GATE Chemical Engineering Solved 2012

8/22/2019 GATE Chemical Engineering Solved 2012

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Q. No.1- 25Carry OneMark Each

1. Consider the fol lowing set of l inear algebraic equat ionsX1 +2x2 + 3x 3 = 2X2 + X = - 12x 2 + ~ x = 0

The sys tem has(A) A un iquesolu t ion (B ) No solution(C ) An infin ite number of solut ions

Answer : - (B )(D ) Only the tr iv ial solution

Ex p _ ~ ~ ]- R""'---=-zR=---?[H -; ]ra nk(A ) = rank (A/ B) = 3So syste m Is inconsistent and has no solu t ion

2. I f a and b are arbitrary constants, then the solu tion to the ordinary dif ferent ia ld2yequation - 2 - 4y = 0 isdx(A) y= ax+b (B ) y = ae -(C ) y = a sin 2x + bcos2x

A nswe r :- (D)(D ) Y = acosh2x + bsinh2x

Exp: - Let us solve it from th e op t ionsd2ydx 2 - 4y = 0; d (s inhx) = cohx; d (coshx)= sinhxConsider option (D) , y= a cosh 2x + b s inh 2x ; dy =2a s inh 2x + 2b cosh 2x ;

dxd2y- 2 = 4acosh 2x +4bsi nh 2x = 4ydx

3. For the function f(t) = th e Taylorseries approx imat ion fort


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4. A box containing 10 id entical com partments has 6 red balls and 2 blue balls . Ifeach compar tment can hold on ly one ba II, then thenumbersof dif feren t possiblear rangements are(A ) 1026 (B) 1062 (C ) 1260 (D ) 1620

Answ e r :- (C)Ex p: - 1 2 3 4 5 6 7 8 9 10I I I I I I I I II I

Total 8 balls an d 10 p laces . lO p 1QIPoss ib le arrange ments are -- = -=2606! 2 ! 6 !2!5. Considerthe following (2 x 2} matrix

Which one of the following vectors is NOT a valid eigen vector of the abovematr ix ?(A) (C ) ( _ ~ ) (D )

Answer :- ( D)Exp:- Let us solve th is question f rom options

Opt ion ) = ( ~ ) = is ane igen ve cto rOption (B) : ~ = t-:J 4 ( -12}s an eigen vecto rOpt io n (C): 4 0 4 = 1 6 ) = 4 ( 4 ) is an e ge n vecto r0 4 - 3 - 1 2 - 3Option (D): ~ ~ ~ = ~ = 4 ~ not an ei ge n vec to r, s in ceei gen vectorshould be a non - zero vector, e igen va lues of A are 4 ,4

6. In a throttling process , the pressure of an idea I gas reduces by 50%. I f CPand Cvare the heat capacities at constant pressure and constant vo lu m e, respect iv ely( Y = ~ J,he specific vo lume will change by a factorof(A ) 2

A nsw e r :- (A )(D ) 0.5

7. I f the temperature of satu rated water is increased Inf in i tes imal ly at constantentropy, the resulting sta te of waterwil l be(A) Liquid(C) Saturated vapour

Answer: - (B)

(B) Liq ud-va pour co existence(D) Solid www.examrace.com


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8. In a para lie f low hea t exchanger operat ing understeady state , hot l iquid entersat a temperature Th,in and leaves at a temperature Th,out . Cold liquid ente rs at atempera ture Tc,n an d leaves at a tempera ture Tcout . Neglect any heat loss fromthe heat exchanger to the surrounding. If Th,in >> Tc,in , then for a g iven tim eInterval, which ONE of the following statements is true?(A ) Entropy gained by cold stream is GREATER than entropy lost by hot stream(B ) Entropy gained by cold stream is EQUAL than entropy lost by hot stream(C ) Entropy gained by cold stream is LESS than entropy lost by hot stream(D ) Entropy gained by cold stream is ZERO

Answ er:- (A)9. For an exothermic re versible reaction, which one of th e following corr ectlydescribes the dependence of th e equi l ibr ium constant (K ) wi th tempera ture (T )and pressure (P)?

(A ) K is independent ofTand P(B ) K increases w ith an increase in T and P(C ) K increasesw ith T and decr eases with P(D ) Kdecreases w ith an increase T and is independent of P

A nsw e r :- (D )10. Water Is flowing under laminar cond it ions in a pipe of length L. I f the d iameter o f

the pipe is doubled, for a constant vo lumetr ic flow rate, the pressure dropacrossthe pipe(A ) Decreases 2 times (B) Decreases 16 t imes(C) In creases 2 tim es (D ) Increases 16 t imes

A nsw e r :- ( B)~

Ex p: - For laminar f low, ~ = 3211VL = Jtri 128 1J.QL[}? [}? ltD4

[V = Volu metri c fl ow ra te = _g_ = 4Q ]

Cross sec t io na a rea of pipe 11:o21:::> ~ a D4 (for canst f low rate )

11. The local ve lo city of a fluid along a stream line can be measured by(A ) Pitot tube (B) Ventur i meter (C) Rotamete r (D) Ori fice meter

A nsw e r :- (A ) www.examrace.com


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12. For un ifo rm laminar flow (in the x -d irect ion) past a flat plate at high Reyno ldsnum ber, the loca I boundary layer thickness (o) varies with the distance alo ng theplate (x) as(A ) o c x11 4

Answer :- (C)(B ) o oc x113 (C ) o c x112 (D )o c X

Ex p :- For a fl ow over a fla t p late , the loca l bo und ary layer th ickne ss (o) var ies w it hx0 5 for Ia m in ar f lowx0 8 fo r f u lly deve loped t urb ulent fl ow

13. I n a mix ing tank operating at very Rey nolds n u m ber (> 104 ) , ifth e d iameter ofthe impeller is doubled (other condit ions rem aining constant), thepower requiredIncreases by a factor of(A ) 1/32 (B ) 1/4 (C ) 4 (D)32

An swe r :- ( D)Exp: - Fo r m ix in g tank,. ~ ~ ~ ~Power requ ired , P= k r n LJ .p => P2 = (P1 ) Di =(P1 ) (D) =32P114. Fo r heat transfer across a so lid fluid in terface, which on e of the following

sta tementsis NOT true when the Biot number is very smal l compare d to 1?(A ) Condition resistance in th e solid is very small compared to convectionresistan ce in the fluid(B) Tempera ture profile w ithin the solid is nearly uniform(C) Temperatu re drop in the fluid is signifi cant(D ) Tempera ture drop in the solid is significant

A nswer :- ( D)Ex p: - Blo it num ber = ~ -t chara cte rist ic leng th

Condu ct ive res istance in so l id= Con vect ive res istance in f lu idOf Blo t num be r (z) , conduct ive resistance is small .:. Tem pe ra ture drop in so l id isno t s ignifica nt.

15. A so lid sphere with an init ial tem pera ture Ti is Immersed In a large therm alreservoir of tem perature T 0 The sphere reache s a steady temperatu re after acertain time t 1 I f the radiu s of the sphere is doubled , th e time re quired to reachstead y state wi II be(A ) ~ (B) ,S_ (C ) 2 t1 (D ) 4t14 2

An sw er :- ( C) www.examrace.com


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Exp:- We know,T - T 0 ( hA tJ::-----'=- = exp - - -T..,- T0 mcp

Here A = U7tr2 : m=pv = p ~ 7 t: The fi nal steady state tempera ture is samefor both the cases,exp ( - hAot tl)= ex p ( - A ~m1cP m2cP~ A 1 t 1 = A 2tz ~ 47trf t1 = 4 X ri t 2

m 1 m2 ( 7trt) P ( Jtri)P~ .!.!_ = ..!L ~ t2 = (t l ) r2 = ( t l ) ( 2r ) = 2tl ~ t 2 =2 tlr1 r2 r1 r

16. I f the Nusse l t number (N u) for heat transfer in a pipe varies with Reynoldsnumber (Re) as Nu ex: Re 0 8 , then fo r constant average ve locity in the pipe, th ehea t transfer coeff ic ie nt varies with the pipe dia m eter D as(A) o-u (B) D-o.z (C ) D0 2 (D ) [ i8

Answer :- ( B)Exp: - Nua Re 0 8 ~ - ""D ,.. V ~ D

KhD v o.apo.sDo.s~ - a ~ h a v o.s po.s D-o .2 KK J..Lo .a:. For constant avera ge ve locity , h a D-a2

17 . In the Mc-Cabe-Thiele d ia gram, if thex-coord inate o f the point o f intersection o fthe q-l ine and the v apour- liquid equil ibrium curv e is greater than th e xcoordinate of the feed point, then the qua l it y of the feed is(A) Superheate d vapour (B ) Liquid below bubble point(C) Saturatedvapour (D) Satura ted liquid

Answ er :- (B )Exp : -

y

X

(1) = Liqu id be low bubb le point(2) = Saturated liq uid(3) = Mixture o f vapor and liq uid

Vapor and liquid(4 ) = Saturated vapor(5 ) = Supe r heated vapor

:. The prese nt case falls under t he case of (1) www.examrace.com


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18. For which of the follow in g combinations, does the absorption operation beco megas-fi lm controlled?P. The solubil ity of gas in the l iquid is very highQ. The solubil ity of ga s in the l iquid is very lo wR. The liquid -side mass transfer coeffi c ient is much higher than the gas-sidemass transfer coefficientS. The liquid-side mass transfer coefficient is muc h lower than the gas-side

mass transfer coefficient(A ) p & Q

A nsw e r :- (B )(B) P & R (C ) p & s (D)Q & R

19. The haIf -life of an nth order reaction in a batch reactor depends on(A) Only the rate constant(B) Only thera te constant and the order of th e rea ctio n(C ) Only the rate constant and in i t ia l reactant concen tration(D ) The rate constant, in i t ia l reactant concentratio n and the order of the reaction

A nsw e r :- (D)Ex p: - Fo r an n th ord e r reaction , - dcA = k Cd t

d cA JcA dcA J, t 1 1:::> -- = kdt :::> - = kdt:::>--- = (k ) (1 - n)en c en 0 c l +n c t+nA AO A A A0For ha lf li fe , t = t 112 and CA= CAo2:::> 1 - - 1 - = kt 1 (1 +n) :::> - 1- [ 21-n- 1] =Kt 1 (1 +n)

(c )-l+n c-l+n - c l+n -~ A 2 Ao 2

2

(0. sn-1 - 1) ct l =2 k (n - 1)

20. Consider the reaction scheme shown below:A : : ~ . ~ - ~ k ~ cBoth the reactions are first-order. The activation energies for k1 an d k2 are 80and 20kJ/m ol 1 respectively. To maximiz e the yield ofBr It is preferable to use(A ) CSTR and hig h temperature (B ) PFR and high temperature(C ) CSTR and low tem perature

A nsw e r : - ( B)(D) PFR and low temperature

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Exp:- For g ven reactions,dC 8d t = K l CA - K 2CB A _K-'- '---4 B

_ 80 x l0 3 20x103_ K e e.3t4xT c - K e -B .3t4xt c- 10 A 20 B

K2 l C

:. High temperature and high concentration o f C A Is needed for ma xim um yieldo f B.

21 . In petro le um refin ing catal y tic reform ing is used to co nvert(A) Paraff ins and Naphth enes to aromatic( B) Paraff ins to hy drogen an d carbon monox ide(C ) Ga s o il to diesel and gasoline(D) L ight o le fins to gasoline

Answer :- (A )22. The final boiling points of gasoline, diesel, a tmospheric gas oil (AGO) andlubricating oils vary as

(A) Gasol ine > diesel > AGO> lubric ating oils(B ) Lubric ating oils > AGO >diesel > gasoline(C ) AGO> lubricating > oils > diesel > gasoline(D) Lubr icating oils > diesel >AGO > gasoline

Answer :- (C)23. The main u n it processes used fo r the pro duction of hydrogen from natural gasare s team reforming (SR), pressure swing adsorption (PSA) , low tempera turew ate r gas sh if t re action (LT WGS) and high tempera ture w ater gas sh ift reaction(HT WGS ). The correct se quence of these in the p lant is

(A) SR; LT WGS ; HTWGS ; PSA (B) PSA ; SR; LTWGS ; HTWGS(C) SR; HTWGS ; LTWGS ; PSA ( D) PSA ; HTWGS ; LTWGS ; SR

Answer :- (C )24. The thermometer in i t ia l ly at 1oooc is dipped at t=O into an oil bath, maintainedat 1sooc. I f the recorded temperature is 13ooc after 1 minute , then the timecon stant of thermometer ( in mm) is

(A) 1 .98 (B ) 1.35 (C ) 1 .26 (D ) 1.09Answer :- (D )Exp: - Fo r th e rm om ete r,

y ( t) = x (t ) [ 1 - e-t /n ] ory ( t ) = A [1 - e -t/n]HereA = SO, y(t) = 30 , t = 1:. 30 = 50 ~ ] => r = 1 .09 www.examrace.com


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25 . The Bode stabi l i ty cr i te rion is appl icab le when(A) Gain and phase curves decrease cont inuously with f requency (B) Gain cu rv e increases and phase curve decreases with f requency(C ) Gain cu rve and phase curve both increase with frequency(D ) Gain curve decreases and phase curve in creases with fre quency

A nswer: - (B )

Q. No. 2 6 - 55 CarryTwo Marks Each

26 . The one-d imens ional unsteady state heat conduct ion equation in a hol lowcy l inder withacons tan t heat source q is oT = ! ~ (r T)+ qot r or orI f A and Bare arbitrary constants,equat ion is then the steady state so lut ion to the above

qr2 A(A) T(r) = - T+r+B qrz(B) T(r) = - 4 + Ainr+B(C ) T(r) = Ainr+B

Answer :- (B)

qrz(D ) T (r) = ""'4 + A In r + B

Exp: - oT = ! ~ ( r


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f (X ) = X- COS 1tX 0 :o; X :o; 1I f the in i t ia l guess for the root is 0.5, th en the value ofx after th e fi rst i terat ion is(A) 1.02 (B) 0.62 (C) 0.55 (D)0.38

Answer:- ( D)Ex p :- f (x ) = x - cosTtx O :o; x :o; 1

29.

Ne wto n-Raph son m eth od to f ind roo ts o f f ( x ): f{X) = X - COS7tX; f' (X) = 1 +1 t Sin 1tX

fG) ~ cos = ~ f ' ( = 1 + 1ts in =1 + lt1

X =_!. - 2 = 0 . 381 2 1 + 1tI f I = .J-1, the valu eof the integ ra l ~ (z +i )dz lzl i z (z + i} z- +- i Z ( Z + i}30. An insulated, evacuated conta in er is co nnecte d to a supply l ine ofan id eal gas atpre ssure P5, temperatureT5 , and specific vo lume V 5 The container is filled withthe gas until the pressure in the container rea ches Ps. There is no hea t transferbetween the supply line to the conta iner , and kinet ic and potent ia l energies arenegligible. I f Cp and Cvare the heat capacit ies at constant pressure and constant

vo lume, re spect ively (r=Cp/Cv), then the f inal temperature of the gas in theconta iner is(A ) yT.

Answer:- ( B)(B) T. (C ) (y - 1)T. (D) (y -1)T. f r

31 . Consider a b in ary l iquid mixture at consta nt temperature T and pressure P. If th eentha lp y change of m issing, D.H = 5x 1x 2 , where x1 and X2 are mole f raction ofspe cies 1 and 2 respect ive ly / and the entropy change of m ix in gD.5= -R [ x 1 1nx 1 +X 2 1nx 2 ] (with R=8.314Jfmoi.K), then the minimum value of theGibbs fre e energy change of mix ing at 300K occurs when(A ) X1 = 0 (B ) X1 = 0.2 (C ) X1 = 0.4 (D) X1 =0.5

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A nsw e r :- (D)


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Exp: - G ive n, AH = 5x 1x2; A5 = - R [ x 1 1nx1 + X2 1nx2]G = H - TSAG = AH - TAS

d(AG)Fo r AG to be m in imum , -- = 0ax1a a~ - (5x 1 x2) - - T [ - R { x 1 1n X1 +x2 1n x2} ] =0axl axl

~ 5 [ x2 - x 1 ] - RT [ 1 + 1n x 1 - 1 - ln x 2 ] = 0~ 5 [ x 2 - x 1 ]- Rr [ ln x 1 - ln x2] = 0T his Is poss ible on ly w hen x 1 = x2 = 0 . 5

32. A be d of sph erical glass beads (dens it y 3000kg/m3, d iamete r lmm, be d porosity 0.5 ) is to be fluidized by a liquid of densi ty 1000 kg/m3 and viscosity 0.1Pa.s.Assum e that the Reynolds number based on particle diameter is small comparedto one. I f g=10m/s2, th en the minimum velocity (Inm/s) required to f luidize the bed is(A) 3.33 x 10-4 (B ) 3.33x10-1 (C ) 3 (D) 30

A nswe r :- (A)Exp: - For pa cke d bed ,

1SO J..l.U (1 - )2-=L ~ AP = gL (1 -) (Pp - p) ( fo r m in imum flu id iza t ion}

gL (l -) (Pp - p) (150)(J..!.} Um(1 -E .f=> = ~ _ _ _ _ ! _ _ . . . . : . : : , . . . ! . . . . _ _ _ _ _ . ! . _L 02 3p(150) (0 .1) (U ) (1 - 0 . 5)

2~ l Ox (1 - 0. 5) (3000 - 1000 ) = 2 m(l x l o -3) 2

~ Um = 3.3 3 x 10- 4 m /s33 . For the enclosure formed between two concentr ic sphere s as shown below(R2=2R1 ) , the fraction of radiat ion leaving the surface area A2 that s tr ikes itselfis

(A ) 1/4( B) 1f2(C) 1 / .f i .

(D ) 3f4 www.examrace.com A nsw e r :- (A )


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:. Fract ion = .!.4

14

34. Heat generatedat a steady rate of 100W due to resistance heating in a long wire(length = Sm, d iameter =2mm } . Th is w ir e is wrapped with an insulation ofth ickness 1m m that has a therma I condu ctivity of 0.1Wlm K. The insu Ia ted wireis exposed to ai r at 3ooc. The convect ive heat transfer between the wire an dsurrounding ai r is characterized by a heat trans fer coefficient of 10Wim2 .K. Thetempera ture in oc at the interface the w ir e and the insulation is(A ) 211.2 (B ) 242.1 (C ) 311. 2 (0)484.2

A nsw e r :- (C )

35. In a counter - f low double pipe heat exchanger, oi l ( m2kg Is, cp = 2.1kJ I kg0 c)Is cooled from 90C to 40C by water ( mlkg Is, c p= 4. 2kJ I kg 0 c) whichenters the inner tube at 1ooc. The radius of the inner tube is 3cm and its lengthIs Sm. Neglecting the wall resistance, th e overall hea t transfer coefficient basedon the in ner radius in (kW lm 2 .K ) is(A) 0.743

A nsw e r :- (A )Exp : - Heat ba lance

(B ) 7.43

~ 2 x 2.1 x (90 - 40 } = 1 x 4 .2 (T - 10}~ T = 60:. LMT D= 30C:. U; A; (Al i )= mcPAT

2 x 2.1 x (50)~ u. = = 0 .7431 6 x 10- 2 xSx tt x (273 + 30 )

(C) 74.3 (D)2475

T = 40no\, = 9 ~ 0 - - - - - - - - - - - - - - - - - -

36. The ra te controll ing step for the solid catalyzed irreversible re actionA + B CIs known to be the reaction of adsorbed A w ith adsorbed B to give adsorbe d C. IfP; Is the part ial pressure of componen t I and K; is the adsorption equil ibriumconstant of component I, then the form of the Langmuir-H inshelwood ra teexpression will be

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rate ex: PAPs


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(A ) (B ) (1 + KAPA + KBPB + KcPc)2(C ) (D ) rate ex: PAPs

PcAnswer :- ( B)

37. Consider the drying operation shown in the f igure bel ow fo r a solid loading (dryba sis) of 50kg/m 2 with a constant drying rate of 5kg/m 2 .h . The fa ll ing rate o fdry ing is lin ear wi th m ois tu re content.X 0 1 .-:-----c = . / jx.= 0 .005

x ...........

The drying time in hours require d to reduce an init ial moi sture conten t of 25% toa final moistu re content of 2% is(A ) 1 .55 (B ) 1.75 (C ) 3.2 5 (D)4.55

A nswer :- (C )

Exp: -50

[(0 .25 - 0 .1)+ (0 .1 - 0 .00S)In (0

1

-0

005

JJ = 3.25hrs5 0.02 - 0 .00538. An equimo la r mixture of A and B (A being more volati le) is flash distilledcontinuously at a feed rate of 100kmol/h, su ch that the liquid product contains40 m ol% of A. Ifthe relative vo lat ility is 6, the n the vapour product in km ol/h is

(A ) 10 (B) 20 (C) 25 (D ) 45A nsw e r :- (C)Exp :- F = L + V ( Y _ ax _ _,_6 ...:...,}(o_. ..!--))- 1 + (a - 1) X - 1 + 5 X 0 .4

50 - 40:::> (100) (0 .5)= (100- V) 0 .4 +V (0 .8 ) = 0 .8 :::> V = = 250 .4

39 . A th ermocouple having a l inear relationship between ooc and 35ooc show s anemf of zero and 30.5mV, respectively at these two temperatures. I f the coldjunct ion temperature is shifted from ooc to 3ooc, then the emf correction (inmV) Is(A ) 3. 13 (B) 2.92 (C ) 2.61 (D)2.02

A nswer :- (C )Ex p: - S in ce, the re lationship is l inear,

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(30.5.0)


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New cold jun ct ion emf= (350 _O) (30 - 0) = 2.614 mV

40. The characteristic equation for the system iss3 + 9s 2 + 26s + 12 ( 2 +KJ = 0Using Routh test, the value of Kc that will keep the system on the verge ofinstability is(A) 20.9 (B) 18.4 (C) 17.5 (D) 15.3

Answer:- (C)Exp: - Routh array

1 269 12(2 + Kc)9 x26 - 12(2 + Kc)

9=>For stabil ity 9 x 26 - 12(2 + Kc) > 0 => Kc > 17.5a:. On the verge of stability Kc = 17.5

41. The elementary reversible exothermic gas-phase reactionA+ 3B 2Cis to be conducted in a non-isothermaI, non-ad a ba tic plug flow reactor. Themaximum allowable reactor temperature is Tmax To minimize the total reactorvolume, the variation of reactor temperature (T) with axial dista nee from inlet (Z)be(A) (B) (C) (D)Tmax l - - - - -

T T

Answer:- (B) z z z

42. The block diagram of a system with proportional controller is shown below

+R - +D ( } - - +1

1

1 1--...----+C' t,S + 1

z

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A unit step input is in troduced in th e set point. The value of Kc to provid e a


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cr i tica ll y d a mp e d re sponse fo r U=O, "P = 8 and "m = 1 Is(A) 3.34 (B ) 2.58 (C ) 1.53 (D ) 1.12

Answe r :- (C )KcEx p: - Y = - - - - : - __ . ; ; : .----=---( ;ps + 1)

1 + Kc 1(-,;PS+ i ) ( -,;nS + i )Ke (s + 1)

8s2 + 9S+ 1 + Ke _ 8_ + _ 9_ + 11 + Ke 1 + K c

For critically d a mp ed sys tem, = 19 9 4 . 5=> 21; =- - => 2-,; =-- => 1; = - -1+ Ke 1+ Kc 1 +Kc

d 2 8an " = --1 +Kc: . ~ = - 8 - :::> 20.25 = 8 (1+ Kc} :::> K 0 = 1 .5 3 1 2 51 + Ke 1 + Kc

43 . A batch reactor produces 1x105 kg of a product pe r year. The to tal batch tim e inhours of th e reactor is k.JP:, where P6 is the pro duct per batch in kg andk = 1. Oh I .jkg . Th e operat ing cost of the reacto r is 200 /h. The tota I ann uaI fixedcharges are Rs. 3 4 0 x Ps and th e annual raw m aterial cost is Rs 2 x 1 06 Theoptimum size in kg of each batc h (a d j usted to the ne ares t In teger) is(A ) 748 (B) 873 (C ) 953 (D ) 1 1 48

A n swe r :- (C )Exp :- Tota l nu m be r of batc hes = i x iOSPB

: . Tota l cost = 200 ( x Jx kJP: +340P6 + 2 x 106() (cost ) 0 __,_ - 20 0 x 105 x i +340 = 0o r op timum ()P -- 3

6 2 x (P6 )23

=> pB2 = 29411.76=>PB = 952.8kg

44 . Hea t In tegra t io n is planned in a process plant at an In ve s tme n t Rs. 2 x 10 6 Thiswould re sult in a ne t energy sav in gs of 20GJ per year. I f th e nominal ra te ofIn te rest is 15%and the plant li fe is 3 years , then the bre akeven cost of energy ,In Rs. Per GJ (ad justed to th e neares t hundred), is(A) 33500 (B) 43 8 0 0 (C) 54 2 00 (D ) 65 400

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A nswer:- (B)


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E R = p i (1 + 1"xp : - (1 +i)" - 12 x 106 x0.15(1 +0. 1 5) 3

(1+0.1 5f - 1(20 )(x ) = 875953 .9237 ~ x = 43797 .696


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(A) 1454 (B ) 1584 (C ) 1676A nswe r : - (B)Exp: - Tota l f lwo of (A+C), I nit ial ly = 1000 kg / h

:. Am oun t of C = 1000 x 0.2 = 200kgAm o unt of A = 1000- 200 = 800 kgFin al co ncen t ra t ion=1 % of 200 = 0.01 x 200 = 2 In A:. Y = 2x~ _ 2_ = 2 x (1 .98)800 mass o f B~ m o f B =1584 kg /h r

(D)1874

49. I f the f low rate of B is 2400kg/h, th en the theo ret ical number of stages in theco lum n, using Kremser's equatio nadjusted to the next In teger is(A) 5 (B) 9 (C ) 11 (D) 13

A nswe r :-

Common Data fo r Questions: 50 & 51

The reaction A(liq) + B(gas) - ~ c ( l i q ) + D(gas) is carr ied out In a reactor fol lowed by asepa ra tor as shown below:

:

FPG~ +~ Reactor - - ~ - Separator1-__ ..,.FeNotat ion :Molar flow ra te of fresh B is FFBM ola r flow rate of A is FAM ola rflow rate of re cycle gas is FRGMole fr act ion of B in re cycle gas is YRaMolar flow rate of purge gas is Fp8M olar flow ra te of C is FeHere FFa= 2mol/s; FA=1m ol/ s; Fs = 5 and A is comple te ly convertedFA

50 . I f YRs = 0.3, th e ratio ofrecycle gas to purg e gas (FRG FPG)Is(A) 2

A nswer :- (A )(B) 5 (C ) 7 (D) 10

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51. I f th e rat ioof recycle gas to purge gas (FRG /FPG) is 4 , th en YRs is


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(A ) 3/8 (B ) 2/5 (C ) 1/2 (D)3/4Answer :- (A )

Statement for LinkedAnswer Quest ions: 52 & 53

A Newtonian fluid o f viscosity 1-L flows between two parallel plates due to th emotion of the bottom plate as show n below, which is m oved w ith a velocity V.The t op plate is sta tionary.

V-4

52. The steady, laminar velocity profile in the x-directi on Is(A ) v[t]

A nsw e r :- ( B)

53. The force per unit area (in the x-direction) that m ust be exerted on the bottomplate to main tain the flow is(A ) I-LV (B ) - ~ - L V (C ) 21-LV (D ) -21-LVb b b b

A nsw e r :- ( B)Statement for Linked AnswerQuestions:54 & 55

The first order liquid phase reaction A -4 P is con ducted is othermally in a plugflow reactor of 5 liter va l u me. The inlet volumetr ic flo w rate is 1 li ter I min andthe inlet concentration of A is 2 mo le /l i te r .

54 . I f the exit concentration of A is 0.5 mole/ l i ter, then the rate consta nt, in min- 1 is(A) 0 .06 (B ) 0.28 (C ) 0.42 (0 )0.64

A nsw e r :- (B )Exp: - For p lug f low re actor,

- d cA I CAo k't = - - : : :> n - = "kC A CA( ln _3_)k - 0 .5 _ ln 4 _ 0277 . _1- " -G)- . mm

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55. The plu g f low reacto r is replaced by 3 mixed flow reactors In series, of 2.0 l it e rsvo lum e. The exact conversion of A (in %) is


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(A) 35.9 (B) 52.5 (C) 73.7 (D) 94.8Answer :- (C )

1Exp : - 1 - XA = 3(1+ kt)1 1

~ XA = 1 - = 1 - = 73 .659 %(1 + k-t f ~ TQ. No. 56 - 60CarryOne Mark Each

56. Which one of the fo l low ing opt ions is the closest in meaning to the word giv enbelow?Mitigate(A) Dim inish (B ) Divulge (C) Dedicate (D)Denote

Answ er : (A)

57 . Choose th e most appropriate alternative from the opt ions giv en below tocomplete the fol lowing sentence:Despite several ----- the mission succeeded in its attempt toresolvethe confli c t.(A) attempts

Answer : (B )(B) setbacks (C) meetin gs (D) de legat ions

58 . The cost function fo r a product i n a firm is given by 5cf, w here q is theamountof product ion . The firm can sell the product at a market pric e of Rs.50 per unit.The number of units to be produced by the firm such that the profit ismaximized is(A) 5

A nswe r : (A)Exp :- P= 50q - 5q2

(B) 10

dp d2pdq = 50 - 10q; dq 2 < 0

(C ) 15

.. p Is m ax imum at 50 - 10q = O o r, q=5Else check w it h opt ions

(D) 25

59. Choose th e most appropr iate alternative fr om the optio ns given belo w tocom plete the fol lowing sentence:Suresh's dog is the one ____was hurt in th e stampede.(A ) that (B) which (C) who (D) whom

A nsw e r : (A)www.examrace.com

60. Choose theg rammatically INCORRECTsentence :(A) They gave us the money back less the serv ice cha rges of Three Hundre d


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rupees.(B ) This country's expenditu re is not less than that of Bangladesh.(C)The com m ittee in it ially asked fo r a funding of Fift y Lakh rupees , bu t la te rsettled for a lesser sum.(D ) This country 's expenditure on educat ional re fo rms Is very less

A nswer : (D )Q. No. 6 1 - 65carry Two MarksEach

61. An automobile plant contracted to buy shock absorbers from tw o su pp lie rs X andY.X supplies 60% and Y supplies 40% of the shock absorbers. All shock absorbers aresubjected to aquality test. The ones tha t pass the quality test are considered reliableOf X's shock absorbers, 96% are reliable. O f Y's shock absorbers, 72% are reliable.The probability that a randomly chosen shock absorber, which is found to be reliable,is made by Y is(A ) 0. 288 (B ) 0 .334 (C) 0 .667 (D ) 0 .720

Answer : (B)Exp: -

SupplyReliab leoverall

X60%96%0.576

:. P (x) = 0 288 = 0 .3340.576 + 0 . 288

y40%72%0. 288

62. A political party orders an arch for the entrance to the ground in which the annualcon vention is being held. The profile of th e arch follows the equation y = 2x- 0.1x 2whe re y is the height of the arch inarch is meters. The m aximum possible he ight of th e(A) 8 m eters (B ) 10 meters

A nswer : (B)Exp: - y = 2x - 0.1x 2

dy = 2 - 0 .2xdxd2 ; < 0 :. y m ax im ises at 2 - 0 . 2x = Odx::::> X= 10: . y = 20 - 10 = 10m

(C) 12 m eters (D ) 14 me ters

63. Wanted Temporary , Part-t ime persons for the postof Field Interviewer to conductpersonal in terv iews to collect an d collate economic data. Requirements: HighSchool-pass, must be available fo r Day, Evening and Saturday work.Transportation paid, expenses reimbursed.Which on e of the follow ing is the best inference fr om the above advert isem ent?

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(A) Gender-d iscr iminatory(B) Xenoph obic


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(C ) Not designed to make the post attractive(D ) No t gender-d iscr iminatory

Answer : (C)Exp: -G ender is not menti oned in the advert ise m ent and (B) clear ly eliminated

64. Given the se que nc e of term s,AD CG FK JP , the next te rm is(A) OV (B ) O W (C ) PV (D ) PW

Answer : (A)+2 +3 +4 +5~ ~ ~ ~AD , CG , FK , JP , 0.J

" ' - . - J ' " ' - . - J J I ~ -+3 +4 +5 y65. Which of the following assertions are CORRECT?

P: Adding 7 to each entry in a list adds 7 to the mean of the listQ: Adding 7 to each entry in a l ist adds 7 to the standard deviation of the listR: Doubling each entry ina I st do ubles the mean of the li s t5 : Doubling each entry in a list leaves the standard de viation of the list unchanged(A) P, Q (B) Q, R (C) P, R (D ) R, S

Answ er : (C)Exp :- P and R a lw ays holds true

Else cons ide r a sam ple set {1 , 2 , 3, 4 } a nd check accord ing ly

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GATE Chemical Engineering Solved 2012