Physical Sciences June

8/12/2019 Physical Sciences June

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SUBJECT CODE BOOQET ODE

2014 I)PPI'BISECAL CIENCES

TEST B O O m E TTime :QO Hours Maximum d arkr: 200

KNSTRUCTH8NS

1 You have opted forEngPish as medium oPQmestionPaper. This T est Booklet containssevcnty five(20 P 'Aq+25 Part 'B' + 30 Parlt C ) MultipleChoice Questions (MCQs).You axe required to ariswera maximum of 15.20 and 20 questions fiom p a t'A' 'B' and

C espectively. If more an required number of questionsare answered, onlyfirst 15,20'28 questions inPapts A B and 'C' respectively,will be taken up for evaluation.

"a Answer skeethas been prnvided separately. Before you s t a t filling up your particulars,

please msure that the bookla contains requisite numbcr of pages and that these are nottorn r mutilated.If it is SO,oi may request the Invigila tor to change the booklet of thesame code. Likewise, check t e answer sheetalso. Sheets for rough work have beenappended to the a s t booklet.Write your Roll No., Name and Serial Number of this Test Bookleton the Answer sheetin the s pa ce provided. Also put your signatures in thespaceearmarked.

4. You musf darken the a~ pm pri a te irc leswith a black bael oen related to RollNumber Suba'ectCode, Booklet Codeand Centre Code on theOMR answersheet.It b the sole responsibilitvof the candidate toaneticmlorsslv follow the instructionsiven on t he Answer $beet, f iing which. th e eo m ~a at erha ll not be ab le to decipher

the 60kkect details whichmav uitirnatelv resultin loss, inciodinp reiection of theOMR answer sheet.

5. Each qlaestiszi in art 'A9 carries2 marks, art 'R' 3.5 marks and Fatt C 5 marks

respectively. There willbe negative marking@ 25% for each wiolrrg answer.6 Below each question in Part'A', B and '13' four alternatives or responses are given.Only one o f these alternatives is the "correct" option to the question .Ygu have to find,for each question, the correct or the best answer.

9 Cand idates found copying or resortingto m y unfair means are liable to be disqualifiedfrom this and future examinations.

I Cand idate should not write anything anywhere except on a ~i sw er heet orsheets for

9. Use o f calculator is notI . After the Best is over, at the perforation point, tear the8 M W answer sheet, hand

m e r the original QMW answer sheet to the invigilator and retainthe carbonlessc o w for your record. -

111. Candidates who sit for the entire duration of the exam will o9ly be permitted to cany

their Test bboklet.

I ,,.-;.. 5 2. ? .o.Y.. _ have verified all the informationfilledf h ~ l ~ in by the candidate.Name

O k I I ~ ~ P ~heet N~ GSA ? CI?


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1. 5 Jcrn 2. 5 a c m

WTO m 4 - l o a m

F Bi 1, c 5 A n d r c h e r climbs to the top of a 10 mI

K P U Z high building and aims at a bird atop aP V D ? t r re 17 r away. The line of sight h m

the archer to the b i d makes angle of

1. P K 45' to the horizontal. What is theh e i g h p3. J 4. L of the tree? pfj1. 117m b 2 7 m \7 42 Consider a right-angled triangle_-ABC 3. 37 rn 4. 47m p a s \where AB = C 3 . A m l e POQ -is drawn inside it, as sh or n . such that the 6 C onsider P t h e set of 1height o f the rectangle is twice its width. (17 , 17 , . - - , 7 ~ ~ ~ 3OWmany of h s

--r---

The rectangle is moved horizontally by a rlumbers e n d with the digit 3?-distance 0.2 2s shown schematically in- 1. 60 2. 75thFdiagram (not to scale). 3. 100 w 150

Find th e m iss ing number in the triangle.

1 . 16Area of AABC 3. 5 4. 80

Wkai is the value of the ratioArea ofPOST

?

8 The time- gap. between the t ~ v on:;tants,,2 400. 625 o n L ~ e f o r e nd one after 12.00 noon,

3L--2Z 3. . i25 w h en th e an gl e betw een s h o u r handand the minute hand is 6 6 Ois

3 8 0 gsm paper is cut into sheets of 200 1. 12 min 2. 16 min; r x x 300 mrn size and assernblz in : 3. 18 min. 4. 24 minpickets of 500 sheets. What will be theweight of iTj5iEket? gSm = g/rn ) 9 A m-an-s eqyal numbe~sf shirts

and t r o u s e r r Z Z p a y s -Rs. PmO. f the1 . 1.2 kg 2. 2.4 kg

- 3 po- c o s t w h i r t s is f 805 ana that3. 3 6 kg 4 . 4.8 kg -tro user d R s . 1 0 0 p h e n how many sh~r ts-

were bqught? 3 3 8 w

4. Three identical flat equilateral-triangular1

60b 5

( & mrp l a t e i d e 5 c m each are j laced 3 . 1 5 . 4. 10together such that t h z orm a trapezium.

60

years of a child, the heightI j

i t~crcasesas the square root of t hezge .0.0-vlltlile the weikht increases in direct-

.... . . .:..... . . . . . . .

.. . . .

..

. . . .

....... c

T~-.-_.-I.-. . ?. . . . . . . . .


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2 reduces with age.L3 increases with age.

4. is constant only if theheigh t at birth are both zero.

11 In 450 g of pure coffee powder 50 g ofchicory is added.A person buys 100g o fthis mixture andadds 5 of chicory tothat . What would. be the rounded-offpercentage of chicory in this final

sh o rn (units t arbitrary)?

1. 10

dra wn, wit out replacement, so that you

blu e and 7 white balls?

1. 140

13 Suppose

+, and x have their usual mea~liags../

W hat is the v a w f( (197 315) 197 315)) (197 315 ) 17.Suppose is a positive integer. -then

- n2 n) Zn 1

I maynot be-divisible by2.2. is always divisible by 2 but-may not


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--.. .

. .

18. There is a train of length 500 m, in which degenerate, while the others are non-a m m is standing at the rear end. At the degenerate. The average., energy atinstant the rear end crosses a stationary inverse tem~eratuie 3 is -observer on a platform, the man startswalking from the rear to the front and thefront tor the rear of the train at a constantspeed of 3 km/hr. The speed of the train 3 zero 4. -E tdnh

is 80 lun/hr The distance of the man

from the observer at the end of30

23 For a particular +hemodynamic systemminutes is thezntropy S is related to the internal-energy U nd Glume V by

1. 41.5 km 2. 40.5 km. /40.0 km. 4. 41.Okm. s = c ~314~11419 A rwtangular area of sides_9 is a constant The ~ i b b ~.is to be covered by s G r e iles C = - TS pV f o s this2, and 5 units. The minimum system isfiles needed for this is . . cu

2. -3

1. 3 2. 11US

4. -3. 12 4. 15 4v

24. An op amp-based voltage follower28. If all horses are donkeys, some donkeys 1. is useful for converting a low impedance

are monkeys, and some monkeys are source into a high impedance sourcemen, then which D .- s useful for converting a high

impedance source into a low il~lpedancey1. Alldonkeysaremen. source

t2 Some donkeys mayr 3 has infinitely high closed loop output

7 3 .- Some horses are men.. impedance-1

4 All horses 4 has infinitely high closed loop gain

25 A particle of mass m in three dimensionsis in the potential

21. One gram of salt is dissolved ie ~ ( r ) = ( ~< a ~that is filled to a height of 5 cm in a cc r

2 aIts ground state energyisbeaker of diametei 16 cm. Tbcc uracy to]-of le, gth wsurement is 0.01 cm while .,. .- . - 7T2 ii2 . . - n 2 f i 2- that of mass measurement is 0.01' mg. 1 2

-----Tma . ma

4

; W h ~ m e a s u r i n g h: the fractional error bC C isr- .8% . . 2. 0.14%

3 0.5%

; 22 A system can have tI E = 0, E . The level- -

~.... .. . .. . .. . _ . . . I . . I . . . . ,. . _ .&_ _ _ . . r _ . _ l . _ ~ _~. . . ~ - - . ~ ~


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, .. .

, .

37. Consider the matrix..

33 particle of mass m and coordinate. qhas the ~ a ~ r a n i i

tvhere is a constant. The Ha nil ton ianfo r the system is given by

The eigenvalues of M are1. - 5 , - 2 , 7 k d - - 7 0 7

3. - i 2i, 21 4. 2 , 3 , 638 Consider the differential equation

with the initial conditions x(O) := 0 nii~ 0 ) 1 . The solution x t ) attains itsmaximum value when is

- -1 /2 2. 1

34 IF^ = yz zxj xyk and C is the 39 A light source is switchedon and offcircle of unit radius in the plane defined .=c---c o C G G q u e n c y ~p c ~ ~ s q r v c ~by z 1, with the centre on the z-axis,

+ + movin? with a velocityc with respect tothen the valueof the.integra1 c A. d t is t u g h t source will obszr-ve the

frequency of the switchingto be

35. GivenEL , X)P= I - xt t2)-'I2, % 2 f/Z3. f ( 1 - ) 4 . . f l - - - 4

f o r I t J < f , t h e v a l u e o f P 5 ( - l) i s C

40. If C is the contour definedby z = : thevalue of the integral z r >

36 A charged particleis& a d i s t a n c e s o m d zan infinite wnducting plane main tained

1 at zero potential. When released fro m is

distance d 2 from the plane. At- wh at

41. The iime period of a simple penduluniunder the influence of the acceleration


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. .. . . ;>:..*.*.*.+,?i?fp@:~..~Tp?-- I; 1

. . . .- f&s.&5:..~* p>.%%??..: .

magnitude f i g in the ho-mn,,.: .,,.< .,* .


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. w u

PART c46. The pressure of a nonrel vistic free

Femi gas . in three-dimensionsdepends, at T = 0, on the density offemi n s1Tn5 3 2 n I3

k3n i3 4 n4i3

47. A double slit interference experimentw e a a laser emitting IW of twoadjacent frequencies vl and v2v;: 15 . The minimum path

difference between the interf ingbeams for which the intergreencepattern disapp'ears is

The recently-discovered Higgs bosonsat the LHC experiment h m e c a ymzde infOa photon and a Z boson7 Ifthe rest masses of the Hig@-and Zboson x 125 @e 89/cL nd 90 ~ e ~ l c ~respectively, and the decaying Higgsparticle is at rest, the energy of thephoton will approximately be

1. 3 5 f i ~ e v 2 35 eV3. 30 GeV 4. 1 5 d . e ~

3. Decreases by 4 .4. Does not change-

.Far the logic circuit shown in the

figur elowI a

a simplified equivalent circuit s

52. A spectral line duk a transition froman electronic state p to an s state splitsinto three Zeernan lines in the presince

of a 3trong lnlagnetic field. Atintermediate field strengths the num6ero9bectral lines is

49. A permanently deformed even-even 10 2. 3nucc w with P 2 has totsional 3. 6 4. 9energy 93 keV. The energy of the nextexcited state is 53. A particle in the infinite square well1. 372 keV 2. 310keV3. 273 keQ 4. 186 keV O x a

= I otherwise

-.- 1 _ ncreases by 2


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The expectationthe particle is

54. The average local internal magnetic

field actingon an

@n i s a'

af-re M is the magnetizationand

The dispersion relation for electronsinan f .c. crystal is given,in t ~ t

%&ing approximati&, by -

k y a k , a :-k 665 - OS

2

+css os -a]a 'is a positive constmt. At atempewtu~eT sufficiently close to (and . where a is the lattice coilstantand q sabovz) the a5tical temperat~lreIc, he a constant vvi& the dimension;ofrnzg,s~etic mce~tEb1Ei~y t zero external energy. h.e w-component ofthe .field is proportional to k B is the velocityof the electrons a?( 0.0) Is .BsHtzmanncernstgnt) 1, - soar~fi . 2. 2 ,a/AI. k,T-a 2. (kBT4- a);' 3. - 4 ~ , a / 4. 4roa/h

.

@k T --a)-- 4. tanh(k,T. a ) .58. The f i ~ i o x ~ i n g zta is obtained in il

59 En o m d i rn~a~ ion , rmdozn w&er experima.ra. CBhdt measure~tht :isc~sityt&es a step with equal pr&asiify to q as a G,'sn.crisn ofmoiecularweight Mthe left 0r.right. W i.lat-is %fie ~obability fix a S ~ I f p~lyiners .that the walker re brmrxs to the s:.ziijragpointaAcr4 steps? fid f D z j Wa-s)

,,/3/8 2. 5/163 , 3./4 4. 1/16 990 0.28 0.03

56 Csnsicier an eleciro-rr In a b.c.c. laitice 5032 30 f 2with Initice constact a i%>inglc

n

partlie v ~ a v e f ~ i n c t i s nhat saisf ies Lbe 10191 259 -t- 10Bloch theorem wiQI have the f01-mf ?) erp( i6 .f ; with f(i) k i n g

I l + c o s ~ ~ ~ + ~ - z ) ] + c o r [ ~ - x + The relation that best describes the+ z j ] + cos[: r +z) ] dependence of q on M is

1. n - W4j9 2. ~ - V 3 I.

cos [? z + . I59. The integral1 fi x is to be & w e d

3. ~ + c o s [ ~ ( x + y ) ] + c o s [ ~ ~ + z ) ] + up to 3 decirnal places osing siFPsoo'scos [f( z f I[) 1 3-pcGnt mle. f the in


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In a classical model, a scalar (spin-8)meson consists of a.--antlquru k bound y a p

where a = 200 MeV f m - b ~ ~ d = 100

MeV fm. If the masses of the quxkand antiquark are negligible the massof the meson can be estimated asapproximatcIy

1Let y . - xl x2 /A where xl and2 . .

x2 are independent and identicallyd l s t r i b u t e ~ ~ s s i mz:dorn variablesof ff n u m starxiarc? deviation o-.~ h E - - { ~ ) j ~ 4s

?'he gaph of a real perit.Bic frariction16) for th.1: razgc: 1-33 cc j s shown

below

satisfy ih l curmuiztiisn relibk3~1as

9. [A li = B C [B ] 0 [C,A] -= i- C

2 . [A,31 = C [B, .I= A, [C ] = B

3. ; ~ , a ]- B ~ B , C I- a Ec.Aa - A41 [A,I?] L Cs a C] = 0 LC A] = B

64. The fur~ction @ x,y, z t == @os z = vt ~ e s i n x y

the equdibn

65. The csordicates a d rnctmenta X j l P ii = 1,2,3) of a particle satisfy-the

canonical Poisson bracket relations.


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-interface at normal incidence. Therefractive index of the dielectricmedium is n and that of the metal isn2 = n l 4 ip). If the beam ispolarisedl parallel to the interface, thenthe phase change e x p x c e d by th;;light upon r e f l e c t i s1 t a n ( 2/ p ) 2 . t a n - ( u p )

1. {C2, C3) = 61 and 6631 Cl) = C22 (C2,C3I = -Cl aqd (C3,C1) = -623. {Cz1C3) = -el and CC3,C1)= C24. (C2,C3)=C1 and {C3rC1)=-C2

A canonical transformation relates _(heold coordigates q, p) to- he new ones

n j y the relations Q = q2 p dP = g / 2 q . The corresponding time-independent generating fiuacti~rr s 7 1 . y cattering grnplitude

f ( 8 ) for the

1. P / q 2- 2. q potential V s) = p e-Pr , where P and

3 q 2 / P 4 q P p are positive constants, is given, in theBorn approximation, by- -

0 Ir2k267 The time evolution of a one- in the followingb = 2ksin; nd = =

dimensional dynkical . system is1. - 4mPP 4 m P ~

described by ~ ~ ( b ~ i ) ~- - i 2b2 b L

If this 6 one stable and two unstablef ed points, then thi parameter bsatisfies

AI o < b & 1 2. b > 3 b < 31 4 b - 2

92. The ground state eigenfunction for thepotential V ( x )= -6 (x ) , where 6 ( x ) isthe delta hctiog, is given by q x ) =~ e - ~ l ~ l ,here A and > 0 are

68. A charge - e is placed in vacwm atthe point (d l 8 ), where d > 0. Tregiozx _< 0 s filled lrnifmly with ametal. The electric field at the point

eonstants, If a perturbation H = b x Zcorrectiouo

b1.

z2.

2

1. A thin, infinitely long solenoid p Wa e t h e z-axis c o n i i a n n e t k f l u x4. W c h of the following vector

-

potentials corresponds to the mag~etic69 An electron is in the ground state of a

. fiel- an arbitrary point (x, y, z) ?hydrogen atom. The probability that rt -

- is within t h e ~ o ~ a d i u s s1- ( ~ X ' AY ' A . ~(- ;r;;;

azoximately equal to Y @ o

70 A beam of lightreflected .. from- f frequency w isa dielectric-rn l


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is designed so that at a fieqrtncy-gas is given by

= l o rads the intemity o theexternal radiation that penetrates theroom is I of the incident radiation.

pressure, volume nd temperaturerespectively, m a nd b are constantparmeters. At the critical point, where its minimum thickness should be given

all the roots of thz ibove- cubic equation that x 10 = 2.3are degenerate, the volume is given by

1 . 4.60 mm 2. 2.30 mm

. . .


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