Gate 2012 Physics Question Paper

fiziks Forum for CSIR-UGC JRF/NET, GATE, IIT-JAM, GRE in PHYSICAL SCIENCES

GAT GA T E -20 -2012 (PH (PHY Y SI CS) Q.1 – Q.25 carry one mark each.

Q1.





Identi dentify fy the correct state statem ment for the foll ollowing owing vectors vectors a  3iˆ  2 jˆ and b  iˆ 2 jˆ 















(a) The vectors a and b are li linearl nearly y inde i ndepe pendent (b) The vectors a and b are li linearly rly depen depende dent nt (c) The vectors vectors a and b are orthogonal orthogonal (d) The vectors a and b are normali alized Q2.

The unifo uniform rm thin thin rods of equa equall length, ngth, L and masses M1 and M2 are joined together along the le length. ngth. The T he moment of inertia nertia of the combi combine ned d rod of length ength 2L about about an axis xis passi passing ng through the mid-point and perpendicular to the length of the rod is,

Q3.

L2 (a) M 1  M 2  12

L2 (b) M 1  M 2  6

L2 (c) (c) M 1  M 2  3

L2 (d) M 1  M 2  2

The space-tim ce-time depe depende ndence of the electric electric field fi eld of a linearly rly polari polarized zed light ght in free space is given by xE0 cos t  kz where E0, ω and k are the ampli plitude, the angula ngular frequency and and the wavevector, ctor, resp respecti ectivel vely. y. The T he tim time average verage energy densi density ty associat associated ed with with the electric field is (a)

Q4.

1

2

 0E0

1 2  0E0 2

(c)  0E02

(d) 2 0E02

I f the pea peak output output volta voltage geof a full full wave wave rectifi rectifier is 10 V , its d.c. volta voltage ge is (a) (a) 10.0 10.0 V

Q5.

(b)

(b) 7.07 V

(c) 6.36 6.36 V

(d) 3.18 V

A parti particl cle e of mass m is confine confined d in in a two dim dimensiona sionall square square wel well potentia ntial of dimension a. This potential V(x,y) is given by V(x,y) =0 for – a < x < a and –a < y < a

=∞ elsewhere The The energy of the firs first excite ited state for for this particle icle is give iven by, (a)

 2 2

ma2

2 2 2 (b) ma2

5 2 2 (c) 2ma2

4 2 2 (d) (d) ma2

fiziks c/o Anand Institute of mathematics, 28-B/6 Jia Sarai Near IIT, Hauz Khas, New Delhi, PIN- 110016 (INDIA) Phone: 011-32718565, +91-9871145498 Website: http://www.p http://www.physicsbyfiz hysicsbyfiziks.com iks.com Email: fiziks.physic [email protected] [email protected]

1


Q6.

The isothe sotherm rma al compressibi pressibillity,  of an idea i deal gas gas at temperature perature T0, and V0, is given by (a) 

Q7.

1 V V0 P T0

(b)

1 V V0 P T0

(c)  V0

P V T0

(d) V0

P V T0

The ground ground state of sodium sodium atom ( 11Na) is a 2S1/ 2 state. state. The The dif difference erence in ene energy rgy leve levels arisi rising ng in the prese presence of a weak weak externa external magne agneti tic c field B, given in terms of Bohr magnet on, on,  B , is (a)  B B

Q8.

(b) 2 B B

(c) 4 B B

(d) 6 B B

For an ideal deal Fermi gas in three three dim dimensions, the the electron velocity veloci ty VF at the Ferm Fermi surface is relat related ed to to ele electron concentra concentrati tion on n as, (b) VF  n

(a) VF  n2/ 3 Q9.

(c) VF  n1/ 2

(d) VF  n1/ 3

Which hich oneof the the foll ollowing owing sets sets correspond corresponds s to fundamenta entall particl rticle es? (a) proton, electron and neutron (b) proton, electron and photon (c) (c) electron, electron, photon photon and and neutrino utrino (d) quark, electron and meson

Q10. In case case of a Geige Geiger-M r-Mul ulller (GM) (GM ) counte counter, r, which one one of the foll fol lowing owing statem tement is CORRECT? (a) Mul M ultipl tipliication cation fa factor of thedete detector ctor is is of the order order of 1010 (b) T ype of the pa particl rticles es dete detecte cted d can can be identif ntified (c) Energy of the particles detected can be distinguished (d) Ope Opera rati ting ng voltage voltage of the det dete ector is is fe few tens tens of Vol V olts ts Q11. A pla plane ele electroma ctromagnetic gnetic wave travel traveling in free space is incide incident nt norma normally on a gla glass pla plate of refracti refractive ve index ndex 3/2. 3/2. If I f there there is no absorption bsorption by the the glass, glass, its its refl refle ectivi ctivity ty is is (a) 4%

(b) 16%

(c) 20%

(d) 50%

Q12. A Ge sem semiconductor conductor is i s dope doped d with with acce acceptor ptor im impurity purity concentration concentration of of 1015 atoms/cm3. For the given hole mobility of 1800 cm2/V-s, the resistivity of the material is (a) 0.288 Ω cm

(b) 0.694 Ω cm

(c) 3.472 Ω cm

(d) 6.944 Ω cm


2


Q13. A cl classical ssical gas of mol mole ecules, cules, each of mass m, is in thermal equilibrium at the absolute temperature, T. The The velocity oci ty compone components nts of the molecules olecules along the Cartesian Cartesian axes axes are are vx , vy andvz . The T he mean value value of vx  vy  is 2

(a)

kB T

(b)

3 kB T 2

(c)

1 kB T 2

(d)

2kB T

Q14. In a centra central force field, the the traj trajectory of a parti particl cle e of mass mand angular ngul ar momentum ntum L in plane polar coordinates is given by, 1 m  1  cos  r L2

where, ε is the eccentricity of the particle’s particle’s motion. Which one of the following choice for for ε gives rise to a parabolic trajectory? (a) ε = 0

(b) ε = 1

(c) 0 < ε < 1

(d) ε > 1

Q15. Identi dentify fy the CORR ORRECT energy nergy band band dia diagram for sil silcon dope doped with with Arsenic. rsenic. Here Here CB, CB , VB, ED and EF are conduction ction band, vale valence band, band, im impurity purity leve levell and Fermi Fermi level, evel, respectively. (a)

(b) CB ED

CB ED

EF

EF

VB (c)

VB (d)

CB

CB

EF

EF ED

ED VB

VB


3


Q16. The first Stokes li line of a rotational Ram R aman spectrum is observe observed d at at 12.96 12.96 cm-1. Considering the rigid rotor approximation, the rotational constant is given by (a) 6.48 cm-1

(b) 3.24 cm-1

(c) 2.16 cm-1

(d) 1.62 cm-1

Q17. The total total energy, nergy, E of an ideal non-relativistic Fermi gas in three dimensions is given by N 5/ 3 E  2/ 3 where N is the number of of parti particl cle es and and V is the vol volum ume of the gas. gas. V

Identify ntify the CORREC ORRECT T equa quation of state (P being the pressure), (a) PV 

1 E 3

(b) PV 

2 E 3

(d) PV 

(c) PV  E

5 E 3

 

Q18. Conside onsiderr the wavefuncti wavefunction on    r1, r2  s for a fermionic system consisting of two spinhalf particles. The spatial part of the wavefunction is given by  

 r1, r2  

1 2









 1r1  2 r2    2 r1  1 r2 

where  1and 2 are single particle states. The spin part χ s of the wavefunction with spin states   1/ 2and - 1/2 should be (a)

1     2

(b)

1     2

(c) αα

(d) ββ



Q19. The electric electric and and the magnetic tic field eld E z,t and B z, t , respectively corresponding to the 

scalar potential  z,t  0and vector potential A z, t  iˆtz are 





(a) E  iˆzand B  j -ˆt 



(b) E  iˆzandB  jˆt





(c) (c) E  iˆz andB  - jˆt



(d) E  iˆzand B  - jˆt


4


Q20. Q20. Consi Consider the the foll following OP-A OP-AM P circuit

 10V 

Vin

 5V

Vout



4k 1k

- 10V

Which one of the following correctly represents the output output V out corresponding to the input V in? (a)

(b)

 5V Vin  1V 0V

 5V Vin  1V 0V

t

 10V

t

 10V

Vout

Vout t

t

 10V

 10V

(c)

(d)  5V

 5V

Vin

Vin

0V

0V

t

 10V

 10V

Vout

Vout t

 10V

t

t

 10V


5


Q21. Deuteron Deuteron ha has only only one one bound bound state state with with spin pari parity ty 1+, isospin 0 and electric quadrupole moment 0.286 efm2. These hese data data sugge suggest that the nuclea nuclear forc forces es are are havi having ng (a) only spin and isospin dependence (b) no spin spin depe dependence ndence and no tensor components components (c) spin spin dependence but no tensor tensor components (d) spin dependence along with tensor components Q22. A parti particl cle e of unit unit mass moves along the x-axis under the influence of a potential, 2

T he parti particl cle e is found found to be be in stable ble equil quilibrium brium at the point x = 2. The V x  xx  2 . The tim time pe period of osci oscilllation of theparticl particle e is (a)



(b) 

2

(c)

3 2

(d) 2

Q23. Which Which one of the foll ollowing owing CANNOT be expla xplained by conside consideri ring ng a harm harmonic approximation for the lattice vibrations in solids? (a) (a) Deby’ Deby’s s T3 law

(b) Dulong Dulong Peti Petit’ t’s s law

(c) Optica Opticall branche nches in lattices

(d) Therm herma al expa expansion

Q24. A particl rticle e is constrained ned to move in a truncate truncated d harmoni rmonic c potentia ntial wel well ( x > 0) as shown in the figure. Which one of the following statements is CORRECT? (a) The T he pari parity ty of the first first excited sta state is even (b) The parity of the ground state is even (c) the ground state state energy nergy is is

V  x

1  2

(d) The first excited state energy is

7  2

Q25. The number of inde i ndepende pendent compone components of the sym symm metric etric tensor tensor Aij with indices i, j = 1, 2, 3 is

(a) 1

(b) 3

(c) 6

(d) 9


6


Q.26 – Q.55 carry two marks each.

1 Q26. Consider onsider a system in the unperturbed unperturbed state descri describe bed by the the Hamiltonia tonian, H0   0   The The system is subjec jected to to a perturbation ion of th the formH'   

0  1  .

  , when δ<< 1. The  

energy energy eigenvalue eigenvalues s of the perturbed perturbed system using using the the first fi rst order order perturbati perturbation on approximation are (a) 1 and (1 +2δ)

(b) (1 +δ) and (1 - δ)

(c) (1+2δ) and (1 - 2δ)

(d) (1+δ) and (1 - 2δ)

χ ) as a function Q27. Inverse nverse susce susceptibi ptibillity (1/ χ unction of temperature, perature, T for a ma materia terial underg undergoi oing ng

paramagnetic to ferromagnetic transition is given in the figure, where O is the origin. The values of the Curie Curie consta constant, nt, C, and the the Weiss Weiss molec olecul ular ar field fi eld constant, constant, λ, in CGS units, are 1 

(a) C  5 105,   3 102

O

(b) (b) C  3 102,   5 105 (c) (c) C  3 102,   2 104

600K T

 2 104 (CGS CGS unit)

(d) (d) C  2 104,   3 102

Q28. A pla plane polariz polarized ed electromag electromagneti netic c wave in free free space space at tim time t=0 is given 



by E x, y  10 jˆexpi 6x  8z . The magnetic field B x, z, t is given by 

1 ˆ ˆ 6k  8i expi6x  8z  10ct c



1 ˆ ˆ 6k  8i expi6x  8z  10ct c



1 ˆ ˆ 6k  8i expi6x  8z  ct c



1 ˆ ˆ 6k  8i expi6x  8z  ct

(a) Bx, z, t  (b) (b) Bx, z, t  (c) (c) B x, z,t  (d) (d) Bx, z,t 


















7


 0 Q29. The eigenva eigenvallues of the the matrix trix 1   0

0  1  are 0  (b) 0, 2, 2

(a) 0, 1, 1 (c)

1 0 1

1 1 , ,0 2 2

(d) 2, 2,0

Q30. M atch thetypical spe spectroscopic ctroscopic regions regions specifi cifie ed in Group I with the corresponding type Group II II. of transitions in Group Group I

Group II

(P) Infra-red region

(i) electronic transitions involving valence electrons

(Q) Ultravi traviol ole et-visibl t-vi sible e region region

(ii (ii) nuclea nuclearr transi nsitions

(R) (R) X -ray ray region region

(ii (iii) vibra vibrationa tional transitions of molec olecules ules

(S) (S) γ-ray regi region

(iv) (iv) transi transiti tions ons involving nvolvi ng inner shell shell electrons ctrons

(a) (P, i); (Q, iii); (R, ii); (S, iv) (b) (b) (P, ii); ii ); (Q, (Q, iv iv); (R, i); i); (S, iii) iii ) (c) (c) (P, iii); iii ); (Q, i); (R, iv); (S, (S, ii) ii ) (d) (P, iv); (Q, i); (R, ii); (S, iii) Q31. In the foll fol lowing owing circuit, circuit, for for the outpu outputt volta voltag ge to be V0   V1  V2 / 2 the ratio R1/R2 is R

(a) (a) 1/2

 VCC

R

(b) 1 (c) 2



V1 V2



R1

(d) 3

R2

Vo

- VCC


8


Q32. The term term  j1, j 2 J arising from 2s13d1electro ectronic nic in j-j coupli coupling scheme are

 1 3  1 5 (a)  ,  and  ,   2 2 2,1  2 23,2

 1 1  1 3 (b)  ,  and  ,   2 21,0  2 22,1

 1 1  1 5 (c) (c)  ,  and ,   2 21,0  2 23,2

 3 1  1 5 (d)  ,  and ,   2 2 2,1  2 23,2

Q33. In the foll fol lowing owing circui circuit, t, the the volta voltage ge drop across the the idea deal diode di ode in forward bias condition is 0.7V. 0.7V. The T he current passing ssing throug through h the the diode is

12k

(a) 0.5 mA (b) 1.0 mA

 

24Volt

(c) 1.5 mA 6k 

(d) 2.0 mA

3.3k

Q34. Choose hoose theCORR ORRECT statem tement from the foll fol lowing owing (a) Neutron interacts through electromagnetic interaction (b) Electron does not interact through weak interaction (c) (c) Neutrino eutrino inte interacts racts through through weak and electroma electromagnetic tic interaction nteraction (d) Quark interacts through strong interaction but not through weak interaction Q35. A rod of proper length l0 orie oriented parallel rall el to the the x-axis axis moves moves with with speed 2c/3 along the x-axis in the S-frame, where c is the speed of the li light in in free free space. The The observer is is also

moving along the x-axis with speed c/2 with wi th respe respect ct to the S-f S-frame. The T he length ngth of the rod as measured by the observer is (a) 0.35 l0

(b) 0.48 l0

(c) 0.87 l0

(d) 0.97 l0


9


Q36. A sim simple ple cubic crystal with with lattice ttice param parameter eter ac undergoes transiti transition on into into a tetragonal structure structure with with latti lattice ce param parameters at  bt  2ac andct  2ac , below a certain temperat perature. ure. The The ratio tio of the interpla interplanar spacing cing of (1 0 1) pla planes nes for for the cubic and the tetragona tetragonal structure is is (a)

1 6

(b)

1 6

(c)

3 8

(d)

3 8

Q37. Consi onsider der thefoll fol lowing owing circuit circuit in which which the thecurrent current gain β dc of the transistor is 100.  15V 900

100 k

100 

Which one of the following correctly represents the load line (collector current I C with respect to collector-emitter voltage V CE) and Q-point of this circuit? (a)

15mA

(b)

Q - point (2V, 13mA)

→

C

I

I

VCE 

VCE 

15V

(d)

15mA

→

Q - point (2V, 10 mA)

→

C

(c)

13mA

Q - point (7.5V, 7.5mA)

C

15V

13mA

→

Q - point (7.5V, 6.5mA)

C

I

I

VCE 

15V

VCE 

15V

fiziks c/o Anand Institute of mathematics, 28-B/6 Jia Sarai Near IIT, Hauz Khas, New Delhi, PIN- 110016 (INDIA) Phone: 011-32718565, +91-9871145498 Website: http://www.p http://www.physicsbyfi hysicsbyfiziks.com ziks.com Email: fiziks.physic [email protected] [email protected]

10


Q38. Consider onsider a system whose three energy energy levels are are given given by 0, ε and 2ε. The The energy level ε is two-f two-fold old dege degenerate nerate and the the other two are are nonnon-de dege generate. The The parti partiti tion on functi function on of the system with with 

1 is given by kB T

(a) 1 2e 

(b) 2e   e2

(c) (1 e  ) 2

(d) 1 e   e2

Q39. T wo infini nfi nite telly exten extende ded d homogeneous isotopi sotopic die dielectric ctric media edia (medium-1and (medium-1and medium-2 edium-2 with with dielectric dielectric constant

 1  0

 2and

2

 0

cti vely) y) meet eet at the z =0 pla plane as shown  5 , respectivel

in the figure. A uniform electric field exists everywhere. For z ≥ 0, the electric field is 

given by E1  2iˆ  3 jˆ  5k . The T he interface nterface sepa separati rating ng the two media is is charge charge free.The ree.The electric displacement vector in the medium-2 is given by

medium - 1

medium - 2

z =0

(a) D 2   0 10iˆ 15 jˆ  10kˆ

(b) D 2   0 10iˆ 15 jˆ  10kˆ

(c) (c) D 2   0 4iˆ  6 jˆ  10kˆ

(d) D 2   0 4iˆ 6 jˆ 10kˆ

Q40. The

ground ground

by 100 

state

1  1    4  a0 

wavef wavefuncti unction on

for for

the

hydrogen hydrogen

atom

is

given given

3/ 2

er / a0 , where a0 is the Bohr radius.

The The plot lot of th the radial ial pr probability ility density ity, P(r) for for the hydrogen hydrogen atom in the ground state state is fiziks c/o Anand Institute of mathematics, 28-B/6 Jia Sarai Near IIT, Hauz Khas, New Delhi, PIN- 110016 (INDIA) Phone: 011-32718565, +91-9871145498 Website: http://www.p http://www.physicsbyfi hysicsbyfiziks.com ziks.com Email: fiziks.physic [email protected] [email protected]

11


(a)

(b)

P(r)

P(r)

r/a0

(c)

r/a0

(d)

P(r)

P(r)

r/a0

r/a0

Q41. Total otal binding energie rgies of O15, O16 and O17 are 111.96 111.96 MeV MeV,, 127.62 MeV MeV and 131.76 131.76 M eV, eV, res respe pectivel ctively. y. The T he energy nergy gap gap betwee between 1p1 and 1d3 neutron shells for for the nucl nuclei ei 2

2

whose mass ass number is is close closed d to 16, is is (a) (a) 4.1 M eV

(b) 11.5 11.5 MeV

(c) 15.7 MeV

(d) 19.8 19.8 MeV

Q42. A particl rticle e of mass m is attached to fixed point O by a weightless inextensible string of length ngth a. It I t is is rotating unde underr the gravi gravity ty as as shown in the figure. gure.

z

The The Lag Lagrangian ian of the particle icle is L ,  



1 2 2 ma   sin2    2   mgacos 2

a

where θ and are the polar polar angles g

The The Hamilto iltonian ian of the particle icles s is p 2  1  2  p  2   mgacos (a) H  2   2ma  sin  

(c) (c) H 

1  p 2  p 2   mgacos 2 2ma

p 2  1  2 p    mgacos (b) H  2   2 2ma  sin  

(d) H 

1  p 2  p 2   mgacos 2 2ma


12

fiziks Forum for CSIR-UGC JRF/NET, GATE, IIT-JAM, GRE in PHYSICAL SCIENCES 





  Q43. Given F  r  B where B  B0 iˆ jˆ  k is constant vector and r is the position vector.





The The value lue of  F  dr , where C is a circle of unit radius entered at origin is, C

(a) 0

(b) 2 B0

(c) (c)  2 B0

(d) 1

C

Q44. The val value of the integra ntegrall  e1/ z dz , using the contour C of circle with unit radius z  1 is C

(a) 0

(b) 1 2 i

(c) 1 2 i

(d) 2 i

Q45. A param paramagneti gnetic c system consisti consisting ng of N spin-half particles is placed in an external magnetic field. It is found that N/2 spin spin are are al aligned gned paral paralllel and and the rem remaining ning N/2 spins are aligned antiparallel to the magnetic field. The statistical entropy of the system is, (a) 2NkB ln 2

(b)

N kB ln 2 2

(c)

3N kB ln 2 2

(d) NkB ln 2

Q46. The equil quilibrium brium vibra vibrati tion on freq freque uency for an oscil oscillator is obse observed rved at 2990 2990 cm-1. The ratio of the frequencies ncies correspo corresponding nding to the fi first and the the fundam fundamental ntal spectral lines nes is is 1.96. Considering the oscillator to be anharmonic, the anharmonicity constant is (a) 0.005 0.005

(b) 0.02

(c) 0.05

(d) 0.1

Q47. At a certain certain temperature perature T, the avera average ge spe spee ed of nitrogen nitrogen mole olecules cules in air is found found to to be 400 m/s. The T he most probabl probable e and and the root mean square square speed of the molecul olecules es are, respectively, (a) 355 m/s, /s, 434 m/s

(b) 820 m/s, /s, 917 m/s

(c) 152 m/s, /s, 301 m/s

(d) 422 m/s, /s, 600 m/s


13


Common Data Questions Common Data for Questions 48–49 ikx ikx  2e ikx The The wavefunction ion of particle icle moving ing in fre free space is give iven by,   eikx

Q48. The energy nergy of the the parti particl cle e is 5 2k2 (a) 2

(b)

3 2k2

k2 (c) 2 

2

(d)



2

k2

Q49. The proba probabil bility current current density nsity for th the real part of the wavefunction is (a) 1

(b)

k

(c)

k

(d) 0

2

Comm ommon Data for for Questions uestions 50 50 – 51

The The disp ispersion ion relat lation ion for for a one dimension ional mo monatomic crystal wit with h lat lattice ice spacing ing a, which which inte interacts racts nearest nei neighbour hbour harmonic onic potenti potentia al is given given by   Asin

Ka 2

where A is a consta constant of appropriat ppropriate e uni unit. Q50. The group group vel velocity ocity at the bounda boundary of the first fi rst Bril rillouin zone is (a) 0

(b) 1

(c)

Aa2 2

1 Aa2 (d) 2 2

Q51. The force orce constant constant between the nearest neigh neighbour bour of the lattice attice is (M is the mass of the atom) MA2 (a) 4

MA2 (b) 2

(c) MA2

(d) 2MA2


14


L inked nked Ans Answe werr Questions Questions Stateme Statement for for L inked Answ Answer er Que Questi stions ons 52 and 53: 53:

In a hydroge hydrogen atom atom,, conside considerr that the the electronic charge charge is unifo uniform rmlly distri distribut buted ed in a spherical volume of radius a (  0.5 1010 m) around the proton. The T he atom atom is pla placed in a uniform electric field E  30 105V / m.Assum .A ssume tha thatt the sphe spheri rica call distri distribution bution of the nega negative tive charge remains undistorted undistorted under under the electri electric c fi field. eld. Q52. In the the equil quilibrium brium condi condition, tion, the the sepa separat ratiion betwe between en the posi positive tive and and the negati gative ve charge charge cente centers rs is is (a) 8.66 1016 m

(b) 2.60 1015 m

(c) 2.601016 m

(d) 8.66 1015 m

Q53. The polariza polarizabi billity of the hydroge hydrogen atomin unit of (C 2m/N) is is (a) 2.0 1040 m

(b) 1.4 1041 m

(c) 1.4 1040 m

(d) 2.0 1039 m

Stateme Statement for for L inked Answ Answer er Que Questi stions ons 54 and 55: 55:

A particle of mass m slides under the gravity without friction along the parabolic path y  ax2 axis shown in the figure. Here a is a constant.

Q54. The L agrang grangiian for this this parti particl cle e is given by, (a) L 

1 2 2   mgax mx 2

(b) L 

1 2 2   mgax m1 4a2x2 x 2

(c) (c) L 

1 2 2   mgax mx 2

(d) L 

1 2 2   mgax m1 4a2 x2 x 2

Q55. The L agrang grange’s e’s equ equa ation of motion otion of the parti particl cle e is (a) x  2gax

2  (b) m1 4a2x2 x  2mgax  4ma2 xx

(c) (c) m1 4a2 x2 x  2mgax 4ma2xx 2

(d) x  2gax


15


GENERAL APTI TUDE TUDE (GA) (GA) QUESTI QUESTI ONS ONS Q.56 – Q.60 carry one marks each.

Q56. Choose the gram grammatica ticallly INCORRECT sentence: (a) They gave gave us the the money back back les l ess s the servi service ce charge of Three Hundred rupees. (b) This his country’ country’s s expe expendi nditure tureis not les less s than that that of Ba B anglad nglade esh. (c) The T he committee initi nitia ally aske asked d for a funding unding of Fi Fifty L akh rupees, but la later settled ttled for a less sum. (d) This country’s expenditure on educational reforms is very less. Q57. Which hich oneof the foll ollowing owing options options is the close closest st in meaning ning to the word given ven bel below? M itigate itigate

(a) Dim Di minish nish

(b) Divul Di vulge ge

(c) Dedicate

(d) Denote Denote

Q58. Choose the most appropria ppropri ate alternative tive from from the options options given given below below to compl complete the foll ollowing owing sente sentence: Despite several _________ the mission succeeded in its attempt to resolve the conflict.

(a) attem attempts

(b) setbacks cks

(c) (c) meeti eeting ng

(d) delega delegations tions

Q59. The cost functi function on for a product product in a firm is gi given by by 5q2, where q is the am amount of production .The .T he firm can sell theproduct product at a market arket price price of Rs. Rs. 50 per uni unit. t. The T henumber ber of units units to be produce produced d by the firm fi rm such that the profi profit is is ma maxim ximized is: is: (a) 5

(b) 10

(c) 15

(d) 25

Q60. Choose the most appropria ppropri ate alternative tive from from the options options given given below below to compl complete the foll ollowing owing sente sentence: Sure Suresh’s dog is the one________ was hurt hurt in i n the stam stampe pede. de.

(a) that that

(b) which which

(c) who

(d) whom


16


Q.61 – Q.65 carry two marks each.

Q61. Which Which of the foll fol lowing owing assertions rtions are CORRECT? P. Adding dding 7 to eac each h entry entry in in a list adds adds 7 to the the mean of the list Q. Adding 7 to each entry in a list adds 7 to the standard deviation of the list R. Doubling each entry in a list doubles the mean of the list S. Doubling each entry in a list leaves the standard deviation of the list unchanged (a) (a) P, Q

(b) Q, R

(c) P, R

(d) (d) R, S

Q62. An automobil obile pla plant contracted to buy shock absorbers absorbers from two suppliers X and Y. X suppl supplies 60% 60% and and Y suppl suppliies 40% of the shock shock absorbe absorbers. rs. All shock shock absorbers bsorbers are are

subje subjected to to a qual quality test. The The ones that that pass pass the qual quality test are conside considered red reli reliable. ble. Of X’s shock absorbers, 96% are reliable. Of Y Y’s shock absorbers, 72% are reliable.

The The probability ility that a randomly chosen shock absorber, which ich is fou found to be reliable, le, is made by Y is (a) 0.288

(b) 0.334

(c) 0.667

(d) 0.720

Q63. A poli political tical party orders an arch for the entrance to the ground in whi which the annual conve convention is is bei being he held. The T he profil profile of the arch fol follows the the equ equa ation y  2x  0.1x2 where y is the hei heigh ghtt of the arch arch in in met meters. ers. The T he maxim ximumpossible possible height of the arch arch is is (a) 8 meters

(b) 10 meters eters

(c) (c) 12 meters eters

(d) 14 meters eters

Q64. Wante anted d Te T emporary, porar y, Par Part-ti t-time me per persons for the post post of Field F ield I nter nterviewer to condu conduct ct personal interviews to collect and collate economic data. Requirements: High School-pass, must be available for Day, Evening and Saturday work. Tra T ran nsporta rtation ion paid, id, expenses reim reimb burse rsed.

Which hich one of the foll fol lowing owing is is the bes bestt inference inference from the the above above adverti dvertise sem ment? (a) Gender-di Gender-discri scrim minatory natory

(b) X enophob nophobiic

(c) (c) Not desi design gned to makethe post attractive ttractive

(d) Not gende gender-di r-discri scrim minatory natory

Q65. Give Gi ven n theseque quence of term terms, AD CG CG FK J P, the next next term term is (a) (a) OV

(b) OW

(c) PV

(d) (d) PW


17



18

Gate 2012 Physics Question Paper

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