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Test Paper : III Test Subject : PHYSICAL SCIENCE Test Subject Code : Test Booklet Serial No. : _______________________ OMR Sheet No. : _________________________________ K-2514 Roll No. (Figures as per admission card) Name & Signature of Invigilator/s Signature: ____________________________________ Name : ____________________________________ Signature : ___________________________________ Name : ___________________________________ Paper : III Subject : PHYSICAL SCIENCE Time : 2 Hours 30 Minutes Maximum Marks : 150 Number of Pages in this Booklet : 16 Number of Questions in this Booklet : 75 A»Ü¦ìWÜÚWæ ÓÜãaÜ®æWÜÙÜá D ±Üâo¨Ü ÊæáàÆᤩ¿áÈÉ J¨ÜXst Óܧ٨ Ü È Ü É ¯ÊÜá¾ ÃæãàÇ ®ÜíÃÜ®áÜ ° ÃæÀáÄ. 2. D ±Ü£ÅP¿ æ áá ÖÜá BÁáR Ë«Ü¨Ü G±Üñ³ ôæ ¨Üá ±ÜÅÍW°æ ÙÜ ®Ü áÜ ° JÙÜWã æ íw¨æ. 3. ±ÜÄàPæÒ¿á ±ÝÅÃíÜ »Ü¨È Ü É , ±ÜÅÍ° æ ±ÜâÔ¤P¿ æ á®Üá° ¯ÊÜáWæ ¯àvÜÇÝWÜáÊÜâ¨Üá. Êæã¨ÜÆ 5 ¯ËáÐÜWÙÜ È Ü É ¯àÊÜâ ±ÜâÔ¤P¿ æ á®Üá° ñæÿ æ áÆá ÊÜáñÜᤠPæÙXÜ ®Üíñæ PÜvÝx¿áÊÝX ±ÜÄàQÒÓÆ Ü á PæãàÃÜÇÝX¨æ. 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OMR EñܤÃÜ ÖÝÙæ¿áÈÉ®Ü AívÝPÜê£ ÖæãÃÜñáÜ ±ÜwÔ ¸æàÃæ ¿ÞÊÜâ¨æà Óܧ٨ Ü È Ü É WÜáÃÜá£Ô¨ÜÃ,æ A¨ÜÃÜ ÊÜåèÆÂÊÜÞ±Ü®Ü ÊÜÞvÜÇÝWÜáÊÜâ©ÆÉ. 1. 6. OMR EñܤÃÜ ÖÝÙæ¿áÈÉ Pæãor ÓÜãaÜ®æWÜÙÜ®Üá° hÝWÜÃÜãPÜñæÀáí¨Ü K©Ä. 7. GÇÝÉ PÜÃÜváÜ PæÆÓÜÊÜ®Üá° ±ÜâÔ¤Pæ¿á Pæã®æ¿áÈÉ ÊÜÞvÜñÜPÜR¨Ü᪠. 8. ¯ÊÜá¾ WÜáÃÜáñÜ®Üá° ×ÃÜíWܱÜwÓÜÖÜá¨Ý¨Ü ¯ÊÜá¾ ÖæÓÜÃÜá A¥ÜÊÝ ¿ÞÊÜâ¨æà bÖæ°¿á®Üá° , ÓÜíWÜñÜÊÝ¨Ü ÓܧÙÜ ÖæãÃÜñÜá ±ÜwÔ, OMR EñܤÃÜ ÖÝÙæ¿á ¿ÞÊÜâ¨æà »ÝWÜ¨È Ü É Ãæ¨ÃÜ ,æ ¯àÊÜâ A®ÜÖì Ü ñæWæ ¸Ý«ÜÂÃÝXÃÜᣤàÄ. 9. ±ÜÄàPæÒ¿áá ÊÜááX¨Ü®ÜíñÜÃÜ, PÜvÝx¿áÊÝX OMR EñܤÃÜ ÖÝÙæ¿á®Üá° ÓÜíËàPÜÒPÜÄWæ ¯àÊÜâ ×í£ÃÜáXÓܸàæ PÜá ÊÜáñÜᤠ±ÜÄàPÝÒ PæãsÜw¿á ÖæãÃÜWæ OMR ®Üá° ¯Êæã¾í©Wæ 10. 11. 12. 13. Pæãívæã¿á PÜãvܨÜá. ±ÜÄàPæÒ¿á ®ÜíñÜÃÜ, ±ÜÄàPÝÒ ±ÜÅÍæ° ±Ü£ÅPæ¿á®Üá° ÊÜáñÜᤠ®ÜPÜÆá OMR EñܤÃÜ ÖÝÙæ¿á®Üá° ¯Êæã¾í©Wæ ñæWæ¨ÜáPæãívÜá ÖæãàWÜÖÜá¨Üá. ¯àÈ/PܱâÜ ³ ¸ÝÇ ±ÝÀáíp ±æ® ÊÜÞñÜÅÊæà E±ÜÁãàXÔÄ. PÝÂÆáRÇàæ oà A¥ÜÊÝ ÇÝW pæàÇ CñÝ©¿á E±ÜÁãàWÜ樆 áÜ ° ¯ÐæàÓÜÇÝX¨æ. ÓÜÄ AÆÉ¨Ü EñܤÃÜWÜÚWæ Má| AíPÜ CÃÜáÊÜâ©ÆÉ . K-2514 1 Instructions for the Candidates 1. Write your roll number in the space provided on the top of this page. 2. This paper consists of seventy five multiple-choice type of questions. 3. At the commencement of examination, the question booklet will be given to you. In the first 5 minutes, you are requested to open the booklet and compulsorily examine it as below : (i) To have access to the Question Booklet, tear off the paper seal on the edge of this cover page. Do not accept a booklet without sticker-seal and do not accept an open booklet. (ii) Tally the number of pages and number of questions in the booklet with the information printed on the cover page. Faulty booklets due to pages/questions missing or duplicate or not in serial order or any other discrepancy should be got replaced immediately by a correct booklet from the invigilator within the period of 5 minutes. Afterwards, neither the Question Booklet will be replaced nor any extra time will be given. 4. Each item has four alternative responses marked (A), (B), (C) and (D). You have to darken the oval as indicated below on the correct response against each item. Example : A B C D where (C) is the correct response. 5. Your responses to the question of Paper III are to be indicated in the OMR Sheet kept inside the Booklet. If you mark at any place other than in the ovals in OMR Answer Sheet, it will not be evaluated. 6. Read the instructions given in OMR carefully. 7. Rough Work is to be done in the end of this booklet. 8. If you write your name or put any mark on any part of the OMR Answer Sheet, except for the space allotted for the relevant entries, which may disclose your identity, you will render yourself liable to disqualification. 9. You have to return the test OMR Answer Sheet to the invigilators at the end of the examination compulsorily and must NOT carry it with you outside the Examination Hall. 10. You can take away question booklet and carbon copy of OMR Answer Sheet soon after the examination. 11. Use only Blue/Black Ball point pen. 12. Use of any calculator or log table etc., is prohibited. 13. There is no negative marks for incorrect answers. ±Üâ.£.®æãà./P.T.O. *K2514* Total Number of Pages : 16 PHYSICAL SCIENCE PAPER III Note : This paper contains seventy-five (75) objective type questions. Each question carries two (2) marks. All questions are compulsory. 4. Which of the following is not a tensor ? 1. Newton-Raphson formula is given by (A) Velocity # (A) ! ! " " ! (B) Acceleration ! ! # " ! (C) Mass # (B) ! ! " # # (C) ! (D) Gradient of a scalar field ! " " ! 5. Let f0, f1, f2, ...fn are known values of a function f(x) at the points x0, x1, x2, ... xn. The first divided difference between xs and xt is ! ! ! # " ! # (D) " ! ! " ! ! ! " (A) ! ! # " ! ! ! ! $ # ! " ! ! ! 2. The value of the integral ! " ! (B) using ! ! ! $ # ! " ! ! Simpsons ! rule is ! (C) (A) 4.86305 ! ! ! $ # " ! ! ! (B) 2.36205 ! (D) (C) 6.46505 ! ! ! $ # " ! ! ! (D) 5.84405 6. Which interpolation formula does not give any information regarding any error committed during approximation ? 3. Error in the Trapezoidal formula of the order of (A) Lagranges interpolation (B) Newton-Gregory backward difference interpolation (A) h 2 (B) h (C) h (C) Newton-Gregory forward difference interpolation (D) h4 (D) Gauss forward difference interpolation 3 Paper III 2 K-2514 *K2514* Total Number of Pages : 16 7. Relation between two finite groups in 10. For conservative system where the many-to-one mapping then it called as coordinate transformation is independent of time the Hamiltonian (A) Isomorphic relation function represents (B) Homomorphic relation (A) Kinetic energy of the system (C) Automorphic relation (B) Total energy of the system (D) Monomorphic relation (C) Potential energy of the system 8. If the Lagrangian does not depend on (D) Difference of kinetic and potential time explicitly energies (A) The kinetic energy is a constant of motion 11. The Poisson bracket of any constant of (B) The potential energy is a constant motion with Hamiltonian H is of motion (A) 1 (C) The Hamiltonian is a constant of (B) 1 motion (C) 0 (D) The Hamiltonian cannot be a constant of motion (D) Infinity 9. For the given transformations. T1 : Q = p, 12. The principle of least action in terms of P = q and T2 : Q = p, P = q where p arc length of the particle trajectory is and q are canonically conjugate variables, which of the following (A) # # " " ! ! statements is true ? (B) (A) Both T1 and T2 are canonical (B) Only T is canonical (C) # 1 # " # # " # # " " ! " ! ! ! (C) Only T is canonical 2 (D) " ! ! (D) Neither T or T is canonical 1 K-2514 2 3 Paper III *K2514* Total Number of Pages : 16 13. If the effective potential energy for radial motion is Veff (r), the condition for stability in radial motion is given by 16. The Poynting vector S is defined as the 1) The existence of a local minimum in V (r) at r = r eff (A) Energy per unit time 0 (B) Energy per unit area ! " & % 2) " # $ # ! # ! " ! " Which of the following is correct ? (C) Energy per unit time per unit area (A) 1 and 2 are false (D) Energy per unit volume (B) 1 and 2 are correct 17. A transmission line whose (C) 1 is false and 2 is correct characteristic impedance a pure (D) 1 is correct and 2 is false resistance 14. Larmor formula is for (A) Must be a lossless line (A) Energy radiated by an accelerated charged particle (B) Must be a distortion-less line (B) Power radiated by an accelerated charge particle (C) May be a lossless line (C) Power radiated by an uniformly moving particle (D) May not a distortion-less line (D) Energy radiated by an uniformly moving particle 18. The velocity factor of a transmission line 15. The dispersive relation for a low density plasma is ! ! " ! ! , where (A) Depends on the dielectric is " the plasma frequency and c is the speed of light in free space. The relation between the group velocity (v g) and phase velocity (vp) is (A) Paper III transmission line ! (C) Is governed by skin effect ! ! (D) Is higher for a solid dielectric ! ! " (D) (B) Increases the velocity along the ! (B) (C) constant of the material used ! than air ! ! 4 K-2514 *K2514* Total Number of Pages : 16 19. Choose the correct answer : 22. Alpha emission is an example of According to Diracs relativistic theory, (A) Barrier reflection orbital angular momentum (B) Barrier tunnelling (A) is a constant of motion in a central force-field (C) Barrier refraction (B) vanishes in a central force-field (D) Barrier absorption (C) is not a constant of motion in a 23. The ratio of Einsteins A and B central force-field coefficients is (D) is a parameter in a central forcefield ! ! (A) ! " ! 20. The WKB approximation often referred as ! ! (B) (A) Classical approximation ! " ! (B) Quantum approximation ! ! ! (C) (C) Semi-classical approximation ! " " ! ! " (D) Weak approximation ! (D) ! ! 21. In partial wave analysis, the expression for total cross-section of scattering is ( 24. The relativistic relation for the total energy E of a free particle with rest mass m0 is # (A) " & % ! $ # ! " ' 2 2 2 (A) E = C p + (B) ! ! " ( # " ' & % ! $ # ! " 2 2 2 (B) E = C p + m0C & 4 # (C) " ' & ! % $ # ! " 2 (C) E = cp + ( ! ! " (D) & # ( " ' & ! % $ # ! 2 " (D) E = ! ! " K-2514 5 Paper III *K2514* Total Number of Pages : 16 28. Fractional fluctuations of number of particles in Bose-Einstein gas is given by 25. In Borns approximation the effective cross-section of scattering depends on (A) Momentum (p) of the incident (A) particle ! " (B) ( (B) Angle of scattering ( ) ! ) ! " ! (C) p and (D) p and in any combination (C) in the combination p sin ! # (D) # " ! ! ! " ! 29. Magnetic susceptibility per electron of diamagnetic materials is 26. Identify which of the following is second order phase transition ? 1) Transition of liquid helium-I into liquid helium-II (A) $ " # " ! " ! ! 2) Transition of water into water vapour (B) ! # $ % " ! # " " ! 3) Transition of non-ferromagnetic state to ferromagnetic state (C) " # " ! " ! ! (A) 1 and 2 (B) 2 and 3 (D) & # $ % " ! " ! " ! (C) 1 and 3 30. According to Curie-Weiss law, which is of the following is correct ? (D) 1, 2 and 3 27. Ising model is to understand the ! (A) behaviour of a substance whose " ! molecules possess ! (B) (A) Non-magnetic nature (B) Random orientation " ! ! (C) " ! (C) Electrostatic nature ! (D) (D) Magnetic moment Paper III 6 " K-2514 *K2514* Total Number of Pages : 16 31. All the materials have ____________ 34. An OP AMP data sheet gives a 15 V property. power bandwidth of 25 kHz. Its slew (A) Paramagnetic rate is (B) Diamagnetic (A) 0.236 V/ s (C) Ferromagnetic (B) 2.36 V/ s (D) Ferrimagnetic (C) 23.6 V/ s 32. The equation of fitting a straight line that gives as a0 + a1 indicates the given below information. (D) 236.0 V/ s ! Statement (A) : " ! ! 35. A piece of semiconducting material is is the centroid of introduced in a circuit. If the temperature the given data points. of the material is raised the circuit current Statement (B) : The fitted straight line will passes through the centroid of the data points. (A) Increase (A) (A) and (B) are correct (B) Remain the same (B) Only (A) is correct (C) Decrease (C) Only (B) is correct (D) Cease to flow (D) (A) and (B) are both wrong 36. The Fourier transform of sin(x)/x is 33. Flash ADC is (A) The slowest of all types of ADCs ! (A) # (B) A converter which uses n comparators for generating a n-bit $ % " ! & (B) digital number # $ % " ! n (C) Fastest of all ADCs and need (2 1) ( comparators for generating a n-bit (C) % & ' " ! # $ % " ! digital number (D) a square function (D) Cannot be practically realized K-2514 7 Paper III *K2514* Total Number of Pages : 16 40. Paschen-Back effect is due to 37. An amplifier has a voltage gain of 500 and an input impedance 20 k without (A) Spin of the electron any feedback. Now a negative feedback with ! " ! (B) Only orbital motion of the electron is applied. Its gain and input (C) Spin-orbit interaction impedance with feedback will (D) Spin of the nucleus respectively be (A) 9.8 and 392 41. In ESR the contribution by nuclear magnetic moment (B) 9.8 and 1020 k (A) Exists but neglected (C) 50 and 1020 (B) Does not exist (D) 50 and 2 k (C) Exists and considered (D) Has very high value 38. The normal Zeeman effect of cadmium red line is 6438 . When the cadmium 42. The Frank-Condon principle is based on the principle on the fact that nuclei are atoms are placed in a magnetic field of 0.009 T, the shift is (A) moving with velocity of light (A) 0.174 (B) are having zero mass (B) 0.0174 (C) are at rest (C) 0.00174 (D) are neglected (D) 0.000174 43. Hyperfine structure and isotope effect are associated with 39. In 4f shell of an atom, there are 6 (A) only splitting of the electronic energy levels electrons. The value of J is (A) 0 (B) only shifting of electronic energy levels (B) 1 (C) 2 (C) both shifting and splitting of electronic energy levels (D) 3 (D) no change in the energy levels Paper III 8 K-2514 *K2514* Total Number of Pages : 16 44. A laser operates at a frequency of 48. The energy separation between two 3 × 104 Hz and has a slit width 102m. The angular spread will be (A) 10 2 radians (B) 10 4 radians (C) 10 3 (D) 10 5 consecutive Stokes line in Raman scattering depends on (A) Energy separation between vibrational levels in the excited state radians (B) Wavelength of the incident light radians (C) Energy separation between vibrational levels in the ground 45. Moseleys law relates state (A) wavelength and intensity of X-rays (D) Intensity of the incident light (B) frequency and applied voltage 49. The number of photons emitted per (C) frequency and atomic number second from one watt Ar-ion laser (D) wavelength and scattering operating at 488.0 nm is approximately (A) 10.23 × 10 46. The possible values of total angular momentum J resulting from the addition of two angular momenta j1 = 1 and j2 = 2 are (B) 2.46 × 10 18 (C) 10.23 × 10 (D) 2.46 × 10 (A) 1, 2 (B) 1, 3 19 17 15 50. The maximum degeneracy of an (C) 0, 1, 2 energy level with principal quantum (D) 1, 2, 3 number n is (A) n 47. Raman spectra is due to collision of (B) n (A) Photon with electron 2 (C) 2n (B) Photon with molecule 2 (D) 2n2 + 1 (C) Electron with atom (D) Electron with photon K-2514 9 Paper III *K2514* Total Number of Pages : 16 51. A two-dimensional lattice has the basis vectors 2i and i + 2j. The basis vectors of the reciprocal lattice are (A) % ! ! " 55. Match the material properties (List I) with the units (List II) : # ! " # $ % $ & ! " # $ % $ & & $ ! ! (B) % ! ! " # " # $ % & ' ( ' & " ) % * + , ! " - ! . / ! ! 0 ! " 1 * 2 2 ' % 2 " . 3 4 ' 5 ' + 6 7 ! " 8 " . 3 ! 5 / $ ! 9 (C) ! $ ! ! " # ! " : ) % 2 . * 5 " & 3 ; < = & + ' > ' + 6 1 ! " ? " / ! " @ (D) % ! ! " ! " : ) % 2 . 3 % 5 % & + 2 ' & " $ 3 A % 2 B ! " . ! " ? ! C (A) 1-A, 2-D, 3-B, 4-C # $ (B) 1-B, 2-C, 3-A, 4-D (C) 1-B, 2-D, 3-A, 4-C 52. Which one of the following pairs of crystal structures can have the same packing fraction of 0.74 ? (D) 1-A, 2-D, 3-C, 4-B (A) BCC and BCT 56. For copper metal, the conduction electron density is 8.45 × 1028 m3. The Fermi wave vector is (B) BCC and FCC (C) BCC and HCP (A) 2.5 × 1010 m (D) FCC and HCP 10 (B) 1.36 × 10 m 10 (C) 4.5 × 10 m 53. Ionic solids are 10 (D) 1.36 × 10 m (A) Soft and brittle (B) hard and brittle 57. If E is the electric field developed in the presence of a temperature gradient T maintained at the ends of a metal rod, under open circuit conditions, then the constant of proportionality in the equation E = c T is (C) Malleable and ductile (D) Malleable, hard and brittle 54. In case of instability in a cubic crystal (A) (A) Peltier coefficient ! (B) C44 > 0 (C) C (D) C Paper III 1 11 11 (B) Joule coefficient >C (C) Seebeck coefficient =C (D) Thermal coefficient 12 12 10 K-2514 *K2514* Total Number of Pages : 16 58. A Frenkel defect in an ionic crystal is a stochiometric defect of 61. In tight binding approximation, for a simple cubic lattice, the band width is (A) a cation vacancy (A) 15 (B) an anion vacancy (C) a pair of cation and anion vacancy (B) 12 (D) a pair of cation interstitial and cation vacancy (C) 9 (D) 6 59. When a dc voltage V is applied across a superconductor-insulatorsuperconductor junction ? 62. Liquid helium does not exhibit 1) Cooper pairs cross the barrier layer (A) Fountain effect 2) An oscillating current of KHz frequency is produced (B) Lambda transition 3) A photon of energy 2eV is emitted/ absorbed (C) Thermo-mechanical effect (D) Photo-mechanical effect 4) A dc current is produced 5) A very precise value of e/h can be obtained 63. Most of the liquid crystal cells used in LCD display are of the type Which of the above statements are true ? (A) 1, 4, 5 (A) Smectic (B) 2, 4, 5 (B) Nematic (C) 1, 3, 5 (C) Twisted nematic (D) 1, 2, 5 (D) Cholestric 60. The relation between resistivity of a metal at high temperature T is 64. Which of the following are probable to be captured by the nucleus ? (A) ! (A) K-shell electrons (B) ! (B) L-shell electrons (C) ! (C) M-shell electrons (D) K-2514 (D) Outermost-shell electrons ! 11 Paper III *K2514* Total Number of Pages : 16 65. The binding energy per nucleon is 68. In the maximum for the nucleus (A) decay, the particles accompanying the daughter nucleus are 56 (A) Electron and neutrino Fe (B) Electron and anti-neutrino 4 (B) He (C) Positron and neutrino (C) 208 (D) 101 Pb (D) Positron and anti-neutrino Mo 69. The reaction # ! # $ & ! % ' ! " 66. According to meson theory of nuclear ___________ is an example of forces a neutron (A) Emits a (A) Alpha decay ° meson and is converted (B) Beta decay into a proton (B) Emits a (C) Positron decay meson and is converted (D) Electron capture into a proton (C) Emits a + 70. meson and is converted 131I, has a half life of 8.04 days. Assuming you start with a 1.53 mg sample of 131I, how many mg will remain after 13 days ? into a proton (D) Cannot be converted into a proton (A) 0.835 (B) 0.499 67. Consider ! particles each having (C) 0.422 an energy of 1 MeV. Arrange these (D) 0.268 particles in the order of increasing distance they travel in air. (A) " 71. Nuclei above the belt of stability can lower their neutron to proton ratio by ! (A) Beta emission (B) " ! (B) Gamma emission (C) (D) Paper III " (C) Positron emission ! (D) Electron capture ! 12 K-2514 *K2514* Total Number of Pages : 16 72. How many neutrons are emitted when a californium-249 nucleus (Z = 98) is bombarded with a carbon 12 nucleus to 74. The decay chain of the radioactive nucleus involves eight alpha decays and six produce a % & ' " ! # $ nucleus ? (A) 1 (B) 2 (C) 3 (D) 4 decays. The final nucleus at the end of the process will have (A) Z = 84, A = 224 (B) Z = 88, A = 206 73. In the case of fundamental particles ? (C) Z = 82, A = 206 1) Conservation of energy is obeyed 2) Conservation of momentum is obeyed but angular momentum is not obeyed (D) Z = 76, A = 200 3) Conservation of parity is not obeyed 75. CPT theorem is also known as 4) Conservation of isotopic spin is obeyed Which of the following options is correct ? (A) Luders-Pauli theorem (A) 1, 2 (B) 2, 3 (C) 3, 4 (D) 1, 4 (B) Briet-Wigner theorem (C) Optical theorem (D) Gellmann theorem K-2514 13 Paper III *K2514* Total Number of Pages : 16 bñÜᤠÃÜÖÜPÝRX ÓܧÙÜ Space for Rough Work Paper III 14 K-2514 *K2514* Total Number of Pages : 16 bñÜᤠÃÜÖÜPÝRX ÓܧÙÜ Space for Rough Work K-2514 15 Paper III *K2514* Total Number of Pages : 16 bñÜᤠÃÜÖÜPÝRX ÓܧÙÜ Space for Rough Work Paper III 16 K-2514