GATE-2021
GG-Geology & Geophysics
GA: General Aptitude
Q.1 – Q.5 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).
1. The people ___________ were at the demonstration were from all sections of society.
(A) whose
(B) which
(C) who
(D) whom
2. A transparent square sheet shown above is folded along the dotted line. The folded sheet will look like ________.
3. For a regular polygon having 10 sides, the interior angle between the sides of the polygon, in degrees, is:
(A) 396
(B) 324
(C) 216
(D) 144
4. Which one of the following numbers is exactly divisible by (1113 + 1)?
(A) 1126 + 1
(B) 1133 + 1
(C) 1139 – 1
(D) 1152 – 1
5. Oasis is to sand as island is to ________
Which one of the following options maintains a similar logical relation in the above sentence?
(A) Stone
(B) Land
(C) Water
(D) Mountain
Q.6 – Q. 10 Multiple Choice Question (MCQ), carry TWO marks each (for each wrong answer: – 2/3).
6. The importance of sleep is often overlooked by students when they are preparing for exams. Research has consistently shown that sleep deprivation greatly reduces the ability to recall the material learnt. Hence, cutting down on sleep to study longer hours can be counterproductive.
Which one of the following statements is the CORRECT inference from the above passage?
(A) Sleeping well alone is enough to prepare for an exam. Studying has lesser benefit.
(B) Students are efficient and are not wrong in thinking that sleep is a waste of time.
(C) If a student is extremely well prepared for an exam, he needs little or no sleep.
(D) To do well in an exam, adequate sleep must be part of the preparation.
7.
In the figure shown above, each inside square is formed by joining the midpoints of the sides of the next larger square. The area of the smallest square (shaded) as shown, in cm2 is:
(A) 12.50
(B) 6.25
(C) 3.125
(D) 1.5625
8. Let X be a continuous random variable denoting the temperature measured. The range of temperature is [0, 100] degree Celsius and let the probability density function of X be f(x) = 0.01 for 0 ≤ X ≤ 100.
The mean of X is _____
(A) 2.5
(B) 5.0
(C) 25.0
(D) 50.0
9.
The number of students passing or failing in an exam for a particular subject are presented in the bar chart above. Students who pass the exam cannot appear for the exam again. Students who fail the exam in the first attempt must appear for the exam in the following year. Students always pass the
exam in their second attempt.
The number of students who took the exam for the first time in the year 2 and the year 3 respectively, are __________.
(A) 65 and 53
(B) 60 and 50
(C) 55 and 53
(D) 55 and 48
10. Seven cars P, Q, R, S, T, U and V are parked in a row not necessarily in that order. The cars T and U should be parked next to each other. The cars S and V also should be parked next to each other, whereas P and Q cannot be parked next to each other. Q and S must be parked next to each other. R is parked to the immediate right of V. T is parked to the left of U.
Based on the above statements, the only INCORRECT option given below is:
(A) There are two cars parked in between Q and V.
(B) Q and R are not parked together.
(C) V is the only car parked in between S and R.
(D) Car P is parked at the extreme end.
Geology (GG)
Q.1 – Q.15 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).
1. Which of the given planets has the highest average density?
(A) Mercury
(B) Venus
(C) Earth
(D) Mars
2. In a multi-electrode resistivity tomography (ERT) survey, using equally spaced electrodes, which of the given configurations will provide the maximum number of data points?
(A) Wenner array
(B) Axial Dipole-dipole array
(C) Axial Pole-dipole array
(D) Schlumberger array
3. In Electromagnetic methods of prospecting, which one of the given options is CORRECT about frequency and type of current source for the Primary field used?
(A) High frequency A.C.
(B) Low frequency A.C.
(C) Both high frequency A.C. and D.C.
(D) Low frequency D.C.
4. ‘Group’ is a unit of:
(A) Lithostratigraphy
(B) Sequence stratigraphy
(C) Biostratigraphy
(D) Chronostratigraphy
5. Furongian is an Epoch of:
(A) Cambrian
(B) Ordovician
(C) Triassic
(D) Cretaceous
6. The stage of textural maturity of a clay-rich sandstone containing poorly-sorted and angular framework grains is:
(A) Mature
(B) Supermature
(C) Immature
(D) Submature
7. Which one of the following structures indicates Synsedimentary deformation?
(A) Festoon bedding
(B) Flaser bedding
(C) Tabular bedding
(D) Convolute bedding
8. Low value in SP log as observed in dispersed shales is mainly due to the impeded movement of:
(A) Na+ ion
(B) Cl ion
(C) K+ ion
(D) OH−ion
9. In Radiometric survey, the g-ray spectrometer count rate depends on:
(A) Cracks present in the target rock volume
(B) Solid angle of the target rock about the spectrometer
(C) Temperature in the target rock
(D) Pressure in the target rock
10. The dimension of radiant emittance of a blackbody as per Stefan-Boltzmann law is:
(A) M0L1T−1
(B) M1L−1T−2
(C) M1L2T−2
(D) M1L0T−3
11. A surface geological process that can create a landform called Cirque is:
(A) aeolian deposition
(B) fluvial deposition
(C) glacial erosion
(D) deposition of volcanic ash
12. If α and β P- and S-wave velocities, respectively, then α2 – (4/3)β2 is equal to:
(κ is the bulk modulus, μ is shear modulus and ρ is density)
(A) κ/ρ
(B) μ/ρ
(C) κ + μ/ρ
(D) κ − μ/ρ
13. Which one of the following phases is P-wave that converts to S-wave during passage through the solid inner core?
(A) PKIKP
(B) PKJKP
(C) PKiKP
(D) PKPPcP
14. In reduction of gravity data, the latitude correction is maximum at:
(A) 35° latitude
(B) 45° latitude
(C) 55° latitude
(D) 65° latitude
15. The most coaliferous unit of the Gondwana Supergroup is:
(A) Talchir Formation
(B) Barakar Formation
(C) Karharbari Formation
(D) Panchet Formation
Q.16 – Q.25 Numerical Answer Type (NAT), carry ONE mark each (no negative marks).
16. A vertical borehole encounters a shale bed of uniform thickness occurring at a depth of 5 m and dipping 60°. The borehole pierces through this shale bed for a length of 10 m to reach a sandstone layer below. The true thickness of the shale bed is ________ m. [in integer]
17. The mass and volume of a fully dried soil sample are 2200 gm and 1100 cm3, respectively. If the specific gravity of the soil particles is 2.5 and water density is 1 gm/cm3, the void ratio of the soil is ________. [round off to 2 decimal places]
18. A constant-head permeability test was performed on a vertical sand column of height 40 cm and cross-sectional area of 25 cm2. During the test, when the loss of head was 50 cm, the volume of water collected in 2 minutes was 300 cm3. Applying Darcy’s law, the calculated coefficient of permeability of the sand column is ________ cm/sec. [round off to 2 decimal places]
19. The radius (r) of the oblate spheroid at 45° latitude with ellipticity of polar flattening of 1/298.25 and equatorial radius of 6378140 m is ________ km. [round off to 2 decimal places]
20. Light passes through two media with refractive indices of 1.75 and 1.55, respectively. The thickness of both the media is 30 μ The resultant path difference of the yellow light component (λ = 589 nm) is ________ πm. (Take λ = 3.141) [round off to one decimal places]
21. The water table in an unconfined aquifer at a place near the coast is 1 m above the Mean Sea Level. Given the densities of fresh and saline water as 1.001 and 1.025 g/cc, respectively, the fresh-saline water interface at the same location should be at a depth of _______ m from the water table. [round off to one decimal place]
22. The volume percentage of galena and quartz in an ore body of Pb are 90 and 10, respectively. The densities of galena and quartz are 7.6 and 2.65 g/cc, respectively. The grade of the ore body in terms of weight percent of Pb is _____. (Atomic weights of Pb = 206 and S = 32) [round off to 2 decimal places]
23. Normal moveout (NMO) for reflected phase of seismic data is 2 milliseconds. Consider the diffraction source at the edge of the same reflector, where the shot point is directly above diffraction source. In this case, the NMO due to diffraction is ______ milliseconds [in integer].
24. In a 2D seismic survey, first receiver location is at (1000 m, 4000 m), second receiver location is at (2000 m, 4000 m) and the source location is at (2000 m, 1000 m). Consider P-wave velocity as 5000 m/sec. The difference in first arrival time of P-wave phase for the two receivers is ________ seconds. [round off to 2 decimal places].
25. The potential difference measured between potential electrodes using Wenner array is 500 mV when a current of 2 A is passed through the subsurface between current electrodes. If the computed apparent resistivity is 100 Ωm then the distance between the current electrodes will be ________ m. [round off to 2 decimal places] (Use π = 3.141)
Q.26 – Q.42 Multiple Choice Question (MCQ), carry TWO marks each (for each wrong answer: – 2/3).
26. Which one of the following statements is CORRECT?
(A) Taphonomy refers to the study of fossilization pathways from death of an organism to its recovery as a fossil.
(B) Biostratinomy refers to the study of fossilization pathways from burial of an organism under sediments to its recovery as a fossil.
(C) Biostratinomy is an integral component of biostratigraphy and refers to the characterization of strata based on fossil content.
(D) Taphonomy refers to the study of fossilization pathways from death of an organism to its burial under the sediments.
27. Based on the three statements given below, choose the CORRECT option:
Statement I: Gunderdehi Formation is a stratigraphic unit of the Chattisgarh Supergroup.
Statement II: Raniganj Formation is a coal-bearing Triassic unit of the Gondwana Supergroup.
Statement III: Pitepani Volcanics is a stratigraphic unit of the Dongargarh Supergroup.
(A) All the statements are correct
(B) Statement I is correct, but statements II and III are incorrect
(C) Statements I and III are correct, but statement II is incorrect
(D) Statements II and III are correct but statement I is incorrect
28. Which one of the following equid genera was a one-toed grazer?
(A) Merychippus
(B) Parahippus
(C) Pliohippus
(D) Mesohippus
29. Match the following invertebrate genera in Group I with their corresponding Class/Phylum in Group II:
(A) P-4, Q-3, R-1, S-2
(B) P-4, Q-1, R-2, S-3
(C) P-4, Q-3, R-2, S-1
(D) P-3, Q-1, R-4, S-2
30. Tillite with faceted boulders and green shale with dropstones characterize the lithology of:
(A) Lameta Formation
(B) Bagra Formation
(C) Talchir Formation
(D) Panchet Formation
31. Match the following structures in Group I with the corresponding environment of deposition in Group II:
(A) P-4, Q-1, R-2, S-3
(B) P-4, Q-1, R-3, S-2
(C) P-3, Q-1, R-2, S-4
(D) P-2, Q-4, R-1, S-3
32. Match the items in Group-I with appropriate items in Group-II
(A) P-4, Q-3, R-1, S-2
(B) P-2, Q-3, R-4, S-1
(C) P-4, Q-1, R-2, S-3
(D) P-3, Q-2, R-1, S-4
33. With regard to superposed folding, the stereographic projection represents a geometry of:
(A) plane cylindrical fold.
(B) plane non-cylindrical fold.
(C) non-plane cylindrical fold.
(D) non-plane non-cylindrical fold.
34. The given outcrop pattern of a bed (shaded in grey) with respect to contours (dashed lines) indicates that the bed.
(A) dips upstream.
(B) is horizontal.
(C) dips steeply downstream.
(D) dips downstream at an angle equal to the valley gradient.
35. With regard to occurrence of groundwater in an area, which of the given statements is CORRECT?
(A) Vadose water occurs in the zone of saturation.
(B) The zone of aeration lies below the zone of saturation.
(C) The water table marks the uppermost surface of the vadose zone.
(D) The depth of the perched water table is less than that of the water table.
36. There are indications of presence of a massive tabular multimetal sulfide ore body at a shallow depth from the surface. Which of the following would be the most efficient geophysical method to confirm the presence of the ore body?
(A) resistivity sounding
(B) ground geomagnetic survey
(C) self-potential method of geophysical prospecting
(D) ground gravity survey
37. The following reaction takes place in the amphibolite grade of metamorphism of pelitic rocks:
kyanite + chlorite ⟺ staurolite + quartz +H2O
Which of the following is a CORRECT statement on this reaction?
(A) The reaction can be represented as a sharp univariant boundary.
(B) Initially chlorite and staurolite are Fe-rich and will gradually become Mg-rich with increasing temperature.
(C) With increasing temperature chlorite becomes Mg-rich and staurolite becomes Fe –rich.
(D) The reaction is independent of fugacity of H2O.
38. Match the items in Group-I with corresponding appropriate items in Group-II.
(A) P-4, Q-1, R-2, S-3
(B) P-4, Q-3, R-1, S-2
(C) P-3, Q-1, R-2, S-4
(D) P-2, Q-1, R-4, S-3
39. The symmetry elements of a point group are: 3 crystallographic axes of 2-fold symmetry and 3 mirror planes perpendicular to the crystallographic axes. The Hermann – Mauguin notation of the point group is:
(A) 2m2m2m
(B) 2mm
(C) 2/m2/m2/m
(D) 2/m
40. An aqueous polyphase (L + V + solid) inclusion contains a halite daughter crystal at room temperature and pressure. Which of the given statements is CORRECT in relation to this inclusion?
(A) The salinity of the bulk aqueous fluid can be determined from the temperature of melting of ice.
(B) The salinity of the bulk aqueous fluid can be determined from the temperature of dissolution of halite.
(C) The density in all cases can be determined from the temperature of liquid-vapor homogenization.
(D) The density in all cases can be determined from the temperature of dissolution of the halite daughter crystal.
41. Match the rock types in Group-I with their most likely corresponding lithospheric/ tectonic settings of formation in Group-II.
(A) P-1, Q-3, R-4, S-2
(B) P-2, Q-4, R-1, S-3
(C) P-2, Q-1, R-4, S-3
(D) P-3, Q-2, R-4, S-1
42. A mantle source rock melts at a time t0 giving rise to melt (M) and residue (R). Which of the following statements is CORRECT about evolution of the (143Nd/144Nd) and (87Sr/86Sr) isotope ratio in M (that crystallized to form a rock) and R?
(A) The growth of Nd isotope ratio versus time is faster in R than M and the Sr isotope ratio grows slower in R than M.
(B) The growth of Nd isotope ratio versus time is slower in R than M and the Sr isotope ratio grows faster in R than M.
(C) Both the Nd and Sr isotope ratios grow at identical rates in R and M.
(D) The growth of Nd and Sr isotope ratio in M and R would depend on the initial concentrations of Sm and Rb in the mantle source rock.
Q.43 – Q.55 Numerical Answer Type (NAT), carry TWO mark each (no negative marks).
43. The mole percentages of SiO2, Al2O3 and K2O in a granitic rock are 84.21, 7.89 and 7.89, respectively. The molar proportion (in %) of K-feldspar in the rock is ______. [ round off to one decimal place]
44. In a zone of active normal faulting, the maximum and minimum in situ principal stresses (compressive in nature) are 30 MPa (s1) and 10 MPa (s3), respectively. The fault plane striking N-S has a dip amount of 60° towards E. Considering Anderson theory of faulting and using the given information, the calculated normal stress on the fault plane is ________ MPa. [in integer]
45. A circular tunnel is being excavated in a blocky rock mass by drilling and blasting. An excavation disturbed zone (EDZ) around the tunnel extends 0.70 m into the rock from the excavation surface. Considering the unit weight of the rock as 25 kN/m3, the support pressure required at the crown of the tunnel to stabilize the loose blocks of the EDZ is _______ kPa. [round off to one decimal place]
46. Under uniaxial compression, a cylindrical quartzite specimen (length = 122 mm and diameter = 60 mm) showed linear elastic behaviour. The uniaxial compressive strength and the modulus ratio of the rock are 150 MPa and 500, respectively. The axial strain at 75 MPa during the loading was _________ milli-strain. [in integer]
47. The sketch shows a triangular rock mass (ABC) resting on a joint plane (AC) inclined at 35° with the horizontal. A rockbolt having an inclination of 25° with the horizontal is used to stabilize the slope. If the bolt tension (T) is 110 kN, the absolute value of shear force along the joint plane induced by the bolt tension is _________ kN. [in integer]
48. A stratified confined aquifer consists of three parallel homogeneous and isotropic horizontal layers with thickness of 10 m, 5 m and 5 m. The layers have the same width. The hydraulic conductivities of the strata are 15 m/day, 20 m/day and 30 m/day, respectively. The water flow follows Darcy’s law and is parallel to the strata. Considering the same hydraulic gradient for all the layers, the effective hydraulic conductivity of the aquifer is ________ m/day. [in integer]
49. A drainage basin of fourth order covers an area of 35 km2. Within the basin, the total lengths of the 1st order, 2nd order and 3rd order drainages are 11.5 km, 8.5 km and 4.2 km, respectively. If the drainage density of the basin is 0.8 km−1, the total length of the 4th order drainage is ________ km. [round off to one decimal place]
50. The grade of copper (in wt%) of an ore body determined at locations 1, 2 and 3 are indicated (in parentheses) below. The grade of copper at an unknown location x calculated using Inverse-Square Distance Weighting (IDW) is ________ wt %. [round off to 2 decimal places]
51. The heat flux at the Earth’s surface is 60 mWm−2. If the thermal conductivity at the surface is 2.5 Wm−1 °C−1, the geothermal gradient is ________ °C/km. [in integer]
52. A rock formed at time t0 = 0 with number of 14C atoms = 105. The number of 14C atoms (in log10) after a time of 8 × 103 years is _______. [round off to 3 decimal places] (Use a decay constant of 1.25 × 10−4 yr−1)
53. In the given reaction,
2Fe2+ + 3H2O → Fe2O3 + 6H+ + 2e−
consider ideal condition, take concentration of Fe2+ as 10−5 molal, E0 = 0.98 V and pH=6. The value of (2.303 × R × T)/F = 0.059 (where F is the Faraday constant). The value of Eh on the Fe2+ / hematite boundary at 25 °C is ________ V. [round off to 2 decimal places]
54. The first and second dissociation constants of H2CO3 are 6.761 × 10−7 and 4.68 × 10−11, respectively. If the concentration of H2CO3 is 1 molal and pH = 6, the ∑CO2 in the solution (assuming ideal condition) is _______ molal. [round off to 3 decimal places]
55. A satellite orbits the earth at an altitude of 700 km on the equatorial plane of the earth and it revolves in the same direction as the direction of rotation of the earth. Considering the radius of a spherical earth as 6300 km and the acceleration due to gravity as 10 m/s2, the tangential velocity of the satellite in the orbit is ____________ km/s. [round off to 2 decimal places]
Geophysics (GG)
Q.26 – Q.42 Multiple Choice Question (MCQ), carry TWO marks each (for each wrong answer: – 2/3).
26. In a horizontally stratified cuboid rock sample (stratified in vertical z direction with various layers of different resistivity), bulk resistivity is measured in three perpendicular directions. If ρ1, ρ2, and ρ3 are the bulk resistivities measured perpendicular to xy, xz and yz planes, respectively, then
(A) ρ1 < ρ2 = ρ3
(B) ρ1 > ρ2 = ρ3
(C) ρ1 = ρ2 ≠ 3
(D) ρ1 ≠ ρ2 ≠ ρ3
27. Which one is the CORRECT sequence of electromagnetic methods in terms of depth of investigation?
P – AFMAG method
Q – VLF method
R – GPR method
S – Magnetotelluric method
(A) P > Q > S > R
(B) P > S > R > Q
(C) S > P > Q > R
(D) S > Q > R > P
28. Which Norm gives the maximum weight to the data points having maximum deviation/outlier from the smoothly fitted curve during linearized inversion?
(A) L1-Norm
(B) L2-Norm
(C) Lp-Norm
(D) L∞-Norm
29. Which one of the following statements is CORRECT for the Quenching agent used in the tube of Geiger-Muller counter?
(A) It enhances the emission of secondary electrons from the cathode.
(B) It reduces the emission of secondary electrons from the cathode.
(C) It enhances the emission of secondary electrons from the anode.
(D) It reduces the emission of secondary electrons from the anode.
30. Which one of the following statements is CORRECT regarding the property of Laplacian operator for vector/scalar fields?
(A) Laplacian of a vector field is zero if the Laplacian of each of its components are zero.
(B) Laplacian of a vector field is zero if the Laplacian of any one of its component is zero.
(C) If the Laplacian of a scalar field is zero then the scalar field is not harmonic.
(D) If the Laplacian of a scalar field is finite (non-zero) then the scalar field is harmonic.
31. The most desirable interaction of γ-ray with matter for γ-ray spectroscopy is
(A) Photoelectric effect only
(B) Both Photoelectric effect and Compton scattering
(C) Both Compton Scattering and Pair production
(D) Photoelectric effect, Compton scattering and Pair production
32. Which one of the following is the CORRECT sequence for a 2D seismic reflection data processing prior to Time-depth conversion?
(A) Migration → Deconvolution → Filtering → Equalization → Coherency
(B) Deconvolution → Migration → Filtering → Coherency → Equalization
(C) Filtering → Deconvolution → Migration → Equalization → Coherency
(D) Deconvolution → Filtering → Equalization → Migration → Coherency
33. Choose the CORRECT procedure to avoid the area of cracked, altered formation in Sonic log.
(A) Measure interval transit times using long-spacing sonic tools.
(B) Use more number of sets of sources.
(C) Measure interval transit times using short-spacing sonic tools.
(D) Use more number of sets of detectors.
34. The factor that DOES NOT influence measurement of Nuclear Magnetic Resonance log is
(A) mineral composition of the rock.
(B) bound water (irreducible water).
(C) free water.
(D) pore fluid pressure.
35. Consider a time-invariant geophysical filter with the given input as:
x(t) = e−αt when t ≥ 0 ; x(t) = 0 when t < 0 and output y(t) = e−βt when t ≥ 0 ; y(t) = 0 when t < 0. The transfer function for the given input and output of time-invariant filter will be:
36. Which of the given figures is the Hilbert transform of the Dirac delta function δ(ξ) :
(A) Figure 1
(B) Figure 2
(C) Figure 3
(D) Figure 4
37. If a mountain range is 100% isostatically compensated (Airy’s type), what would be the expected nature of the Bouguer anomaly and free air anomaly?
(A) Bouguer anomaly is very large and negative; free air anomaly is small and positive.
(B) Bouguer anomaly is very large and negative; free air anomaly is large and positive.
(C) Bouguer anomaly is exactly zero; free air anomaly is very large and positive.
(D) Bouguer anomaly is very large and negative; free air anomaly is large and negative.
38. Which of the following is INCORRECT for a recorded nuclear explosion event?
(A) The first P-wave from an explosion to arrive at any seismic station, irrespective of Azimuth, should be compressional.
(B) Nuclear explosions are not as good as earthquakes at generating surface waves or S-waves.
(C) In general, earthquakes have Mb values same those for nuclear explosions with same Ms values.
(D) Nuclear explosions have all been shallower than 2 km depth.
39. Focal depth can be determined from measurement of the difference in the travel time between:
(A) pP and P
(B) PP and P
(C) PcP and P
(D) PPP and P
40. Of the following options, at which discontinuity both P-wave and S-wave have maximum velocity drop?
(A) Conard
(B) Mohorovicic
(C) Gutenberg
(D) Lehman
41. In data enhancement techniques, what is the advantage of magnetic anomaly being ‘Reduced to the pole’?
(A) Enhances the signal to noise ratio.
(B) Estimates the depth to the basement.
(C) Takes care of variation of the magnetic anomaly with latitude.
(D) Helps in pseudo-gravity transformation.
42. Match the source in Group – I with their half-width (X1/2) / δgmax and depth (d) relation in Group –II.
(A) P-1, Q-2, R-4, S-3
(B) P-1, Q-4, R-3, S-2
(C) P-3, Q-4, R-1, S-2
(D) P-3, Q-1, R-4, S-2
Q.43 – Q.55 Numerical Answer Type (NAT), carry TWO mark each (no negative marks).
43. If a gravity determination is made at an elevation of 150 m above mean sea level, the Bouguer correction required for a density contrast of 250 kg m−3 with the surroundings is________ mgal. [round off to 2 decimal places]
44. An infinite horizontal cylinder of radius 40 km is buried at a depth of 100 km and yields the same maximum gravity anomaly as that of an infinite horizontal cylinder of radius 1 km, buried at a depth of 1 km having density contrast with the surroundings of 200 kgm−3. The density contrast of the deeper cylinder with respect to the surrounding is ________ kg/m3. [round off to one decimal place]
45. An earthquake causes an average of 25 m strike slip displacement over a 50 km long, 25 km deep portion of a transform fault. Assuming that the rock rigidity is 3 × 1010 Nm−2, the moment magnitude (Mw) of the earthquake is ______ . [round off to 2 decimal places]
46. Lithological unit X is sandwiched between Y1 above and Y2 below it. Now consider a log across lithology X, where Gamma ray (GR) reading is given by 100API; Y1 lithology, where minimum GR reading is 10API; and Y2 lithology of shale, where GR reading is 200API. Then the shale-free fractional volume in the X lithology will be________. [round off to 2 decimal places]
47. In a 2D seismic survey, 25 receivers are placed in a group and 25 sources are placed in another group, where random noise is present. The signal to noise ratio for this arrangement will be_______. [in integer]
48. In a VSP survey, the tube wave passage through borehole causes cross-section area change from 0.79 m2 to 1.13 m2. The transmission coefficient will be ______. [round off to 2 decimal places]
49. In a cratonic region, radioactive heat generation decreases exponentially with depth. Assuming characteristic depth as 10 km and surface heat generation as 3 μWm−3 and neglecting mantle heat flow, the heat production per unit volume for a 30 km thick layer will be_______ μWm−3. [round off to 2 decimal places]
50. In an Induced Polarization survey, 50 milliseconds chargeability was measured for steady state voltage (full saturation reached) of 200 V between potential electrodes. When the current was switched off, the voltage across potential electrodes drops instantaneously (time t = 0 s) to a level Va and thereafter decays linearly with time and becomes zero in 10 seconds. The magnitude of instantaneous voltage Va (at time t = 0 s) will be________ mV. [in integer]
51. Apparent resistivity sounding data for Schlumberger array is theoretically generated by the teacher for the following 4-layer model as: ρ1 = 100 Ωm, ρ2 = 20 Ωm, ρ3 = 500 Ωm, ρ4 = 10 Ωm and layer thicknesses h1 = 50 m, h2 = 20 m and h3 = 50 m. If the student interprets this theoretical sounding data for ρ3 as 750 Ωm, then according to the Principle of Equivalence, the thickness h3 would be ________ m. [round off to 2 decimal places]
52. A 3D conducting body is located at a depth of 50 m in a homogeneous medium of resistivity 500 Ω A frequency of f1 Hz is appropriate to detect this conducting body in a plane wave EM survey. When the same conducting body is located in a host medium of resistivity 100 Ωm at the same depth then a frequency of f2 Hz is found to be appropriate. Then the value of f2/f1 will be __________. [round off to 2 decimal places]
53. The apparent resistivity and phase computed for MT measurement at 10−3 Hz frequency is 500 Ωm and 30°, respectively. Ratio of Imaginary to Real component of the Impedance tensor is ______. [round off to 2 decimal places]
54. The diagonal elements of a covariance matrix computed for a linearized inverse problem having model parameters m1, m2, m3, m4, m5 are 49, 15, 3, 200, 40, respectively. The standard deviation (uncertainty) in the estimation of model parameters m4 is ________. [round off to 2 decimal places]
55. Electric current density incident at an angle 40° from vertical at the horizontal interface between two layers with resistivity ρ1 = 100 Ωm and ρ2 = 500 Ωm (from layer 1 to layer 2). The current density will enter into the second layer at an angle ________ degrees from vertical. [round off to 2 decimal places]