QP-CGeoScnstPrelExam-24-GEOPHYSICS-PAPER-190224

Combined Geo-Se! DO NOT OPEN THIS TEST BOOKLET UNTIL YOU ARE TOLD TO DO SO T.B.C. : SBVP-B-GPH or ol Test Booklet Series F. Serial ol 4004 TEST BOOKLET 1777 Paper II (GEOPHYSICS) Time Allowed : Two Hours Maximum Marks : 300 INSTRUCTIONS 1. 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. 2. Please note that it is the candidate’s responsibility to encode and fill in the Roll Number and Test Booklet Series Code 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. 8. You have to enter your Roll Number on the Test Booklet in the Box provided alongside. DO NOT write anything else on the Test Booklet. 4, 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. 5. You have to mark all your responses ONLY on the separate Answer Sheet provided. See directions in the Answer Sheet. 6. All items carry equal marks. 7. 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. 8. 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. 9. Sheets for rough work are appended in the Test Booklet at the end. 10. Penalty for wrong answers : THERE WILL BE PENALTY FOR WRONG ANSWERS MARKED BY A CANDIDATE. @ There are four alternatives for the answer to every question. For each question for which a wrong answer — given by the candidate, one-third of the marks assigned to that question will be deducted as penalty. Gi) Ifa 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. Gii) If a question is left blank, ie., 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 SBVP-B-GPH (1-A) SBVP-B-GPH Consider the following statements regarding the different geophysical methods : 1. Seismic methods using ambient noise come under passive seismology. 2. Gravity and magnetic methods are wave field methods. 3. Seismic exploration methods investigate structures shallower than the earthquake seismology. Which of the statement(s) given above is/are correct ? (a) lonly (b) land 3 only (c) 2and 3 only (d) 1,2and3 Consider the following statements regarding different geophysical methods : 1. The time variation of magnetic field is complex whereas the gravity field is smooth. 2. The study of the Earth’s magnetism is the oldest branch of geophysics. 3. Exploration seismology is an offspring of earthquake seismology. Which of the statements given above are correct ? (a) 1,2and3 (b) land 3 only (c) 2and3only (d) 1 and 2 only 3. (2-A) Bode’s law gives the distance of a planet from the Sun. Which one of the following does not follow this relationship ? (a) Venus (b) Asteroid belt (c) Uranus (d) Neptune What is the major constituent in the core of Vesta asteroid ? (a) Iron (b) Nickel (c) Aluminium (d) Copper After passing through the shock front, the solar wind is diverted around the Earth in a region of turbulent motion called : (a) Magnetosheath (b) Magnetosphere (c) Magnetopause (d) Van Allen belts Which one of the following statements regarding the angle of obliquity and eccentricity of Earth’s orbit is not correct ? (a) Eccentricity varies with a period of about 1,00,000 years. (b) Obliquity varies with a period of about 41,000 years. (c) The difference in insolation between summer and winter seasons is high for very small values of eccentricity. (d) Obliquity is the main factor that determines the seasonal difference between summer and winter in each hemisphere. SBVP-B-GPH The remanent magnetization related to the meteoritic impact is : (a) Piezo remanent magnetization (b) Shock remanent magnetization (c) Anhysteretic remanent magnetization (d) Isothermal remanent magnetization The horizontal component of Earth’s magnetic field at a place on the Earth’s surface is 1:5 times its vertical component. What is the inclination at the place ? (a) tan™}(1/1:5) (b) sin"? (1/15) (c) cos! (1/1:5) (d) tan} (1:5) International Geomagnetic Reference Field (IGRF) correction removes : (a) Effect of Earth’s dipolar field only (b) Effect of Earth’s non-dipolar field only (c) Effect of both, Earth’s dipolar and non-dipolar fields (d) Diurnal variations 10. 11. (3-A) Which one of the following is the correct geomagnetic anomaly order across the starting from Vine-Matthews-Morley ? Pacific-Antarctica _ ridge, its ridge axis, as suggested by (a) Brunhes-Matuyama-Gilbert-Gauss (b) Brunhes-Gilbert-Gauss-Matuyama (c) Brunhes-Gauss-Matuyama-Gilbert (d) Brunhes-Matuyama-Gauss-Gilbert Consider the following statements regarding passage oof seismic waves during earthquakes : Statement 1: Rocks and minerals in the Earth react differently to stresses that may be brief and sudden. Statement 2: The stress response of rocks and minerals at depth in the Earth is affected by temperature, pressure and time of burial that exists at that depth. Which of the statement(s) given above is/are correct ? (a) lonly (b) Both 1 and 2 (c) 2only (d) Neither 1 nor 2 12. The ground motion during an earthquake is recorded on a three-component seismometer. Which one of the following components will show the maximum amplitude of Rayleigh wave ? (a) Vertical (up-down) only (b) East-West only (c) North-South (d) East-West and Vertical (up-down) both 13. Consider the following statements regarding the phase and group velocities of surface waves : bs For Earth, the phase velocity of both Love and Rayleigh waves generally increases with period. 2 Love waves are intrinsically dispersive even when the surface layer and underlying half-space are uniform. 3. Rayleigh waves over a_ uniform half-space are dispersive. Which of the statements given above are correct ? (a) land 2 only (b) land 3 only (c) 2and8 only (d) 1,2and3 SBVP-B-GPH 14, 15. (4-A) Consider a simple layer over a half-space model for the continental crust as shown in the diagram : 40 km 7 P, =2-7g/em®, B, =3-5 km/s Py = 3:3 g/em?, B, =4-5 km/s (where p = density, B = shear wave velocity; arctan 2:58 ~ 1-20 rad) What will be the period of fundamental Love wave travelling with a phase velocity of 3-8 km/s ? (a) 12:28 (b) 23-48 (c) 381s (d) 426s If the upper and lower mantle are convecting separately, what will happen to the temperature structure of the Earth’s mantle compared to the whole mantle convection ? (a) Increase in temperature of lower mantle only (b) Increase in temperature of upper mantle only (c) Increase in temperature of both upper mantle and lower mantle (d) Decrease in temperature of lower mantle only 16. 17. 18. SBVP-B-GPH Which one of the following layers of the Earth has almost the same density as the average density of the Earth ? (a) Inner Core (b) Upper Mantle (c) Lower Mantle (d) Outer Core What will be the value of Reynolds number for mantle layer with density, large scale of the flow, viscosity and velocity of flow as 5000 kg/m®, 2900 km, 1:5 x 10?! Pa.s and 5 cm/year, respectively ? (a) 15x 10° (b) 1-6 x 107° (c) 15x 10? (d) 1:5 x 10-20 What portion of the upper mantle appears to attenuate seismic waves the most ? (a) 40-60km (b) 80-220 km (c) 240-410km (d) 410-660 km 19. 20. 21. (5-A) Which one of the following statements regarding the response function of an inertial seismometer is correct ? (a) It includes the effects of various forces that act on the suspended mass. (b) It is independent of the forces acting on the suspended mass. (c) It includes the effects of spring forces on the suspended mass only. (d) It includes the effects damping force on suspended mass only. of viscous The Wadati-Benioff zone is related to : (a) Seismicity at subduction zone (b) Seismicity at conservative plate boundary (c) Seismicity at mid-oceanic ridge (d) Seismicity in the plate interiors Consider the following statements regarding the earthquake seismology : ky Long-period seismometers record the signals with periods in the range of 0-1 to 1:0 sec. 2. PKiKP is a P-wave that travels through mantle, outer core and inner core. 3. In the _ earthquake (N), magnitude (Mg) relationship given by frequency log N = a — bMg, the value of ‘b’ varies between 8 and 9 from region to region. Which of the statements given above are correct ? (a) land 2 only (b) 2and 3 only (c) land3 only (d) 1,2and3 22. 23. 24. 25. (a) 2 (b) 4 ¢ 8 (0 12 SBVP-B-GPH (6- The special class of strike-slip fault that joins active segments of the ridge is known 5 : (a) Normal fault (b) Reverse fault (c) Transform fault (0) Listric fault Which one of the following earthquake the amplitude around 0-8 sec and 15 highly useful magnitude scales considers wave in engineering seismology ? (a) Surface-wave magnitude scale (2) Body-wave magnitude scale (c) Local magnitude scale (d) Moment magnitude scale If x = a sin 6 608 ¢ and y = asin 9 sin , then the value of a? - x? _ 772 is: (8) 8 8026 00) ` 82 5122 9) 2 (6) ` 82 (082 0 (1) & cos” ¢ What is the value of (1, 2, 3) for a function defined as ¢ (, y, 2) = 3 x2z? - xy? - 15? 26. 27. 28. A) 2 What is the value of | F(x) dx, if 1 A 4 ¢ £ F(x) = 31 + =; j+2xk ? x 1 = 28 Pak‏ ` 43k‏ 31-21 60 (c) 81 + 21 + 86‏ 48k‏ )3142 )4( Which one of the following relations‏ represents Stokes’ theorem ? (where all symbols have their usual meaning) oh ( . (2) 1: भ = ట్రీ. ਰਤੇ 5 > >> =» -> (0) [2.१8 = [૪૦૭.૫૭ 6 (0 [ட்கள்‌ .]]>] )4( 8 0 The inverse of the matrix A = A ia: @ 43 1 @ ¢ >| te 29. The eigenvalues of the matrix 1 i are : (a) 1,2 (b) 0,2 (ce): F251 Cay 05,1 30. The acceleration due to gravity at the Earth’s surface is : (where G is the gravitational constant, My is the mass of the Earth and Rg is the radius of the Earth) GMz (a) Re GM. (b) _ RE GM (©) a Ry R2 a (d) GM, SBVP-B-GPH 31. 32. (7-A) The time period of a satellite moving in a circular orbit of radius r around the Earth is proportional to : (a) yl2 (bo)? (c) 32 (a) rl The spin of the graviton is : (a) > (b) 0 io Baie | (d) 2 Which one of the following statements regarding work done by a conservative force is not correct ? (a) It is given by the difference between the initial and final values of a potential-energy function. (b) It is not reversible. (c) It is independent of the path of the object and depends only on starting and ending points. (d) The total work done is zero for a closed path. The moment of inertia of a rotating body is decreased to i times and its angular velocity is increased to 4 times; then kinetic energy of the rotating body will : (a) be decreased by a factor of ‘ (b) be increased by a factor of 4 (c) not change (d) be increased by a factor of 2 35. 36. SBVP-B-GPH A rigid body rotation in (X, Y, Z) ` is given as : x x’ ‎ 6+ ¥ =. 0 10 2 2‎ -1 0 0152 then : (a) Z-axis is the rotation axis and the angle of rotation is ; (2) Y-axis is the rotation axis and the angle of rotation is 7 (c) Z-axis is the rotation axis and the angle of rotation is 7 (0) Y-axis is the rotation axis and the angle of rotation is The correct expression for time dilation is : (where y is the Lorentz factor relating the two frames and Aty is the time interval between two events measured in the rest frame of the clock) Aty ) 40/7, (1 2/ (8- 7. 39. A) What is the first-order correction to the non-relativistic kinetic the relativistic energy of a particle given as K = († - 1) me?? (here is the Lorentz factor, the particle has energy mass ‘m’ and speed , and © is the speed of light) (a) am () am (0 (4) am What is the speed of an electron accelerated from rest due to potential increase of 5-11 MV of electric field ? (where ‘c’ is the speed of light) (a) 0:096 (2) 08166 (6) 09960 (0) 0086 x ©> and are standard errors in the measurement of x and y respectively, and both x and y are independently measured quantities. If 0 = x — y, then standard error in 00 18 : (8) (जेर قرتی‎ (७) പ്രത) i+)? Vo)? 1 (0) 40. 41. SBVP-B-GPH Consider the following set of measurements : [7-2; 7-0, 7-1) The variance of all the measurements is : (a) O1 (b) 0:2 (c) 0-01 (d) 0:02 The solution of the differential equation 2. any which passes through the origin (0, 0) and the point (In 2, =) is: e*~+e * (a) (b) (c) (d) Consider the following differential equation : ay _ gay te ee + 9y =0 The solution of the above equation can be written as : (a) (Ax +B)e* (b) (Ax+B)e* (c) Aes re Be (d) Ae®* Es Be-3* (9-A) The solution of the partial differential equation x +xy =u Satisfying u = 2y on the line x = 1 may be worked out to yield : (a) xy(2+lnx) (b) xy (2-Inx) (c) xy(2+lny) (d) xy(2-Iny) Which one of the following statements is correct for the wave equation é7u ite 1 au -0? ax? 2 at? (a) Itis an elliptic equation. (b) Itis a parabolic equation. (c) The appropriate boundary conditions are Cauchy conditions on an open boundary. (d) The appropriate boundary conditions are Dirichlet or Neumann conditions on a closed boundary. Which one of the following equations is the correct representation of the heat equation ? (where symbols have their usual meaning) (a) V2u=0 1 du Vu & u <2 at 1 au () va v2 at? ja as ves ieee 2m y: ot 3 637 3 46. Given 771 = sin 2” and ‎ = cos 25, the 49. The Taylor series method is applied to solve dy of the Wronskian W 01]; Yo) 18 : the equation x? + y? under the condition 2 () —abz’ y(x) = 1 when x = 0. The first few terms in the () 822 series are : (০) ಇತಿಖುಬೆ 2.28 8 (8) 1+x+x () 3822 (0) 5100 ox! 47. Let f(x) =x sin + cos x, then the iteration nes formula by the Newton-Raphson method is : 6‎ 7 X_sinx + cosx ee n+1 n ± 8!‏ X_sinx_ + 006% n n n b + ¥ ¬ 0) n ad cosx,, 50. Which one of the following statements X_sinx - cosx £ 3 . 415 ‎ + - ‎ regarding equipotential surfaces is correct ? × 510 ®. x sinx + cosx (a) 10 electric field lines and equipotential , Six ‌ 3 81042 surfaces are always in the same direction. 48. Use Simpson's rule, given by the formula ) The electric field lines and equipotential 1 I= = 4 in th 1 tion, to 6 60 + in the usual notation surfaces are always mutually 1 evaluate I = | ‎ . Then I equals : perpendicular. id 0 (c) The angles between the electric field () 06970 lines and equipotential surfaces depend 07083 on the potential on the surface. 0 () The directions of electric field lines and (4) 0:6988 equipotential surfaces are unrelated. SBVP-B-GPH (10-A) 51. Suppose that at a certain location on the globe, the Earth’s magnetic field of 40 pT is horizontal and directed northward. Let there be a long, straight, horizontal wire, carrying a uniform current I. If the Earth’s magnetic field be cancelled by the magnetic field due to the wire at a distance 8 cm above it, then what would be the magnitude of the current I in ampere ? (The free space permeability Ho =4nx 10-7 H/m) (a) 4 (b) 2 (c) 24 (d) 16 52. Consider a particle of charge q = -2x10-°C placed in an electric field produced due to a charged cloud near the Earth’s surface. If the electrostatic force acted on the particle is downward (i.e. towards the centre of the Earth), and of magnitude 3x10°N, then the magnitude and direction of the electric field yy E are given by: (a) 15 N/C, upward (b) 1500 N/C, upward (c) 15 N/C, downward (d) 1500 N/C, downward SBVP-B-GPH e —— (11-A) Consider a charge Q on a tiny sphere. Let a portion of it, say q, be transferred to a nearby tiny sphere. If both the spheres are treated as then the electrostatic force of would be particles, repulsion between them maximum for : (a) q=Q/4 (b) q=Q/8 () q=Q/2 (d) q=3Q/4 An electron is allowed to transit through a region of space in which there is an electric field of magnitude 1:5 kV/m and a magnetic field 0:25 T is applied as shown in the figure. If the electron leaves the region without being deflected, then it would have entered the [ QB region with speed : Q@QVSL®S@#o®B @QB®LS®@®S#®# (a) 15km/s (b) 3:5 km/s (c) 45 km/s (d) 60km/s 55. 56. SBVP-B-GPH Consider a particle of mass 100 mg and charge —5x10°C moving in the Earth’s gravitational field. Let the particle’s initial velocity be horizontal, due north, and of 40 km/s. A horizontal, eastward magnetic field will keep the particle magnitude moving (under the influence of gravity) in the same horizontal, northward direction, if the magnitude of such a field has the minimum value : (taking the acceleration due to gravity g =9'8 m/s”) (a) 0-98T (b) 0-49T (c)2 1-965 (d) 1:47T A uniformly charged solid sphere, of radius R and total charge Q, is centered at the origin and spinning at a constant angular velocity @ about the z-axis. The magnitude of the curl of the magnetic field B at a point (r, 0, o) within the sphere is : Yo Q (a) a RS | | r?sin 20 Ho (b) re 4 |o|rsin@ bal ©) 2 |8)r?sine 4n R Ho 4n (d) = | @|rsin 20 R 57. (12-A) Consider the circular acceleration of singly charged ions (of mass number A) that are projected perpendicularly into a magnetic field of magnitude B. When the ions are accelerated to a kinetic energy E,, the radius of their circular orbit, non-relativistic motion, can be expressed in assuming terms of the charge and mass of a proton, e and Mp, as: E, JA m, eB [A KE, m, 2eB j2AE, m, eB E, [2A m, eB (ale: ras Oytirs (c) r= (dd) r= Consider an electric field in a certain region of the Earth’s atmosphere. Let the electric field be directed vertically down, and have magnitude 100 N/C at an altitude 200 m and 60 N/C at an altitude 300 m. In terms of the free space permittivity 9, the net amount of charge contained in a cube of sides 100 m, and with horizontal faces at altitudes of 200 m and 300 m, would be : (a) q=2x 104 e, (b) q=4%x 10° e (c) q=2x10%e, (d) q=6x 10% e% 59. A long, cylindrical wire carries a current I | 61. The electric flux through a certain area of a distributed uniformly over its cross-sectional dielectric varies with time as के « కేటీ, If at area A. Let By be the magnitude of the a time t = 3 sec, the displacement current magnetic field strength, due to the current I, through that area is 24 A, then its value is at the surface of the wire. The magnetic 6 A ata time: field strength is half of 80 (in magnitude) at a (a) 15sec distance (from the axis of the wire) : ila (b) 24sec (a) 24/7 (©. “1 see 0) V2A/n ar (0) 6500 ( 2&/7 (0) ~ 62. Consider a short current element 0} = by, and a point 2 located at Y=b( +32) where b is a constant, and 2 ; 9, 9 denote 60. 00580 1 ‎ h havi ee ਮਦ ಅರಯದ ಕಾರ ભા the unit vectors along the x, y, z directions, area A, parallel to the xy plane and separated respectively. The magnetic field at P, due to 4 by a distance d along 2. If the upper plate is the current I carried by the element 61 along held at a fixed potential Vo and the lower the y direction, can be expressed in terms of plate (250) is grounded, then the the free space permeability [10 85 : potential distribution along the z-direction is Ho .5 3 A 3 given by : (a) 1940 5” ) () 7-7 (285 + 2) / 0 0‎ Brat b 0 (b) क्रं ® ` 7 = 270 9 I 79 ‎ ( - 5) 167 (6) = 0 (xy + 22) / 0 1 V3 A A () ¬ (8 ± - 2 ) (0) V=Voz/d 327 SBVP-B-GPH (13-A) 63. An electrical circuit is placed in a magnetic SBVP-B-GPH field. An emf can be induced in the circuit by changing : (a) The magnetic field only (0) The area of cross-section only (€) The electric current in the given electric circuit only (d) The magnetic field or the area of cross-section or the angle between the magnetic field and the plane of the circuit Suppose that magnetic charges 8001, 2, --- exist, and there is a Coulomb’s law for such Ho 001 122 47 for a given magnetic charge moving with a => A charges, given by F = 7, then, > + velocity v , through electric and magnetic > > fields, E and B respectively the force law using the principle of electromagnetic duality can correspondingly be expressed as : > $ ‎ =» = 8. + x 2/02) +» ¬» 2 0) F ಎಣ್ಣಿ ૪ x ૪/૦૯ > > () = १०८८ - ए x E/c?) 0 (0) (14-A) If the peak magnetic field in a plane electromagnetic wave is 2 x 1074 , then the average energy density corresponding to the electromagnetic wave is : (a) 1 J/m? 207 0) 591 7 1 3 — J/ () 97 m () 2 3/m3 7 A source of sinusoidal electromagnetic waves radiates in all directions. If at a distance 15 m from this source, the amplitude of the electric field of the wave is 2 N/C, then at a distance 30 cm from the source, the electric field amplitude would be : () 60N/C 00) 01100 (6) 100N/C (0) 68/0 67. The total intensity of electromagnetic radiation from a star, as measured by a space probe at a distance 2 x 10!° m away from it, is 5000 W/m2. If the star radiates uniformly in all directions, then its total average power output is : (a) 8nxx10% w (b) 2nx10%4 W (c) 8nx10 W (d) 2nx10 W 68. Which one of the following factors is responsible for different density values measured during in-situ and laboratory conditions ? (a) Surrounding rocks density (b) Porosity (c) Mineral constituents (d) Measurement principle 69. What is the factor by which the true resistivity of 25% water saturated formation increases in comparison to fully water saturated formation according to Archie’s equation ? (Given saturation exponent = 2) (a) 2 (b)2,2:8 (c) 16 (d) 0-062 SBVP-B-GPH 70. 71. (15-A) In an aeromagnetic survey at a flight altitude of 1000m above sea-level, the maximum total field anomaly over an ore body measured 160 nT. 2500 m In a_ repeated altitude, the maximum amplitude of the anomaly was 20 nT. What will be the depth of the ore body below sea-level assuming a monopole sphere at centre was measurement at source for the ore body ? (a) 375m (b) 500m (c) 625m (dq) 750m A plane electromagnetic wave of wavelength 2um is being used to infer subsurface properties across a geological region. The land surface in the region consists of soil A and soil B with electrical conductivities as. 107 Om!’ andi: 10 eam respectively. Which one of the following statements regarding the wave penetration in soil A and soil B is correct ? (a) The wave penetrates soil A up to 10 times greater depth than soil B. (b) The wave penetrates soil B up to 10 times greater depth than soil A. (c) The wave penetrates soil A up to 100 times greater depth than soil B. (d) The wave penetrates soil B up to 100 times greater depth than soil A. 72. Consider the following statements regarding remanent magnetization : : Thermoremanent magnetization results when magnetic material is cooled above the Curie point in the presence of external field. 2: Lightning strikes produce isothermal remanent magnetization over a very small area. Which of the statement(s) given above is/are correct ? (a) land 2 both (b) lonly (c) 2only (d) Neither 1 nor 2 73. Consider the following statements regarding geoelectrical methods : 1. Dipole-dipole array is least influenced by inductive coupling. 2. In Schlumberger gradient profiles obtained over faults, dikes/veins show gentler gradient than the Wenner profiling. 3. For resolution of horizontally layered structures, the Schlumberger and Wenner arrays are preferred over the other arrays. Which of the statement(s) given above is/are not correct ? (a) land3 (b) lonly (c) 2only (d) 2and3 SBVP-B-GPH 74, 75. (16-A) Match List-I with List-II and select the correct answer using the code given below the lists : List-I List-II (Frequency range) (Geophysical method) P. 10-4Hzto1Hz 1. VLF Q. 400Hzto2000Hz 2. GPR R. 20 kHz to 25 kHz 3. MT 8S. 25MHztol-2GHz 4. Slingram Code: P Q@RsS (a) 2 aie ad (10th: Bea Re aka (G22 Uae! ae | (Gh oe eit Let sphere ‘A’ of mass excess (MA) in metric tons lying at a depth Z (km) produce a maximum anomaly of ga (mGal). Suppose sphere ‘A’ is now replaced by another sphere ‘B’ at the same depth with its mass excess as 0-5 times Ma (metric tons) and produces a maximum anomaly of gp (mGal). Which one of the following is the correct relation between ga and gp? (a) ga=0-5 gp (b) ga=2-0gp (c) gp=6-5ga (d) gp=2-0ga 76. What will be the ratio of critical distance (X,it) to the crossover distance (X,) for a model having a layer of velocity V, lying above another layer of velocity V2 (>V,) ? (a) ea 1 (b) me ae 1 Sa wi es) 1a ye 77. What is the P-wave velocity of a fully-fluid saturated formation having 25% porosity, if P-wave velocity in rock matrix and saturating fluid is 3000 mst and 1500 ms? respectively ? (a) 2700 ms (b) 2400 ms? (c) 2100 ms (d) 1800 ms 78. Consider the following statements regarding the shallow reflection technique : 1. Smaller energy sources with longer detector spreads are used in the survey. 2. Mapping of low velocity channels is possible. 3. Resolve the depositional features within the overburden material. 4. Appropriate for surveying when the surface layer is clay or silt with shallow water table. Which of the statement(s) given above is/are correct ? (a) land 2 only (b) 2,3 and 4 only (c) lonly (d) 1,2,3and4 SBVP-B-GPH 79. 81. 82. (ATA) If ‘d’ is the depth of shot below the reflector producing the ghost in seismic survey, what is the effective path difference between the direct wave and ghost wave ? (a) e+d d b £ (b) eer (ec) At+d (a) 42d The minimum frequency at which a signal comprising of 30 Hz, 50 Hz and 70 Hz frequencies should be sampled to avoid aliasing is : (a) 25 Hz (b) 35 Hz (c) 70Hz (d) 140 Hz The band-limited signal is uniquely represented by its samples. In practice, however, narrow, large amplitude pulses, which approximate impulses, are also relatively difficult to generate and transmit. What is the convenient form of sampled signal generated ? (a) Zero-order hold (b) First-order hold (c) Ideal low-pass filter (d) Cascade combination A wave filtered at 200 Hz is aliased due to the sampling process. The sampling rate of the signal is 350 Hz. What is the output frequency ? (a) 175 Hz (b) 150 Hz (c) 125 Hz (d) 100 Hz SBVP-B-GPH 83. Consider the following statements regarding the Fourier Transformation (FT) of a time series ‘g(t)’ : 1. FT converts g(t) into its equivalent amplitude and phase spectra. 2. FT converts g(t) into a complex function of frequency. 3. FT converts g(t) into its equivalent phase spectra only. 4. FT converts g(t) into a real function of frequency. Which of the statements given above are correct ? (8) land3 (0) land2 (c) 2768 (0) 83004 Consider the following statements regarding the scaling of a signal in time and frequency domains : 1. Linear expansion in time domain gives rise to linear contraction in frequency domain. 2. Linear contraction in time domain gives rise to linear expansion in frequency domain. 3. Linear expansion in time domain gives rise to linear expansion in frequency domain. Which of the statement(s) given above is/are correct ? (a) land2 2and3 (6) 30017 (6) lonly 85. 87. (18-A) The 0083) - 4 sin4(x) - 3 cos*(2x) contains : Fourier series expansion (a) Sine terms only (b) Constant terms only (c) Both non-zero cosine and sine terms (d) Cosine terms only Consider a two-dimensional function 1 (x,, 22) in the spatial domain and F(¢,, 2) be its Identify the relation between 1 (±, ) and †' (81, 52) if x, Fourier transform. correct and x, are scaled independently by a factor of a, and ag, respectively : (2) 1{ (11, 282) <> 189 ‎ 8] 2 1 & 8 ) f(a,x,, Fr, (b) (11, 9232) 5 6 ) () (8.51, 282) 182 F (8151, 292) (0) ) 8285) (1861, 292) 8182 The axis of complex plane at which the Laplace and Fourier transforms converge is : (a) Real axis (b) Imaginary axis (€) Positive side of real axis only (1) Positive side of imaginary axis only 89. Cross-correlate the wavelet g[n] = (2, 5, ¬ 2, 1} with another wavelet (6, - 1, - 1). For what shift are these functions being mostly alike ? (a) 0 (b) 7 0.1 (0) -2 The value 6 ` 8 ( + 1) 47 is: 1=0 (where, 5 (1) is delta function) (a) 4 00).. -1 (1 (0) 0 The near field displacement record of an earthquake was found to be _ closely approximated as the function 0, £ < 10 t) = ১ रि ৮৯৮০ What would be the velocity record look like ? (8 represents a Dirac-Delta function) (8) 0 (Zero) 6 (£ ¬ 109 (1) 50 SBVP-B-GPH 91. 93. (19-A) In an eight-bit remote sensing image, the digital number (DN) value lies between 64 and 128. After doing linear contrast enhancement of the whole data, what will be the value of DN = 98 after transformation ? (a) 34 (b) 64 (c) 135 0) 168 Ratio of radiating capability or exitance of a surface to that of a black body is defined as : (a) Emissivity ) Reflectivity (c) Reflectance (d) Radiance Which one of the following parameters does not govern the spatial resolution of an optical remote sensing image ? (a) Modulation Transfer Function (MTF) (b) Signal to Noise Ratio (SNR) (c) Object Contrast (d) Object Temperature Which colour of the visible light has the highest sensitivity for the human eye ? (a) Violet ) Yellow-Green (c) Blue () Orange-Red 95. 97. 98. SBVP-B-GPH Sunlight strikes the surface of the Earth with an average intensity of 1400 W/m”. The maximum value of the electric field associated with electromagnetic radiations is approximately : (a) 1060 V/m (b) 1400 V/n (c) 2800 V/m (d) 700 V/m The radiant emittance of a blackbody at a temperature of 400 K is : (a) (b) (c) 1452 x 10? Watts/m? (d) 1452 x 10° Watts/m? 1452 x 10! Watts/m? 1452 x 103 Watts/m? The entropy for a black body radiation is : (where T = temperature, V = volume and ‘a’ is the constant which appears in the expression for radiation energy density u : u = aT‘) Da (a) aT°V wo (b) aT°V (c) aT°V (d) aT°V wl wip cwlp What is the temperature at which the Kelvin and Fahrenheit scales coincide ? (a) (b) (c) 374-25 (d) 274-25 574-25 -—40 99. 100. 101. (20-A) A Carnot engine absorbs 200 J of heat from a reservoir at the temperature of 273-17°C. What is the work done by the engine, if it rejects heat to the reservoir at a temperature of triple point of water ? (a) 3003 (b) 4003 (c) 1505 (d) 1003 Which one of the following statements regarding molar heat capacities for all ideal gases is true ? (where T is temperature and other symbols have their usual meaning) (a) C_is not a function of T. (b) Cp is a function of T only and is less than C,. (c) Cp—C, is not a function of T. (d) The ratio Cp / C, is not a function of T and is less than 1. The electric quadrupole moment for a spherical nucleus is : (a) Positive (b) Negative (c) Zero (d) Dependent on the atomic number of the nucleus 102. Which one among the following best describes nuclear force ? (a) A strong long-range force between two nucleons which depends on their electric charges (b) A weak short-range force between two nucleons which depends on their electric charges (c) A> strong short-range force which is responsible for the attraction between a proton and a neutron (d) A weak long-range force which is responsible for the attraction between a proton and a neutron 103. Which one of the following set of charges can be possessed by quarks present in a nucleon ? (a) -2/3 and — 1/3 times the electron charge (b) + 2/3 and — 1/3 times the electron charge (c) -2/3 and + 1/3 times the electron charge (d) + 2/3 and + 1/3 times the electron charge 104. The binding energy is often expressed in mass units. One atomic mass unit is equivalent to : (where c is the speed of light in vacuum) (a) 931-494 MeV/c? (b) 93-1494 MeV/c? (c) 9:81494 MeV/c? (d) 9814-94 MeV/c? 105. Which of the following moderator(s) can be used in fission reactors fuelled by natural uranium ? (a) Beryllium (b) Boron (c) Cadmium (d) Cin the form of graphite or D,O SBVP-B-GPH 106. 107. 108. (21-A) Among the stable nuclei, the ratio of neutron number (N) to proton number (Z) increases with atomic mass (A) because of : (a) Large Coulombic repulsion among protons as Z increases. (b) Increase in pairing effect between neutrons and protons. (c) Magic number of neutrons, provides more stability as A increases. (d) Large surface energy of the nucleus as Z increases. 137 ; ‘ Decay of ;-Cs radioactive source is an example of : (a) Alpha decay (b) Beta plus decay (c) Beta minus decay (d) Neutron decay When gamma-rays are scattered by an electron at rest then : (a) The wavelength of the scattered gamma-ray is less than that of the incident ray and it does not depend on the angle of scattering. (b) The wavelength of the scattered gamma-ray is greater than that of the incident ray and it depends on the angle of scattering. (c). The wavelength of the scattered gamma-ray is less than that of the incident ray and it depends on the angle of scattering. (d) The wavelength of the scattered gamma-ray is greater than that of the incident ray and it does not depend on the angle of scattering. 109. 110. The probability of photoelectric absorption for gamma rays incident on a medium depends on: (a) Energy of the gamma rays and atomic mass of the absorber medium (b) Energy of the gamma rays and atomic number of the absorber medium (c) Atomic mass of the absorber medium but not on the energy of the gamma rays (d) Atomic number of the absorber medium but not on the energy of the gamma rays Which one of the following radioactive minerals has Thorium (Th) radioactivity ? (a) Alunite (b) Carnotite (c) Monazite (d) Muscovite 111. The daughter nucleus produced after beta-plus decay of Cd is: (a) 13m (b)s “ggCd © “4rAe (ds FgaPd SBVP-B-GPH 112. oU cannot spontaneously emit a proton 113. (22-A) as: (a) pe Uis not a radioactive element (b) 0 is a heavy element (c) The proton is a stable particle (d) The process has a negative Q value In a typical gamma-ray detector, what processes occur for an incident high-energy photon ? 1. It undergoes Compton scattering a few times and may leave the detector before depositing all its energy. 2. It undergoes multiple’ Compton scattering, followed by photoelectric absorption and complete energy deposition. 8. It produces an e*e™ pair, followed by annihilation, scattering and photoelectric absorption positron Compton and complete energy deposition. 4, It produces an ete pair, followed by positron annihilation, and one or both annihilation photons escape. Select the correct answer using the code given below : (a) land 3 only (b) 2and 4 only (c) 1,8 and 4only (d) 1,2,3and4 114. below : (a) land2 (b) 2and3 (c) lonly (d) 3only 115. The magnitude of spin angular momentum of the electron is : 1 (a) cE h ue (b) i h 3 (c) 7 h 4 (d) z h SBVP-B-GPH (23- Geiger-Miiller counter is used to measure : 1. Energy of the incident radiation 2, Charge of the incident radiation 3. Number count of the incident radiation Select the correct answer using the code given 116. 117. A) In which one of the following situations will a proton and an alpha particle have the same de Broglie wavelength ? (Assume the non-relativistic approximation holds) (a) The velocity of the proton is four times the velocity of the alpha particle. (b) The velocity of the alpha particle is four times the velocity of the proton. (c) Both the particles move with the same velocity. (d) Both the particles move with the same kinetic energy. Consider a particle of mass ‘m’ enclosed in a box of length ‘L’ with impenetrable walls. The longest wavelength of the particle trapped in the box is : (a) 2 (b) 2L L 2L a) cee (d) 3 118. An excited atom de-excites through the emission of photon with a lifetime of 105 sec. The inherent uncertainty in the frequency of the photon is about : (8) 107 Hz 10-26 Hz ` 1011 Hz (4) 1019 Hz 119. Which one of the following radiations takes place in the visible region ? (a) Lyman Series (0) மண்ண Series () Pfund Series (d) Balmer Series SBVP-B-GPH (24-A) 120. According to Bohr Model, the potential energy () for an electron in 7" orbit is : (b) (c) (d) 01 12 2me |‏ 500 4me 212 11 SPACE FOR ROUGH WORK SBVP-B-GPH (25-A) SPACE FOR ROUGH WORK SBVP-B-GPH (26-A) SPACE FOR ROUGH WORK SBVP-B-GPH (27-A) SPACE FOR ROUGH WORK SBVP-B-GPH (28-A)