonal. (0s Marks)

o, 4x2 'n ^, 2x4x2o'rr*s, c),"9- D) None oftbese'

ii) x'z+f =*f is symmehic aboutA) x-axis B) y-axis C) the line y : x D) All of these

iii) Surface area ofa solid ofrevolution ofthe curve y - f(x), if rotated about x-axis, is:

iy) Asymptote to the curve f(a - x) : x3 isA)v=o B)x=0

IOMAT1l

D) None ofthese.(01MrrlG)

(06 Mrrks)

C)x=a

'l--o rb. Evaluate l1----id{, q>0.

; log xrlz

c. Derive the reduclion formula for [sin' x dx .J0

d. Compute the perimeter ofthe car<liod r = a (l + cose).

(0s Mrrts)

(0s Msrks)

6 a. Chqose the correct answ€r :

i) For the differential_ - \2 / - \6Id'vl Id'vl

eouahon I ---r. I +l ---:- I' I dx'./ ldx'Jrespectively areA)2,6 B)3,2

..- dv vll I --i-+a={l rs'dx x

A) Variabte separable and homogeneous B) LinearC) Homogeneous and exact D) All of

+y=x', the order and degee

D) None ofthese.(01Marlc)

(06 Marl(s)

(0s Marks)

- coso) , using the differential(05 Mrrls)

c) 2,4

iii) ydx - xdv 0 can be reduced to exact, ifdivided byi.1*'*f B)l c)xyiv) Olthogonal trajectory ofl = 4aG + a) is

e; x'?= +a 1y i a; ' nj x'? + f = uu '

C) Selforthogonal

Solve:'(1 + f)dx + (x -e-d 'Y)dy = O

Solve: (y'ze*v' + 4x3 )dx + (2xye.' - 3y'?)dy = 0

Find the ofihogonal trajectory of the cardiods r : a(lequation method.

7 a. Choose the conect answer :

i) Ilhich ofthe following is not an elementary transformation?A) Adding two ro\1s B) Adding two columrlsC) Multiplying a rcw by a non-zero number D) Squaring all the eiements of the matrix.

fr 23'lii) RaDt( of rhe matrixA= l2 4 6lis

l: o o.l

A) 3 B) I C)2 D) None ofthese.iii) The solution of the simultaneous equations x + y = 0, x -2y = O is

A) orly trivial B) onty unique C) unique aad trivial D) None ofthese.iv) Which of rhe following is in rhe normal form?

c) c= D) All ofthese.

b.

c,

d.

lr ool lr oolara=lo r ol nrs=l orol

Lorol Lor,.]

10000100001000010000

3 of4

(04 Mrrk)

f

lOMATlI

b. Fitrd the mnk of the matrix

91 92 93 94 95

92 93 94 95 96

93 94 95 96 97

94 9s 96 97 98

95 96 97 98 99

-r

(06 Msrk)

d.

8a.

b,

d.

Fqr what \Blu€s of l" and p , the following simultaneous equations have i) No solutiofl ii)a mique solrtion iii) an inlinite number of solutions?x+.y+z:6 t x+2y+32=10. x+2y+Xz=lt. (os Mirks)Solve. usiug tbe Causs-Jordan meLhod.,t+y+z:g; x-2y+32=8; 2x+y-z= 3. (0s Marks)

Choose the collect a.nswer :i) The eigen values ofthe matrix A exist, if

A) A is a square malrix B) A is singular matrixC) A is aay matrix D) A is a null matrix.

ii) A square Darrix A oforder .n' is similar ro a square mahix B ofthe order .n. if.... Al A: P-'BP B) AB = Null matll\ C) AB = Unit matrix D) None of these.iii) Which ofthese is in quadratic form?

A1x2 t f +) -2xy t yz- rx B)x3.l yl-22C) (x y - z)' D.l None ofthese.

iv) Quadmtic form rX'AX) is positive detuire, ifA) All the eigen values ofA are > 0 B) At least ore eigen value ofA is > 0C) All eigen values ) 0 and at least one eigen value = 0 D) No such condition.

Find the eigetr values and eigen vector coresponding to ttre largest eiu"rr rufo" of#JHiH11 r3l

a:Ir s r]'' l - 'l (o6Mark)p I 1l

[-l r rlttIfP:10 1 2 I

is a modal mahi.( of the ryiatdx A in e.No.8(b)raad ioverse of p is

Lr 1 1l

[-3 o ]lI-t = I 2 -2 2 J, then transform A in to diagoral folm and hence find Aa. (0s Marks)lr z tl

Fird the trature of the quadratic forms for which coresponding eigen values of theconesponding mahices are given asas

Matrix Eigen values2, 3,4

BC 0, 1,6D 0,3,-4E 1, 3,4

4 ol4

(0s Mark!)

c.

d,

Ee

3

a

t,t

Ea5h

Aq=.9sE3d

EE}E

">6

E+

l6

:g

5g:>

.i 6igzE

Notet L Answer at y FIYE full questions, choosing at least t\)o fiot , each part.2. Answet all objectiye rype quesrions orrbt ih OMR sheet page j of the dhsu'et bookleL3. Anst'er lo obJective lrpe qaestiohs on sheets othel than OMR uill not be ralued.

PART*A1 a. Select the conect answer :

i) 'An expression for the radius ofcurvature in parametric fonn is1l(3/],.,2\,}

A) p=,''.,,, B) p=ll-tJ; ", o=i,li,-{lj} D)Norcor$eseI: ); |.*Y-rx]

ii) The curvature ofa circle is aA) constant B) variable C) 1 D)0

iii) Ifa firnction {x) is continuous in [a, b] ther ril(x)=f(x)-kr is alsoA) differentiable B) continuous C) Both A and B D) None ofthese

xdviv) ll Y= --:-,,11.n - atx=0isrlr

Time: 3 hrs.

1v)

b. Evaluate :

(04 Marks)(06 Mark)(06 Mrrks)

Second Semester B.E. Degree Examination, June/July 2011

. Engineering Mathematics - IlMax. Marks:100

A)l B)0 C) Both A and B D) 2 (04 Mrrkl

O6MAT21

4a'zQa - x\, where the curve meets theFind the radius of cuivahne for the cuwe y2 =

x-axis-State and prove Cauchy's mean value theorem.

2 a. Select 1ft9 cortect atsw€r I

i1 Theralueof Lh logl

1,x -r 0 cosec x

A)0 B)1

ii)

iii)

If f '(a) = O and g'(a) = O, th"o *" hurre Lh lG)*=

x -+ a c(x)

Lim tanx-x

A) Li- -t]u B) Li' t-l*l a, t'' {Q D) Non" orrh"r"x-)a g(x) x--+a g (x) xra g"(x)The ni:cessary conditions for f(x, y) = 0 to have extuemum arcA) f-r=6=1* B) f-=o=f,y C) fx=o=fy D) None oftheseThe point (a, b) is called a statiomry point and the value (a, b) is calledA) stationary point B) stationary value C) m4ximum value D) minimum value

x --) 0 x'tan xc. Examine the function f(x,y) = xa 1ya - 2(x - y)'? for exheme values.

d. Ifxyz = 8, find the values ofx, y, z for whicb u= 5.xyz, is a maximum.x+2y+42

1of4

(04 Marks)

(04 Marks)

(06 Marks)

(06 Marks)

O6MAT21

PART _ B5a. Select the correct answer :

The-differential equation !I = y' is

A) Linear B) Quasi linearThe P.I of y'+y = cosxis

IA) -sitrx2iii) The P.l. of(D2+ 3D + 2)y = I + 3x + xr is

A) *2 B)!)

6 a" Select the correct answer :i) The homogeqeous linear Citbrentiall, l, and -2 isAJ (Dr - Dz - :ti - 2)y - 0C) @'-3D+2)y=0

ii) The general solutioa of (x-2D2 _ 1p;, = 6 i,

iv) Tie general solution of 2a qb 61d91 6ilferential equaiior, rontainsA) Atleast 'n' ind:oendent constrnts n; Airaos ,n. inaefendent cc'stantsC) Exactly n' ind;pendent constants D) Exactly ,n, dependent consraal:

Solve ; (;r - 252 ..4p - gy, = O. (04 Marks)

Scivt : y'- 2y'+ y = xe' 5ii; . (o1M'rks)

Sotve : y' - 4y' + 3y = 20 aos :{ ,by the methcd of undetermined cosffic,iejs. [: #::]

B) 1"or*

C) NonJinear

c) I "si ,

a) 2x2

D) )lone ofthese

_. IU) -xsrn x

2

D) 4x'z

D) cof I 1s - I.1

b.

c.

c..

equatili y,,665e auxiliary equation has roots

B)(D3+3D-2)y=0D) None ofthese

b.

.i.

7a.

.. A) y=C,+Cre* B) y=C,+Cr* C) y=C,+Czx, D)y=C,x+Crx,iii) The equarion ao 1ax + b), y, + a,(ax + b)y, + ary = O(x) is4 ) Legencire s linear equation 81 Cauchl.s ijrrcar equauor,C) Borh A and B

iv) The differential equatior y,+ 5y,+ 61 = , , ,idr1T"J:;1;;; = , ,. *A)

_Initial value ryoblem B) Boundary val-ue problems

C) Both A aird B D) All ofthese (04 Msrks)Solve by the method ofvariation ofparaoeters y,+ury =.gsuj.. (05 Marks)Solve {x + 1)'y' + (x + 1)y'+ y = 4cos log(l + x) . (0d Marks)Solvey'+4y'+4y=8x'],giveny(0)=landy(l)=1.

(05 Marks)

Select the corect answer ;

i) L[ry]=LtJA) cot-rs B);+

ii) L[3sin h 2t]=

.q)-6 B) 6

s'-4 s'+4

C) tan-r s

c,) i6,s'+4

3 of4

D) None of these

.lt-"-l7 a. 1ll)

LI-Ja1 rogfr] . n; r"rf:ll cl rrfr-l

\s+a/\s,/\s,/

B)es

O6MAT2I

D) Noae ofthese

- (04 Mrrks)s

(04 Mrrk)

(06 Mrrk)

(06 M{rks)

iv) Ifu(t * a) is a unit step filnction then Laplace transform ofu(t - a) is

A)-s

C)Ls

D)

b.

c,

d.

8a,

nlPrcve that Llt"l = +tf f(r) = t'7. 0 < t < 2. is a periodic tunction witb period 2, then find L[ (r)1.

fsint 0<t<4Find Laplace transform of f(0 = .{ using unit step function.- [cosr r> i

Select rhe correct lnswer :

l r,l-1-l=Ls- +5J

.,* D)sin.G.t$* B)

--- - ,[s3 +6s':+l2s+8.lfl) l,'l.......................- l='Ls"lt',tottA) -+t- +-+-'21 2t 15

c) t'+t'+tn+f

a; Jrlu; 96 -u;au

q lr6)duiv) L [y"(t) ] is equal to

A) s'2 Lty(t)l * sy(o) - y'(0)

c) s' Lty(t)l - sy'(o) - y(0)

-2B) i-+t'+ tt + t''2

D) None ofthese

B) F(u) s(t+u)du

D) Jg(u) du

B) s'? - sy(0) - y'(0)

D) None ofthese

sinJ5t-T-

iii) Convolution of(t) and g(t) is given by (0 ,i g(t) is equal to

c.

d.

Fiod , L'f s+2, )\G+l).,

rl.a l.'l' - l-), by using convotution theorem.\s(s" + a'),

Solve by Laplace traosfom method, given y" + k'y = 6 and y(0) : 2, y'(0) = 0.

4of4

(04 Mukr)

(0{ Mrrks)

(06 Mrrl(s)

(06 M&ks)

USN lOMAT?1

Second Semester B.E. Degree Examination, June/July 2011Engineering Mathematics - tl

Time: 3 hrs. Max- Marks: l0O

Notei l. Answer an! FfWfull questions, choosing dt leoat two lrom each pdtL2. Answer all obJective lype questions onl! in OMR sheet page 5 oJ lhe ans$'er booklet,3. Afis$,er to objective q,pe quations oa sheels othet lhan OMR teill not be valued.

PART-A1 a. Choose your answem for ttre following :

i) A differential equation of the first order but of second degree (solvable for P) has thegeneral solutioo as,

A) 4 (x,y, c) + F, (x, y,c) = 0

C) F, (x, y,c) - F, (x, y,c) = 0ii) Ifthe given differential equation is solving for x then it is ofthe form,

B) \ (x, y,c) x I (x,y,c) = 0

D) F, (x, y,c) /F. (x, y,c) = 0

s

E

=.9bE

nB6CAR

'U

:>-.i 6i

cz

a1 x=f(y'1) B) y=f(x,P) c) x=f(i) D) x=f(y,P)

iii) Clairaut's equation of P = sin(y - xP) is,

A) y=llrio-rp B) y=Px+siqP c) y=Px+sinrPx

iv) The di.fferential equation lor R, L series circuit is.

Ar {+tu=E BtL{+i=e cr di+Ri=E'dt dr dr L

D) Y=x+sin-'P

o)r-$+ru=r

b. solve P(P+ y) = x(x + y) by solving for P.

c. Solve P3 - 4xyP + 8y'z = 0 by solving for x.

d. Solve (Px - y)(Py +x) = a'P, use the substitutionX = x2,

2 a. Choose )our answers for the following :

i) Roots of y'-6y'+ 13y = 6 ale,

A)2t3i ,- B) 2+i C) 31

ii) The value of *(f(x)) is,

A) f'(x) c) F(x)dx

iii) The pa icutar integat of (D'? - 6D + 9)y = log 2 is,

A) 61o9 2 C) 91o92

A) Cj cos Ft + C, sinptC) Cr cospt t C, sinpt

b. Solve (D3 -D)y = 2e* +4cos x.c. Solve (D'? +2)y = x2er* +aos2x

(04 Mrrk)(0s Marks)

(05 Mark)

(06 Marks)

Br I'f'(x) or []-a*

' 1( x.)

or llosz'6 -gt ltosz9'

iv) The displacement in the simpte harmoni" rno,ior, {=-p'* ir,

B) C, cos pt - C, sin prt

D) cosfrtt sirpt (04 Mrrks)

(0s Marks)

(05 Mark)

d. Solve the simultaneous dilfcrential equations, $+5x-2y = r, 9+2*+y =g. 196 vu.l",' .dt ' dt1of 4

q=x

-8 e *rC,r2

10MAT21 -

3 a. Choose your answels fol the following :

i) If y, and yrare the solutions of second ordq differentiat equation and u and v are

vadation of paBmeters of yo = uy, + ry, then v =

iD

ii0

.. r (y,x)dx ., I fulx)dx .,., t X& n\ f dx

"'t :*,-viv, '' ti,i',tviv, -' rv,v',-viv, ')v,Y',.'viv'

lt x1 y' + 4xy' + 2y =e' if x = e' then we get for x2y' as,

A) (D-l)y B) D(D-l)y C) D@+l)v D) D@+2)v

ro tu iot (ax+b)'?y'+K,(ax+b)y'+Kry=x iito Legendre's linear equation we

B)l C) 1+ e'

b. Solve v'-6y'+9v=1. usine variation ofparameters.-xt

c. solve x2 y'+ xy'+ y = 2cos'](log x )

d. solve 2xy'+3y'- y = 0 by Frobenius medtod'

a. Choose your aoswers for the following :- 1) iattil Aferentia equation by eliminating a and b ftom the relation

Z = (x'?+ a)(y'z +b) is,

put ax+b =

A) e-'

iv) Series solution is a regular singutarity of the equation Poy' + P,y

A) x<0 B) x> 0 C)x=0

A) Z*2, =xYz B) 2,, = xY2

The solution of Z}y = sinxy is Z = -

Ct Z = 4xvz D) Z,Z, = 4aY2

B) -1cos xy + f(x) + g(Y)x

D) -sinxy+ f(x) + xg(Y)

differential equation, Pp+Qq - R' &e subsidiary

-. -dx -dY dzt'.) p = a =R

D) g=q=E,P, Q, R,

iv) In the method of separation of variables to solve un-2ux+q = 0, the trial solution is

o) x(x)",8(0

D) 1-et

'+PrY = 0 when

D)x *0 (o4Mark)

(05 Marks)

(05 Marb)(05 Mrrks)

(04 Mrrks)= 0 when y is an odd

(0S Mark)

(05 Mrrks)

(06 Mrrks)

A) sinxy+f(x) + g(y)

IC) - . sitr Ky+ f(x) + g(y)

x'iii) For the Lagraage's linear partial

equations are

.. dx -dv dzA' -=-=-PQR

^. dx dy dz,P Q R

b.

A) x(x)r@

Solve Z*y = sinxsiny_, -1tmultrple ol ,.

srX(*) o E' T(t) ll r(t)

for ruhich Z, = -2siny when x = 0 and z

c Solve (xr - yr -Z'z)P +zx-yq= 2xz.

d. Solve 3u* + 2uy = 0, u(x, 0) = 4e-" by the separation ofvariables.

2of4

PART-BChoose your answers for the following :

i) The value of ijij-ra-o h

A) 6 B)1,lTiii) The ntegral f j1* * yyoyo* after changing the order of integration is

,,fi ,l-' ,.Fi ,"/iTA) J ilx + v)dxdv B) i lr**vu*av c) iit"*vx*avD) J lx'v)dxdv

iii) The value of 'Je idx is

--l,) r,D qz../; q J2"

rv) rhe value of r(][(;) =

-

1OMAT21

(0s Mrrk)

c)8 D)9

")+

$ 2Ji

contained in the fEst octant between z = 0 and z = 2.

c1 rJi

B) Vector volume integralD) Vector surface integral

il+ Dr !a rol nr".tst'2

(05 M.rks)

(05 Mrrk)

(06 Mrrk)

b b"-Y"

b. Evaluate J Jvaxdrtr chans,as the order ofintegmtion.

c. Evaliate JJ J("+r+zXra"az-l0 r-z

d. show that I(l+ x)'-'(l - x)*'dx = 2-."-'p(m,r).I

a. Choose your answers for the following :

1 r Jr.i=o then F is caltedc

A) Rotational B) Solenoidal C) Irotational D) Depend€nt

ii) If f is the vector field over a region of volume V in tbree dimensional space then F.dv

is calledA) Scalar volume integralC) Scalar surface integral

iii) In oreen's theorem in rhe plane J'|f+- +I-dyir

-

^\4, alA)

J(Mdx - Ndy) B) I (Mdx) x (Ndy) C) IOdx-Mdy) D)

[tuax + uay)

iv) IfC be a simple closed curve in space and S be the open surface, fbe the vector field

oen Jr.ar =

A) f(cwlfl.nds B) Ioxf).ds C) lN2DJlas D) Jo.0.nds (04 Mrrks)

b. Evaluale lJt."a" *irer" f = tzi+2y'j+xzlk ar,d S rs the surface of rhe cyiinder x1 +y2 =9

s

c. Veri& Greeu's theorem for f1ry+y2px+x2dywhere C is the closed curve made up ofthe line

y = x and the parabola y = x2.3 of4

(05 Marks)

6 d, Veriry Stoke's theorem fs1 1=(2x-y)i-yz2j-y2z* fot the upper half of the sphere

x +Y +z =1.7 a. Choose your answers for the following :

i) L{coshat}.

1OMAT21

(06 Marks)

c) -l

b.

c. Find L{f(t)} *h"o ,,,t = {t' 0 < t <-o where rhe period is 2a Sketch Lhe gaph also.

L-E.aslsza

d. Expt""t (t) in terms of unit step fimction and hence find the

f,'. o ... ,r1t1= lar, z. r < l'

|.'. ''n8 a. Choose your answers fo! the following :

l ,-rJ I l=Ir,_"1,, r,]

A)-s +a

ii) L{t'?er'} =

-I

G+3)'iii) Tlaasfolm ofunit frmction L{(u(t - a))} =

A)Liv) Unit impulse firnctior 5(t-a)is6(t-a)=.o

I6(t-a)dt =

-

0

A) r B)0

Find L{t(sin3 t - cos3 t)}.

A) L.o"ttb

B)-s

... , ["' - r. *+ll1) L {-}=I r )-A) 1-3t+2tr s) r*i

;fol t:a;0fort+asuchthat

o1 /, lotu*xs1

(05 MrrLs)

B)z-s -a

B) -i--(s + 3)-

q--

o-l .(s + 3)"

c)

C) I "o"

utb

C) t -:t' +:t'21

D)-j,s +a

_2:' (s+ 3)'

D)?s

D) 1* "i.

tt

D) t+ at'+l

(05 Marks)Laplace transfom given that

(06 M.rl(s)

B) le" sin ot

iii) ln cowolutioD th"or"..,{i1,,r,, -,,0,} =

-B) F(s)xc(s) c) ffi

b. Find the iwerse Laptace transforo of 6"-lf]1.\s'ic, Find. rl s I using con r'olution tbeorem.

l(s rj s' ' tl

d. Solve y'(t) + 4y'(t) + 4y(t) = et with y(0)=0 ard y'(0) = 0

A) F(t)C(o

iv) The expression S'rL{x(O} - s3x(0) - s'!x'(o) - Sx'(o) - x"(0) is due to,

A) L{y'(r)} B) L{x"(t)} c) L{y'(t)} D) L{x'l(t)}.

D) F(t) -G(t)

(04 Mrrks)

(05 M.rks)

(0s M6rl(s)

using Laplace tansform method.(06 Marks)

4of4

USN 06ccPt3t23

Max. Marks:100

First/Second Semester B.E. Degree Examination, June/July 201IGomputer Goncepts and G - programming

E

E

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=.9

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Notei L Arrswer an), FIVE full q estiot s, choosing dt least t\o frorn each pai.t.2. At swer all objeclite Ope quesliohs only in OMR sheet pdge S of the answer booklet.3. Answer 1o objeclire q)pe questions o sheets orher tha Otr[R ;ill not he valued-

Time: 3 hrs.

PART - A

I a. Choose your answers for the following:i) A computer converts data into

A) Inlormation B) ChMsC) Softwae D) Inpur/Output

ii) Which ofthe following is a soft copy device?A) Dot matrix pdntemC) Laser printers

iiD The quality ofthe monitor does not depend onA) Size

Choose your answers for the following :

i) The process ofmapping magnetic disk surface is called

.. A) Polarizing B)Charging C) Formaningii) The back ofa CRT monitor,s scrcen is coated with.. A) Phosphors B) Elecnons C) Elenrentsiii) Which ofthe following is the uait ofdata?

. A) Tem b),te B) Nibble C) Biriv) The temr dots/inch (dpi) refers to a printersA) Speed B) Resolurion Ct Ortpur

Differentiate between :

i) Primary memory and secondary memory.ii) Floppy disk and hard disk.What are the steps to be taken to optimize the computet drive? Explain.

B) Inkjel pdnlelsD) Monitors

B) Resolutionc) Dot pitch D) speediv) The common key boaxd arrangement is called the lavoutA) QWERTY B) QUWTYRC) QYWERT D) e\\.ERryb. Explain in briefthe t pes ofcomputeN used in an orgadzation.

c. What are ouhut devices? What are the various outpui devices?

2a.

b.

D) Accessing

D) None of these

D) A1l ofthese

D) Colours(04 Marks)

(04 Marks)(08 Marks)(08 Marks)

(03 Marks)(08 Marks)

c.

1of 3

3 a. Choose your arswers for the following :

i) A device that connects two or mote LANS is a

iii) Which ofthe following is not an O.S?

A) HUB B) SWITCH C) BRIDGE D) ROUTERii) A program which is used to access the contents ofweb and view webpages is

A) Website B) Web brouser C) Hot mail

C) Apple

C) Single user

C) scanf ( )

C) 10.5 e 10.5

06ccPt3t23

D) None ofthese

D) Macintosh

D) All ofthese(04 M8rks)(06 Marks)

D) None oflhese

D)^

D) fgets ( )

D) 10.s E 10

b.c,

4a.

A) Windows B) Linuxiv) The O.S. is used in _ systems

A) Real time B) Multi user

What is an operating system? Mention its functioDs.What are the various t ?es ofnetwork topologies? Explain in briel with their advantagesand disadvartages. (10 Marks)

Choose your answers 1br the following :

i) A digital integer coDstant aan be ary combination ofdigits fiomA)'1'to'10' B)'0'to '10' C)'0'to'9'

ii) Whicb of the following is nor a biMse operator?A)<< B) | c) &&

iii) Identiry formatted console input fimction

iv) The valid floating point number isA) r0 E 10.5 B) 10,s55.55

b. What is an algoritbm? Write an algodthm to find the biggest of ,hr"" ,,r-b"* *f:tH:flstatemelrt.What is a variable? List oul the rules to define a variable.!!&at is an operator? Explair the different types of an operator.

PART - BChoose your answers for the following :

i) Identifu the invalid statemeflt

c,d.

A) get char ( ) B) sets ( )

A) case 4

(05 Marks)(05 Mrrks)(06 Mrrks)

B) case'a' C) case4ii) Identifu the conditional bmnch statemetrt

A) goto B) break C) conrinueiii) The break statemert is used

A) to skip the statement B) in switch statementC) in looping statements D) Atl ofthese

iv) The oulput ofthe following program is# include <stdio.h>void main ( ){

inti=8;print("%d", i>>l) ;

B)4 c) 16

Explain the various unformatred Vo tunctions in C. [:ffi:[iDiffercrtiate between nested ifand ladder ifstatements. (03 Marks)Write a prcgram to find the roots ofa quadmtic equation with switch statemeot. (05 Marks)

)A)8

D) case I

D) switch

D) Invalid printf

b.c,

d.

2of3

6 a- choose your answers for the forlowing : 06ccPl3l23

i) Ideotif, the conect syntax for .for' loopA) for (Exp1 ; exp2 ; exp3) B) for (Expl : Exp2 : expj)C) for @xpl ; exp2 ; exp3) ; D) for (Expl : ExpZ ; exp3)ii) The minimum mrmber oftimes the do-while loop will be exec;ted.A)0 B)1 c)2

iii) The kel.word 'else' can be used withA) switch B) while C) if

iv) mat is the output of the foltowing progam?# include <stdio.h>void main ( ){

inti;for(i= l;i<=4;i++)printf ('%d", i) ;

D) both A and B

D) for

c) 234 D) None of these

B) Subscripted variableD) Size ofanay

B) inr a[s], [s] ;D) int b (10, 10) ;

B) float a [4] = {10.0, 1s.00, 17.6,6.0}D)AandB

B) Integer variableD) All of these

C) void D) None of these

)A) 1214 B) t23

b. Differentiate between while and do-white statement. I3:#::Bc. Write a flow chart and C - program to check the given number is prime or noL (10 Marks)

7 a. Choose your answe$ for the following :i) The anay elernenls are represented by

b.c.

8a-

A) Index valueC) Array name

ii) Idefltiry the corect declarationA) int a[6] [5] ;c) int a (10) (10) ;

iii) Idertifu the correct anay initializationA) inra [5] = {10,20, 15,30,40}C) char s [8] = welcome

iv) An array subscript may beA) Integer constantC) Integer expression

A) float B) int

What is an array? How you are initializing an array in C? [l:ffi:[]Write a 'C' progam to find the product oftwo mitrices with suitable messages. (r0 Marks)

Choose your a-nswers lor rhe lollowing :

i) \\4rich is the user defined firnction?

... 1) qT"_( ) B) sqrt ( ) C) cllscr ( ) D) gets ( )ii) Identiry the statement used to rchrm the contol to the ;hrg functio; -

.... A) continue B) break C) rerum D) exitiii) A function connot be called as

.. ! ^91d: B)procedure C) subprogram D) applicarionrv) lhe defaull retum q?e offunctjon is

b.c.d.

Differcntiate between call be value end call by refetence.Differentiate global and local variables.Wdte 'C' progmm to sort the elements by bubble sort techrdque using functions.

3 of 3

(04 Marks)(0s Marks)(04 Msrks)(07 Marks)

USN

Time: 3 hrs.

r0ccPl3/23

FirsUSecond Semester B.E. Degree Examination, June/July 2011Gomputer Goncepts aad C programmlig

r)

iD

b.

d.

b.

d.

!

-cg

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2',=;

EC

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Noler l. Ans$,et FIUE lall questions choosing at least two from eqch port2. Answet qll abiecrive lype questions onl! in OMR 6heet page i olth. onswer booHeL3. Answer b oUe(tive 4)pe questions on sheets orhet tha$ OIJ{R iill not be eataed.

PART-A

1 a. Select th€ correct answer :

i) Which ofthe foltowing device stored instuctioos that help computfl to start up?A) Ioystick B) RAM C) ROM D; Morrito.

ii) A collection of 8-bits is called

Max. Marks:100

A) Blte B) Wold C) R€€ord D) File

D) CRT Screen

iii) Which ofthe follo\f,ing is not an output device?A) Printer B)Keyboad C) VDU

iv) Which ofthe following is not a t ?e ofkeyboard cormector?A) 5-pin cornector B) 6-pin connector C) 8-pin comector D) USB comector.

'\{ith a neat diagram, explain th€ basic stucturc of a computer.

Explain two typ€s ofmodtors based oo the techdque used to

Convert the decimal number 371n to biaary form.Convert the binary aumbor 001 I I 10 to decimat.

ii) A magurtic disk's h6€ks ale divided into snaller pafts call€dA) clusters B) sqctols C) bytes D) dices

iii) A translator which reads an eatire program Pritten in high level lang03ge atrd qonvert$ itinio machine langruge code is

Select the corectanswer: \i) Unlike a transistor, a magnetic disk can storc data without a

A) etectdcity B) RPMs C) poladty

- A) Assembler B) Translator C) Compiler D) System softwareiv) A dishibuted [etwork configuration in which all data./information pass tbrough center

computer isA)Bus network B) Star nctwo* C) Riry network D) poid-to-point Detwork

(0t Msrlc)What is an operating system? List alrd explain ditrerent Spes of opqaiing systsB based oqusage atrd requirsm€nt, (08 Msrls)What is OSI model? Explain the principle used to develop sevco layers ofOSI model.

(0{ Mrrk)(08 Mrrb)

(0{ Mrrln)

({X Mrr}r)

(0l Marks)

(04 Mrrks)List the basic corrpotcnts of a nctwork.

D) Ucht

I of 3

3 ' a. Selea the correct answer :i) Which ofthe followirg are not valid id€ntitrers?

A) studeot_natne B) _total C) 2naEes- ii) Which ofthe following are not character c.oDstants?

A) .C' B) "C" c) ,bb,

,d) displayf B) rcad

b. List ad q.plaiD coding constants.

C)priutf D) scanf

10ccP13/23

D) int

D) '?'

D) prinary

D)Assigna€nt iorMrrkt)

(0{ Mrrk!)

using the following

(0t M.rls)

D) None ofthese.(01M.rks)

4a.

q. What is variable? Exphin yariable iuitializatiotr.

d. Explain the stucture of'C' plognm,

iii) Which ofthe following iB not an €xpressio! formaflA)assignmcnt B)conditional C)bitr8ry

iv) Which ofthe fotlowilg has high€st pie-oederce?A) prefix i:acrcment B) Multiply C) Modulus

iii) Which field specificstiotr is used to read or write shon heger?A)o/oc B) %d q%t D) %hd

iv) Which fiructiou reads det' tom the ke)toard?(lX [..f.)({}5 Mrrt!)(1,4ltllrL.)

(06 M.rb)

SelEet ihe corrert a$wer :

i)

-

is used to determi[e the order il which difierent operations in an expressionare evaluated-A) Associarivity B) prec€dence C) evaluatio! D) fomar

ii) Which ofthe fottowing is not a vatid assignm€ €xprcssiotr?A)x=23 B)4x=8=3 C)yo/o:s D)x=r=5

b. lfa = 2, b = 8, c = 4, d -- 10, what is the value ofeach ofthe following?i) a+b/c.d-c/a \ gta'1%ciii)a+++6-- 1 6a1 iv) +ra + b-- + +*uWrite a program to convgrt temp€ntur€ ftom Fafu€nheit to Celsiusformula.

ca,ius = [!!91* (ramrheit - 32)u80/

c.

5a.

Convert the following matheEatical expEssions into .C, expressions:orLi)a+bxc ii); iii) Js(s - a) x (s - b) x (s - c, iv)x2+l+2ry (04 Mrrk)

. PAR,T - BSelect the correct ans*er :

i) A fimption that calls itselffor its processing is knoun asA) lJine fiuction B) Nested fimction C) Overtoaded flrnction D) Recurcive functiou

ii) We declare a firnction with _ if it do€s not have any rctum typ€.A)long a;aoubli- C)void ojir:tiii) Vaiables iruide parc[tlEsis ofa fimction declaration have level access,

A) local B) global C) module --5["i"enaiv) AryurDents ofa fiuctiou are separated with

A) conma(,) B) semicolon (;) C) colon (:)

).of3

0rccPt3.t23USN

First/Second Semester B.E. Degree Examination, December 2010Gomputer Goncepts & G-programming

Time: 3 hrs. Max. Marks:1ooNoaeil-Aneter an! FIVEfull quesrions, choosit g at least th,o fiom rrch pon

z,Ansh'et all objective type questions onl! on OMR sheeipage S ofthe answer boohlet3.Ans.t et to objective type que;tions on sheets other than'OitIR *7 nu be vatued

i) Dot matix ir) I8ietSelect the correct answer:

iii) Laser

2a. i) The CPU uses a_ to store and retriretrieve each piece of data in the memory.

Select the cor.rect lnswer:I a. i) Which tlTle of computer will

vehicles?A) Smaxt phone

A) PS2C) HDX

iii) Disketts spin at aboutA)3

Select the correct answer:3 a. i) In many GUl-based programs, a

commands quickly.A) Meuu barC) Cornmand base

ii) DOS stands foXA) Distdbuted operating systemC) Disk operating system

... C) Super comput€r D) Minicomputerii) Which of the following devices stores the instruction ua-:t helps the computsr start up?

A) Joystick B) RAM.... 9l RoM D) Mooitoriii) When ydu pess a key, this device notifies the system software.

A) Key board B) Keyboard bufferC) Key board controllo D) Netwo* CpU

iv) A compgter's resolutiotr is deterrdned by _A) Monitor B) Video controlersC) CPU D) System unir

b. Explain the four categodes ofhardware devices.c. What is Lhe difference between impact and oon-impact printers? Classify

printers into impact and non-impact pdnter:

PART-A

you most likely encotmtet at the department of motor

B) Main&ame

(04 Msrl6)(10 Marks)

the following

(06 Mrrks)

B) CacheD) Memory location

A) Cof,lrcl unitC) Post

ii) Most popular extemal connection for a pC is,B) USBD) MIDI

revolution per minute.B) 30

c) 300 D) 3000iv) To remove a system program Aom yoru compuler you can

A) Uninsrall Sl OeteteC) Store D) Transfer

b. Explain the-componenls required to process the data in a computer.c. Biefly explain the following processors:i) AMD ii) Free scale iiD IBM

(04 Markr)(07 Marks)

(09 Marks)

displays burtoru that let you

B) Sooll barD) Tool bar

B) Driver operating systemD) Diskless operating system

I of4

lssue

Q3 (a)- contd...iii) ln a

communicate through i!A) BUSC) Ring

B) Stax

D) Mesh

B) Delete and paste

D) Cut and delete

06ccPt3l23

r.etwo*, all devices are aonnected to a device called the hub and

iv) Which command is used to rcmove data from one docurnent and place it in another?

b. What is an operating system? Explain the four fypes of OS with examples.

c. what is the need of network topology? Explain the following network lopologies:i) Bus topology ii) Star topology iii) Ring topotogy

Select the correct .answcr:4 a. i) The step by step procedue to solve a particular problem, is called

A) Copy and paste

C) Cut and paste

A) Flow chartC) lnstuction

ii) An infmite loop in a programenor is it?A) Syllta{ errorC) Run-time error

A) AssemblerC) Compiler

iv) Basic building blocks of C are,

A) Ke,.wordsC) Constarts

A) put char ( )C) set ch o

ii) Which opemtor has the highest precedence?

A)+C) N"

iii) Switch expression can be

A) FloatC) Integer

iv) Which is the formatted console output function?A) get char ( )C) scan f( )

B) Pro$amD) Algorithm

sequelce; causes no output but oeates error. wlat type of

B) Logical errorD) None ofthese

B) ComputerD) Interpreter

B) IdentifieND) Variables

B) get char ( )D) put ch o

(04 Mark)(08 Mark)

(08 Marks)

iii) Which taoslator conyerts high level language progam iDto machine language?

Wdte a flowcha( to find the factorial of a given number.

What is the value of x, if i= 10, b : 15 and x = (a > b)? a : bi

What would be the value of c, if a: 1, b:2 ? Mention the steps involved.

i) c=(a> 0 && a<= 10)? a+b : a/b1

ii) c=(a<0 && a<= 10)? a+b : a/bj

PART _ BSelect the correct answer:

5 a. i) To read a single character, which ofthe following equation is used?

b.c,

d.

(04 Marks)(06.Marks)

(02 Ma*s)

(08 Mark)

B)*D) >>

rype.B) VoidD) Double

B) set ch oD) print f( ) (04 Mark9

(04 Mark)b. what is the difference between IF..ELSE and switch statement?c. Wdte a C pro$am that will read the value ofx and evaluate the following flnction:

y:1+x,whenn:1:1+xn,whenn:2:1+nx,othetwise

using (i) else ifstatement (ii) switch statement

2of4

(12 Marks)

06ccPt3/23

Selcct the correct answer:6 a. i) Identiry the unconditional control statement in the following:

A) If ElseC) Switch

B) Nested ifD) goto

ii) What is the output of the following? For (i = 0; iL = 3; i*); priritf (.,%d,,, i);A) 0123c) 012

iii) Which statement is called as blT,asses?A) goto

C) co inue

Select the correcl answer:7 a. i) Array elements must be enclosed within

. A)tlc){}

ii) Size ofatr anay is indicated by,A) integerC) char

iv) In the following, identiry the ron-looping statemeot;A) whileC) for

B) 01

D) garbage value

B) breakD) switch

B) do-whileD) swi&h

to initialize the arrav-

(09 Marks)

(04 Maiks)dimension aray?

(06 Mrrks)

(10 Marks)

b. Explain the following statements: (i) break (ii) goto.c- Write a progam to pdnt the fdllowing output using for loops:

(04 Marks)(02 Marks)(0s Marks)

I2244445 5 5s5

d. Write a Eogram to find the sum of ODD number beginning with i : 1 and upto n number,_!-

sum: )x, usihg

while loopdo_while loopfor loop

i)ii)ii)

iii) What is the output of the following pogam segment?Main ( ){ int K [s] = (3, s, 6, 8, 10);

Prinl f("o/od". K[0):

B) floatD) double

B)()D)"

B) 32D) EIIor

)A)3c)8

iv) Alray is which data t]T,e?A) User defiaed B) Built inC) Pdmary datat ?e Oj Oerivia aata type

What is an array? How do you declare and initialize OIIE anA TWOExplair u ith an example.Write a program that accepts a 3 x 3 matuL\ and computes,i) Transpose oflhe marrix.ii) Addition ofdiagonal elements.

3 of 4

06ccP13t23

8a.Select the correct answer:i) Ifthe retum t}?e oIa function is int, tbeb wbat is the value retumed?

A) null B) voidC ) int D) char

ii) Identiry the mathematical function ia the fotlowing :

iii) The plocess of splitting a lengthy and complex program into a number of smallerprograms is calledA) rmit program B) modules

D) logical prcgamC) built in progamiv) How many number of functions carr be used in a program?

A) one onlyC) eight only

Distinguish between:i) Actual and formal argumetrtsii) Global and local variables.Describe the two ways of passing parameters to finction. When do you prefer to use each ofthem? Give examples (10 Marks)

A) clrscr ( )C) fabs ( )

B) printf( )D) maiu ( )

B) two onlyD) any [umber (04 Marks)

(06 Marks)

g

Eg

g

Eh

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ta

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I

4of4

Seleca the correct onswer:8 a. i) Ifthe rctum type ofa firnction is irt, then what is thc valueietumed?

A) null B) voidC) int D) char

ii) Identiff the mathematical fimction iir the following :

A) clrscr ( ) B) printf( )C) fabs ( ) D) main ( )

06ccPt3t23

(r0 Marks)

;

iii) The process of splitting a lengthy and complex program into a number of smallerprograms is called

B) modulesD) logical program

iv) How many number of functions can be used in a proglam?A) orconly B) two onlyC) eight onty D) any number (04 Mxrks)

Disiinguish between:i) Actual and lormal argumentsii) Global and local variables. (06 Marks)Descdbe the two ways of passing parameters to function. wheo do you piefer to use each of

A) unit progamC) built in program e

E

E

39!9=

=?

8a

rb

a3

tUtsEEP

=ioi;z

E

thern? Give examples.

4of4

USN 05ELN1s/2s

Max. Marks:100

C) di{tusion D).alzlaache break do*,n

B) decreases its resistanoeD) increases the potenlial tranier height

B) decreases with teo1lret&tweD) depeflds on the method ofits fabricatiol

(04 Msrks)

i) No bias; ii) Forward bias;(10 Mark!)

value, ii) Rectifier(06 Mrrk)

D),four (04 Marks)

First/Second Semester B.E, Degree Examination, Juno/July 2011Basic Electronics

Note,l.Anst er FIWfull questions choosihg al least t rofrorfi each part-2-4nswer dll objective Ope q estions onl! in OMR;heet page i althe Arrstaer Booklet,3.Ahswrefi to objective type questioks on sheets other th;4 6MR;i n of be valued.

PART - A1 a. Seiect the correct answ€r :

i) An excessively high reverse voltage applied to a junction diode will cause an effectknown as:

Time: 3 hrs.

b.

E

g

ty

E

2E

t,!.9

!-o

?s

,.' B

5!

E6"-E

Eg.

gz

E

A) punch through B) satuation

ii) Forward biasing a P-NjunctiotrA) increases its resista[ceC) shorts the junction

A) is due to majority carrie$C) is in mA or pA range

iii) When a diode is heavily doped,A) the zener voltage will be low B) the avalanche voltage will be highC) the depletion region will be thin D) the leakage currentivil be low.

iy) Leakage curent of a junctiotr diode

b. W1lal is a P-N j'rction? Discuss its behaviour underiii) Reverse bias.

c. For a bddge rectifier circuit, derive theefficiency.

2 a. Select the corect answei :

i) The e{ficiency ofhalfwave rectifier isA) 40.6% B) 0.46% c) t.2to/o

A) one B) two C) thrce

ii) A zenerdiode \A) is always forward biased B) is'C) has a sharp breakdo.rm at low reverse vottug" O) t u. u ,"gutio, .".iri*"".

iii) A filter circuit is used to remove theA) AC voltage B) DC voltage C) Both A and B D)None ofthese.

iv) if, by mistake, AC source in a bridge rectifier is connected across ttre dc termitals. it willbum out aad heoce short -.- diodes.

In a firll wave bridge rectifier, the transformer secondary voltage is lO0 sin ot. The fona?idresistance ofeach diode is 25O and the load resistance is g5ocr]Calcolatt, DC output volt.ge ii) ripple factor iil; em"ien"y oiiecmrccti* iv) plv acrossnon-condu$ing diode. (09 Marks)Sketch t]lical transistor commor-base curent gain chamctedstics. Eqilain the shape ofthecbaracledstics. -

1oz mar*y1of4

6*--X)\37 --.<er& \"c4l ee:- dtrY l?

' )'.---.--'J:\G NAGAqi/-z

06ELN15/25

3 a. Select the correct aDswer :

i) The biasing circui! v,/hich givos most stable operating point isA) Base bias B) Coll€ctor to base bias C) Voltage divider bias D) None oflhese

ii) Ttie anow on tlrc emitter ofa transistor indicatesA) the direction of electron flow B) the positive voltage poiatC) the direction of positive curent flow D) the ground connections.

iii) The common eEitter hansistor circuit configuration is most often used because of itshigherA) power gainC) output impedanc€

iv) in a t ansistor with normal bias, the emitterjuuction

B) fiequencyD) voltage gain.

B) has a high resistarceD) emits carriers in base which are in majority there

A) is leversed biasedC) has a low rcsistaoce

b.

c.

d.

DeEDe'cr' and' p' of a transistor. Sbow thal P = --e -' (l-(r)

Discuss the causes of unstability in a tansistor.

In the circuit shown in Fig.Q3(d), a NPN Traasistor with P = 100 is used. Find Ic and Vce.

Draw the DC load tine output charaatelistics and indicate the Q point. Take Vge = 0.7 Volts.

(06 [krkl)

(0a Marks)

(04 Mirks)

(06 Mirls)

4 a. Select the oorect aoswer :i) A IFET behaves like a

A) ResistorC) CoNtant voltage sourc€

A) increases sharplyC) st3lts decreasing

ii) Wher JFET is op€rakd above pinch offvoltage, its dmin curent

B) Corlsta curertD) Al1the above iD different regioDs.

B) becomes constantD) b€comes zero,

iii) The output of a UJT cart be taken ftom itsD) any one ofthrce tenrdnalsA) base I B) base 2 C) emitter

iy) W1rcn a UJT is tumed ON, the resistance between eBitter temdnal atrd base I isA) increased B) decreased C) zero D) infinite (0aMrrk)

Sketch the voltanpere charactelistic of a t,?ical silicon-controlled rcctifier. Explah the

behavior ofthe SCR reference to its V-I oharacteristic. (0E Mrrk)

DIaw the output characteristics of a P-channel JIET with extemal bias. lndicale various

rcgions ofopemtion and explain the shapes ofthe curves qualitatively. (0t Mrrks)

Fis.Q3(d)

2 of 4

PART - B

5 a. Select the coEeit ans*er :

i) As coDpared to the resistaoce of the source, the input impedance of a good voltage

amplitrer should be

A) hiCh B) low C) equal D) twice'

ii) Coupling capacitors mainly affect

A) uppei cut-offftequency B) lower cut-offfiequencyC) with upper and lower culoff ftequency D) gain in high ftequency range'

iii) The volrage gain of a common-base amplifier depends upon- A) load resisior RL B) Input resistance oftansistor

B) high cunent gainD) all theabove.

06ELNl5/25

(04 Marks)

(r0 Marks)

C) ac atpha D) All the above.

iv) In a common base amplifier, a smaller load resistance will produce:

A) high voltage gain

C) low power gain

salied points on it.

6 a. Select the conectanswer:

b. What is an oscillator? Wlite the circuit of a phase-shift oscillator and descdbe its operation

giver the expression lor irs Aequeocy ofoscillation. (09 Marks)

c. Sketch a tlpical frequency response graph'fol an RC coupled ampliher. Briefly explain the(07 Merks)

i) An advantage of an inverting amplifier is its ability to handle - irput at a time'

A) more tban one B) less than one C) equal to one D) None ofthese'

ii) Op-amp is adiect coupled multisrage

iii) The commor-mode rejection ratio ofar ideal op-amp is

A) zero B) low C) hiCh D) infinite.

iv)

-

convefts physical quantity to electrical signal.

a) neceirer B) TraDsducq C) Modulator D) Tlansmitter. (04 Marl$)

A) voltage amplifierC) voltage-cunent amplifier

C) electro-mechanical signal

ii) (762)s=(?)oA) (468)to B) (248)ro

ii, (0.125)ro=(?),A) (0.001), B) (0.010>

B) cunent amplilierD) power amplifier

b. Dedve an expression for output voltage of an op-amp

i) Inverting amplifier ii) Adder iii) Idegator.

c.

la.

What do you meao by the terE modulation? Why is it required in communication system?(06 Marks)

Select the correct answer :

i) Radio communication is the process of s€oding information in the form ofA) mechanical signal B) electrical sigoal

D) all ofthese.

c) 028)10

c) (0.100)

D) (498)ro

D) (0,110),

iv) Computer system only support numbers for theA) binary data B) decimal number c) hexadecimal number D) octal NnnbeL

Mr.k".

3of4

b.

06ELN15/2s

Convert: i) (434.514)s =(?)ro=(?)16ii) (44030)ro, (?),t?)r"iii) To subtract (10l0ll), fron (100110)2 using 2's compleBed. (0e Mark!)

t 5-m Y, f _W., carier is amplihrde modulated with a sinusoidal signal of I kHz. Thedepth ol modulatio[ is 60%. Calculate the band width power in the sid;ands aDd the totalpower transmitted. (04 Marks)

d. Wdte the syrbol, tnnh bble and output exprcssio[ for EX-OR gate.

8 a. Select the correcl a.nswet :

i) In a halfaddet when both th€ inputs A ard B are high then

4lluy=1andcarry=0 B) SUM=0andcarry=0C) SUM=0 and carry = | D) All ofthese.

ii) NAND gale is a combination of ea[e.A) OR and NoR -- s,) NoT;a NaND 'C) NOT ard AND

iii) Demorgan theorem states that A]E =

(0.! Msrks)

D) None ofthese.

D) Noae ofthese. (04 Marks)

b.

c_

Simplify and realize the expression (A + B + CXA + B + C)(f +B) using only NAND gates,

(06 Merks)Draw the circuit of a TWO input traosistor logic NAND gate. Explain its operation.

(07 Marks)

(03 Mrrks)

A) {+B B) A.Biv)A+A=_

A)0 B)1

D) None ofthese.

C) AB

c)A

d. Draw the logic circuit of Full adder.

4of4

USN06ELN15/25

one ofthesein Fig.Ql(aXiii)?

First/Second Semester B.E Degree Examination, December 2010

Basie Electronics

Max. Marks:100

NoteJ.Answer any FIW full questions, choosing at least two queslions from each pdtt.2.Ansteet all objective qrye questions onl! on OMR sheet page 5 oflhc onsuer hooklet'

3.Ans$,er to objecrtve 4tpe queslions on sheets othel rhLn OMR teill aot be valaed

Time: 3 hrs.

PART - A1 a. Select the dght answer :

i) What kind ofa device is a diode?A) Bilateral B) Linear C) N

ii) How is nonconducting diode biased?A) Forward B) Reverse

What is the value of the current (I)CivenV=0.7V.

r3,

E

gg

!')

ih

E_E

=-2

=b

8e

i€3;

EO

Iz

E

It-

I

i

C) Poorly -:l--{e -vrPin the circuit sho-$,n

'.i-

Y Fis.el(axiii)

A) 0.s A B) 0.4 AC) 0.1A D) None ofthese

iv) lf the line ftequency is 60 Hz, the output ftequency of a half wave rectifier rs

A) 30 Hz B) 60 Hz C) l20Hz D) 0 Hz (0a Mark)b. For a tDical P.N junction diode, define the tems : i) Knee voltage and ii) Reve$e saturation

currer$. Also indicate them on a t)'pical V-l charactedstic curve.

c, Design a zener voltage regulator to meet the following specifications:Output voltage = 5 V load cunent = 10 mAzener waltage = 100 mW input voltage : 10 V i2 V.

d. Derive an expression for ripple factor and output dc voltage, in case ofa full wave rectifierwith a capacitor filter. (08 Mrrk)

2 a. Selecl fie right ans\rer :

i) In a CE configuation circuit, ifthe base resistor is open the Q point will be :

A) In the middle ofthe load line B) At the upper erd of the load lineC) At the lower erd ofthe load line D) OFF the load line.

ii) In a BJT the collector current is 10 mA, ifthe curent gain is 100, the base curent isB) 10 pA C) 100 pA

(04 Mark)

(04 Mark)

iii) Find the collector current in the circuit shown in Fig.Q2(aXiii)

1 l^svFig.Q2ra)( iii)

iv) 'o' and 'p' in a BJT are connected by the equalion

A)1pA

' 1-0

D)lmA

A) 2mAB) 3 rBAC) 10 mAD) None ofthese

D) Both B and C

(04 Marks)

' l+B

i'^n)h-/

B) p=l-cl

1of 4

2b.

c,

.t Va,(:3ov

Skrr-Fie.Q2(b)

Explaitr the iryEt and output charactedstics for a CEregioE o}1 the citamcteristics.Compae variots BJT circuit co.figuations.

Select fr6 rigkt answer :

i) Majodty carriers in the emitter ofpry transistor are

06ELN1s/21

the DC load line and mark the dcV66q and I6q values. Given B : 100

(06 Marks)

configuation BJT circuit. Discuss each(06 Marks)(0,{ Marks)

For the CE ci?euit sho n below in Fig.e2(b), drawoperatiEg pdm in lhe actire region. lndicare respecti\eand negtect VB+-

iD

d.

3a-

A) Holes B) Free elecmons C) Trivalent aioms D) Pentavalent atomsVoltage divider bias is noted for itsA) Urrstahle collector voltageC) Large base curent

B) Varying emitter currentD) Stable Q pointof 10oC results iniii) In a FN junction a temperature

leakage ettrrentA) Doubling B) Tripling

iv) Therrral runaway in a BJT is aA) Useft phenomenonC) Destruclion pheoomenon

change

A) Holditrg currentC) Trigger current

ii) Irput impedance ofJFETA) Appmachcs to zero

Q Approaches to oriii) A ufpolar tra$istor uses

Is continEous gate current necessary to switch theswitched OFF?Sketch the V-I characteristics of VJT, iodicate eachcharacteristic curve.Illustrats SCR as a controlled rectifier.

C) No change D) Both B and C

B) Tolerable phenomenonD) Both A and B (04 Marks)

stability factor. (0S Marks)82 KQ and Vc! = 5 V.

(04 Marks)(04 Msrk)

B) Break over curentD) Latching curent

B) Approaches oneD) Is impossible to predict

of reveNe

b.

c.

d.

4a.

b.

c.

Draw a voltage divider bjas circuit and dedve an expression for itsA collector to tlase bias has Vcc = 15 V, Rc = 5.6 KO, RB =DeterEtine the transistor ht value. Assume a siiicon transistor.Explain tbermal runaway in thc case a BJT.

Select the dg*t answer :

i) The miaimum anode curent that keeps a thyristor tumed ON is called the

A) Both ftee electons and holes B) Only free electronsC) Only boles D) Eilher one or the olher but rot bothiv) IFET acts-like a yoitage cottrolled rcsistance in _ region.A) Cut off B) ohmic regioo C) Saturation D) None ofthese

d

(0,t Mark)SCR ON? Justifu. How the SCR is

(04 Marks)region and expiain the shape of the

(06 Marks)(06 Marks)

2of4

06ELNls/25

5 a. select the right answer : PART-B

i) Al oscillator always needs an amplifier withA) Positive feedback B) Negative feedbackC) Both A andB D) A1LC tank cjrcuitii) Overatl voilage gain with negatjve feedback (AcL) in rems of open loop gain (AoL)and feedback factor (p) are given by

A) A-t B) Aor ,-i Ao'" l-0AoL "',-PTo, t' ,,ffi D) Noneofthese

iii) For high ftequency oscillators normally _ elements are useei in the fee<ibackcircuit.

. A)LC B) RC C) EitherAorB D)BorhAandBiv) Frcquency output ofan RC phase shifl oscillator is given by

A) f = I' znRC

B) f=- l- Cr r=2rRC J6

l

2TJLRCD) None ofthese

b. Draw the circuit of a two stage R-C coupled CE amplifier. Erpluio ,igoifi"-":04oT::Ticompolent. Plol ils fleque[cy rcsponse. (r0 Marks)Discuss the effect ofnegative feedback on the batdwidth and voltage gain ofan amplifier.

(06 Marks)

Select the right arswer :

i) OPAMP voltage follower has a voltage gain ofapproximately

... L) U_rlY B) Zero C) Intrnity D)None of ttreseii) Ideal OPAMP has a CMRR equal to

.... 1l-?"ro . _, B) Infiniry C) Uniry D) None ofrheseIl) lt v I and Vz are input voltages ofa non inverting adder circuit, output voltage Cyo) isgiven by

. A) (Vr + V, B) -(Vr + vrt CI vr V2 D) None of theseiv) An OPAMP has a voltage gain of 5 , I05. If fie output vohage is I V, the inputvoltage is

_-. . A) 2 pV B) 5 mV C) 10 mv D) I V (04 Marks)Write

_expressions for outtrut voltage at points A, B, C, D and E in t(e circuit shown inFig.Q6(t).

(10 Marks)(06 Marks)

c.

6a.

:EC/r)\

,a+1 , !. r

,o. ' i-1J

-::,i:l'

3of4

Select the iight answer :

i) (ABCD)I6 = ( )8A) t2571s B) 13715

A) I, = I.

c) I. =t, D) None ofthese

B) Intoductory frequercyD) None of these

C) AM tansmitter D) None ofthese

c) 12s710 D) None oftheseii) Relation between modulation index (mJ, total modulated current (It) add unmodulated

(tc) curIent. ir case ofAM wave is given by

ut,,=,"[,.4)

iii) Term "lF' in an AM receiver refers toA) Intermediate ftequencyC) Interlock frequency

iv) Mixer is a building block ofA) AM receiver B) FM receiver

b.Obtain an expression for total average power of simuoidal AM wave.When the modulation percentage is 75%, an AM tansmitter radiatedthis is carrier power?Draw the clock diagram of

(04 Mrrks)(0s Mrrks)

10 KW. How much of(0s Marks)

d. stage,

a. Select the right aoswer :

i) Boolean expression for )O"IOR gate is

41 Y=eb+BA B) Y-AB+Aa c) Y=AE,eBii) Iftwo inputs ofNAND gate are shorted and input is applied its

of the inputA) complement

iii) Universal gates are

A) NAND and NOR

iv) A+B+1=A)0

a super heterodyne receiver and explain the functioll of each(06 Mark!)

D) None oftheseoutput will be

b. Simplifu the following expression and implement using NAND gates only:

B) Double

B) AND ard OR

B)1

C) No charge

C) Both A and B

c) a+s+i

D) Both A and B

D) None ofthese

D) A.B.i (oa Mark)

(06 Mark)a truth table for the circuit given

00 Marks)

ii) AB + BAc. Draw the output waveform (Y and Y') and also prepare

below h Fig.Q8(cxi) and (ii).

i) XYZ+YZ+Z

4of4

2ma2

Fig.Q8(cXii)Fig.Q8(c)(i)

USN tof,,LNl5/25

3

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s

9:

-EE!F:,

q;

ET

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tU

i3

Ei

-l.i

z

First / Second Semester B.E. Degree Examination, June/July 2011

Basic EiectroniesTime: 3 hrs. Max. Marks:t00

A) 0.3V B) 0.7V c) -0.7v D)-0.3V

D) open

Natet l, .{n$wer ont FIVE full questions,'chooting a leost *oJfiom each parlL Ans*,er all objective We qaestions onl! it OMR shea poge i o1f the ansyter bookla.3. Ansr.'et to objective t pe questioLs orl sheets olher thor, OMR iill not be valued.

PART-AI a. Choose the corgct answers for the following :

i) Forward voltage across a condulting silicotr diode is

ii) Zener diode regulates only u,hen it is connected in mode.A) forward bias B) reverse bias C) shoi--

iii) l* for halfiryave rectifier is _A)+ B)+ c)2 'Jaiv) Peak inverse voltage lor bridge rectifier is

A) v. B) 2Vn

b. Deduce the following for FWR :

i) I-" irld" iii) Ripple factor iv) Effciency of rectification.

c) (04 Mqrkr)

(08 Msrks)

c. i) Calculate the ripple voltage ofa firll wave rectifier with a 120 pf capacito! com€cted toa load and load current of60 mA, frequercy of50 Hz.

ii) Ifthe peak voltage ofthe rectified wave is 60V, calculate the DC voltage.iii) Calculate the ripple factor. (0E MlIk )

Choose the correct answers for tbe following :

i) When a traosistor is ',rsed as a switch, it works in the following region :

A) active and cut-off B) saturation anicut-_offC) saturation atrd active D) none oftheseii) If the traDsistor aoplifier has voltage gain of i00, if the input voltage is 15 n0V, thentbe output voltage is

.... ! 1.:v B) l5v c) o.1sv D) 1.15viii) The phase difference betw€en input and oupui of an emitter follower is

.. A) i"*B:e B) out-of-phase C) 90" D)45"iv) An amplifier is generally connected in mode.A) sahuation B) cut-o{I

-c) *tir" D) shon (04 Mart r)

A transistor amplifier connected in CE mode has g = 100 ancl Is = 50 td Compute thevalues ofIs, 16 and o.Draw a skitch to show the various cunents in a

'.N tansistor aad d"dr". ,h" ,"lXl#;ffi

between various components. (r0 Mrrk!)

2a.

rs?',,[ c

"e\lG. uepE-2

I of 3

3a.

b.c,

4 a."

c.

(0d Mrkt)(08 Markt)(08 Mork)

10ELN15/25

Choos€the corect aDswen for the following :

il Which is the bias technique that is very widely used

" ;ifid *' -*'--' si"oti""tot c) emitter. ^ . . D) voltage divider

iil flfui"i tr"*i"t* bias circuit has poor stabitity b€cause its Q-point varies with p6f

A) collector feedback B) base

Cjvottage divide D) eminer

iii; Emitter follower is a

-.

'--' e) uortug" t-pru",

-

B) ourent-amplifier

C)attEouat$ D) oorc ofthes€ .

iv) E;tter followel hrs 8tr iEput of I volt, the! its output voltage ls --- ' .-' Arn{v Bllov C)lv D)5v (04 Mrrk!)

S*pf"ioG"-*n""pt of voltage diYider bias technique using tansistor'-,- - . (10 Mtrks)

;:.li;;;:; ;t'"",t-nas v, = 24v, RB = 180Ko' Rc = 33Fo Tg vcg = 10v'

A;;il;#;il" v"B when a new transistor is replaced having h6s = 120' (06 Mrrk)

Choose the correcl aruwers for the following :

i) The fitnction of gate in SCR is to conhol drc

-'' ei n"* "r",-"it

B) voltage regulation

C) volEge amPtification D) noDe ofthese

ii.1 1 ofUJT is known as

-

ratio'' A)oN B) Pulse

Cinegative - D) intrinsic sand-off .--iiil lie ;idmum Doint in V-l charactetistic ofUJT is knoru as

-

poun'-' ,a.i;;;d;-'-"'- sl uar"v c) latchitrs D) tubg

iul 'rG ""Fei,

rrr" "au"

oi v* ur t't'i"l 16 becomes essentially constant is the

' A) pinch-ofivoltag" ' B) cut-offvoltag€

cjit urao*orotig" D) ohmic voltage

Explain vl chaEcteristic ofSCR,Explain working princiPle of UJT.

b.c,d.

PART;-B

Choose dre conect aDswers for the following :

i) Cut.offftequencies ofan amplifier are also called as' A) haHpower points B) squale poirts

O amoiified points D) none ofthese

ii) fie objcctive of using a crystal oscillalor is to get' A)Dc B) 50'70H2-

i) stable fiequeocy D) variable &equency

O An oscillato! uses -' A) negative feedback B) +v€ feedback

Ci +v-e anrt -"e feedback D) none ofthese

iv) Which of the following oscillatoB i5 used !o gercrale hlgh fi€quencles 'A)RC-phaseshifr

- B)wielbride ...C) L-C oscilator D) blocking oscillator (04 Mrrkt)

e*ptnio tt. *o*iog ofRC coupled amptifier with its ftequency r€spotrse (0t M'rl6)

f*iiuio srtkho*oi "ritt.io".

- (02 Mrrkt)

tn u Hurttev orcillator Lt = 20 lt*, L2 = 2 tDIt and capacitor is variable Find the range of C

nt**i"y ir raril m. I Ilfozto 2.5 MlIz (06 Mrrk')

2 of 3

6a.

b.c.

8a.

Choose ttrc c-orrect aDswers forthe following :

i) An id€d OP-AMP hasA) infinite hput impedancac) zero ouQut Esistanca

ii) Ths differential amplifier has

A) one input ard one outputC) tu/o inputs and one output

B) infinite voltage BainD) all ofthese

B) two iDputs and two outpdsD) one input and two outpuls

10ELN15/25

(08 Mrrks)

D)A+B

D) none of these

D) a+B

D) 4 (04 Mrrk!)

c.

iir) An OP-AMP shorted betwern inverting terminal aDd ouhut termhal is called

A) adder B) volage follower C) iotegalor D) inverte!iv) The vokage gain ofan OP-AMP in the open loop condirion is ofthe order of

A) l0r B) l0z c) l0' D) l0' (04 Mcrkr)Draw the follou/tng circuits using OP-AMP:i) adder ii) voltage follower iiii integl8tor iv) ditrercntiator (0t M!rk)Explain the working ofCRT. (0E Mrrks)

Choose the correct atrswers for the following :

i) The two complement of (l 001)2is-.A) 1001 B) 0010 c) or 10 D) 10r0

D) 4loii) The decimol trumber 20 in hexadecimal code is

A) 41 B) 14 c) r40iii) The principle used to aa$mit the signal is

A) modulation B) de-modulation C) amplification D) attetruationiv) 9's complementation is used for

-.

A) additioD B) subtraction C) multiplication D) division(04 M'rl(3)

Explain the working of super heterodyne receiver with & suitable btock diaglam. (0E Msrk)Perform the followiag :

i) (l0t0l0lltl00;r=i?)5-(?)ioii) (240)ro = ( ? h = ( ? )ecoiii) (28)ro - (19)ro usiag l's and 2's complement methodiv) (1100), + (1111)z and (123)r + (126)r

Choose the correcr aaswers for the following :

i) Simplified form ofBoolean expression of I + AB is

C) AB+AB

C) A+B

A)l B) AB c) ABii) Expression for EX-OR gate with inputs 'A.' and 'B' is

A) A+B -

B) AB+BAiii) Simptification of AB is _A)A+B B) A+Biv) Full addor has _ inputs.

A) l B)2 C)3b i) R"ulize v=eet1g by using ninitoum number of NAND gates.

ii) SimpliS ABC+ABC+ABC+ABC and realize using basic ga&s.

c. Stak and prove Demorgan's theorem,

d. Simpli& XY + XYZ + X(Y + XY) .

(0t Mrrk)(04 Muks)

(04 Mark)

3 of 3

USN..

1OCED14

Max. Marks: 100

First Semester B,E. Degree Examination' Dec 2010 - Jan 2011

COMPUTER AIDED ENGIIIEERING DRAWINGTime: 3 Hours (GO OI{ TO ALL BRAI{C}|E$)

OfficeUse

Note: 1. Artswer three full aueslions3. Druw to actusl scale

2. Use A1 sheets suoolied4. Missing data, d any, rrroy be assbmed suitabb)

ll.92

19 Q 1. a)t

259 b)

118 b)

115 Q2.

218 03. a)

Apoinlis 40 mm behind VP, l5 mm above HP and 25 mm in fiont / behind / (10 Marks)from LPP .Draw its projections and name the side view.

The top view ofa line PQ 75 mm long measures 50 mm and the ftont view (20 Marks)measures 60 mm above HP and 15 mm hfront ofthe VP. Draw the

projections ofthe line and find its true inclinations with HP and VP. And

find distance betueen lhe end projectorsOR

A rectangular plate of negligible thickness of size 35l0mm has one of its (30 Marks)shorter edges i[ VP with that edge inclined at 40" to HP. DIaw the top view

if its front view is a square of side 20mm.

A hexagonal plramid 25 mm sides ofbase and 50 mm axis length rests on (40 Marks)HP on one ofits edges ofthe base. Draw the projections ofthe p1'ramid when

lhe axis is inclined to HP at 45" and VP at 30".

A square pyramid ofside ofbase 45mm, altitude 70mm is resting with its (30 Marks)base on IIP with two sides of the base parallel to VP. The pyramid is cut by a

section plaoe which is perpendicular to tie VP and inclined at 40" to the HP.

The cutting plane bisects the axis of the pltamid. Obtain the development ofthe lateml surfaces the trucated pyraqfd.

ORA sphere of diameter 30mm rests on the frustum ofa hexagonai pyramid (30 Marks)base 30mm, top face I 8mm side and height 50mm, such that their axes

coincide. Draw the isometric projection ofthe combined solid.

USN

Time: 3 Hours

1OCED14

2011

Max- Marks: 100

First Semester B.E. Degree Examination, Dec 2010 - Jan

COMPUTER AIDED ENGINEERING DRAWING(GO ON TO ALL BRANGHESI

Oflic€Use

320

Note: 1. Ahswer thrce full questions 2. Use A4 sheets suoolied3, Druw to actual scale 4, Missing dala, if any, may be assu ed suitdbly

1. a)i. Two Points P and Q are on HP. The point P is 30 mm behind VP, while Q is (10 Marks)50 mm in front ofVP .The line joining their top views makes an angle of40deg with XY. Find the ho zontal distance between their projectoN parallel

to XY line.

ii. Two lines AB and AC make an atrgle of 120'between them in their ftont

view and top view. AB is parallel to both the HP and the VP. Determine the

real angle between AB and AC.OR

b) An equilateral triangular lamina of 25mm side lies with one of its edges on (30 Marks)

HP such that the surface ofthe lamina is inciined to IIP at 60" The edge on

which it resls is inclined to VP at 60". Draw the projections.

Q 2. A hexagonal prism 25 mm sides ofbase and 50 mm axis length is suspended (40 Marks)fteely from one of its comers. Dmw the projections of the prism when the

axis appears to be inclined to VP at 45'.

Q3. a) A rectangular prism ofbase 40mm x 25mm and height 65mm rests on HP on (30 Marks)its base with the longer base side inclined al 30' to vP lt is cut by a plane

inclined at 40'to !{P, perpendicular to VP cuts the axis at its mid heighl,

Draw the development of the remaining portion of the prism.

ORb) A hemisphere of diameter 70mm is placed on the grcutrd ort its curved (30 Marks)

surface. A cone ofbase diameter 70mm and heighl 70mm is placed centrally

on it. Draw the isometric projection ofthe combination of solids.

(20 Marks)89

101

165

201

216

USN

.. First Semester B.E. Degree Examination, Dec 2010 - Jan 2011-. COMPUTERAIDED ENGINEERING DRAWING

Time: i] Hours (coMMox To ALL BRAI{CHES)

1OCED14

Max. Marks: 100

OfficeUse

11 0

Note: l. Answer lhree fall oaestions 2. Use A4 sheels suoolied3. Draw lo aclaal scale 4. Missihg dqta, d any, may be assurued saitably

1. a)i. Draw the projections ofpoiEt G which is in fi$t quadrant such that it is (10 Marks)equidistanl from IIP, \ry & PP. The point is 25 mm from RPP. Determine itsdistances liom HP&VP.

ii. A lire AB 60 mm long has one of its extremities 20 rlln infomt of VP and (20 Marks)15 rlrn above HP. The line is inclined at 25'to }IP and 40" to VP. Draw itstop alld f.ont views.

ORb) A pentagonal lamina of edges 25mm is resting on VP with one of its sides (30 Marks)

such that the surface makes an angle of60'with VP. The edge on which it.ests is inclined at 45'to I{P. Draw its prcjections.

Q 2. A square plmmid 35 mm side ofbase and 65 mm axis length rests on HP oa (40 Marks)one ofits edges ofthe base which is inclined to VP at 30". Dmw theprojections ofthe plaamid when t}le axis is inclined to HP at 45'.

O3. a) A pentagonal prism ofbase sides 30mm and axis length 60mm rcsts with its (30 Marl..s)base on HP and an edge of the base inclined at 45" to VP. It is cut by a planeperpendicular to VP, inclined at 40'to HP ard passing through a point oa theaxis, at a distance of30 mm from the base. Develop the rcmaining surfacesofthe tuncated pdsm.

ORb) A fiIstum of cone base diameter 50mm, top face diameter 25nrm and height (30 Marks)

50mm is placed centally on the top face ofa cylinder diameter 60mm andheight 60mm. Draw the isometric projection ofthe combination of solids.

59

129

166

213

274

, . 3 : - a. Select the correct answer :

i) Which of tha following are not valid identifiers?A) student_name B) _total C) 2Darcoes D)iff

ii) Which ofthe following are not character constants?

toccPt3l23

iii) Which field specification is used to read or write shoft integ€r?A','k B) yo6 c) o/of

A)'c' B) "c" c)'bb' D),?,

iv) Which firuction reads data ftom the keyboard?,d) displayf B) read C) printf

D) %hd

(04 MrrLs)

(06 M.rk)(0C M.rk!)(06 MxrLs)

4 a^ Select the corre.t arswer :

i) _ is used to det€rohe tlte order in which different operations in an expression 'are evaluatcd.A) Associativity B) precedence C) waluatiou D) format

ii) Which of the following is not a valid assigm€nt exprcssiof

b. Lisr. and explain coding constants.

c. What is variable? Explain variable iuitialization.

d. Explair the structure of'C' program.

A)assignment B)condition8l C)biraryiv) Which ofthe following has highest prEcederce?

A) prefix incrcueat B) Multiply C) Modulus

i) a+b/c'd-c/aiii)a++b-- + d++

n) Sta)%civ) #a+ b-- + +t

D) scanf

D) primary

D) Assignment (0{ Mrrki)

(0{ Mrrkr)

lsing the following

D) None of these.(04 Mrrks)

A)x= 23 B)4x=8=3' C)Yo/o: s D)x-r=Jiii) Which ofthe foltowing is not an exprcssio! format?

b. If a = 2, b = 8, c = 4, d = 10, what is the valuc of each of the fottowing?

ca,u = (ffi)rF,r*.u"it-rz) (08 Mrrk)

d. Convert the following mathematical expressions into 'C' expressious:

",1 ,.

'2

. PAR,T - B5 a. Select the correct aDswer :

i) A fimctiotr that ca.lls itseu for its processing is knoum asA) Inline fimction B) Nested firnctiotr C) Overloaded fimction D) Recursive firnction

ii) We declare a function with

-- ifit does not have any retum tlpe.

A) tons B1 douuF- C) void oj intiii) Variables inside parenthesis ofa fimction declaratioq have level access.

A) locat B) glob&l C) module O1 uni"ersAiv) Arguments ofa flmction are separated with

c. Wdte a program to convert temperat$e ftom Fahrenheit to Celsiusfonnula-

A)coErr(,) B) semicolon (;) C) colon (:)

2 of 3

10cw18

USN

Time: 2 fus.l

First Semester B.E, Degree Examination, January 2011

Environmental Studies

(COMMON TO ALL BRANCIIES)

[Max. Maxks: 50

/}IS TRUCTIONS TO THE CANDIDATES

1. Answer all the fifty questions, each question carries ONE mark.

2. Use only Black balt point pen for wdting / darkening the circles.

3. For each questiou, after selectitrg yonr answer, darken the appropriate circle

correspondiug to the same question number on the OMR sheet.

4. Darkening t\ o circles for the same question makes the answer invalid.

5. Damaging/overwriting, using whiteners on the OMR sheets are strictly

prohibited.

l. The lerm ecosystem was introduced by

a) Haekel b) Odum c) Tansley d) All of these

2. The short term properties ofthe atmosphere at a given place and time are refened as

a) Climate b) Season c) Micro climate d) None ofthese

Source of sr.rpply is calleda) Resoucesc) Substance available

A maior niaogen storage reservoir isb) Atmosphere

b) A means of meeting n""A, .,@d) Natural substance

a) fuver c) Oceans d)

5. The pan ofthe eanh in which life exists is known as

a) Lithosphere b) Biosphere

6. Enviroment meaNa) A beautiful landscapec) Sum total ofall condition

c) Atmosphere d) lonosphere

b) Irdustial Productiond) Ah ard water

7, The UN general assembly proclaimed the urliversal declaration ofhumar dghts in Pads inthe year :

a) 1948 b) 1992

-Al -

c) 1,972 d) 1962

8.

9.

The lead<r ofrte Chipko movement is :a) AtrbdtltaDevi b) Jashibhai parel

World ear& dav is :a) 7ii April -'

b) 56 Jrme

12. Taj Malal atAgra may be damaged bya) CO2 b) Chlorine

IJ. Troposphere hEs an altitude range ofa)ll-50km

c) Medha Patekar

c) 16th September

c) Chlorofluorocarbons

c) Hydrogen

c)20-80km

c) Exhaustible

c) Micro organism

c) 23%

c) All ofthese

c) Taste and odour

c) Temperature

c) Spanish

b) Sun and waterd) Mountain and water

c) Both a and b

c) Jhum

10cwr8 .

d) Vandhari Shiva

d) 22'd Apdl

d) Ali ofthese

d) Non€ ofthese

d) s0 - 200 km

d) Mining

d) Rocks and soiJ

d)25%

d) None ofthese

d) Irritation

d) All of these

d) Urbanization

d) English

d) Nore ofthese

d) None ofthese

10. Ecosyste6 has the following major components :

a) Plants. animals ard micro organisms b) Flora and Faunac) Producers, consumers and decomposers d) Bolh a and c

11. Which ofthe following is a green house gas?a) O),Tgetr b) so,

b)0-tlkm14. TaLngya systsE is

a) AgIo forestry b) Inexhaustible

15. Lithospherc meansa) Air b) Water

16, How much percentage of Jand is covered with forest?a)26o/o b) t9%

17, Human rcsource_ is sa) Renewable b) Inexhaustible

18. Excess fluoride in drinking water is likely to cause :a ) Blue babies b) Fhrorosis

20. The basic requiremetts ofhuman beings are provided bya) Industrialization b) Aglicultule c) Deveiopment

I9, Wlrich among the foliowing is a climatic lactor?a) Prcssue b) Humidity

21. The word "ecology" is deived Aoma) Greek b) French

22. Hy&ological cycle mainly involvesa) Air aDd &?terc) Animai ard B?ter

23. The forest isa) Abiotic b) Biotic

Most biotic rcsorEces area) Non renewable b) Renewable

24.

-A2

c) FoEst

c) Spanish

b) Climate factord) None ofthese

lOCIVIS

d) All of these

d) English

a) Soil b) Water

26. The word "environment, is dedved fr6ma) Greek b) irrench

27. Abiotic comporents include thea) Climate and edaphic factorsc) Edaphic factor

28, Natural ecosystem is called

29_

a) Anthropogenic b) Human activity c) Both a and b d) None of these

Hydrosphere denotesa) Water b) plads c) Microorganisms d) Soil

b) Thermal Plantsd) Hydroelectric plants

c) l" December d) 2"d October

30. Both power and manure is provided bya) Nuclearplarrsc) Biogas plaots

31. World AIDS dav is :

a) 1'r July b) 5h June

34.

Study trends in human population gowth and prediction df futue $owth is calleda) Demography b) Biography c) Kalogrprhy ,l a) p.y"lorogy

Name the species lo which human belongsa) Animals b) Plants c) Homosapiens d) All ofthese

What was rhe human population al tle beginning olthe 20d cennry?a) 1.2 billion b) 1.6 billion

"; t.t tittion d)2.0 biltion

38.

Ozone hole isa) Antarctica b) Kaulilya

Greetr house effect is related toa) Greeo treesc) Chlorofluorocarbons

Expand WWFa) World Wide LiG Fundc) Both a and b

Decomposers area) Bacteda and Fungi b) Reducers

c) Earth surdmit d) All ofthese

b) co,d) Methane

b) World Wide Forestd) None ofthese

c) Both a aad b d) None of these

d) All ofthese

d) None ofthese

39. Large rcgional rmit characterized by Flora ard Fauna isa) Biosphere b) Biome

40. One ofthe inexhaustible resources is

c) Ecosystem

. c) Solar energy

-,A3-

a) Minerals b) Fossil tuels

loclvl S

41. A distinct unit oflife itr natwe is: *a)Population b)Ecoiystem q) Organisms d) LanGcape

42. Name ofthe scientist who gavo the dilfereoce between }'{iche alld Habitat, is :a) OduD b) Emest Haeckel c) Grinnell d) Both'a and c

43. Construction of dams hasa) ODly merits b) OnlY demerits

c) Neither merits nor demerits d) Merits as wetl as demedts

44. The sequence of eating and being eaten in an ecosystem is called

a)Food-chain b) Hyclrological cycle c) Carbon cycle d) Anthropogenic

45. B.O.D. measuresa) lndustrial pollutioob) Air pollutionc) Polluting capacity ofef{luentsd) D.O. needed by mioobes fordecomposition

46- What is the unit ofmeasuemert ofsound?a) dB b) Decibel c) Both a and b d; None ofthese

4?, what is lhe percentage oxygen present in air?

a)18.08r/. b)21% c)71o/o d)'13%

48. Weather conditions determinea) Wind b) Tempenture c) Orgadsms d) Al1 ofthese

' 49. Soil conservation is a process in whicba) Soil is aerated b) Soil erosion is allowedc) Sterile soit is made fertile d) Soil is Fotected against loss

50. Expand E.I.A.a) Environmental Protection Act b) Environmental Impact Assessmed

c)Envirc n€ntal lEpact Adminishation d) All ofthese

-A4-

USN

06crv18/28

Question Paper Version : D

Time: 2 hrs.l

First/Second Semester B.E Degree Examination, June/July 2011Environmental Studies

(COMMON TO ALL BRANCIIES)

[Max. Marks: 50

INSTRUCTIONS TO TIIE CANDIDATES

l.

4.

Answer all the fifty questions, each question caries ONE mark.

Use only Black ball point per for {riting / darkening the circles.

For each question, after selecting your atrswer, darken the appropriate circle

corresponding to the same question number on the OMR sheet

Darkening two circles for the same question makes the answer invalid.

Damaging/overwrititrg, using whitetrers on the OMR sheets are strictly

prohibited.

2. Air pollution ftom automobile car be conholled by fitting

l.

5-

6,

Global warming could affecta) Climatec) Melting ofglacier

a) Eiectostatic precipitatorc) Catal).tic converter

b) Increase in sea leveld) All ofthese

b) Wet scrubberd) A11 ofthese

c) 1994

c) l8th July

3. About 3/+ ofthe courtries coal deposits are found ina) Kamataka b) Tamil Nadu c) Kashmir d) Bihar and Odssa

4. The water (prevention and control ofpollution) act was enacted in the yeara) 1986 b) t974

World Environment dav is on

a) 5ih May 'b) 5s June

d) 2004

d) 16ib August

d) Kidney

d) Kaiga

d) Marble stones

A chronic disease called 'silicosis' involvesa) Hea( b) Lungs c) Liver

7. Nuclear power plant in Kamalaka is located ata) Bhadravathi b) Sandur c) Raichur

8. Klrctri (Rajasthar) is famous forb) Copper mines c) Granite stonea) Gold mines

-D1

9.

06cIv18/28Vasectomy is the inethod of sterilization ina) Man b) Womenc) Both man aod women d) None ofthese

Which ofthe following is not an ideal solution for tackling the water crisisa) Drilling targe numbers of deep bore wellb) Population $ou'th controlc) Water conservation in irrigationd) Water pollution contuol

The study ofi[teraction between living organisms and elvionment is called as

10.

11.

12.

13.

14,

a) Ecosystemc) Phl4ogeography

Soil erosion can be prevented bya) Overgrazingc) Afforestation

Fossil fuels and metallic minerals arca) Renewable resourcesc) Non-renewable resouces

The area reserved for the welfare of wildiife isa) Nationat parkc) Sanctuary

a) Oxygenc) Chloroflurocarbon

22. The maximum number of irdividuals thatcalleda) Biotic potentialc) Population size

b) Ecologyd) Phl.tosociology

b) Removal of vegetationd) Deforestation

b) Inexhaustible resourcesd) None ofthese

calledb) Botaiical garden

d) Forest

15. Which one ofthe following is an abiotio componenl ofthe ecosystema) Bacteria b) Ptant c) Humus d) Fungi

17.

18.

16. Acid rain is called by increase in the atmospheric concentation ofa) Ozone and dust b) SO, and NO, c) SO3 and CO d) SO, and CO

Gas teaked in Bhopal tragedy wasa) Potassium isothiocymtec) Ethyl isocynate

Biochemical oxygen demand measuresa) Industrialpollutionb) Air pollutionsc) Polluting capacity of effluentd) Dissolved oxygen required to decompose orgaric waste

19. Which ofthe following is not a "green house gas"

b) Sodium isothiocynated) Methyle isocyanate

b) Carbon dioxided) Methane

c) Sulphur dioxide d) Argon

can be supported by a given environment

b) Carrying capacityd) Resistance

20. Study of trends in human population grouth and prediction ofi.rture growth is calleda) Demography b) Biography c) Kalogaphy d) Psychology

21. The ultraviolet radiation ilr the statosphere are absorbed bya) Ozone b) Oxygen

-t)2-

23,'thewortd"AlDS"dayisrecalledon 06CIv18/28

a) lsJuty b) 5'n June c) l't December d) 2d october

24. 'ICDS' is a welfare scheme fora) Public b) Women c) Men d) Children

25, The lalgest reservoir of nitogen in our pianet isa) Ocears b) Atmosphere c) Biosphere d) Fossil fuels

26. The wo d population in the year 2000 was arouoda) 8 billioa b) 6.1 bitlion c) 4 biltion d) 4.5 bi ion

27. Which ofthe fotlowing is the iil effect ofubanization?a) Decrease in agricultural land b) Loss of greeneryc) Loss ofwarer bodies d) All ofthese

28. Environmental (prolection) Act was enacted in the yeara) 1986 b) t992 c) 1984 d) t9'74

29, Which of the following is a biodiversity hotspot in Indiaa) Gulf of Mannar b) Westem ghats c) pachmarhi d) Sunderbans

30. In an aquatic ecosystem ph)-toplanldon can be considered asa) Consumer b) producerc) Saprotropic orgai sms d) Macro consumers

31. Which ofthe following devices is suitable for the removal ofgaseous pollutant?a) Cyclone sepamtor b) Fabric filterc) ElectIosraric precipirator d) Wet colleclor (scrubber)

32. What is the permissible range ofpH for drinking water as per the Iadian standarda) 6to9 b\6.5to7.5 c)5to8.5 d)6.51o8.5

33. Minamata episode of Japan is due to the poisoning ofa) Lead b) Nickel c) Mercuy d) Cadmium

34. Amor1g ftesh water availability oll earth, the percentage of grou[dwater occu$ is abouta) 0.2% b) o.so/" c) 0.8% d) 1.0%

35. Liquid waste generated from bathrooms and kitchens are calleda) Domestic sewage b) Runoff c) Sullage d) Allof these

36. Eutrophicalionmeansa) Waste water teatment processb) Neutralization ofwaste waterc) Enrichment ofplant nutrients in water bodiesd) Water purificadon techniques

37, EIA is related toa) Environmental and industdal activities b) Envionmental impact assessmentc) Environmenta_l impact activities d) Environmental intenBl activities

38. Organisms who directly feed on producers are calleda) Camivores b) Omnivores c) Herbivores d) Decomposers

-D3-

39. Ozone layer thickness is measued ina) Millimeter b) Centimeter c) Decibels

b) Methatre and hy&ogen sulPhide

d) None of these

d) Smallpox

b) Himachal Pmdesh

d) West Bergal

06CrV18/28

d) Dobson units

d) 1996

d) Dengue fever

d) None ofthese

44, Silent valleY is located ina)Andhra Pradeshc) Kerala

47. Electromagtretic radiation can cause

a) Plague b) Maleria

41.

40. Chemobyl nuclear disaster took place in the year

a) 1986 b) 1982 c) 1992

Biogas is gaseous fuel composed mainly ofa) Methane and carbon dioxideci Methane and catbon monoxide

42. The required iron oontent in &inking water as specified by BIS is*' ;il60';il"-".'"'-ui-lorgnli'lr*gnit d)0'30meAit

43. Which of the following is a water bome disease

a) Anthax b) Tuberculosis c) Cholera

45, Existing oil reserves ofthe earth could last for about

a) 5O0dyears b) 500 Years c) 50 Years d) 5 years

Water quality involves measuring the number of colonies ofa) iotliiorrrbacteria b) Protozoa c) cells d) Ckomozomes

c) Caocer

c) pH48-

49.

50.

Phvsical pollution ofwater is due to

a) Dissoived oxygen b) Tubidity

which ofthe following is not a palt olthe hydrological cycle

a) Precipitation -

b) Infiliration c) Transpiration d) Perspiratron

What would you do to prevent enviroEnental darnages

a) Plant hee b) Halt deforestalion

cj Control pollution d) All ofthese

-D4-

O6MAT21

3 a. Select the correct answer :t/r

i1 The value of J jxy dydx is

A)I B) I- c)I D)l''' 24 -' 48 ' 25 50

ll I = j Jdx dy represents the area ofriangle wirh vertices.

00A) (0, 0) (0, l) (1, 0)C) Both A alld B

iii) The tunction ,,6+1 is defired for allA) Positive integersB) Real oumbersC).Both A and BD) Real numbels except for negative fractions

/1 1\iv) The value of ttl j - .' I is'\2 2)

A)3.1416 B) 1.1416 C) 2.1416 D) None ofthese

r ,I-", (04 Marks)

b. Change the order ofintegralioo and hence evaluate J J v'a"af. (04 Msrks)oc

c. prove rhar pt*,oy = 6lE

B) (0, 0) (0, r)D) None ofthese

(06 M&rks)

(06 Msrks)d. show that t-L, t--gl- =-4.jJt-x' iJt+*' 4',12

4 a. Select the correct answe! :

i) If F = x'zi+xyj, rfren JF.ai , from 10,0) to (1, l) along the liee y = x isc

A)? B)i c) 2 Dt4'2 3

ii) Green's theorem in the plane is applicabie toA) xy - plane B)yz-plane C) xz - plane D) All ofthese

iii) With usual notations Gauss-divergence theorem st3te thal JfJdiv F dv is etiual to

A) J.JF.

nds B) IFxnds O IIF-a.ds D) None oftheseSS

iv) Cyiindrical polar coordinates (p, $, z) are given byA)x=pcoso y=psin$ z=1 B)x=qosg y=psinQ z=pC) x=pcoso y=psn$ z=z D) None ofthese (04 Mrrk)

b. find the total worl done b; the force represenLed Uf F-:rli-yjr:xzkir ooving a

paticle around the circl e x2 + y1 = 4 . (04 Mrrks)c. State and prove GrEen's theorem on the plane. (06 Msrk!)d. Express divergence of F, where F = xi - yj + z k in spherical polar coordinates. (06 Markr)

2of4