W lsqm-f I r-a'rtl Ev$

S"t : #rn- I -D"*r i tulo s):-o | 6QP Gode: 28579

ITotal Marks : 100

h€il/ 1ol{

REYISED COIJRSE(3 !"Iours)

^,J\.v ;{\l5*ts :

"- n i],.restioa No. 1 is compulsory.

: l Acemspt any three questions from question No. 2 to question no. 6.

:" figrrre to the right iudicate full marks.

Solne &e eqration Tcoshx+Ssinhx : I for real values of x

( u az\z-: z i'x---v): (x-y) find , * -T I\dx q)

"sz)tz\-w\\\

=]F^'n\-\\a<-J t>-'

1\r\

bJqI'j'

a-rv\,0(u, v)I:-':: Ccos2o , V: t' sin 2 0 nnaffi

p:ove tirat Seczx - 1+x2 *4* -.....5

. = -.:-,-:erivativesof cr;11_m{ _d

r\w-=\v

r){y

-.7\/\:\yv

{yI r :: q f, are the roots of the equatioq@i -2'13'x + 4 = 0

=:d rhe value of cr3 + Fr +U: Ltamine whether the vecotrs +'

Xr=[3 1 t],xr$'o -tJXr=[+ z 1] A"1,\

a- Lnearly independpff: (il State and prolp,Eulet's theorem for a Homogeneous function in two

variables. ^$'- '::i Ify=x$dfixd ttValue of xzu**+ Zxy u*, * y'uw

,O$r ITURN ovER

I\,*\<\\_

r.'.TFW€on.8276-{6.

\,--.\-r\

N"s

4

4

.-.:.: t-: rarl< of the Matrix by'reducing it to normai fonn gO.a_r-r I 1l {t

4

6

rl I 1l *.;

;I -l -Il .(rS13 I 1-l ,(r+-

QP Code: 28579

2

3. (a) Is the following system has trivial or non triviai solution ? Obtajn the nontrival soiution if exist.

3x.- 4x:- xr- 9xo:0?v-iwr-?v-?y:O.nl ) i1 LL3- J

^1-U2x,r- y-- l4x-- i2xr:0x,+ 3xr+ 13xr-r 3xo:g

(b) Discuss the stationary points for Maxima and Mininima of*:-1- xy2- l2x2-2y1 +ZLx + l0

(c) (i) If tan (x+iy) : a * ib prove that tanlr Zy = -$ -i + 3- * b-(ii) Separate into real and imaginary parts ef Log (3+4i)

:'\*5$>+*

orr\'s

-q\

t\11,r\J.)\\

,0Y4, (a) Ifx=ucosv,y:usinv

J,C,

*4, ?!*,rJ=, ...$sProve that ffi, AG{=. ;x-r. ^'r l- - ''(b) Show that togfeio -.'']=,"*j r""r(#)j-ffi

(c) (i) Solve rhe system of .iution uy cigpo;"rdan Methodx * Z,y * 62: ZZ, 3x+4yiz: Z6,Qlx - y - z: 19

(ii) Soive the system of equation.bp5dauss Siedel Method.Correct upto rhree decimal. (7"2x- 4y * 492= 49 X,43x+ 2Y + /$2:23 +\-/3x+53y+32=gl +-

- qv"s (a) Prove that Cos60*q$-d=]pcos+o+s]

.(sr- I'(b) Find the value of*Cnd b

:n r{i-u.ck;)-bsinx I.: x-ro-=r\" x'

(c) (i) ifF e* cos2xcosx find y^

{ii) .$-y = stan-rx prove that (tixz)y n*z+l2 (n+li x -' '.f/4

4

B*J_<\-

a-'\Y.^'il'

1tY,tY,^\

*,' Ftt€on. 8276-{5.

^V-$\.V\J

i]yn*, 'f n(n+l) y,:0

ITURN OVER

6

6

QP Code: 28579

3

Fi-i no:-Silgular Matrices P & Q such that, U $^ \J-I z 3 4l ,.)'

t{

^= ,2 1 4 ' I t, redued to normal form. Also find rank. ;S3 0 s -1ol .q\is'

v--'6-\\---- : r*5.4 5:-x e'-o'; find 3*3*P -h.

: Frr a sraight liae ro the following data , -aSFo1961 79i't 198l i99i

t2 6 10 15

c'{

/a..v\,1+/

r\-.x-(x

i:: a secoad degree parabolic curve to the following(9u ,

z)r

^\U1r'

-

T \. \./nY

'j"_C.o-

.tOV:.\,'

- q\"

'-\5/9'.c"

""-.F-(-/c

*r.H

_..$*n.g2TG-{6,

4 5 6 ,a\1,x-/\/ 8 9

8 i0 r1; i1 10 9

F E t(e*] l*"*-s !Ce{rS

i 'l H"l & 2c r6 / frricrlttlorl

QP Gode : 28584

r6

CN

{3 Hours)

3i.B-r i:-) QLestion No. 1is compulsory'

i2]Arer,rot any three questions frorn remaininB five questions'

{3;Assume suitable data if necessary and mention the sarne clearly'

i4ila<e g=9'81 rn/sz

i.1 a. letermine the resultaut of the forcss aoting as given in figure bolow.

arde which the resultant makes with the positive x-axis'

[Total Marks 80

'i\-.F

,"J.--\=:

Find the talot'.l'-\\srY{'

25N

.v. o spheres A and B are kept in a horizontai charure.l@et31r:rin1t:t "*:T t4l

ai jiCmm respectively. Take Wa =500 N and Wg!

rJ*-* lzornrn--;{

t>-\q\HJ

nYt{'

nVt)^v-.U

')\\/-\tlJ

\-./

,^(): l,:iine Angle of Frictiq?SrAd Angie of Repose

:. Car A starts fro* rq$b accelerates uniformiy on a straighi road. Another car B

stans from tire .qde place 5 seconds 1u*g; r','.:h ::::iai veiociry zero & itr.---.eierates uqi€Nty ai 5 *is"r'. If buih :h; cr;s o'reral<.: at 500 rn frorn the

stardne nlace-End the acceleration of car A"

, Find ,,{. dfui; the force P makes rvith horizontai such that the block of mass 4

i; ;.r-6r)f"celerarion of l0m/sec2, when it is sublectecl to a force of 35 N.

:rs =&91 rrk:0 6.r:- -?A-V

,-,+ \- "- iTtrRNovER.

'bk

t4lt4l

[4]

+-,F^\).i/

FIY-Con, {O{{g'16'

ITURN OVER

QP Code: 28584

Q.2 a. Repiace the force system by a single icrce ri' :. 'io poi:rt C

20N/m

i- 3m J, 3m +o 6rn -r.i Saoot

b. A unifonn beam AB hinged ar a is kept horizontal by supporting & setting " -{Ei100 N weight by using a string tied at B & passing over a smooth pulley at C- c-FThe beam also loaded as shown in figure beiow. Find the reactions at a &

QY--

2

l5l

A -:\-

rl\'/^V

rL/'?s

AH--- 3m

I

______-+{

r\'s/c_ Prove that for a perfectly elastic body,($wo equal masses participating in

^^lIi.in-o-^1"o-ao+hor'.,.lnnifiec ^Xcollision exchange their velocities. O*Q.3 a- Fino Centroid of snaded area with,rSf"rence to X an-d Y axes.

{'+ .V! -' -CfI \-/tr

t6l

l8l

i.\5-. ^e-: \Cr-rv\.c-' I

.'+r'- i t0Cnr

c}* t ---z?7,4/4-* "'*)" 0'

=\b. @ the resultant of the spatial ccncur:ent fbrce slrstem concurent at A(1,0,0)

$d passing through point.s B(-i,-?,5). C(i,5,?), D(0,4,0). Ir,Iagnitude of forces

rI,,'F^e= 100N, FAC =i50N. Far:200N^\i

<i)'

I6l

\4\\

i>\'\\.

,^./:

r^!^\,.$' Fll\l-Gon . 1O1{ 9-{ 6.

\-

i , 3m o[o_ sm i+ :rn. - - *l

ITURN OVER

QP Gode r 285843

A coliar of mass 1 kg is attached to a spring aci siides without friction along a i$lc:rcular rod which lies in a horizsntal plane. The spring is undeformed when the .*'ccliar is at B. knowing that the collar is passing through the point D with a b 'soeed of 1.8 m/s, determine the speed of the collar when it passes through ,',)point c and B- Take Stlffness of the spring, k= 250 N/m, Radius of the circular ,ivpath = 300 mm and distance OA = 125 mm.

^F.'\..\\^u'$

-v-D-J

+'" r;\'

ov./+/

1V€,+-,\)

Q.4 a. Find the reactions at supportsfigure below.

1,vA and E for the beamloYCed as shown in the I8l

ITURN OVEi

.9"A fighter Plane Moving t orlfiYf fy with a ccnstant velocity oi 200 nr/seconds releases

a bomb from an altitude-oF-4OO m. Find the vebcitl'arc ,jirect:o;i of the bomb just4 Uulltu !ulll ol @Lrluuu/-uHvv

beforp it strikes the ggr{aa. Also deterrnine the cistanre travelled by the plane before

'Jre bonrb just strikes ft*lround.Find veiocity of Cgrh point D at the hstant sh*',n ,l.s : I rad lsec ciockwise'AB:400mm. .1i

^\v(1 ' hU

lDl

i6l

.c.' *t,$' -\ay \'*-

-O-A\\- t- \+.{-a\*/1. 3-J

Slu '{-'I \..p' ['*^ \

3" "--I------------------ --l\-f

1$.,Fjs'}J.r:

FW-Con, 1 O{ { 9-{ 6.

:

8P Gode : 285844

Q.5a.FindtheforcesinCFanclCDbymethcdofs:":i;':'::::|:::r:aiiing:yN{ethodoftSl.Joints"

*:iF

L-^v\

z)vr\-z.-\

=.\H\

Q'+-

H\

\F

6.-\

n\x-

Tikn

_t-\1/n'

^\-/is as shpqpin figure t6l

.s"ti

(9"u mls

b.

B

Foravehiclemovingalongastraighttine'v-tdiagrambelow. Plqt a-t & s-t diagrams for the given time period'

t rec

A rr.,heel is rolling along a -straishtqf#,w':1*',::lOiT'netermine

velocitv of

points A,B and P. Op = aoo**Z-QXo raci/sec' vo = 4rnls

tol

\+I .J1B't*-'-

.\ i o Ir3\i.$\/o\/-\a)(J

-,4.6 3. ",c;

of magnitude 500N is acting from ,4{2,3.6) and passes through a point i4l

e$i, Oi' Ccmpute its moment about point C(4' 6' 3)'l>'r\c

6v

lruRN OVER

FW-Gon' 101 19-16'

QP Gode : 28584

5

A stone is thrown with a velocity (u) m/sec at a:r angle of 200 with horizontal ftom a t4lpoint 2 m above the ground. The stone strikes the ground 5 m away from the originalposition- The rnotion of stone is subjected io gravitational acceieration & windrx:s+-ance of 0.82 m/sec? , opposing the horizontal motion. Detennine the time of flightof the stone.

A heary metal bar AII rests with its lower end A on a rough horizontal floor having t8]cceffioient of frictian pr& the other end B on a rough vertical wall having ooefficiontcf ficdon irw. If the cente of gravify of the bar is at distances a & b from tho ends A& B respectively, show that at impending motion, the inclination of the bar with the

-i-- --.1 ,, il''^..

.iNV,s

\b

'ry+-rI

mil-li(

---d

6-

ts

Iu-,r

a - bpvltwd+l)

a'r\\-

\1rt)r

l4l

.1 r\

,di'r(zTr,, o masses are interconnected with t*he pulley sy'pSNeg,ecii:g i:.cr..r. & fiictional:ffect of pulleys & cord, determine the acccleqlgflcf the :nass m;.

Take m1= 50 kg & mr:40 kg , o..

FW-Gon. { 0119-{ 6.ro'

slo'$

i

I - r a.I :r crl,.t- fuo t at-rfuf'u

EF Sl-=lq-I.l-

( A t-t-) S"-b I AP -T-

QP Gode: 285O3

:( 2 Hours) [ Total ]Vlarks :60 . '''.

i, t: ,, n\

:i.B.:(I)Queetionno',tr,isciimpulsory.l:.;.::.^;(2i, Ate:rpt rluy three gtrestiol$'from'Q:2"t+ Q'-6' ' r<tr"

(3) Use suirible dati urler v* t";;;'-i :' - t-\si4 y-:.to*,1,*ti,d:€atetuIl*If ,,,, ,,, ,:.,,,,,,... ,. r . :, - ,,: :

,o"qi-{cemgt my Eve from the follorving:-

,

,.al Draw (a) ' i tl Z1 461 (0 14 O) ,,(c).

:[O'-4.CI] wi& refeib# tc 'ir cnbicl unit "e1L

V-\'

ron being therm"Uy p'o*o'ed to the "ooau"t1#'t.: .*td

is rhe probabiliiy of an'elect

baad in diamo.ad 11 i7oc, lf thq Uanagap, i1 5 '6 , 9\' *i1:'^--^ ^^ -. , ' -- frt :

' '

{sj o=4"* aiA ;r*t"{ 9ifq"9n or:rryry.a1! ryobifiU oj charge caffierf '/at-,

,st \rtat is di"te;;;o1i#ation and diotreotuic silsieptibititvt write-$$*elationl

oetweenthem. ,: .sDC{raYgClI l{fvs. : ."-. : ' . ;.

: Si::e and explain Ohm's law in magnetic circuil' '

!.i. ,.

in solids

"'',' . ', ,af.., -:-; T;r;:l;i"rmula ard exptain?* u.rr,, used Lr it. (-: !- - ^-:^_: carcuiare the tength of an iron rod which can ire used;poroduce uitrasomc

LafcLIatE ue tvuSu

waves of Z,ak1lzGiven - y = 1 1,6 x 1010}Ii*', O 1 1.1s0'o*,'*'classrfication on the 8

FHJ-Con' 12035'16.

',1etomlc !

alornic

*tgtt"rsi*:.Draw u uystrr.rpd6p for ferromagnetic material aud expiaiu I

-: .li Ilaer is hysteresls'J ljraw a nysre Ua'arous important paramsters' ( '-* *-g""tii material a51v maErretizatioo. o-f 2300 Alm and produces a

ftc deosit-v "flo.o

oi * *i7-Lffi--irtt mapetizine fc,Ice aBd relative petmeability

of the marerial. ...,\,-: Eqlais a"'J,.**t l€dtal act as three dimesional grating with X-rays"' 7

ftono.troa$? X-ray beam of wavelength L = 5.8189 A0 is reflected

, " ffig angle of 0 = 75.860 in f*st order by ce*ain planos of

mcc- o, r*i@ffi, g;;. pou*rioe Miller indices of the possible reflecting

:;e33S' rrf- +L/

, !" n rrg;p}.r. Fiad the value of criticai radius.ratio for ligancy 4' 5

,,-!,: *ap$rriry- of 0-01 ppo is -added

to Si. The semiconduotor has a resistivity of 5

,]5yrE ,rioor crr*oiat" &e hoie concentration aod its mobility' Atouic weight

t$t, is 28.1, drrrsitl of gi=2'4v103kg/m3 -^.,^-i-^+i^-o-,{ramqtF g=pr"u ee c'igin of eiectsric, ionic and orien:ationalpolarization andtemperatrrre 5

i5- +rp*A"".r1lr"rpective polarizability. t TUm,.[ OVER

.l;.

GP Gode : 286$3

\-c+

o\\<.Dh-'

5.(a)

6. (a)"

(b)

(o)

(b)(c)

The densif of copper is 8980kgim3 a:rd unit ceil dimension is 3'61 A0' Atomic 5

weight of copper is 63.54.Determine type of crystal strucfi'ue' caiculate atomic

ruai.L and iaterplaaar spacing of (1 I 0) plane' rr-,-^r1^.r ri^-a* s .,Q

What is HaO effect? D"i"; t*!r.rri* fo, faU voit"rge with neat labelled diagram' si*'Explain how the roverberariia time is affecte<i t v fU size (ii) nature of wd\a',*rifo"" (iii) audience in an auditorium'

-.=Y-^v--Esrimate rhe ratio of vaoancies at (r) -1190C (ii) 800C where alerage rt$'ed 5

to create vacaosy is L.8eV' {A

IIow a p-n juncrion diode is used to generate a potential. difference in uj5PKoftui" S

solar ceil? r\-/

Explair with naat labelled diagram the coabtruction and workingqspiezoelectric 5

,\Josciliator. {I(nt/\v

,r\-/Y

tYt-*-z.rN

,+-xf

.9:,b'

,-a+.VLJ/

lt

AJJV

;-.$

aY,tt)

.(":\-/r\l

rv

-\-..\J\

rF.v(i"

N\

^SirH.

-(Ns.l'FHf-Con. 12035'16.

;!':\"

$)1)r\ii

2

!r=tr f ,*t-t'| ctrs9s I semll*u Y -Ju.,^r- &ot{. il bf*,,

Chapter-1i of the Environmental Protection,St 1986?

(e Which are the various renewabie sources,S-nerBY?

(g) What is the role of technology with t5$d"t to environment and

health? $',,c

?. Answer the following:- . C*(a) How is environmental "4{fution

important for sustainabie

development? ^iy-(b) What are the constituen6rlfi tire municipal solid waste?

(c) What are the limitati&fu of conventional sources of energy?

ic3. Answer the foliowing:- ..-Ft

(a) How ozon..1*.$tti"g depleted from the atmosphere? Explain with

chemical,$bdtions.(b) What uryfii important functions of Central Poiiution ControlBoard?

(c) fxplslfre main aspects of Disaster Management Technique in detail'

=\"4. Answer q[Sfoilo*ing,-

(*NOVnte a note on depleting nature of environmental resources-

.E minerals.

-V'Ul What environmental clearances are required' to set up an industrial

iS unit?

$t (c) Explain the working principle of generating electricity by using wind

,,\ energy.

Sul, I EV S

Q.P. Code : 28604

(2.Hours) [Total Marks : 60

N.B. : (i) A11 questions are compulsory.

{2) Answer any three from Question No 2 to 6

+(j) Draw neat diagrarns wherever necessary ^Fq'.\-\\{\s,.

-. Arempt any five from the following: - ._f ' l)

(a) Discuss the global environmental crisis. +-fib) Explain in briefthe concept of socio-economical aspect of sr2sAiilable

development. - C"

(c) Discuss coaguiation and flocculation in water treatmS@t

(d) Define the term "Noise Pollution" and explain its p,$)ses.

(e) What are the general powers of the Central G(bdnment stated in

^,-t"6\.r\zI(",

15

st' FW-Con, 122910-76,(1..Q-

\

TURN OVER

s3

Q.P. Code : 28604

2

i. Answer the foliowing:- 15

(a) What do you mean by "3R" with respect to sustainable development? S'(b) What cio you understand by ''Green l{ouse Effect"? ,q"(c) State the working of Photovoltaic Celi used for solar energy, _+*

qY

6. Answer the following:- "$(a) Discuss the importance of Environmentai Study

" tr{t(b) Draw a neat iabelled diagram of "Venturi scrubber" and bgfitsworking, -{.,

ic) Explain the terms Tsunami and Earthquake, OUr\J

.x\r)\(?-

$\,

^s<,.S

$_/1r\-

(.Yrr)L-/

O,(qu.k"

dI)r\.Uv.\v--

rrYY,-")d/,\.V

.-Uc--Li

-r*'..Lit>'r\

\tJr1\)

ky\rf$.v-

\:-AA\r1\^.bn

iq"Y

Fll\l-Con,12290.16.

tf SqnnTCroses) Fr'tn h*ti faetr

.ADa.[r-: -'t+ls{te

Q.P C':cie:28592

(2. F{ours) i Total [4arlcs : 60

N.B" : (1) QLrestion No. I is compr,rlsory.

(2) Answer arry three questions from renrainiug five cluestrons.

(3) Figure to tlre right indicates luli nrarks. -q(4)Atomicweights: Ca=40, lvtg:24,C1="35,5.S:32, I-i= l. C= i2. {'\

C=16. i\"FJ

+Y:. Atternpt any five from the following , ^O*'

15

(a) Write two baianced equations to describe tiie changes.Sil occurwiren hard water is boiled. ,+"-'i ci,a 1's656ns to explain why naturatr r'ubber needs vpt$)nization..- i UlYv lwsJUI]J Lv v Plsrrl YYIIJ ll.tlu!cL! rrtuuv.

)S-f *.,,-*-

,.c) Give the preparation and uses of silica bricl<s" <y

id) Give the number of phases in tlre following tyg@., (arrv tirree) :

(i) Sarurated soiution of NaCl ,J&*'(ii) Mixture of rirombic and nronocliniq$phur(iii) Ivlixture of O, and N, -:,C(iv) lce * Wut"r rqJ'ilibriu,"^UO>-

:.ei What is grease ? What are llre cor4lltlons irr whiclr greases are used?

,.1 Thermosetting poiymers .a,rq$?-be reshal:eci ancj reuseci. Givereasons. ,-\*

:gr Caiculate the COD of an Ghluent sarnple it Zlc.c. of the effluent

sarnple required 8.3 ag1h,f 0.00iM I(C::rO- for oxiciation.

I ,2., rl:lguiate the ouanti{ g$h- and soda requirecl fbr softening 50.000 L of',r.'eier ccntaining foilU$inS salts per Iitre.

Ca,"HCO.).: i6.2Ifb; Mg(l{CO,), = 7.5mg;,laSC. : i3.6T{.r\" MgSoo : 24.onrg,

:.i=C,- = :C'0€.

^-C=: :>::.ailP following terms :

.:r .$dnciensed Phase rule

'::,firiple poinr

*r1.1$5o, are carbon nanofubes ? Describe the laser methoci of preparation of 4

3['cxr'$

9qb:

24 l€

c-r

A\--Y6Q

V

'+\'-_\'r:rr

A/1\A\

^.6'soNt

Fhl-Con. 11225-16.TURN OVER

)

Q.P. Cocle:28592

j.(a}(i)Discusst1remechanismofExtremepreSSureIubricatiorr(il) Name any f,our additives in blended oi and give two exarnples of 6 ,Jieach. S-(b) Desuibe a rnouiding method suitable for ihernroplastic resins" aF(c) Discuss the limitations of plrase rurle.

=S'*rY +

(ai Give the preparation, properties and uses of (any two) , &f(i) PMMA (;i) Siiicone rubber (i;i) BunaS" q G

(b) Wlite brief notes on any two nretirocis of disinf'ecting municipatr w$''rvithreactions. ^vU 5

(c) 1.5g of an oii was saponified with 50nri of 0.1N KOI-I srq\ri;on Afterrefluxing the u:ixture required 7.5nrl of 0.1N.dCl fol ne,4p)isation, Find 4

the saponification value of oii. "^"*-+"

(a) Draw a neat diagram of rctary l<iin in the manr-rfa@)e cf portlan,j cernent

and rnention the reactions in each zone. _r)" 6

(b) Wirat is giass transition temperature ? Whate(dthe factols affecting glass

transition temperature ? What is its signifiqtte ? s(c) The I'rardness of 10,000 litres of a watgqbAnrple was completeiy removed

by passing it through a zeoiite ,oft*nq{Xl. .oft.n., tlren required 4001itres 4

of sodiurn chioride soiution cont4ipltig 1C0g,/i- of NaCl for regenelation.

Calcuiate ilre irardness of the vra6$/sampie.

6. (a) (i) Discuss the softeni"*#O'-r**eneratiorr leactions in the Ior.r-exchangesplccess. .J(ii) Discuss tire Re.r€rX Osmosis rnethod of'purificatiorr olwater.

(b) Explain the functi,q$:of the following constituients in tire compounding ofpiastic (any twof(i) Plasticiofi (ii) Lubricants (iiii Stabiliser.

..c) Define anagliain the significance of the folio',ving propei'ties of lubricarrts

(ariy twqf\(,) .Stf, and Fire point

{ii)fXcict value

.S" viscositY and

A,^\rl 7

^\./.v'.\'FW-Con. 11225-16.

viscosity index.