UPSC Previous Year Question Paper-Combined Geo-Scientist (Preliminary) Examination-2026-GeoPhysics
1. The geophysical methods used for investigating the shallow features of the Earth's crust are
(a) static methods only
(b) dynamic methods only
(c) static and dynamic methods both
(d) relaxation methods only
2. The units of magnetic field strength and magnetic flux density, respectively are
(a) ampere metre⁻¹ and volt second metre⁻²
(b) volt second metre⁻² and ampere metre⁻¹
(c) volt second and ampere metre⁻¹
(d) ampere metre⁻¹ and volt second
3. The angle of obliquity of the Earth ranges from
(a) 21.1° to 25.3°
(b) 21.9° to 24.3°
(c) 21.9° to 25.3°
(d) 21.1° to 24.3°
4. Which one of the following planets of the solar system has the highest mean orbital velocity?
(a) Mercury
(b) Venus
(c) Earth
(d) Mars
5. Which one of the following relations is correct among the radius of sphere, R and equatorial and polar radii of the international reference of ellipsoid, a and c respectively, if the volumes of the sphere and ellipsoid are equal?
R - c = (a - R)/2
R - c = a - R
R - c = 2(a - R)
R - c = 4(a - R)
6. The difference between geographic and geocentric latitudes is maximum at
(a) 0° latitude
(b) 23.5° latitude
(c) 45° latitude
(d) 90° latitude
7. The acceleration of a point mass m₁ due to the attraction of another point mass m₂ at distance r is equal to
G m₁ / r²
G m₂ / r²
G m₁m₂ / r²
-G m₁ / r
(where G = universal gravitational constant)
UPSC Previous year question paper Geo scientist exam
8. A circular coil having axis length L and number of turns n is wound around a magnetic core. A current of I units passes through this coil. The magnetic excitation inside the core will be
(a) nI/L
(b) nIL
(c) nL/I
(d) L/I
9. The angle between magnetic north and total magnetic field is
(a) magnetic declination
(b) magnetic inclination
(c) magnetic total angle
(d) magnetic vertical angle
10. Which one of the following minerals has negative magnetic susceptibility?
(a) Pyrrhotite
(b) Ilmenite
(c) Sphalerite
(d) Quartz
11. The ratio of S-wave to P-wave velocities for zero Poisson's ratio value is
(a) √3
(b) 1/√3
(c) √2
(d) 1/√2
12. What fraction of the normal incident wave energy will be transmitted into the second layer, if a layer with density 3 g/cc and wave velocity 4 km/s is overlain by a layer having density 2 g/cc and velocity 3 km/s ?
(a) 0.11
(b) 0.22
(c) 0.44
(d) 0.89
13. Which one of the following seismic phases results from a P-wave turning within the crust?
(a) P_g
(b) P_mP
(c) P_n
(d) PP
14. The slowness vector of a 1 Hz plane P-wave propagating at 6.5 km/s velocity in +x direction is
(a) {1/6.5, 0, 0}
(b) {0, 1/6.5, 0}
(c) {0, 0, 1/6.5}
(d) {1/6.5, 0, 1/6.5}
15. Which one of the following correctly describes the attenuation property of the Earth expressed in terms of quality factor (Q)?
(a) The Q value is infinite for the Earth.
(b) The Q value is zero for the Earth.
(c) The Q value of P-wave is lower than the Q value of S-wave in the Earth's core.
(d) None of the above
16. What type of changes in the mineral phase takes place at 410 km discontinuity inside the Earth?
(a) Olivine-type to spinel-type lattice
(b) Graphite-type to γ-spinel-type lattice
(c) α-spinel-type to pyrite-type lattice
(d) γ-spinel-type to β-spinel-type lattice
17. What is the approximate pressure at the centre of the Earth?
(a) 180 GPa
(b) 280 GPa
(c) 380 GPa
(d) 480 GPa
18. A weak P-wave diffraction is observed in the epicentral distance range of
(a) 0° - 30°
(b) 30° - 90°
(c) 90° - 102°
(d) 103° - 120°
19. Which one of the following is the correct epoch sequence from 0 to 4 Ma age as estimated from normal and reverse geomagnetic data?
(a) Brunhes, Gauss, Matuyama, Gilbert
(b) Brunhes, Matuyama, Gauss, Gilbert
(c) Brunhes, Matuyama, Gilbert, Gauss
(d) Brunhes, Gilbert, Matuyama, Gauss
20. The scalar seismic moment (M₀) of an earthquake is related to density of medium ρ, seismic velocity c, hypocentral distance r and radiation pattern U_φθ as
(a) ρc³ / rU_φθ
(b) ρc² / rU_φθ
(c) ρc³r / U_φθ
(d) ρc²r / U_φθ
21. What approximate percentage of the total annually released seismic energy is due to the intermediate focal depth earthquakes at the global level?
(a) 85%
(b) 20%
(c) 12%
(d) 3%
UPSC Previous year question paper Geo scientist exam
22. What is the ratio of the number of earthquakes having surface wave magnitudes greater than 5 and 7 occurring in a region, if the intercept, α and slope, b values of earthquake magnitude-frequency relation are 8 and 1, respectively for that region?
(a) 1000
(b) 100
(c) 32
(d) 10
23. The approximate value of free-air correction at a station located at 1 m height above the datum plane at the equator is
(a) 0.3072 mGal
(b) 0.3388 mGal
(c) 0.3491 mGal
(d) 0.3516 mGal
24. What is the ratio of maximum values of gravities directly above the centres of two spherical bodies of radii 1 m and 2 m situated in a homogeneous moraine having density contrast of 1 g/cc and 2 g/cc, respectively and depth to the centre of sphere as 2 m and 4 m, respectively?
(a) 1
(b) 1/2
(c) 1/4
(d) 1/8
25. What is the approximate range of the Earth's magnetic field variation due to change in latitude value?
(a) >100 nT/km
(b) 50-100 nT/km
(c) 10-50 nT/km
(d) <6 nT/km
26. What is the approximate direction of polarization of protons with respect to the Earth's magnetic field (F) due to applied external field in proton precession magnetometer?
(a) Parallel to F only
(b) Antiparallel to F only
(c) Normal to F
(d) Both parallel and antiparallel to F
27. What is the coefficient of anisotropy for a medium having vertical and horizontal resistivities ρ_v and ρ_h, respectively?
(a) (ρ_v / ρ_h)^(1/2)
(b) (ρ_h / ρ_v)^(1/2)
(c) ρ_v / ρ_h
(d) ρ_h / ρ_v
28. What is the equivalent horizontal resistivity for a vertical stake of n beds with resistivities ρ₁, ρ₂, ρ₃, ..., ρ_n and thicknesses z₁, z₂, z₃, ..., z_n from top to bottom, respectively?
29. What is the ratio of effective resistivity of the rock (ρ_e) to the resistivity of the groundwater (ρ_w) if the formation has 1% porosity, water saturation constant 1.0 and parameters a = 1, m = 2 and n = 2 are constants of Archie's formula?
(a) 10⁻⁴
(b) 10⁴
(c) 10⁻²
(d) 10²
30. Which one of the following potentials is relatively more variable electrical potential used in geophysical prospecting?
(a) Diffusion potential
(b) Nernst potential
(c) Electrokinetic potential
(d) Telluric potential
31. What is the ratio of seismic velocities of the second layer to the first layer for a seismic wave incident on a horizontal interface at an angle of 30° to the normal in the first layer and refracted at 45° angle to the normal in the second layer?
(a) 1/√2
(b) √2
(c) 2
(d) 2√2
32. The ground roll in seismic data can be attenuated by
(a) grouping of geophones
(b) reducing the number of geophones
(c) increasing geophone spacing
(d) decreasing geophone spacing
33. What is the reflection coefficient for a seismic wave incident at normal to the interface between the first and second layers characterized by densities 3 g/cc and 2.5 g/cc and velocities 5 km/s and 4 km/s respectively?
(a) 0.2
(b) -0.2
(c) 1.2
(d) -1.2
34. A point scatterer is observed at 2.5 km depth within a layer with a uniform velocity of 4 km/s. What is the observed two-way travel time for the source and receiver with an offset of 3 km?
(a) 1.25 s
(b) 1.35 s
(c) 1.60 s
(d) 1.95 s
UPSC Previous year question paper Geo scientist exam
35. The phase shift between ghost multiple and primary reflection in seismic data is
(a) 90°
(b) 180°
(c) 270°
(d) 360°
36. What is the Nyquist frequency for a seismic data recorded with a sampling rate of 100 Hz?
(a) 250 Hz
(b) 200 Hz
(c) 100 Hz
(d) 50 Hz
37. Which one of the following filters is used to avoid the aliasing problem in seismic data processing?
(a) Low-pass filter
(b) High-pass filter
(c) Band-pass filter
(d) Notch filter
38. The convolution of a signal with a delta function
(a) alters the shape of the signal only
(b) does not alter the shape of the signal but produces a time shift in the original signal
(c) makes the signal zero at all times
(d) alters the shape of the signal as well as produces a time shift in the original signal
39. The only non-zero Fourier series coefficients for the signal x(t) = sin ω₀t, having fundamental frequency ω₀, are
(a) ±1/8i
(b) ±1/6i
(c) ±1/4i
(d) ±1/2i
(where i = √-1)
40. The radix-2 fast Fourier transform requires the sequence length of the input time-domain signal to be an integral power of
(a) 2
(b) 3
(c) 4
(d) 5
41. The Laplace transform of a function f(t) is given as F(s). The Laplace transform of a time-domain signal f(t) = A e^(-at) (A = constant, a > 0) is
(a) A/s
(b) A/s²
(c) A/(s + a)
(d) A/(s + a)²
42. What would be the length of the output signal, generated after convolution of two signals of lengths D₁ and D₂?
(a) D₁ + D₂ - 1
(b) D₁ + D₂ + 1
(c) D₁ + D₂ - 2
(d) D₁ + D₂ + 2
43. Which one of the following is not correct about the Dirac delta function?
(a) The Fourier transform of a Dirac function is equal to a nonzero constant.
(b) The Dirac function can be used to delay a time series function.
(c) The product of a function with a Dirac function gives a Dirac function of amplitude equal to the sample of that function.
(d) The Fourier transform of a Dirac function is equal to zero.
44. With the increase in number of input data points, the difference between the number of complex multiplications required by the radix-2 fast Fourier transform (FFT) and the discrete Fourier transform (DFT)
(a) remains constant
(b) increases
(c) decreases
(d) becomes zero
45. Which one of the following microwave bands will have the maximum penetration in dry sand?
(a) P
(b) S
(c) X
(d) K
46. Which of the following ground parameters are measured during field survey using thermal infrared region of electromagnetic spectrum?
(a) Ground temperature and spectral emissivity
(b) Rainfall pattern and backscattering coefficient
(c) Spectral emissivity and backscattering coefficient
(d) Ground temperature and rainfall pattern
47. Which one of the following statements is not correct regarding body's emissivity?
(a) The spectral emissivity values range from 0-1.
(b) Blackbody radiates a continuous spectrum.
(c) The Sun and the Earth as whole bodies radiate a near-continuous spectrum.
(d) The spectral emissivity values of a gray body are not constant at all wavelengths.
48. Consider the following statements :
1. Stefan-Boltzmann relation applies to all wavelengths of the spectrum shorter than microwaves.
2. Rayleigh-Jeans law is valid for longer wavelengths such as microwaves.
Which of the statements given above is/are correct?
(a) Both 1 and 2
(b) 1 only
(c) 2 only
(d) Neither 1 nor 2
UPSC Previous year question paper Geo scientist exam
49. Which one of the following is the correct sequence of the electromagnetic waves in the order of their increasing frequencies?
(a) Radio wave, Microwave, Infrared, Visible, Ultraviolet, X-ray
(b) Radio wave, Infrared, Microwave, Visible, Ultraviolet, X-ray
(c) Microwave, Radio wave, Infrared, Visible, X-ray, Ultraviolet
(d) Infrared, Visible, Ultraviolet, Microwave, Radio wave, X-ray
50. A hot blackbody emits energy at the rate of 25 J m⁻² s⁻¹ with most intense radiation corresponding to wavelength of 20000 Å. If the temperature of the body is further raised, its most intense radiation corresponds to wavelength of 10000 Å. Then the rate at which energy is emitted is
(a) 100 J m⁻² s⁻¹
(b) 200 J m⁻² s⁻¹
(c) 400 J m⁻² s⁻¹
(d) 800 J m⁻² s⁻¹
51. The correct value of the Stefan-Boltzmann constant is
(a) 5.6704 × 10⁻⁷ W m K⁻⁴
(b) 5.6704 × 10⁻⁸ W m⁻² K⁻⁴
(c) 4.6704 × 10⁻⁸ W m K⁻⁴
(d) 4.6704 × 10⁻⁷ W m⁻² K⁻⁴
52. The energy of an oscillator of frequency ν is equal to
(a) h/ν
(b) hν
(c) h²ν^(2/3)
(d) h^(2/3)ν²
(where h is Planck's constant)
53. The Kelvin-Planck statement of the second law of thermodynamics deals with
(a) conservation of energy
(b) conservation of mass
(c) conversion of work into heat
(d) conversion of heat into work
54. Which one of the following thermodynamic laws relates the change in internal energy of a system with the heat supplied to the system and the work done by the system on its surroundings?
(a) Zeroth law
(b) First law
(c) Second law
(d) Third law
55. An infinite plane carries a uniform surface charge σ. Its electric field is
(a) σ/(2ε₀) n̂
(b) σ/ε₀ n̂
(c) σ/(4ε₀) n̂
(d) σ/(8ε₀) n̂
(where n̂ is a unit normal vector pointing away from the surface)
56. The velocity of ground-penetrating radar signals depends on
(a) electrical properties of the material only
(b) magnetic properties of the material only
(c) both electrical and magnetic properties of the material
(d) neither electrical nor magnetic properties of the material
57. The electric field in polystyrene (relative permittivity = 2.55) filling the space between the plates of a parallel-plate capacitor is 10 kV/m. The distance between the plates is 1.5 mm. The potential difference between the plates is
(a) 4 V
(b) 10 V
(c) 60 V
(d) 15 V
58. A particle of charge Q moves with speed ν, in a circle of radius R, in a uniform magnetic field of magnitude B perpendicular to the plane of the circle. The momentum of the particle is
(a) QνB
(b) QB/R
(c) QB/ν
(d) QBR
59. Which one of the following laws describes the force F experienced by a charged particle of charge q, while moving through a magnetic field B with velocity v?
(a) Faraday's law
(b) Biot-Savart law
(c) Coulomb's law
(d) Lorentz's law
60. Which one of the following statements regarding solenoid is not correct?
(a) The wire is wound closely in the form of a helix.
(b) The wire is coated with a conducting material.
(c) Adjacent turns of the wire physically touch each other.
(d) Ampere's law is valid.
UPSC Previous year question paper Geo scientist exam
61. According to Biot-Savart law, the magnitude of the magnetic field due to a current element is
(a) directly proportional to the square of the distance between the current element and the point where the field is calculated
(b) directly proportional to the cube of the distance between the current element and the point where the field is calculated
(c) inversely proportional to the square of the distance between the current element and the point where the field is calculated
(d) inversely proportional to the cube of the distance between the current element and the point where the field is calculated
62. According to Faraday's law of electromagnetic induction, the magnetic flux through a coil can be changed by
1. changing the magnitude of the magnetic field within the coil
2. changing the portion of the area of the coil that lies within the magnetic field
3. changing the temperature of the experimental setup
4. changing the angle between the direction of the magnetic field and the plane of the coil
Select the correct answer using the code given below.
(a) 1,2 and 4
(b) 2,3 and 4
(c) 1 and 4 only
(d) 2 and 4 only
63. Two parallel plates are separated by a distance d/2 as shown in the figure below :
[Figure: Parallel plates with 2V]
The surface charge density at x = 0 is
(a) 4Vε₀/d
(b) Vε₀/d
(c) Vε₀/4d
(d) 2Vε₀/d
64. Which one of the following boundary conditions is not satisfied by the electric potential (V) while solving Laplace's equation ∇²V = 0 in electromagnetic method?
(a) V is continuous.
(b) The component of current density normal to the boundary is continuous.
(c) The component of current density normal to the boundary is discontinuous.
(d) V is finite at any point where there is no source or sink of current.
65. The equation
d/dx (1/ρ dV/dx) + d/dy (1/ρ dV/dy) + d/dz (1/ρ dV/dz) = 0
(where V = electric potential, ρ = resistivity)
reduces to Laplace's equation for
(a) a homogeneous and anisotropic medium
(b) a homogeneous and isotropic medium
(c) an inhomogeneous and anisotropic medium
(d) an inhomogeneous and isotropic medium
66. A uniform magnetic field B exists in a direction perpendicular to the plane of a square frame made of copper wire. The wire has a diameter of 2 mm and a total length of 40 cm. The magnetic field changes with time at a steady rate dB/dt = 0.02 T s⁻¹. The current induced in the frame is
(a) 4.5 × 10⁻² A
(b) 9.3 × 10⁻² A
(c) 2.5 × 10⁻¹ A
(d) 8.5 × 10⁻³ A
(Given : Resistivity of copper = 1.7 × 10⁻⁸ Ω m)
67. Which one of the following Maxwell's equations is generalized due to displacement current?
(a) Gauss's law for electricity
(b) Gauss's law for magnetism
(c) Faraday's law
(d) Ampere's law
68. "The parallel components of H are discontinuous by an amount proportional to the free surface current density."
For a linear medium, which one of the following relations is the correct boundary condition for the statement given above?
(a) (1/μ₁)E₁|| - (1/μ₂)E₂|| = K_f × n̂
(b) E₁|| - E₂|| = 0
(c) (1/μ₁)E₁|| - (1/μ₂)E₂|| = 0
(d) (1/μ₁)E₁|| + (1/μ₂)E₂|| = K_f × n̂
(where the symbols have their usual meanings)
69. An electromagnetic wave propagates through a linear homogeneous medium. The speed of the wave in this medium is
(a) c√(ε₀μ₀/ε₀μ₀)
(b) c√(ε₀μ₀/ε₀μ₁)
(c) c√(ε₀μ₀/ε₀ μ₀)
(d) c√(ε₀μ₀/ε₀μ₁)
(e) c√(ε₀μ₀/ε₀μ)
(where the symbols have their usual meanings)
UPSC Previous year question paper Geo scientist exam
70. Consider the following statements regarding skin depth of electromagnetic waves in conductors :
1. It is the distance taken by the electromagnetic wave to reduce the amplitude by a factor of half.
2. It measures how far the electromagnetic wave penetrates into the conductor.
3. It is determined by the real part of the wave number.
4. It is determined by the imaginary part of the wave number.
Which of the statements given above are correct?
(a) 1 and 3
(b) 1 and 4
(c) 2 and 3
(d) 2 and 4
71. The number of inhomogeneous Maxwell's equations for a good conductor is
(a) one
(b) two
(c) three
(d) zero
72. Which one of the following pairs is an example of mirror nuclei?
(a) ¹⁴C and ¹³C
(b) ¹³C and ¹⁴N
(c) ¹³C and ¹³N
(d) ¹³C and ¹²B
73. The ground-state spin (J) and parity (P) of most of the even-even (even protons, even neutrons) nuclei, i.e., J^P, is
(a) 3⁻
(b) 0⁺
(c) 5/2⁺
(d) 0⁻
74. The approximate radius R of ¹²⁵Sn nucleus is
(a) 1.2 fm
(b) 12.5 fm
(c) 6 fm
(d) 10 fm
75. According to the liquid drop model, when a nucleus is bombarded by neutrons, the compound nucleus before undergoing fission attains the shapes in the sequence of
(a) ellipsoidal, spherical, dumbbell
(b) spherical, ellipsoidal, dumbbell
(c) spherical, dumbbell, ellipsoidal
(d) dumbbell, ellipsoidal, spherical
76. The total binding energy of ²⁰₁₀Ne nucleus is 160.647 MeV. The binding energy per nucleon for ²⁰₁₀Ne is
(a) 160.647 MeV
(b) 16.064 MeV
(c) 8.032 MeV
(d) 5.354 MeV
77. In the asymmetric fission of ²³⁵₉₂U, the maximum energy appears as
(a) kinetic energy of the emitted neutrons
(b) energy of the emitted gamma rays
(c) kinetic energy of the lighter fission fragments
(d) kinetic energy of the heavier fission fragments
78. Which one of the following nuclear fusion reactions has the highest release of energy?
(a) Proton-proton reaction
(b) Proton-deuteron reaction
(c) Deuteron-deuteron reaction
(d) Deuteron-triton reaction
79. The half-life of a radioactive nucleus is 6 nanosecond (ns). The decay constant of this nucleus is
(a) 1.16 × 10⁹ s⁻¹
(b) 1.16 × 10⁸ s⁻¹
(c) 1.60 × 10⁹ s⁻¹
(d) 1.60 × 10⁸ s⁻¹
80. ⁹⁹₄₃Tc nucleus decays to ⁹⁹₄₄Ru nucleus by a radioactive decay process. This radioactive decay is an example of
(a) alpha decay
(b) positive beta decay
(c) negative beta decay
(d) orbital electron capture
81. Which one of the following statements is correct for a nucleus undergoing gamma decay?
(a) The number of neutrons increases by one.
(b) The number of protons increases by one.
(c) Neither the number of protons nor the number of neutrons changes.
(d) Each of the proton and neutron numbers increases by one.
82. The minimum photon energy required for a pair production by a gamma ray, in the presence of a nucleus, is
(a) 0.511 MeV
(b) 1.022 MeV
(c) 937 MeV
(d) 4.0 MeV
83. For an incident gamma-ray energy of 1 MeV, which one of the following absorbers has the highest probability of photoelectric absorption?
(a) ¹²₆C
(b) ²⁸₁₄Si
(c) ⁶⁰₂₈Ni
(d) ⁷⁶₃₂Ge
UPSC Previous year question paper Geo scientist exam
84. The maximum energy that can be transferred by an incident photon of energy hv to an electron in a single Compton interaction is
(a) hv (2α/(1 + 2α))
(b) hv (1/(1 + 2α))
(c) hv (1/(1 - 2α))
(d) hv (2α/(1 - 2α))
(where α = hv/m₀c²; m₀c² is the rest mass energy of the electron)
85. Which one of the following is the correct equation to represent a pair-production process of gamma-ray interaction?
(a) hv - m₀c² = E_e⁻ + E_e⁺
(b) hv + m₀c² = E_e⁻ + E_e⁺
(c) hv + 2m₀c² = E_e⁻ + E_e⁺
(d) hv - 2m₀c² = E_e⁻ + E_e⁺
(where hv is the energy of incident gamma ray; E_e⁻ and E_e⁺ are the electron and positron kinetic energies, respectively; m₀c² is the rest mass energy of the electron)
86. Which one of the following radioactive minerals has thorium (Th) element?
(a) Alunite
(b) Carnotite
(c) Monazite
(d) Muscovite
87. A radioactive source having a half-life of 5 years has an initial activity of 400 kBq. The activity (in kBq) after 15 years will be
(a) 200
(b) 100
(c) 50
(d) 25
88. The parent nuclide of the (4n + 2) radioactive series is
(a) ²³²Th
(b) ²³⁸U
(c) ²¹⁰Bi
(d) ²²⁷Ra
89. Which one of the following inorganic scintillators has the maximum light yield per MeV?
(a) BaF2
(b) BGO
(c) NaI (Tl)
(d) LaBr3(Ce)
90. The different regions of operation of gas-filled detectors are ion saturation, proportional region, limited proportional region and Geiger-Muller region. The region not used for detector operation is
(a) Geiger-Muller region
(b) ion saturation region
(c) proportional region
(d) limited proportional region
91. The de Broglie wavelength associated with an alpha particle emitted with a kinetic energy of 1 MeV by the nucleus of an atom of radon is of the order of
(a) 10⁻¹⁴ cm
(b) 10¹⁴ cm
(c) 10⁻¹² cm
(d) 10¹² cm
92. The magnitudes of total angular momentum given by J = L + S for l = 1 and s = 1/2 are
(a) √3/4 ħ and √15/4 ħ
(b) √3/2 ħ and √1/2 ħ
(c) √3/2 ħ and √15/2 ħ
(d) √3/2 ħ and √4/3 ħ
(where the symbols have their usual meanings)
93. In the X-ray spectra, the K_β line originates
(a) when an n = 4 electron undergoes a transition to a vacant n = 2 state
(b) when an n = 3 electron undergoes a transition to a vacant n = 2 state
(c) when an n = 3 electron undergoes a transition to a vacant n = 1 state
(d) when an n = 2 electron undergoes a transition to a vacant n = 1 state
94. A completely antisymmetric tensor ε_μνλ in 3-space dimensions possesses
(a) rank = 3 and independent components = 3
(b) rank = 1 and independent components = 1
(c) rank = 1 and independent components = 3
(d) rank = 3 and independent components = 1
95. Which one among the following pairs is not correctly matched?
(a) ∇ · (∇ × A) : 0
(b) ∇ × (∇ × A) : ∇(∇ · A) - ∇²A
(c) ∇ × (∇φ) : 0
(d) ∇ × (φA) : (∇φ) × A - φ(∇ × A)
(Given: φ and A are differentiable scalar and vector functions, respectively)
96. Let P(4 cos t, 4 sin t, 4t) be a point on a curve, where t is some parameter. The magnitude of the tangent vector at point P is
(a) 4
(b) 2√2
(c) 2
(d) 4√2
97. The eigenvalues of the matrix
[Figure: Matrix]
are
(a) 1, 2
(b) 5, 2
(c) 2, 6
(d) 1, 6
UPSC Previous year question paper Geo scientist exam
98. For a matrix A, the diagonal matrix A' is obtained using the similarity transformation A' = S⁻¹AS, where S is a transformation matrix. If A = ((0, i), (i, 0)) then the diagonal matrix A' is
[Figure: Options]
99. The isostatic gravity anomaly is defined as the difference between
(a) Bouguer gravity anomaly and computed anomaly of the root zone
(b) free-air gravity anomaly and computed anomaly of the root zone
(c) Bouguer gravity anomaly and free-air gravity anomaly
(d) regional gravity anomaly and residual gravity anomaly
100. The gravity value on the surface of the Earth at the equator is approximately
(a) 6.78 m/s²
(b) 7.78 m/s²
(c) 8.78 m/s²
(d) 9.78 m/s²
101. The spherical shape model mass in the gravity method is particularly used as a first approximation in the interpretation of
(a) asymmetrical 2D anomalies
(b) approximately symmetrical 2D anomalies
(c) asymmetrical 3D anomalies
(d) approximately symmetrical 3D anomalies
102. Which one of the following fundamental forces is mediated by massive particles?
(a) Strong force
(b) Electromagnetic force
(c) Weak force
(d) Gravitational force
103. The range of weak interactions is
(a) 10⁻¹² m
(b) 10⁻¹⁵ m
(c) 10⁻¹⁸ m
(d) 10⁻²¹ m
104. The engine of a rocket in outer space, far from any planet, is turned on. The rocket rejects burned fuel at a constant rate. In the first second of firing, it ejects 1/100 of its initial mass m₀ at a relative speed of 2000 m/s. The initial acceleration of the rocket is
(a) -20 m/s²
(b) +20 m/s²
(c) -2 × 10⁵ m/s²
(d) +2 × 10⁵ m/s²
105. In the centre of mass frame of reference, the magnitudes of the velocities of particles
(a) remain unchanged in an elastic collision
(b) remain unchanged in an inelastic collision
(c) remain unchanged in both elastic and inelastic collisions
(d) change in both elastic and inelastic collisions
106. The angular speed of 3600 rpm in rad/s is equal to
(a) 251
(b) 277
(c) 351
(d) 377
107. If the kinetic energy of a proton is 3752 MeV, then its Lorentz (relativistic) factor is approximately
(a) 5
(b) 4
(c) 3
(d) 2
108. The total energy of a 3.53 MeV electron is
(a) 3.02 MeV
(b) 3.53 MeV
(c) 4.04 MeV
(d) 4.55 MeV
109. The regularization parameter in nonlinear least-squares inversion technique describes a trade-off between
(a) the best fitting and the most reasonable stabilization
(b) the worst fitting and the most reasonable stabilization
(c) the best fitting and the most unreasonable stabilization
(d) the worst fitting and the most unreasonable stabilization
110. Which one of the following is the additive rule of probability P(X ∪ Y) for mutually exclusive events X and Y?
(a) P(X ∪ Y) = P(X) - P(Y) - P(X ∩ Y)
(b) P(X ∪ Y) = P(X) - P(Y) + P(X ∩ Y)
(c) P(X ∪ Y) = P(X) - P(Y)
(d) P(X ∪ Y) = P(X) + P(Y)
111. Match List-I with List-II and select the correct answer using the code given below the Lists :
List-I (Distribution) | List-II (Probability distribution)
A. Binomial | 1. 1/σ√2π e^-(x-μ)²/2σ²
B. Poisson | 2. q^(x-1)p
C. Geometric | 3. λ^x e^-λ/x!
D. Normal | 4. nCx p^x q^(n-x)
(where the symbols have their usual meanings)
Code :
(a) A B C D = 4 2 3 1
(b) A B C D = 4 3 2 1
(c) A B C D = 1 2 3 4
(d) A B C D = 1 3 2 4
UPSC Previous year question paper Geo scientist exam
112. Consider the following differential equation :
d²y/dx² = y
The solution of this equation y(x) passing through the origin and through the point (ln 2, 3/4) is
(a) sinh x
(b) cosh x
(c) 2 sinh x
(d) 2 cosh x
113. Consider the following statements regarding a system of linear equations :
1. A system of linear equations is consistent if it has one or more solutions.
2. A system of linear equations is inconsistent if it has one or more solutions.
3. A system of linear equations is consistent if it has no solution.
4. A system of linear equations is inconsistent if it has no solution.
Which of the statements given above are correct?
(a) 1 and 3
(b) 2 and 4
(c) 2 and 3
(d) 1 and 4
114. The order and degree of the differential equation
[1 + (dy/dx)²]³ = (d²y/dx²)²
are, respectively
(a) 1, 2
(b) 2, 2
(c) 3, 1
(d) 2, 3
115. Let y₁ = e²ˣ and y₂ = e³ˣ be two solutions of a linear second-order differential equation. Which one of the following is correct about the Wronskian (W), y₁ and y₂?
(a) W = 0, y₁ and y₂ are linearly dependent
(b) W = e⁵ˣ; y₁ and y₂ are linearly dependent
(c) W = 0, y₁ and y₂ are linearly independent
(d) W = e⁵ˣ; y₁ and y₂ are linearly independent
116. Consider the second-order partial differential equation for a function u(x, y), defined by
∂²u/∂x² + ∂²u/∂y² = 0
Which one of the following is correct regarding the equation given above?
(a) Laplace equation, hyperbolic type
(b) Laplace equation, elliptic type
(c) Wave equation, parabolic type
(d) Wave equation, elliptic type
117. Consider the heat flow in a two-dimensional (x, y) metal plate. The temperature u(x, y, t) at any point (x, y) at time t for diffusivity d² of the plate is governed by
(a) ∂²u/∂t² = d² ∂²u/∂x²
(b) ∂u/∂t = d²(∂²u/∂x² + ∂²u/∂y²)
(c) ∂²u/∂x² - ∂²u/∂y² = d² ∂u/∂t
(d) ∂²u/∂t² = d²(∂²u/∂x² + ∂²u/∂y²)
118. The numerical value of the integral ∫₁²(x³ + 1) dx using trapezoidal rule (considering only one interval between the end points) is
(a) 5.50
(b) 5.60
(c) 5.75
(d) 5.55
119. The Newton-Raphson method is used in numerical analysis to
(a) solve a partial differential equation approximately
(b) find the root(s) of nonlinear equations approximately
(c) solve an ordinary differential equation exactly
(d) solve an algebraic equation exactly
120. Which one of the following rules/methods is used to numerically find the solutions of linear differential equations?
(a) Trapezoidal rule
(b) Boole's rule
(c) Newton-Raphson method
(d) Euler's method
UPSC Previous year question paper Geo scientist exam
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