**GATE-2023**

**GG: Geology and Geophysics**

**General Aptitude**

**Q.1 – Q.5 Carry ONE mark each.**

1. The village was nestled in a green spot, _______ the ocean and the hills.

(A) through

(B) in

(C) at

(D) between

2. Disagree : Protest : : Agree : _______

(By word meaning)

(A) Refuse

(B) Pretext

(C) Recommend

(D) Refute

3. A ‘frabjous’ number is defined as a 3 digit number with all digits odd, and no two adjacent digits being the same. For example, 137 is a frabjous number, while 133 is not. How many such frabjous numbers exist?

(A) 125

(B) 720

(C) 60

(D) 80

4. Which one among the following statements must be TRUE about the mean and the median of the scores of all candidates appearing for GATE 2023?

(A) The median is at least as large as the mean.

(B) The mean is at least as large as the median.

(C) At most half the candidates have a score that is larger than the median.

(D) At most half the candidates have a score that is larger than the mean.

5. In the given diagram, ovals are marked at different heights (h) of a hill. Which one of the following options P, Q, R, and S depicts the top view of the hill?

(A) P

(B) Q

(C) R

(D) S

**Q.6 – Q.10 Carry TWO marks Each**

6. Residency is a famous housing complex with many well-established individuals among its residents. A recent survey conducted among the residents of the complex revealed that all of those residents who are well established in their respective fields happen to be academicians. The survey also revealed that most of these academicians are authors of some best-selling books.

Based only on the information provided above, which one of the following statements can be logically inferred with certainty?

(A) Some residents of the complex who are well established in their fields are also authors of some best-selling books.

(B) All academicians residing in the complex are well established in their fields.

(C) Some authors of best-selling books are residents of the complex who are well established in their fields.

(D) Some academicians residing in the complex are well established in their fields.

7. Ankita has to climb 5 stairs starting at the ground, while respecting the following rules:

(1) At any stage, Ankita can move either one or two stairs up.

(2) At any stage, Ankita cannot move to a lower step.

Let F(N) denote the number of possible ways in which Ankita can reach the Nth stair. For example, F(1) = 1,F(2) = 2,F(3) = 3.

The value of F (5) is _______.

(A) 8

(B) 7

(C) 6

(D) 5

8. The information contained in DNA is used to synthesize proteins that are necessary for the functioning of life. DNA is composed of four nucleotides: Adenine (A), Thymine (T), Cytosine (C), and Guanine (G). The information contained in DNA can then be thought of as a sequence of these four nucleotides: A, T, C, and G. DNA has coding and non-coding regions. Coding regions—where the sequence of these nucleotides are read in groups of three to produce individual amino acids—constitute only about 2% of human DNA. For example, the triplet of nucleotides CCG codes for the amino acid glycine, while the triplet GGA codes for the amino acid proline. Multiple amino acids are then assembled to form a protein.

Based only on the information provided above, which of the following statements can be logically inferred with certainty?

(i) The majority of human DNA has no role in the synthesis of proteins.

(ii) The function of about 98% of human DNA is not understood.

(A) only (i)

(B) only (ii)

(C) both (i) and (ii)

(D) neither (i) nor (ii)

9. Which one of the given figures P, Q, R and S represents the graph of the following function?

f(x) = ||x + 2| – |x – 1||

(A) P

(B) Q

(C) R

(D) S

10. An opaque cylinder (shown below) is suspended in the path of a parallel beam of light, such that its shadow is cast on a screen oriented perpendicular to the direction of the light beam. The cylinder can be reoriented in any direction within the light beam. Under these conditions, which one of the shadows P, Q, R, and S is NOT possible?

(A) P

(B) Q

(C) R

(D) S

**GG: Geology and Geophysics**

**PART A: COMPULSORY SECTION FOR ALL CANDIDATES**

**Q.11 – Q.17 Carry ONE mark Each**

11. Which of the following is a chronostratigraphic unit?

(A) Member

(B) Stage

(C) Acme Zone

(D) Period

12. During contact metamorphism, with increasing temperature,

(A) the ratio of volume to surface area of mineral grains increases.

(B) the ratio of volume to surface area of mineral grains decreases.

(C) the reaction kinetics becomes slower.

(D) hydrous minerals become more stable.

13. The dimension of dynamic viscosity is

(A) M^{1}L^{−}^{1}T^{−}^{2}

(B) M^{1}L^{1}T^{−}^{1}

(C) M^{0}L^{2}T^{−}^{1}

(D) M^{0}L^{0}T^{0}

14. At a depth of about 400 km inside the Earth, which one of the following occurs?

(A) Conversion of most silicates to perovskite structure

(B) Conversion of plagioclase-peridotite to spinel-peridotite

(C) Transformation of olivine to spinel structure

(D) Conversion of spinel-peridotite to plagioclase-peridotite

15. Equatorial radius of which one of the following planets is closest to that of the Earth?

(A) Mercury

(B) Venus

(C) Mars

(D) Neptune

16. Variation of Bouguer anomaly obtained along a profile after applying all the necessary corrections is due to

(A) topographic undulation above the datum plane.

(B) increase in densities of crustal rocks with depth.

(C) lateral density variations.

(D) vertical density contrast across Moho.

17. The heat production (Qr) of a granitic rock due to decay of the radioactive elements U, Th and K having concentration CU, CTh, and CK, respectively, is given by the expression

Q_{r} = αC_{U} + βC_{Th} + γC_{K}

Which one of the following correctly represents the relation between the magnitude of coefficients α, β, γ (in μWkg^{−1})?

(A) α > β > γ

(B) α < β > γ

(C) α > β < γ

(D) α < β < γ

**Q.18 – Q.26 Carry TWO marks Each**

18. Which one of the following Phanerozoic periods has the shortest duration of time?

(A) Cambrian

(B) Devonian

(C) Cretaceous

(D) Silurian

19. Based on the given mineral proportions, which one of the following statements is CORRECT?

(A) Y is more felsic compared to X & Z

(B) X is more felsic compared to Y & Z

(C) Z is more felsic compared to X & Y

(D) Y is the most felsic and Z is the most mafic

20. The CORRECT sequence(s) of electromagnetic radiations in terms of increasing wavelength is/are

(A) Gamma ray < UV < Near-IR

(B) X-ray < Visible light < Thermal IR

(C) Microwave < Visible light < Radio wave

(D) Microwave < Thermal IR < Near-IR

21. Which of the given folds is/are represented by the stereoplot?

(A) Horizontal fold

(B) Vertical fold

(C) Upright fold

(D) Recumbent fold

22. The bulk density and water content of a soil are 1800 kg/m3 and 18%, respectively. The dry density of the soil calculated from the given information is __________ kg/m^{3}. [round off to 2 decimal places]

23. In a seismic reflection survey over a two-layered Earth model having densities and seismic velocities ρ_{1}=2000 kg/m^{3}, V_{1}=1800 m/s for the first layer and ρ_{2} = 3000 kg/m^{3}, V_{2} = 2100 m/s for the second layer, the normal incidence P-wave reflection coefficient is ____________. [round off to 3 decimal places]

24. The resistivity of a rock, 100% saturated with water of resistivity 0.25 Ωm, is 60 Ω Assuming tortuosity and cementation exponents to be 1 and 2, respectively, the porosity of the rock is ________ (in %). [round off to 2 decimal places]

25. Let us consider that a student misses cancelling the self-potential between potential electrodes before injecting current into the subsurface, in a Wenner electrical resistivity survey using DC resistivity meter over a horizontally stratified Earth. In direct and reverse modes of measurement (when current flows from C1 to C2 and C2 to C1, respectively) with the same magnitude of current flow, the potential differences recorded are +158 mV and −214 mV, respectively. The self-potential between the potential electrodes before injecting current was _________mV. [in integer]

26. For the given figure, considering Pratt’s model of isostatic compensation at the crust mantle boundary, the crustal density (ρ_{1}) that explains 1.5 km deep lake is __________kg/m^{3}. (Consider density of water ρ_{w} = 1000 kg/m3) [round off to 2 decimal places]

**PART B (SECTION 1): FOR GEOLOGY CANDIDATES ONLY**

**Q.27 – Q.44 Carry ONE mark Each**

27. Which one of the following mineral pairs shows solid solubility through coupled substitution of elements?

(A) Albite – Anorthite

(B) Albite – Orthoclase

(C) Grossular – Andradite

(D) Jadeite – Aegirine

28. The behavior of trace elements in magmatic systems follows

(A) Henry’s Law

(B) Raoult’s Law

(C) Fick’s Second Law

(D) First Law of Thermodynamics

29. Choose the CORRECT statement regarding crystallization of a single feldspar of composition Or50Ab50 in the Albite-Orthoclase system.

(A) The mineral can form in hypersolvus but not in subsolvus feldspar system.

(B) The mineral can form in subsolvus but not in hypersolvus feldspar system.

(C) The mineral can crystallize in both hypersolvus and subsolvus feldspar system.

(D) The mineral can crystallize neither in hypersolvus nor in subsolvus feldspar system.

30. Given ΔV_{r} and ΔS_{r} are the volume and entropy of reaction, respectively, the most suitable conditions for the reaction to be used as a geothermometer are

(A) small ΔV_{r} but large ΔS_{r}

(B) small ΔS_{r} but large ΔV_{r}

(C) positive ΔV_{r} but negative ΔS_{r}

(D) negative ΔV_{r} but positive ΔS_{r}

31. In which one of the given mass extinction events, global cooling that resulted in glaciation and lowering of sea level, is considered as major cause of extinction for more than 50% of marine fauna?

(A) Cretaceous – Paleogene

(B) Permian – Triassic

(C) Ordovician – Silurian

(D) Holocene

32. Processes of fossilization affecting an organism from its death to burial under sediments come under the study of

(A) Biostratinomy

(B) Biostratigraphy

(C) Taphonomy

(D) Taxonomy

33. The dip and dip direction of the lee side of a straight crested ripple on modern sediments are found to be 15° and N10°W, respectively. Considering unidirectional water movement, the flow direction is towards

(A) N10°W

(B) N70°W

(C) S10°W

(D) S70°W

34. Rhodocrosite in hand specimen is most likely to be confused with certain varieties of

(A) Wollastonite

(B) Orthoclase

(C) Gypsum

(D) Biotite

35. Which of the following is NOT an essential property of a mineral?

(A) Natural occurrence

(B) Regular internal structure

(C) Fixed composition

(D) Solid state

36. The number of lattice points in a face-centered cubic unit cell is

(A) 1

(B) 2

(C) 3

(D) 4

37. All the faces of an octahedron can be collectively symbolized by

(A) 111

(B) [111]

(C) (111)

(D) {111}

38. Shallow-focus earthquakes with tensional focal mechanism are characteristic of

(A) subduction zones.

(B) continental shear zones.

(C) transform faults.

(D) mid-ocean ridges.

39. 90% of the bulk Earth is constituted of Fe, Si, O and

(A) Al

(B) Ca

(C) Mg

(D) Na

40. Which of the following is/are slope stabilization method(s)?

(A) Bolting

(B) Application of shotcrete

(C) Use of impression packer

(D) Use of geogrid

41. The amount of Fe in a sample of 25 g of pyrrhotite (FeS) is __________ g. (Atomic wt. of Fe = 55.85 and S = 32.06) [round off to 2 decimal places]

42. The rate of spreading about a symmetric spreading center at the middle of a 4000 km wide sea is 40 mm/year. The spreading began ________ million years before present. [in integer]

43. A vertical aerial photograph is obtained over flat terrain with a 30 cm focal-length camera lens from an altitude of 18288 m. If the width of a dolerite dyke on this vertical photograph is 2 mm, its actual width on the terrain is ____________ m. [round off to 2 decimal places]

44. The decay constant of a radioactive isotope is 1.21 × 10^{−4} year^{−1}. The half-life of the isotope is __________ years. [round off to nearest integer]

**Q.45 – Q.65 Carry TWO marks Each**

45. The given outcrop pattern on a flat topography represents

(A) antiform with axial culmination.

(B) horizontal fold.

(C) plunging antiform.

(D) synform with axial depression.

46. Match the following fossil taxa in Group I with their corresponding features in Group II.

(A) P-4, Q-3, R-2, S-1

(B) P-3, Q-4, R-2, S-1

(C) P-4, Q-1, R-2, S-3

(D) P-3, Q-1, R-4, S-2

47. In the given schematic diagram, cross beds are exposed on a vertical rock face. The feature XY (bold line) represents a/an

(A) reactivation surface.

(B) foreset of cross bed.

(C) scoured channel base.

(D) angular unconformity.

48. The schematic diagram represents thin section of a carbonate rock. The type of cement formed by large calcite crystals is known as

(A) overgrowth cement.

(B) poikilotopic cement.

(C) isopachous cement.

(D) meniscus cement.

49. Based on the three statements given below, choose the CORRECT option.

**Statement I:** Echinoids have water vascular system.

**Statement II:** Delthyrium and pedicle foramen are found in the brachial valve of brachiopods.

**Statement III:** Cardinal teeth, adductor muscles and chondrophore are found in bivalves.

(A) Statements I and III are correct, statement II is incorrect.

(B) Statements II and III are correct, statement I is incorrect.

(C) Statements I and II are correct, statement III is incorrect.

(D) Statements I, II and III are correct.

50. The total number of symmetry elements in the crystal class represented by the point group

(A) 21

(B) 22

(C) 23

(D) 24

51. The ratio of bridging to non-bridging oxygen atoms in the amphibole structure is

(A) 4:11

(B) 5:6

(C) 2:7

(D) 1:2

52. Match the following basins in Group I with their corresponding formations in Group II.

(A) P-4, Q-3, R-1, S-2

(B) P-3, Q-4, R-2, S-1

(C) P-4, Q-1, R-3, S-2

(D) P-2, Q-3, R-1, S-4

53. Based on the three statements given below, choose the CORRECT option.

**Statement I:** Gigantopithecus is a genus of the family Hominidae

**Statement II:** Equus is a living genus of the family Equidae

**Statement III:** Gomphotherium is a genus belonging to the order Proboscidea

(A) Statements I and II are correct, statement III is incorrect.

(B) Statements I and III are correct, statement II is incorrect.

(C) Statements II and III are correct, statement I is incorrect.

(D) Statements I, II and III are correct.

54. In porphyry copper deposits, the order of alteration zones from the intrusive body outwards is

(A) propylitic→argillic→phyllic→potassic

(B) argillic→phyllic→potassic→propylitic

(C) potassic→phyllic→argillic→propylitic

(D) potassic→argillic→phyllic→propylitic

55. Which is the CORRECT sequence of ore minerals in their increasing order of reflectance?

(A) Galena, Sphalerite, Magnetite, Pyrite

(B) Magnetite, Sphalerite, Galena, Pyrite

(C) Sphalerite, Magnetite, Galena, Pyrite

(D) Galena, Magnetite, Sphalerite, Pyrite

56. Which of the following stratigraphic successions is/are arranged in CORRECT chronological order?

(A) Muth Quartzite-Syringothyris Limestone-Fenestella Shale-Panjal Volcanics

(B) Barakar Formation-Bijori Formation-Pachmarhi Formation-Bagra Formation

(C) Chiravati Group-Papaghni Group-Nallamalai Group-Kurnool Group

(D) Kaimur Group-Semri Group-Bhander Group-Rewa Group

57. Which of the following options represent(s) simultaneous crystallization of two minerals in the given feature(s) ?

(A) Granophyric texture

(B) Myrmekite

(C) Corona of orthopyroxene around anhedral olivine

(D) Cumulate pyroxene with interstitial plagioclase

58. Which of the following textures suggest(s) post-kinematic growth of the mentioned mineral?

(A) Randomly oriented chlorite grain aggregates pseudomorphing porphyroblast

(B) Garnet porphyroblast wrapped by external foliation

(C) Foliation defining biotite wrapping around a porphyroblast

(D) Porphyroblastic garnet containing helicitic fold as internal schistosity

59. In the schematic cross-section of a hill, a planar discontinuity intersects a planar slope face. Using kinematic analysis, which of the following conditions favor(s) plane failure to occur?

(A) The dip of the discontinuity surface is less than that of the slope face.

(B) Friction angle on the discontinuity surface is more than the dip of the slope face.

(C) Friction angle on the discontinuity surface is less than the dip of the discontinuity.

(D) The dip direction of the discontinuity surface is same as that of the slope face.

60. In a drainage basin, the number of the 1st, 2nd, 3rd, 4th and 5th order streams are 240, 40, 8, 2 and 1, respectively. The average of all calculated bifurcation ratios is __________. [round off to 2 decimal places]

61. A sandstone follows Mohr-Coulomb failure criterion. If the uniaxial compressive strength and the angle of the internal friction of the sandstone are 7 MPa and 30, respectively, the calculated cohesion of the rock is _____________ MPa. [round off to 2 decimal places]

62. At a certain depth in the crust, the maximum and minimum principal compressive stresses are 150 MPa and 75 MPa, respectively, which lead to normal faulting. If the average density of the crust is 2700 kg/m3, the crustal depth of fracture initiation according to Anderson’s theory of faulting is __________ km. (g = 10 m/s^{2}) [round off to one decimal place]

63. A cylindrical soil sample of 10 cm diameter is tested in a constant-head permeameter. A volume of 250 cm^{3} of water is collected in 5 minutes when the constant-head difference between tapping points 15 cm apart is 5 cm. Considering Darcy flow, the absolute value of coefficient of permeability in cm/s is ____________. (π = 3.14) [round off to 3 decimal places]

64. The minimum anion-to-cation radius ratio at which a 3-fold coordination becomes possible is _________. [round off to 2 decimal places]

65. The mole fraction of jadeite in the pyroxene of composition (Ca_{667}Na_{0.333}Fe^{2+}_{0.121}Fe^{3+}_{0.125}Mg^{0.546}A_{l0.208})Si_{2}O_{6} is _________. [round off to 3 decimal places]

**PART B (SECTION 2): FOR GEOPHYSICS CANDIDATES ONLY**

**Q.27 – Q.44 Carry ONE mark Each**

27. Young’s Modulus of granite is

(A) 5 × 10^{10} to 7 × 10^{10} Newton/m^{2}.

(B) 5 × 10^{10} to 7 × 10^{10} Newton/cm^{2}.

(C) 5 × 10^{10} to 7 × 10^{10} Newton.

(D) 5 × 10^{10} to 7 × 10^{10} Newton m.

28. The resultant stress obtained from normal stress measurements that are corrected for the mean stress is

(A) hydrostatic stress.

(B) lithostatic stress.

(C) deviatoric stress.

(D) shear stress.

29. Which one of the following options is CORRECT for the arrangement of magnetic moment of dipoles in ferrimagnetic material?

(A) Equal and anti-parallel in nature

(B) Unequal and anti-parallel in nature

(C) Equal and parallel in nature

(D) Unequal and parallel in nature

30. Choose the CORRECT earthquake body wave phase which travels as S-wave through the inner core of the Earth.

(A) SKIKS

(B) SKKS

(C) PKJKP

(D) PKiKP

31. If the divergence and curl of a vector field are zero, then the field will be

(A) solenoidal and irrotational.

(B) solenoidal but not irrotational.

(C) irrotational but not solenoidal.

(D) neither solenoidal nor irrotational.

32. The equipotential surface due to a line current electrode placed horizontally over the surface of a homogeneous Earth is

(A) cylindrical.

(B) spherical.

(C) half-cylindrical.

(D) hemi-spherical.

33. The basic working principle of a standard Proton Precession Magnetometer is based on

(A) Faraday’s law of induction.

(B) Nuclear magnetic resonance.

(C) Zeeman effect.

(D) Gauss’s law for magnetization.

34. The working principle of a modern absolute gravimeter is based on

(A) free-fall method.

(B) simple pendulum method.

(C) Hooke’s law.

(D) principle of zero length spring.

35. The given figure shows the self-potential (S.P.) anomaly observed over a polarized spherical body. The direction of polarization with respect to horizontal is

(A) 0°

(B) 45°

(C) 60°

(D) 90°

36. Geiger-Muller counter responds primarily to

(A) α-radiation.

(B) β-radiation.

(C) γ-radiation.

(D) α, β, γ-radiations all, equally.

37. The damping parameter in the Damped Least-squares solution of a geophysical inverse problem is primarily used to

(A) stabilize the inverse solution.

(B) increase the resolution of estimated model parameters.

(C) decrease the non-uniqueness of the solution.

(D) obtain a unique solution.

38. A seismic wave with a wavelength of 25 m propagates through a sedimentary basin with a phase velocity of 280 m/s. The rate of change of phase velocity with respect to wavelength is 4 per second. The group velocity of the seismic wave propagating in the same dispersive medium is _________ m/s. [round off to nearest integer]

39. The gravity anomaly value estimated at the base of a 10 m tall building is 20 mGal. The gravity anomaly value at the top of the building is ________ mGal. (Ignore the mass of the building in both cases) [round off to 1 decimal place]

40. In a VLF EM measurement, the vertical and horizontal components of secondary magnetic field observed at any observation point are +10 SI units and -2 SI units, respectively. If the magnitude of the primary magnetic field at the observation point is +50 SI units, then magnitude of the measured dip angle with respect to the horizontal at the observation point is_________ degree. [round off to 2 decimal place]

41. A geothermal gradient of 32°C/km is measured in the upper few meters of sediments covering the ocean floor. If the mean thermal conductivity of the oceanic sediments is 1.9 Wm^{−1}°C^{−1}, then the absolute value of local heat flow is _________milli-Wm^{−2}. [round off to 1 decimal place]

42. A seismic refraction survey is done over a two-layered Earth having P-wave velocities of 2000 m/s and 3500 m/s for the first and second layers, respectively. Given the thickness of the first layer to be 2000 m, the critical distance for the refracted wave is ________ m. [round off to nearest integer]

43. The given figure shows the time domain convolution of two boxcar functions. The duration (t) of the output pulse as shown in the figure is _________ milli-second. [in integer]

44. For a given rock formation, the porosity (ϕ) is 23 % and water saturation (S_{w}) is 25 %. The proportion of water (bulk volume of water) in the total rock formation is ________%. [round off to 2 decimal places]

**Q.45 – Q.65 Carry TWO marks Each**

45. Electrical Resistivity Tomography (ERT) survey is performed in a noisy background along a 1000 m long profile with 10 m equi-spaced electrodes using different electrode configurations. Which electrode configuration will produce maximum number of negative apparent resistivity data?

(A) Dipole-dipole configuration

(B) Wenner-Schlumberger configuration

(C) Wenner configuration

(D) All configurations will produce the same number of negative apparent resistivity data

46. Consider a signal whose original real part is given by f(t) = sin (t) and its Hilbert transform is given by f(t)_{H}. Then, the complex signal f_{C} is

(A) sin(t) – isin(t)

(B) cos(t) – icos(t)

(C) sin(t) – icos(t)

(D) cos(t) – isin(t)

47. Mathematically, the geometrical factor for a Two-electrode array and Wenner array is the same. Which one of the following statements is CORRECT?

(A) Lateral resolution of Two-electrode array is better than the Wenner array

(B) Lateral resolution of Wenner array is better than the Two-electrode array

(C) Lateral resolution of both arrays will be the same

(D) Vertical resolution of both arrays will be the same

48. Laminar shale, structural shale and dispersed shale can be distinguished by which one of the following cross-plots?

(A) Self-potential (S_{P}) log value and formation water resistivity (R_{w})

(B) Laterolog Deep (LLD) resistivity and formation resistivity (Rt)

(C) Sonic log value and Sonic porosity

(D) Neutron porosity and Density porosity

49. The factor by which the magnetic field decreases with respect to the gravity field caused by the same source at a distance (r) is

(A) 1/r

(B) r

(C) 1/√r

(D) 1/r^{2}

50. The total excess mass of an irregular shaped body can be calculated from the corresponding gravity anomaly measured over a horizontal plane on the surface of the Earth using

(A) Divergence theorem.

(B) Stoke’s theorem.

(C) Newton’s law of gravity.

(D) Laplace’s equation.

51. Select the CORRECT equation for Euler deconvolution solution of the total magnetic field B_{T} observed along a profile on the surface of the Earth for ith point, with background magnetic field value B, and structural index N.

52. The potential field U due to a source follows a spherical symmetry. Which among the following is/are CORRECT statement(s)?

53. In Magnetotelluric survey, three magnetic field components (H_{x}, H_{y}, H_{z}) and two electric field components (E_{x} and E_{y}) are measured and two apparent resistivities ρ_{xy} and ρ_{yx} are computed. Which of the following is/are CORRECT?

(A) ρ_{xy} = ρ_{yx} over horizontally stratified layered structure

(B) ρ_{xy} = ρ_{yx} when 2D strike is in x-direction

(C) ρ_{xy} = ρ_{yx} when 2D strike is in y-direction

(D) ρxy = ρyx when 2D strike is at 45° from x-direction

54. Singular Value Decomposition (SVD) decomposes a matrix A into 3 orthogonal matrices. If V is one of the orthogonal matrices, then which among the following is/are CORRECT? (superscript T-represents transpose and I is the Identity matrix)

(A) V^{T}V = VV^{T} ≠ I

(B) V^{T}V ≠ VV^{T} ≠ I

(C) V^{T}V = I

(D) VV^{T} = I

55. If g_{A}, g_{B} and g_{C} are the observed gravity values in a valley below mean sea level, on a plane surface at mean sea level and on the top of a mountain above mean sea level at the same latitude, respectively, then which of the following option(s) is/are CORRECT?

(A) g_{A} and g_{B} less than g_{C}

(B) g_{A} and g_{C} less than g_{B}

(C) g_{A} and g_{B} more than g_{C}

(D) g_{C} and g_{B} less than g_{A}

56. The CORRECT option(s) for the generation of point M in a seismic reflection survey as shown in the given figure is/are

(A) The curvature of the reflector is greater than that of the incident wavefront

(B) Focusing effect

(C) Migration

(D) The curvature of the incident wavefront is greater than that of the reflector.

57. In the X^{2} – T^{2} seismic reflection method, the travel time (T) is expressed as

T_{0} is the normal incidence two-way travel time at zero offset distance (X = 0), RMS velocities Which of the following options apply(ies) to the third term?

(A) Heterogeneous medium

(B) Isotropic medium.

(C) Homogeneous medium

(D) Geometrical spreading to correct AVO data.

58. The coefficient of electrical anisotropy and mean resistivity of a horizontally stratified rock sample is 1.10 and 150 Ωm, respectively. The longitudinal resistivity of the rock sample is _______ Ω [round off to 2 decimal places]

59. The amplitude of a plane EM wave travelling vertically downward in a homogeneous medium of resistivity ‘ρ’ decreases with depth as where z is depth. If the frequency of the EM wave is 10 kHz, then the resistivity of the medium is _______ Ω (use μ = μ_{0} = 4π × 10^{−}^{7} H/m and π = 3.14)

[round off to nearest integer]

60. In a seismic survey using a Vibroseis source, the source wavelet used is S(t) = (0.3, 0.5, 0.6, 0.7) and the data acquired is X(t) = (0.5, 0.3, 0.7, 0.2) (as shown in the figure). Consider the unit delay (lag) to be 0.1 second (i.e., two-way travel time), which corresponds to a depth of 300 m. The cross correlation of S(t) with X(t) leads to maximum cross-correlated value of ________. [round off to 2 decimal places]

61. In the given figure, the rupture propagates from left to right along a fault with a rupture velocity of 1.5 km/sec. Given the P-wave velocity of the medium to be 6 km/sec, the apparent rupture time observed at point ‘O’ at the right edge of the fault is _________ sec. [round off to nearest integer]

62. Given the following well logging parameters

Flushed zone resistivity R_{XO} = 0.4 Ωm, Formation resistivity R_{t} = 5 Ωm, Mud-filtrate resistivity R_{mf} = 0.02 Ωm, Formation water resistivity R_{w} = 0.10 Ωm, Tortuosity factor 𝑎 = 1, and Cementation and Saturation exponents m = n = 2, Porosity = 30 %.

The movable hydrocarbon saturation is _________%. [round off to 1 decimal places]

63. The horizontal and vertical components of the geomagnetic field at a location are 40000 nT and 30000 nT, respectively. If the horizontal and vertical components of the induced field at the same location are −1000 nT and −600 nT, respectively, then the total magnetic field anomaly for that location is _______ nT. [round off to nearest integer]

64. There is a major water supply well in a fully saturated sandy medium which has a porosity of 40% and a density of 2600 kg/m^{3}. Water extracted from this well creates a depression in the shape of a vertical cylinder to a depth of 300 m from the surface and with a radius of 1000 m about the well. The maximum change in gravity anomaly due to the 100% extraction of water is __________ mGal. (use π = 3.14 and G = 6.67 × 10^{−11} Nm^{2}kg^{−2}) [round off to 2 decimal places]

65. The given figure is a seismogram of a local earthquake which occurred at a depth of 10 km. Considering the P-wave and S-wave velocities as 6 km/s and 3 km/s respectively for the medium, the epicentral distance is________ km. [round off to nearest integer]