QP CGSPE26 Geophy II 09022026

Combined Geo-Scientist (Preliminary] Examination, 2026 DO NOT OPEN THIS TEST BOOKLET UNTIL YOU ARE TOLD TO DO SO T.B.C. : BBSP-T-GPS Test Booklet Series Serial No. 1000109 TEST BOOKLET PAPER—II ( Geophysics ) Time Allowed : Two Hours Maximum Marks : 300 1. 2. 10. . You have to enter your Roll Number on the Test Booklet in INSTRUCTIONS IMMEDIATELY AFTER THE COMMENCEMENT OF THE EXAMINATION, YOU SHOULD CHECK THAT THIS TEST BOOKLET DOES NOT HAVE ANY UNPRINTED OR TORN OR MISSING PAGES OR ITEMS, ETC. IF SO, GET IT REPLACED BY A COMPLETE TEST BOOKLET. Please note that it is the candidate’s responsibility to encode and fill in the Roll Number and Test Booklet Series A, B, C or D carefully and without any omission or discrepancy at the appropriate places in the OMR Answer Sheet. Any omission/discrepancy will render the Answer Sheet liable for rejection. the Box provided alongside. DO NOT write anything else on the Test Booklet. . This Test Booklet contains 120 items (questions). Each item comprises four responses (answers). You will select the response which you want to mark on the Answer Sheet. In case you feel that there is more than one correct response, mark the response which you consider the best. In any case, choose ONLY ONE response for each item. - You have to mark all your responses ONLY on the separate Answer Sheet provided. See directions in the Answer Sheet. . All items carry equal marks. . Before you proceed to mark in the Answer Sheet the response to various items in the Test Booklet, you have to fill in some particulars in the Answer Sheet as per instructions sent to you with your Admission Certificate. After you have completed filling in all your responses on the Answer Sheet and the examination has concluded, you should hand over to the Invigilator only the Answer Sheet. You are permitted to take away with you the Test Booklet. . Sheets for rough work are appended in the Test Booklet at the end. Penalty for wrong answers : THERE WILL BE PENALTY FOR WRONG ANSWERS MARKED BY A CANDIDATE IN THE OBJECTIVE TYPE QUESTION PAPERS. (i) There are four alternatives for the answer to every question. For each question for which a wrong answer has been given by the candidate, one-third of the marks assigned to that question will be deducted as penalty. (ii) If a candidate gives more than one answer, it will be treated as a wrong answer even if one of the given answers happens to be correct and there will be same penalty as above to that question. (iii) If a question is left blank, i.e., no answer is given by the candidate, there will be no penalty for that question. DO NOT OPEN THIS TEST BOOKLET UNTIL YOU ARE TOLD TO DO SO 1. The geophysical methods used for investigating the shallow features of the Earth’s crust are (a) static methods only (b) dynamic methods only (c) static and dynamic methods both (0) relaxation methods only 2. The units of magnetic field strength and magnetic flux density, respectively are (a) ampere metre! and volt second metre 2 (b) volt second metre~? and ampere metre! (c) volt second and ampere metre~! () ampere metre~! and volt second 3. The angle of obliquity of the Earth ranges from (a) 21:19 to 25:39 (0) 2197 to 24:39 21:99 to 25:39 (0 21:19 to 24:39 4. Which one of the following planets of the solar system has the highest mean orbital velocity? (a) Mercury (b) Venus (c) Earth (‌) Mars BBSP-T-GPS/62A 5. Which one of the following relations is correct among the radius of sphere, R, and equatorial and polar radii of the international reference of ellipsoid, and respectively, if the volumes of the sphere and ellipsoid are equal? a-R (a) R-c= 5 (b) R-c=a-R () R-c=2(a-R) (d) R-c=4(a-R) 6. The difference between geographic and geocentric latitudes is maximum at (a) 0? latitude (0) 23:55 latitude (c) 45° latitude () 90° latitude 7. The acceleration of a point mass m, due to the attraction of another point mass m, at distance r is equal to He (6) -3 © 6 6-2- 7 (where G = universal gravitational constant) 8. A circular coil having axis length L and 12. What fraction of the normal incident number of turns n is wound around wave energy will be transmitted into a magnetic core. A current of J units the second layer, if a layer with density passes through this coil. The magnetic 3 g/cc and wave velocity 4 km/s is excitation inside the core will be overlain by a layer having density 2 g/cc ni and velocity 3 km/s? (a) im (a) 0-11 (b) 0:22 IL (b) n (c) 0-44 (c) * (a) 0:89 13. Which one of the following seismic E phases results from a P-wave turning ia within the crust? (a) P, 9. The angle between magnetic north and (are, total magnetic field is () Py (a) magnetic declination (da) PP (b) magnetic inclination 14. The slowness vector of a 1 Hz plane P-wave propagating at 6°5 km/s velocity (c) magnetic total angle in +x direction is (ad) magnetic vertical angle (a) {ate 0, o| 10. Which one of the following minerals has 1 negative magnetic susceptibility? (b) {o 6.5 o| (a) Pyrrhotite 1 a foo JI (b) Ilmenite @ { 6-5. (c) Sphalerite ‘d fe a (a) 6.5’ 0, Sa (d) Quartz 15. Which one of the following correctly 11. The ratio of S-wave to P-wave velocities describes the attenuation property of for zero Poisson’s ratio value is the Earth expressed in terms of quality factor (Q)? (a) V3 oe (a) The Q value is infinite for the i Earth. (2).== ? V3 (b) The Q value is zero for the Earth. () v2 (c) The Q value of P-wave is lower than the Q value of S-wave in the 1 Earth’s core. (= 2 (d) None of the above BBSP-T-GPS/62A 3 [ P.T.O. 16. What type of changes in the mineral phase takes place at 410 km discontinuity inside the Earth? (a) Olivine-type to spinel-type lattice (b) Graphite-type to y-spinel-type lattice (c) a-spinel-type to pyrite-type lattice (a) y-spinel-type to B-spinel-type lattice 17. What is the approximate pressure at the centre of the Earth? (a) 180 GPa (b) 280 GPa (c) 380 GPa (d) 480 GPa 18. A weak P-wave diffraction is observed in the epicentral distance range of (a) 0°-30° (b) 30°-90° (c) 90°-102° (d) 103°-120° BBSP-T-GPS/62A 19. Which one of the following is the correct epoch sequence from 0 to 4 Ma age as estimated from normal and _ reverse geomagnetic data? (a) (b) (c) (a) 20. The an of Brunhes, Gauss, Matuyama, Gilbert Brunhes, Matuyama, Gauss, Gilbert Brunhes, Matuyama, Gilbert, Gauss Brunhes, Gilbert, Matuyama, Gauss scalar seismic moment (My) of earthquake is related to density medium p, seismic velocity c, hypocentral distance r and radiation pattern Uy as (a) (b) (c) (a) pes TU 49 pe?r Uy9 21. What approximate percentage of the total annually released seismic energy is due to the intermediate focal depth earthquakes at the global level? (a) (b) (c) (@) 85% 20% 12% 3% 22. What is the ratio of the number 25. What is the approximate range of the of earthquakes having surface wave Earth’s magnetic field variation due to magnitudes greater than 5 and 7 change in latitude value? occurring in a region, if the intercept, a and slope, b values of earthquake (a) > 100 nT/km magnitude-frequency elation are 8 and 1, respectively for that region? (b) 50-100 nT/km (a) 1000 (c) 10-50 nT/km (b) 100 (a) <6 nT/km (3) 32 (a) 10 26. What is the approximate direction of polarization of protons with respect to the Earth’s magnetic field (F) due 23. The approximate value of free-air to applied external field in proton correction at a station located at 1 m precession magnetometer? height above the datum plane at the equator is (a) Parallel to F only (a) 0:3072 mGal (b) Antiparallel to F only (b) 0-3388 mGal (c) Normal to F (c) 0:3491 mGal (ad) Both parallel and antiparallel to F (ad) 03516 mGal 27. What is the coefficient of anisotropy for 24. What is the ratio of maximum values of a medium having vertical and horizontal gravities directly above the centres of resistivities p, and p,, respectively? two spherical bodies of radii 1 m and 2 m situated in a homogeneous moraine fe having density contrast of 1 g/cc and (a) (E+)? 2 g/cc, respectively and depth to the centre of sphere as 2 m and 4 m, respectively? ; (a) 1 Pn i (b) [i lies p (jE—= Ce Ph 1 qy Ph @ 3 BBSP-T-GPS/62A 5 [Rtoi 28. What is the equivalent horizontal resistivity for a vertical stake of n beds with resistivities Py Pa» Payee »P, and thicknesses Zyy Zags Zags eves ,Z, from top to bottom, respectively? in (a) | 2a Yin: Pp; (b) = Yin1?i mM u uN (c) Pls in aii n =P; a of M N (4) M 29. What is the ratio of effective resistivity of the rock (p,) to the resistivity of the groundwater (p,,), if the formation has 1% porosity, water saturation constant 1:0, and parameters a=1, m=2 and n = 2are constants of Archie’s formula? (a) 10+ (b) 104 (10-4 (a) 10? 30. Which one of the following potentials is relatively more variable electrical potential used in geophysical prospecting? (a) Diffusion potential (b) Nernst potential (c) Electrokinetic potential (ad) Telluric potential BBSP-T-GPS/62A 31. What is the ratio of seismic velocities of the second layer to the first layer for a seismic wave incident on a horizontal interface at an angle of 30° to the normal in the first layer and refracted at 45° angle to the normal in the second layer? (a) (b) (c) (a) 2V2 * & bl 32. The ground roll in seismic data can be attenuated by (a) grouping of geophones (b) reducing the number of geophones (c) increasing geophone spacing (d) decreasing geophone spacing 33. What is the reflection coefficient for a seismic wave incident at normal to the interface between the first and second layers characterized by densities 3 g/cc and 2:5 g/cc, and velocities 5 km/s and 4 km/s, respectively? (a) 0-2 (b) -0:2 (c) 12 (d) -1-2 34. A point scatterer is observed at 25 km depth within a layer with a uniform velocity of 4 km/s. What is the observed two-way travel time for the source and receiver with an offset of 3 km? (a) 1:25s (b) 1:35 8 (ce) T:60es (@) 195s 35. The phase shift between ghost multiple 39. The only non-zero Fourier series and primary reflection in seismic data is coefficients for the signal x(t) = sin Wot, having fundamental frequency Wy, are (a) 90° 1 (ae (b) 180° 8i 1 pe (c) 270° (b) Si (d) 360° (ike 4i 1 36. What is the Nyquist frequency for a (a) + 3 seismic data recorded with a sampling : rate of 100 Hz? (where i = y-1) (a) 250 Hz 40. The radix-2 fast Fourier transform requires the sequence length of the (b) 200 Hz input time-domain signal to be an integral power of (c) 100 Hz (a) 2 (a) 50 Hz (b) 3 (c) 4 37. Which one of the following filters is (da) 5 used to avoid the aliasing problem in : seismic data processing? 41. The Laplace transform of a function f(t) is given as F(s). The Laplace transform (a) Low-pass filter of a time-domain signal f(t)=Ae™ (b) High-pass filter (A= al a>0O)is ayia (c) Band-pass filter (a) s A (a) Notch filter LE eer s A 38. The convolution of a signal with a delta (c) sta function m (a) (a) alters the shape of the signal only (s+ a)? (b) does not alter the shape of the 42. What would be the length of the output signal but produces a time shift in signal, generated after convolution of the original signal two signals of lengths D, and D,? (c) makes the signal zero at all times a ie sae ac (b) D,+D,+1 (ad) alters the shape of the signal as (c) D,+D,-2 well as produces a time shift in the original signal (a) D,+D, +2 BBSP-T-GPS/62A 7 [PiTtO: 43. Which one of the following is not correct about the Dirac delta function? (a) The Fourier transform of a Dirac function is equal to a nonzero constant. (b) The Dirac function can be used to delay a time series function. (c) The product of a function with a Dirac function gives a Dirac function of amplitude equal to the sample of that function. (a) The Fourier transform of a Dirac function is equal to zero. 44. With the increase in number of input data points, the difference between the number of complex multiplications required by the radix-2 fast Fourier transform (FFT) and the discrete Fourier transform (DFT) (a) remains constant (b) increases (c) decreases (d) becomes zero 45. Which one of the following microwave bands will have the maximum penetration in dry sand? {a).-P (b) S (c) X (a) K BBSP-T-GPS/62A 46. Which of the following ground parameters are measured during field survey using thermal infrared region of electromagnetic spectrum? (a) Ground temperature and spectral emissivity (b) Rainfall pattern and _back- scattering coefficient (c) Spectral emissivity and _back- scattering coefficient (da) Ground temperature and rainfall pattern 47. Which one of the following statements is mot correct regarding body’s emissivity? (a) The spectral emissivity values range from 0-1. (b) Blackbody radiates a continuous spectrum. (c) The Sun and the Earth as whole bodies radiate a near-continuous spectrum. (a) The spectral emissivity values of a gray body are not constant at all wavelengths. 48. Consider the following statements : 1. Stefan-Boltzmann relation applies to all wavelengths of the spectrum shorter than microwaves. 2. Rayleigh-Jeans law is_ valid for longer wavelengths such as microwaves. Which of the statements given above is/are correct? (a) Both 1 and 2 (b) 1 only (c) 2 only (ad) Neither 1 nor 2 49. Which one of the following is the 52. The energy of an oscillator of frequency correct sequence of the electromagnetic v is equal to waves in the order of their increasing frequencies? (a) A (a) Radio wave, Microwave, Infrared, Visible, Ultraviolet, X-ray (b) hv (b) Radio wave, Infrared, Microwave, Visible, Ultraviolet, X-ray () h2v2/3 (c) Microwave, Radio wave, Infrared, Visible, X-ray, Ultraviolet (d) n2/3 y2 (a) Infrared, Visible, Ultraviolet, Microwave, Radio wave, X-ray (where h is Planck’s constant) 50. A hot blackbody emits energy at the rate of 25 J m~2 s~! with most intense radiation corresponding to wavelength 53. The Kelvin-Planck statement of the of 20000 A. If the temperature of the second law of thermodynamics deals body is further raised, its most intense with radiation corresponds to wavelength of 10000 A. Then the rate at which energy (a) conservation of energy is emitted is (b) conservation of mass (a) 100 J ms"! (c) conversion of work into heat (b) 200 J ms} (d); conversion of heat into work () 400 J ms"! (d) 800 Jm~s7} 54. Which one of the following thermo- dynamic laws relates the change in internal energy of a system with the 51. The correct value of the Stefan- heat supplied to the system and the Boltzmann constant is work done by the system on its surroundings? (a) 5-6704x10-?’ WmK~* (a) Zeroth law (b) 5-6704x10° Wm~? k* (b) First law € -8 -~4 (c) 4-6704x10-°§ WmK fc) Mecano (d) 4.6704x10-7 Wm? k* (a) Third law BBSP-T-GPS/62A 9 [PekO.; 55. An infinite plane carries a uniform 58. A particle of charge Q moves with speed surface charge o. Its electric field is v, in a circle of radius R, in a uniform = magnetic field of magnitude B (a) ala perpendicular to the plane of the circle. 0 The momentum of the particle is (b) — A (a) -QuB A) QB () A st 4E, B (dj =A (c) 2 8e (where fiis a unit normal vector pointing (d) QBR away from the surface) 59. Which one of the following laws describes the force (F) experienced by a charged particle of charge gq, while moving through a magnetic field Bwith velocity 0? 56. The velocity of ground-penetrating radar signals depends on (a) electrical properties of the material only (b) magnetic properties of the material only (a) Faraday’s law (c) both electrical and magnetic (b) Biot-Savart law properties of the material 1 ’s lay (d) neither electrical nor magnetic 1. renee properties of the material (a) Lorentz’s law 57. The electric field in polystyrene (relative permittivity = 2-55) filling the space 60. Which one of the following statements between the plates of a parallel-plate regarding solenoid is not correct? capacitor is 10 kV/m. The distance ae : between the plates is 1:5 mm. The (a) The wire is wound closely in the potential difference between the plates form of a helix. a (b) The wire is coated with a (a) 4V conducting material. (b) 10V (c) Adjacent turns of the wire (c) 60V physically touch each other. (@) 15V (d) Ampere’s law is valid. BBSP-T-GPS/62A 10 61. According to Biot-Savart law, the magnitude of the magnetic field due to a current element is (a) directly proportional to the square of the distance between the current element and the point where the field is calculated (b) directly proportional to the cube of the distance between the current element and the point where the field is calculated (c) inversely proportional to the square of the distance between the current element and the point where the field is calculated (d) inversely proportional to the cube of the distance between the current element and the point where the field is calculated 62. According to Faraday’s law of electro- magnetic induction, the magnetic flux through a coil can be changed by 1. changing the magnitude of the magnetic field within the coil 2. changing the portion of the area of the coil that lies within the magnetic field 3. changing the temperature of the experimental setup 4. changing the angle between the direction of the magnetic field and the plane of the coil Select the correct answer using the code given below. (a) 1, 2 and 4 (b) 2, 3 and 4 (c) 1 and 4 only (d) 2 and 4 only BBSP-T-GPS/62A 11 63. Two parallel plates are separated by a distance d/2 as shown in the figure below : The surface charge density at x = 0 is ia, oy =e 9 2 i 2 64. Which one of the following boundary conditions is not satisfied by the electric potential (V) while solving Laplace’s equation V?V=0 in electromagnetic method? (a) Vis continuous. (b) The component of current density normal to the boundary is continuous. (c) The component of current density normal to the boundary is discontinuous. (a) V is finite at any point where there is no source or sink of current. [ P.T.O. 65. The equation - [14 |, [ 1 | , [ 1 / =0 dx\p dx} dy\p dy) dz\p dz (where V = electric potential, 2 = resistivity) reduces to Laplace’s equation for (a) a homogeneous and anisotropic medium (b) a homogeneous and medium isotropic (c) an inhomogeneous and anisotropic medium (0) an inhomogeneous and isotropic medium 66. A uniform magnetic field B exists in a direction perpendicular to the plane of a square frame made of copper wire. The wire has a diameter of 2 mm and a total length of 40 cm. The magnetic field changes with time at a steady rate The current induced‏ ,8¬1 7 0-02 2 in the frame is‏ (0) 4-5x107A (b) 9-3x1072 A © 2-5x1071A (0 8.5%10 A (Given : Resistivity of copper = 1.7× 10-8 ) BBSP-T-GPS/62A 12 68. “The 67. Which one of the following Maxwell’s equations 15 generalized due 10 displacement current? (a) Gauss’s law for electricity () Gauss’s law for magnetism ( Faraday’s law (9 Ampere’s law parallel components of H are discontinuous by an amount proportional to the free surface current density.” For a linear medium, which one of the following relations is the correct boundary condition for the statement given above? (a) +8! ! = . xf 141 2 - = 0‏ © LB! ! = 0 141 () ‎ +! ex. 141 (where the symbols have their usual meanings) 69. An electromagnetic wave propagates through a linear homogeneous medium. The speed of the wave in this medium is fa) | 0110 (b) () (> (where the symbols have their usual meanings) Consider the following statements regarding skin depth of electromagnetic waves in conductors : 1. It is the distance taken by the electromagnetic wave to reduce the amplitude by a factor of half. 2. It measures how the electromagnetic wave penetrates into the conductor. 3. 115 determined by the real part of the wave number. 4. It is determined by the imaginary part of the wave number. Which of the statements given above are correct? 1 and 3 1 and 4 (0) (b) () (0) 2 and 3 2 and 4 71. The number of inhomogeneous Maxwell’s equations for a good conductor is (a) one (b) two (c) three () zero 72. Which one of the following pairs is an example of mirror nuclei? (a) 140 and 130 (b) 130 and 14] (9) 1%€ and 150 (0 130 and 128 BBSP-T-GPS/62A 13 73. 74. 75. The ground-state spin (J) and parity (P) of most of the even-even (even protons, even neutrons) nuclei, i.e., © (a) 3 (b) (4 5/2* (0 The approximate radius R of 12537) nucleus is (a) 1:2 fm (b) 12:5 fm (c) 6 fm (0 10 fm According to the liquid drop model, when a nucleus is bombarded by neutrons, the compound nucleus before undergoing fission attains the shapes in the sequence of (a) ellipsoidal, spherical, dumbbell (b) spherical, ellipsoidal, dumbbell (c) spherical, dumbbell, ellipsoidal (d) dumbbell, ellipsoidal, spherical [ P.T.O. 76. The total binding energy of en Ne nucleus is 160°647 MeV. The binding energy per nucleon for ay Ne is (a) 160-647 Mev (b) 16-064 Mev (c) 8-032 Mev (d) 5354 Mev 77. In the asymmetric fission of S2, the maximum energy appears as (a) kinetic energy of the emitted neutrons (b) energy of the emitted gamma rays (c) kinetic energy of the lighter fission fragments (a) kinetic energy of the heavier fission fragments 78. Which one of the following nuclear fusion reactions has the highest release of energy? (a) Proton-proton reaction (b) Proton-deuteron reaction (c) Deuteron-deuteron reaction (da) Deuteron-triton reaction 79. The half-life of a radioactive nucleus is 6 nanosecond (ns). The decay constant of this nucleus is (a) 1-16x109 s7} (b) 1-16x108 sg"! (c) 1-60x109 s7} (@) 1-60x108 s7} BBSP-T-GPS/62A 14 80. gate nucleus decays to seRu nucleus by a radioactive decay process. This radioactive decay is an example of (a) alpha decay (b) positive beta decay (c) negative beta decay (d) orbital electron capture 81. Which one of the following statements is correct for a nucleus undergoing gamma decay? (a) The number of neutrons increases by one. (b) The number of protons increases by one. (c) Neither the number of protons nor the number of neutrons changes. (d) Each of the proton and neutron numbers increases by one. 82. The minimum photon energy required for a pair production by a gamma ray, in the presence of a nucleus, is (a) 0-511 Mev (b) 1-022 MeV (c) 937 MeV (d) 40 Mev 83. For an incident gamma-ray energy of 1 MeV, which one of the following absorbers has the highest probability of photoelectric absorption? (jy ce (0) 22S} (c) SONi (a) 38Ge 84. The maximum energy that can be 87. A radioactive source having a half-life transferred by an incident photon of of 5 years has an initial activity of energy hv to an electron in a single 400 880. The activity (in 880) after Compton interaction is 15 years will be 20. ) (a) 200 = 6‎ (b) 100 ( ) (0 50 ( ) () 25 88. The parent nuclide of the (4n+2) (0) ho ) radioactive series is ; (6) 232 , (where a = ; 7102 is the rest mass myc? (0) “580 energy of the electron) (9 3108 85. Which one of the following is the correct () 227Ra equation to represent a pair-production process of gamma-ray interaction? 89. Which one of the following inorganic (4 1-6 = E+ EW. scintillators has the maximum light 2 yield per MeV? (b) ‎ + = 23% +E. (a) BaF, ‎ 7 +2#1062 =E_ +E, e e (b) BGO 22‎ (9 1-2 =& 75 (c) Nal ( (where hv is the energy of incident (0 12873 (06) gamma ray; E_ and are the electron and positron kinetic energies respectively; moc? is the rest mass 90. The different regions of operation o gas-filled detectors are ion saturation, energy of the electron) proportional region, limited proportional region and Geiger-Miiller region. The 86. Which one of the following radioactive region not used for detector operation is minerals has thorium (Th) element? (a) Geiger-Miller region (a) Alunite ) Carnotite (b) ion saturation region (© Monazite (c) proportional region () Muscovite (0) limited proportional region BBSP-T-GPS/62A 15 व्हि. 92. The 91. The de Broglie wavelength associated with an alpha particle emitted with a kinetic energy of 1 MeV by the nucleus of an atom of radon is of the order of ( 1015 cm (b) 1014 cm & 1012 cm (0 1012 cm magnitudes of total angular 7 ‎ momentum given by J =L +S for 1= 1 and s=1/2 are (a) 037‎ 315, 4 4 v3 v1 (b) ‌ iy ( ¥3 ana 15 # ‌ 2 (0) 33 # and 34, 2 8 (where the symbols have their usual Which one among the following pairs is not correctly matched? (a) V-(VxA) : 0 Vx(VxA) V(V-A)-V2A‏ : ‏ .4) ( x 4 - 0) × A)‏ (Given : 0 and A are differentiable scalar and vector functions, respectively) 96. Let P(4cost,4sint,4t) be a point on a curve, where £ is some parameter. The magnitude of the tangent vector at point P is meanings) (a) 4 93. In _the X-ray spectra, the Ke line (b) 22 originates (a) when an n=4 electron undergoes (0: 2 a transition to a vacant n = 2 state (b) when an n=3 electron undergoes (a) 442 a transition to a vacant n = 2 state (c) when an n=3 electron undergoes a transition to a vacant n = 1 state (0) when an n=2 electron undergoes a transition 10 a vacant n = 1 state 97. The eigenvalues of the matrix . 30 94. A completely antisymmetric tensor in 3-space dimensions possesses (a) rank =3 and independent components = 3 (b) rank = 1 and independent ( 1,2 components = 1 (c) rank = 1 and independent 0‎ components = 3 2,6 (97 rank = 3 and independent components = 1 (0 1,6 BBSP-T-GPS/62A 16 98. For a matrix A, the diagonal matrix A’ is obtained using the _ similarity transformation A’ =S7!A S, where S is 0 i a transformation matrix. If A -(j > then the diagonal matrix A’ is 99. The isostatic gravity anomaly is defined as the difference between (a) Bouguer gravity anomaly and computed anomaly of the root zone (b) free-air gravity anomaly and computed anomaly of the root zone (c) Bouguer gravity anomaly and free-air gravity anomaly (d) regional gravity anomaly and residual gravity anomaly 100. The gravity value on the surface of the Earth at the equator is approximately (a) 678 m/s? (b) 7-78 m/s? (c) 878 m/s? (d) 9-78 m/s? 101. The spherical shape model mass in the gravity method is _ particularly used as a first approximation in the interpretation of (a) asymmetrical 2D anomalies (b) approximately symmetrical 2D anomalies (c) asymmetrical 3D anomalies (ad) approximately symmetrical 3D anomalies BBSP-T-GPS/62A 17 102. Which one of the following fundamental forces is mediated by massive particles? (a) Strong force (b) Electromagnetic force (c) Weak force (a) Gravitational force 103. The range of weak interactions is (a) 10°12 m (b) 1075 m () 10718 m (a) 10°21 m 104. The engine of a rocket in outer space, far from any planet, is turned on. The rocket rejects burned fuel at a constant rate. In the first second of firing, it ejects ‘doe of its initial mass my at a relative 100 speed of 2000 m/s. The __ initial acceleration of the rocket is (a) -20 m/s? (b) +20 m/s? (c) -2x105 m/s? (ad) +2x10° m/s? 105. In the centre of mass frame of reference, the magnitudes of the velocities of particles (a) remain unchanged in an elastic collision (b) remain unchanged in an inelastic collision (c) remain unchanged in both elastic and inelastic collisions (d) change in both elastic and inelastic collisions [ P.T.O. 106. The angular speed of 3600 rpm in rad/s is equal to (a) 251 (b) 277 (c) 351 (a) 377 107. If the kinetic energy of a proton is 3752 MeV, then its Lorentz (relativistic) factor is approximately (a) 5 (b) 4 (c) 3 (a) 2 108. The total energy of a 3-53 MeV electron is (a) 3:02 Mev (b) 3:53 Mev (c) 404 MeV (d) 455 Mev 109. The regularization parameter in non- linear least-squares inversion technique describes a trade-off between (a) the best fitting and the reasonable stabilization (b) the worst fitting and the reasonable stabilization (c) the best fitting and the unreasonable stabilization (a) the worst fitting and the unreasonable stabilization BBSP-T-GPS/62A most most most most 110. Which one of the following is the additive rule of probability P(X UY) for mutually exclusive events X and Y? (a) P(XUY)=P(X)-P¥)-P(XAY) (b) P(XUY)= P(X)- P(Y)+P(XAY) (c) P(X UY)=P(X)-P(Y) (d) P(XUY)=P(X)+P(Y) 111. Match List-I with List-II and select the correct answer using the code given below the Lists : List-I List-IT (Distribution) (Probability distribution) 1 _(x-p)? A. Binomial a, ee eT 207 oV2n B. Poisson 2) tgxaly x C. Geometric 3. Ment x! D. Normal 4. E Cipiq' sx (where the symbols have their usual meanings) Code : (a) A B Cc D 4 2 3 1 (b) A B € D 4 = 2 1 (c) A B c D 1 2 3 4 () A B Cc D a 3 2 4 18 112. Consider the following differential equation : The solution of this equation y(x) passing through the origin and through the point (m2 2) is (a) sinhx (b) coshx (c) 2sinhx (a) 2coshx Consider the following statements regarding a system of linear equations : 1. A system of linear equations is consistent if it has one or more solutions. 2. A system of linear equations is inconsistent if it has one or more solutions. 3. A system of linear equations is consistent if it has no solution. 4. A system of linear equations is inconsistent if it has no solution. Which of the statements given above are correct? (a) 1 and 3 (b) 2 and 4 (ce) 2 and 3 (d) 1 and 4 BBSP-T-GPS/62A 19 114. The order and degree of the differential equation are, respectively (a) 1,2 (b) 2, 2 (c) 3,1 (a) 2,3 115. Let Vee and aes be two solutions of a linear second-order differential equation. Which one of the following is correct about the Wronskian (W), y, and y,? (a) W=0; y, and Yq are linearly dependent (b) W=e%*; y and yp are linearly dependent (c) W=0; y and y, are linearly independent (dj) W=e*; y, and y, are linearly independent [ P.T.O. 116. Consider the second-order partial 118. The numerical value of the integral differential equation for a function ‎ +1) de using trapezoidal rule u(x, y), defined by (considering only one interval between the end points) is 82 82 ao 0 ax? 982 (a) 5:50 5-60 Which one of the following is correct regarding the equation given above? (9 575 (a) Laplace equation, hyperbolic type (0 5:55 (0) Laplace equation, elliptic type 119. The Newton-Raphson method is used (c) Wave equation, parabolic type in numerical analysis to (0) Wave equation, elliptic type (a) solve a partial differential equation approximately (b) find the 10009) of nonlinear 117. Consider the heat flow in 8 two- equations approximately dimensional (x, y) metal plate. The temperature u(x, 0 at any point (25 ) solve an ordinary differential at time £ for diffusivity d? of the plate equation exactly is governed by (0) solve an algebraic equation exactly 22 = 2 82 (2) - : at? ax? 120. Which one of the following ‘rules/ du _ 42 22. 921/ methods is used to numerically find ( ax2 as 2 the solutions of linear differential equations? 22 82 2‎ au (a) Trapezoidal rule 2 2 os oy (5) Boole’s rule 0) Newton-Raphson method 7 ‎ (6) n-Raphson metho at? ax? (0) Euler’s method BBSP-T-GPS/62A 20 SPACE FOR ROUGH WORK BBSP-T-GPS/62A 21 [ P.T.O. SPACE FOR ROUGH WORK BBSP-T-GPS/62A 22 SPACE FOR ROUGH WORK BBSP-T-GPS/62A 23 9:3:9 SPACE FOR ROUGH WORK kkk BBSP-T-GPS/62A 24 26BS—1344