GATE 2025 Question Paper Geomatics Engineering (GE)

GATE
2025
Question Paper | Answer Key
Graduate Aptitude Test in Engineering
(GATE) is a prestigious national-level exam
that assesses candidates for
comprehensive understanding in various
undergraduate-level subjects in
Engineering, Technology, Science,
Architecture, and Humanities.

General Aptitude
Q.1 – Q.5 Carry ONE mark Each

Q.1 Here are two analogous groups, Group-I and Group-II, that list words in their
decreasing order of intensity. Identify the missing word in Group-II.

Group-I: Abuse → Insult → Ridicule

Group-II: ________ → Praise → Appreciate

(A) Extol

(B) Prize

(C) Appropriate

(D) Espouse

Q.2 Had I learnt acting as a child, I ________ a famous film star.

Select the most appropriate option to complete the above sentence.

(A) will be

(B) can be

(C) am going to be

(D) could have been

Page 1 of 49

Q.3 The 12 musical notes are given as 𝐶, 𝐶 # , 𝐷, 𝐷# , 𝐸, 𝐹, 𝐹 # , 𝐺, 𝐺 # , 𝐴, 𝐴# , and 𝐵.
12
Frequency of each note is √2 times the frequency of the previous note. If the
frequency of the note C is 130.8 Hz, then the ratio of frequencies of notes 𝐹 # and 𝐶
is:

(A) 6
√2

(B)
√2

(C) 4
√2

(D) 2

Page 2 of 49

Q.4 The following figures show three curves generated using an iterative algorithm. The
total length of the curve generated after ‘Iteration 𝑛’ is:

Note: The figures shown are representative.

1
Iteration 0:

1 1
Iteration 1: Length of each segment:
3 3

1
1
Iteration 2: 9 Length of each segment:
9

𝑛
(A) 5 2
( )
3

(B) 5 𝑛
( )
3

(C) 5 2𝑛
( )
3

(D) 5 𝑛(2𝑛−1)
( )
3

Page 3 of 49

Q.5 |𝑥|
Which one of the following plots represents 𝑓 (𝑥 ) = − , where 𝑥 is a non-
𝑥
zero real number?

Note: The figures shown are representative.

f(x)
(A)
(0,1)

x
(0, −1)

f(x)
(B)
(0,1)

x
(0, −1)

f(x)
(C)

(1,0)
x
(−1,0)

f(x)
(D)
(0,1)

x
(0, −1)

Page 4 of 49

Q.6 – Q.10 Carry TWO marks Each

Q.6 Identify the option that has the most appropriate sequence such that a coherent
paragraph is formed:

P. Over time, such adaptations lead to significant evolutionary changes with
the potential to shape the development of new species.

Q. In natural world, organisms constantly adapt to their environments in
response to challenges and opportunities.

R. This process of adaptation is driven by the principle of natural selection,
where favorable traits increase an organism’s chances of survival and
reproduction.

S. As environments change, organisms that can adapt their behavior, structure
and physiology to such changes are more likely to survive.

(A) P→Q→R→S

(B) Q→S→R→P

(C) R→S→Q→P

(D) S→P→R→Q

Page 5 of 49

Q.7 A stick of length one meter is broken at two locations at distances of 𝑏1 and 𝑏2 from
the origin (0), as shown in the figure. Note that 0 < 𝑏1 < 𝑏2 < 1. Which one of the
following is NOT a necessary condition for forming a triangle using the three
pieces?

Note: All lengths are in meter. The figure shown is representative.

(A) 𝑏1 < 0.5

(B) 𝑏2 > 0.5

(C) 𝑏2 < 𝑏1 + 0.5

(D) 𝑏1 + 𝑏2 < 1

Page 6 of 49

Q.8 Eight students (P, Q, R, S, T, U, V, and W) are playing musical chairs. The figure
indicates their order of position at the start of the game. They play the game by
moving forward in a circle in the clockwise direction.

After the 1st round, 4th student behind P leaves the game. After 2nd round, 5th student
behind Q leaves the game. After 3rd round, 3rd student behind V leaves the game.
After 4th round, 4th student behind U leaves the game. Who all are left in the game
after the 4th round?

Note: The figure shown is representative.

P

W R

U T

Q
V

S

(A) P; T; Q; S

(B) V; P; T; Q

(C) W; R; Q; V

(D) Q; T; V; W

Page 7 of 49

Q.9 The table lists the top 5 nations according to the number of gold medals won in a
tournament; also included are the number of silver and the bronze medals won by
them. Based only on the data provided in the table, which one of the following
statements is INCORRECT?

Nation Gold Silver Bronze

USA 40 44 41

Canada 39 27 24

Japan 20 12 13

Australia 17 19 16

France 16 26 22

(A) France will occupy the third place if the list were made on the basis of the total
number of medals won.

(B) The order of the top two nations will not change even if the list is made on the basis
of the total number of medals won.

(C) USA and Canada together have less than 50% of the medals awarded to the nations
in the above table.

(D) Canada has won twice as many total medals as Japan.

Page 8 of 49

Q.10 An organization allows its employees to work independently on consultancy
projects but charges an overhead on the consulting fee. The overhead is 20% of the
consulting fee, if the fee is up to ₹ 5,00,000. For higher fees, the overhead is
₹ 1,00,000 plus 10% of the amount by which the fee exceeds ₹ 5,00,000. The
government charges a Goods and Services Tax of 18% on the total amount (the
consulting fee plus the overhead). An employee of the organization charges this
entire amount, i.e., the consulting fee, overhead, and tax, to the client. If the client
cannot pay more than ₹ 10,00,000, what is the maximum consulting fee that the
employee can charge?

(A) ₹ 7,01,438

(B) ₹ 7,24,961

(C) ₹ 7,51,232

(D) ₹ 7,75,784

Page 9 of 49

PART A: Common FOR ALL CANDIDATES
Q.11 – Q.27 Carry ONE mark Each

Q.11 For a sample drawn from normally distributed population, the statistic

Y=
( n − 1) s 2 , where n = sample size,  = population standard deviation,
 2

s = sample standard deviation, has

(A) Chi-square distribution with ( n −1) degrees of freedom

(B) Chi-square distribution with n degrees of freedom

(C) Chi-square distribution with ( n + 1) degrees of freedom

(D) Gaussian distribution with n degrees of freedom

Q.12 The reflectance geometry of white-sky albedo can be represented as______.

(A) bi-directional

(B) bi-conical

(C) bi-hemispherical

(D) directional-conical

Page 10 of 49

Q.13 Clouds appear white in optical visible spectral bands of remote sensing images due
to ______ scattering.

(A) Rayleigh

(B) Mie

(C) selective

(D) non-selective

Q.14 If the absolute temperature (greater than 0 K) of a body is doubled, it would emit
______ times more radiation.

(A) 2

(B) 4

(C) 8

(D) 16

Page 11 of 49

Q.15 If the emissivity of an object varies with wavelength, it is called as ________.

(A) grey body

(B) black body

(C) selective radiant

(D) non-selective radiant

Q.16 In the context of Global Navigation Satellite System positioning, the Saastamoinen
model provides a correction for________.

(A) zenith hydrostatic delay

(B) slant hydrostatic delay

(C) zenith total delay

(D) slant total delay

Page 12 of 49

Q.17 In the context of Global Navigation Satellite System positioning, which of the
following statement is correct?

(A) In Differential Global Navigation Satellite System, the corrections to the
coordinates of the user are transmitted from the reference station

(B) Real-time kinematic positioning and stop-and-go positioning are both kinematic
methods

(C) Rapid-static positioning is not a relative positioning technique

(D) Double differencing eliminates the clock errors and improves the noise in the
differenced pseudorange observations

Q.18 In the choke ring antenna there are concentric cylinders placed around the antenna
that are of a certain depth to minimize the multipath effect. If the signal wavelength
is 𝜆, then the depth of the cylinders in the choke ring antenna should be

(A) 
exactly
4

(B)  
slightly more than and far less than
4 2

(C) 
exactly
2

(D) 
slightly more than and far less than 𝜆
2

Page 13 of 49

Q.19 Which one of the following statements is NOT correct in the context of Geographic
Information System?

(A) A raster data model makes use of grid of cells that are organized into rows and
columns for representation of features on earth

(B) Vector data model represents the spatial features on Earth’s surface in terms of
points, lines or polygons

(C) Resampling is applied after georeferencing of vector datasets

(D) Topology is used in vector data models to ensure spatial data integrity

Q.20 Which one of the following statements is NOT correct in the context of shapefile?

(A) It is an example of georelational data model

(B) It is a topological data model

(C) It treats points as pairs of ( x, y) coordinates

(D) In this, polygons can have duplicate arcs for shared boundaries

Page 14 of 49

Q.21 The table below is an attribute table about employee records. Which attribute can
be used as a primary key?

(A) Emp_Name

(B) Emp_ID

(C) Emp_Dept

(D) Emp_Desig

Page 15 of 49

Q.22 Find the best match between column I and column II for the following scenario
related to spatial operators.

(A) P-2; Q-3; R-1

(B) P-1; Q-3; R-2

(C) P-2; Q-1; R-3

(D) P-1; Q-2; R-3

Page 16 of 49

Q.23 For the weighted least squares adjustment, which of the following statements is/are
correct?

(A) Weighted sum of the squares of the residuals is minimized

(B) The expected value of the residuals is equal to zero

(C) Redundancy of observations is maximized

(D) Weights are taken inversely proportional to the variance of the observations

Q.24 The geophysical variables that can be measured/derived from the Global Navigation
Satellite System observations is/are

(A) ocean color

(B) precipitable water vapor

(C) soil moisture

(D) seismic motion

Q.25 For a given set of observations for distance measurements, the standard error was
computed as ± 2.5 cm. Assuming that the observations conform to normal error
distribution theory, the probable error will be given by ± ______ cm (rounded off
to 2 decimal places).

Page 17 of 49

Q.26 In a two-dimensional coordinate system, it is proposed to determine the size and
shape of a triangle ABC in addition to its location and orientation. For this, all the
internal angles and sides of the triangle were observed. Further, the planar
coordinates of point A and bearing/azimuth of line AB were known. The redundancy
(r) for the above system will be equal to _____________ (Answer in integer).

Q.27 The covariance matrix, , for the planar coordinates of a surveyed point is given as:

 25 mm2 0.500 mm2 
= 2 
0.500 mm 100 mm2 

The coefficient of correlation is________ (rounded off to 2 decimal places).

Page 18 of 49

Q.28 – Q.46 Carry TWO marks Each

Q.28 Match the following SAR sensors to their frequency bands

(A) P – 3, Q – 2, R – 4, S – 1

(B) P – 4, Q – 2, R – 1, S – 3

(C) P – 2, Q – 4, R – 1, S – 3

(D) P – 1, Q – 4, R – 3, S – 2

Q.29 The relativistic effect in Global Navigation Satellite System satellites has two parts,
of which the first part is the time dilation due to the shift in the fundamental
frequency of the satellite clock. The second part is due to the satellite’s semi-major
axis and __________.

(A) eccentricity

(B) inclination

(C) argument of perigee

(D) right ascension of the ascending node

Page 19 of 49

Q.30 A country has 7 permanent Global Navigation Satellite System stations covering its
territory. Their surveying organization generates a network solution after applying
double differencing to the observations. These 7 permanent stations can view 5 to
10 common satellites at any given epoch. What is the range (minimum, maximum)
of the number of independent double differenced observables possible?

(A) (35, 70)

(B) (30, 56)

(C) (28, 48)

(D) (24, 54)

Page 20 of 49

Q.31 Consider the nodes of a square grid A, B, C and D (shown in figure below), where
a certain parameter is measured. The distances between the points is also indicated
in the same figure. For example, the value observed at point A is 120 and is
indicated as A (120), and the distance between points A and B is 1.0 units. The
value at point ‘X’ computed using bilinear interpolation, using the values at points
A, B, C and D is _________.

(A) 175

(B) 152

(C) 198

(D) 210

Page 21 of 49

Q.32 The first value in the output of a SQL query (given below) when run on a table
having name “Table-1”is?

SQL Query: SELECT LastName FROM Table-1 WHERE State=“IN” ORDER BY
FirstName

(A) Ramirez

(B) Douglas

(C) Paul

(D) Squires

Page 22 of 49

Q.33 Consider the three input raster images given below. A geospatial analyst decided to
use the overlay operation to generate a new raster showing the average values. The
values of the cells P, Q and R in the output raster are:

(A) P = 3, Q = 3, R = 2

(B) P = 4, Q = 4, R = 3

(C) P = 3, Q = 3, R = 3

(D) P = 4, Q = 4, R = 2

Page 23 of 49

Q. 34 In a Geographic Information System database, a stream is represented by a line and
houses are represented by polygons. The pollution in the stream is affecting houses
within a distance of 500 m on both sides. Which vector data analysis operations
should be performed to identify houses affected by the pollution in the stream?

(A) Buffer and Overlay

(B) Dissolve and Overlay

(C) Buffer

(D) Split

Page 24 of 49

Q.35 In a given weighted graph shown below, what is the value of the expression
(p+d)
2

where,

i. Alphabets A, B, C, D, E and F denote the nodes
ii. Numbers 1 to 6 denote the weights between two nodes
iii. d = shortest distance between node A and node E
iv. p = number of paths with distance d

(A) 100

(B) 64

(C) 81

(D) 121

Page 25 of 49

Q.36 In a plane triangle, the observed angles 𝑃, 𝑄 and 𝑅, assumed uncorrelated, with
given weights are:

𝑃 = 401902″ weight = 1

𝑄 = 703001″ weight = 2

𝑅 = 691100″ weight = 1

The most probable values of these angles (𝑃̂, 𝑄̂ , 𝑅̂ ) will be given by:

(A) 𝑃̂ = 401900″, 𝑄̂ = 703000″, 𝑅̂ = 691100″

(B) 𝑃̂ = 401901″, 𝑄̂ = 703000″, 𝑅̂ = 691059″

(C) 𝑃̂ = 40190.8″, 𝑄̂ = 70300.4″, 𝑅̂ = 691058.8″

(D) 𝑃̂ = 401858.4″, 𝑄̂ = 70300.4″, 𝑅̂ = 69111.2″

Q.37 Which of the following statements is/are correct in the context of Voronoi polygon?

(A) A Voronoi polygon may contain more than one point, especially where the density
of points is higher

(B) The center of a Voronoi polygon is a circumcenter of a Delaunay triangle

(C) Each intersection of Voronoi edges belongs to at least three Voronoi polygons

(D) Voronoi polygons and Delaunay triangles are geometric dual of each other

Page 26 of 49

Q.38 Which of the following conditions is/are essential for geostationary satellite orbits?

(A) Eccentricity is zero

(B) Inclination is close to zero

(C) Prograde

(D) Retrograde

Q.39 Two adjacent angles 𝐴 and 𝐵 have been observed with the following mean values
and correlation matrix, 𝜌:

𝐴̅ = 10°20′10″ ± 10″ 1.0 0.6
} 𝜌=[ ]
𝐵̅ = 25°35′15″ ± 20″ 0.6 1.0

The standard deviation of the sum of the estimated angles 𝐴̅ and 𝐵̅ will be
______________ (in arcseconds) (rounded off to 2 decimal places).

Q.40 The residual error in a measurement comprises a bias of + 0.08 m and a random
component given by the following density function:

1  − x 2  −1
f ( x) = exp  m
0.15  0.0072 

For this system, the mean square error (MSE) is ________ m. (rounded off to 2
decimal places)

Page 27 of 49

Q.41 For the following ten angle observations, the standard error of the mean angle is
given as ____________ arcsecond (rounded off to 2 decimal places).

25°40′12″ 25°40′14″ 25°40′16″ 25°40′18″ 25°40′09″

25°40′15″ 25°40′10″ 25°40′13″ 25°40′15″ 25°40′18″

Q.42 The velocity ( Vs ) of a satellite moving in a circular orbit at a height of 1000 km above
earth surface is ______ km s-1 (rounded off to 2 decimal places).

( G = 6.67 10−11 m3 kg -1 s-2 , M e = 5.972 1024 kg and re = 6378 km )

Q.43 If the radiant temperature of a body is 360 K and its emissivity 0.6, then the kinetic
temperature of that body is ______ K (Answer in integer).

Q.44 Energy carried by a part of short-wave infrared ray at 1000 nm wavelength is ______
eV (rounded off to 2 decimal places).

h = 6.626 10−34 J s , 1 J = 6.242 1018 eV , c= 3 × 108 m s-1

Page 28 of 49

Q.45 The scattering matrix for a fully polarimetric synthetic aperture radar pixel is given
below. The C11 element of the covariance matrix computed with a 1 × 1 window
will be ____? (rounded off to 2 decimal places).

Here, i = −1 .

0.1 + 0.5i 0.1 − 0.1i 
 0.1 + 0.1i 0.3 − 0.5i 
 

Q.46 Global Navigation Satellite System can be used for positioning and timing. The
average geometric dilution of precision (GDOP) at a location is 1.0 and positional
dilution of precision (PDOP) is 0.8. With the precision of the measurements being
300 m, the achieved precision of timing is ____ns (Answer in integer).

Consider the speed of light is 3108 m s-1

Page 29 of 49

PART B: FOR Section I: Surveying and Mapping CANDIDATES ONLY
Q.47 – Q.54 Carry ONE mark Each

Q.47 Two positions on the Earth’s surface are given in the form of Cartesian coordinates
in the WGS84 reference frame and ellipsoid. The norm of difference of these two
position vectors is the____________.

(A) spherical distance

(B) ellipsoidal distance

(C) Euclidean distance

(D) planar distance

Q.48 Which one of the following map projections is NOT conformal?

(A) Transverse Mercator

(B) Stereographic

(C) Lambert Conformal Conic

(D) Sinusoidal

Page 30 of 49

Q.49 In a Survey of India topographic map of scale 1:50,000, the contours are drawn
conventionally at intervals of _______ m.

(A) 10 and 20

(B) 20 and 40

(C) 30 and 50

(D) 25 and 50

Q.50 Figure below shows an open traverse PQRS, where P is the starting point of traverse
and S is the end point of traverse. Which one of the following is correct?

(A) ∠𝑅 = Bearing = 32 , ∠𝑃 = Deflection Angle = 75 , ∠𝑄 = Included Angle = 120

(B) ∠𝑃 = Bearing = 75 , ∠𝑄 = Deflection Angle = 120 , ∠𝑅 = Included Angle = 32

(C) ∠𝑃 = Bearing = 75 , ∠𝑅 = Deflection Angle = 32 , ∠𝑄 = Included Angle = 120

(D) ∠𝑅 = Bearing = 32 , ∠𝑄 = Deflection Angle = 120 , ∠𝑃 = Included Angle = 75

Page 31 of 49

Q.51 When conducting a survey using a total station, a zenith angle is measured as
841356 in the direct mode. What is the equivalent zenith angle in the reverse
mode?

(A) 2641356

(B) 05

(C) 275

(D) 185

Q.52 In a closed traverse PQRST the following data were collected in the field. What is
the correct sum of deflection angles for this traverse?

(A) 38200

(B) 36000

(C) 54000

(D) 72352

Page 32 of 49

Q.53 Which one of the following parameters does NOT affect the scale of a vertical aerial
photograph?

(A) Size of the photograph

(B) Focal length of the camera

(C) Flying height

(D) Terrain elevation

Q.54 Select the correct statement in the context of relief displacement in vertical aerial
photographs.

(A) It is zero for principal point, irrespective of whether the point is above or below the
datum

(B) It increases with increased flying height above datum

(C) It occurs radially from one of the image corners

(D) It has no effect on the appearance (in the aerial photograph) of the straight roads
over an undulating terrain

Page 33 of 49

Q.55– Q.65 Carry TWO marks Each

Q.55 Given hP = HP + NP, where hP is the ellipsoidal/geodetic height at point P, HP is the
orthometric height and NP is the geoid undulation along the ellipsoidal normal. Which
one of the following statements is correct?

(A) Two points on the Earth’s surface that have the same ellipsoidal height will be on the
same equipotential surface

(B) The geoid undulation is the separation of the equipotential surface at the ground
surface with respect to the ellipsoid

(C) The points on an equipotential surface will not have the same orthometric height

(D) The orthometric height of the instantaneous sea level is zero

Page 34 of 49

Q.56 In the figure below, I1 and I2 are the two instrument stations. The instrument stations
and the object (P) lie in the same vertical plane. Assume all instruments and staff are
levelled.

L = horizontal distance between the object and the station I2

b = horizontal distance between the instrument stations

S = staff reading at the Benchmark (BM) for horizontal line of sight

H = reading on the staff at P

r = height of the point sighted by instruments at the staff kept at P from the line of
sight of the instruments

1 and  2 = vertical angles to the reading on staff at P from I1 and I2, respectively

Which one of the following relationships is correct for L?

(A) b tan 1
L= ( )
tan 1 − tan  2

(B) b tan  2
L= ( )
tan  2 − tan 1

(C) b tan 1
L= ( )
tan  2 − tan 1

(D) b tan  2
L= ( )
(tan 1 − tan  2

Page 35 of 49

Q.57 In a closed traversed with five sides, the closing error found from the fore bearing
and back bearing of the last line is +0.5. The correction to the fourth line will be

(A) –012

(B) 018

(C) –024

(D) 030

Q.58 Consider a pair of overlapping vertical aerial photographs taken from a flying height
of 665 m above a point A on the ground, with a camera having a focal length of
152.4 mm. The height of the point A above the mean sea level is 535 m. The parallax
bar reading of the point A as measured from the photographs is 10.96 mm. Assuming
the air base to be 400 m, the parallax bar constant is ___________ mm.

(A) 80.71

(B) 457.96

(C) 39.84

(D) 24.18

Page 36 of 49

Q.59 The statements below show the relationship of Whole Circle Bearing (WCB) with
the Quadrantal Bearing (QB) for quadrant designations North-East (N-E), North-
West (N-W), South-East (S-E) and South-West (S-W). Which of the following
statements is/are correct?

(A) For the quadrant S-W, QB = WCB −180

(B) For the quadrant S-W, WCB = 180 − QB

(C) For the quadrant N-W, WCB = 180 − QB

(D) For the quadrant N-W, QB = − WCB 360

Page 37 of 49

Q.60 Consider an infinitely sized square grid pattern (as shown in the figure below)
overlaid on a flat ground at an elevation of 120 m above mean sea level. An image is
taken by a camera from flying height of 450 m above mean sea level. Assume that
the flying height remains constant throughout the operation of the flight. The flying
direction is along the line FL, as shown in the figure below. The camera is looking in
the off-nadir in the flight direction resulting in a low oblique photograph. Which of
the following statements for the resulting low oblique photograph is/are correct?

(A) Scale of the photograph is not uniform along the flight direction

(B) Parallel lines on the ground do not always appear parallel in the resulting photograph

(C) Horizon is visible in the photograph

(D) Cells A, B and C appear as squares in the resulting aerial photograph

Q.61 A point is specified along the Greenwich Meridian at 60 N latitude on an ellipsoid.
The parameters of the ellipsoid are semi-major axis a=6378137 m and flattening
1 4 a 2b
factor f= . The volume of the ellipsoid is given by , where b is the
298.224 3
semi-minor axis. The latitude of the point on the sphere whose volume is the same as
the volume of the ellipsoid of reference is _________ N (rounded off to 2 decimal
places).

Page 38 of 49

Q.62 In a map based on the UTM projection, the grid distance is in error with respect to
the geodetic distance by about one in four thousand. If the map distance is 3 cm and
the map scale is 1:25,000, then the geodetic distance is_________ m (rounded off to
2 decimal places).

Q.63 A level with the height of the instrument being 2.550 m has been placed at a station
having a Reduced Level (RL) of 130.565 m. The instrument reads 3.665 m on a
levelling staff held inverted at the bottom of a bridge deck. The RL of the bottom of
the bridge deck is______m (rounded off to 3 decimal places).

Q.64 In levelling between two points P and Q on opposite banks of a river, the level was
set up near P, and the staff reading on P and Q were 2.165 m and 3.810 m,
respectively. The level was then moved and set up near Q and the respective staff
readings on P and Q were 0.910 m and 2.355 m. The true difference of level between
P and Q is______ m (rounded off to 3 decimal places).

Q.65 A 23 cm square format camera with a focal length of 152.4 mm is used for taking
vertical aerial photographs with 60% end-lap. These photographs are viewed under a
stereoscope with a base-height ratio of 0.15. The vertical exaggeration while
stereoviewing these photographs is __________ (Answer in integer).

Page 39 of 49

PART B: FOR Section II: Image Processing and Analysis CANDIDATES ONLY
Q.66 – Q.73 Carry ONE mark Each

Q.66 Which one of the following image processing methods employs standard deviation?

(A) Band ratio

(B) Parallelepiped classification

(C) Correction of skew distortion in raw satellite image

(D) Nearest neighbor classification

Q. 67 Which one of the following is NOT used to assess the quality of remote sensing
image?

(A) Univariate statistics of image

(B) Histogram

(C) Multivariate statistics of image

(D) Swath of the image

Page 40 of 49

Q.68 Which one of the following techniques is NOT used to atmospherically correct the
satellite image?

(A) Image normalization using histogram adjustment

(B) Radiative transfer model

(C) Image to image registration

(D) Image normalization using regression

Q.69 A remote sensing instrument measures only in Green, Red and Near-Infrared
frequency bands. The remote sensing index/indices that CANNOT be derived using
data of this instrument is/are______.

(A) Normalized Difference Vegetation Index

(B) Atmospherically Resistant Vegetation Index

(C) Soil Adjusted Vegetation Index

(D) Enhanced Vegetation Index

Q.70 Principal Component Analysis is performed on a 4-band IRS satellite image. The
eigen values (𝐸 = [𝜆1,1 , 𝜆2,2 , 𝜆3,3 , 𝜆4,4 ]) computed from the covariance matrix are
887.60, 75.20, 37.60 and 6.73, respectively. The percentage of total variance
explained by the third principal component (𝜆3,3 ) is ________ (rounded off to 2
decimal places).

Page 41 of 49

Q.71 Piecewise linear contrast stretch is performed on an 8-bit image. The output (𝐵𝑉𝑜𝑢𝑡 )
would be zero for input value 𝐵𝑉𝑖𝑛 ≤ 80. The output (𝐵𝑉𝑜𝑢𝑡 ) would be 255 for
𝐵𝑉𝑖𝑛 > 120. For the remaining input values, 𝐵𝑉𝑜𝑢𝑡 = (2 × 𝐵𝑉𝑖𝑛 ) − 20.

If 𝐵𝑉𝑖𝑛 = 120, then 𝐵𝑉𝑜𝑢𝑡 is _____ (Answer in integer).

Q. 72 A CCD array element in a remote sensing sensor measures incoming radiation and
its output voltage varies linearly between 0 V to 5 V. This voltage is converted to
an 8-bit digital image using an analogue to digital convertor (ADC). The ADC has
a linear response without bias or noise. If the output image pixel has a digital
number of 100, the input voltage to the ADC would be _____ V (rounded off to 2
decimal places).

Q.73 In supervised digital image classification, the number of combinations to be
evaluated to select three best bands out of five bands is___________ (Answer in
integer).

Page 42 of 49

Q.74– Q.84 Carry TWO marks Each

Q.74 The figure below shows a one-dimensional function, 𝑓, and a filter 𝑤. Consider 𝑓
is padded with zeros on both sides. Which one among the following will be the final
convolution output of 𝑓 with 𝑤 after the padding zeros are removed from the
output?

(A)

(B)

(C)

(D)

Page 43 of 49

Q.75 Figure below shows the scatterplot of training pixels of water (w), sand (s), forest
(f) and commercial (c) in bands 1 and 2. Pixel ‘A’ having digital number 4 and 6
in band 1 and band 2, respectively, is to be classified using k-nearest neighbor
classifier having the value of k equal to 5. The assigned class for the pixel ‘A’ is
_____.

(A) forest

(B) sand

(C) water

(D) commercial

Page 44 of 49

Q.76 A remote sensing image is acquired from an IRS series satellite. Initially a two-
−𝐷 2 (𝑢,𝑣)
dimensional filter with transfer function 𝐻(𝑢, 𝑣) = exp ( ) is applied to
2𝐷02
reduce scan line effects. Here 𝐷(𝑢, 𝑣) is the distance from center of the frequency
rectangle, and 𝐷0 is the cutoff frequency. Which one of the following will be the
transfer function for the corresponding filter to detect the edges in the image?

(A) −𝐷2 (𝑢, 𝑣)
1 − exp ( )
2𝐷02

(B) −𝐷 2 (𝑢, 𝑣)
exp ( )
2𝐷02

(C) −𝐷2 (𝑢, 𝑣)
1 + exp ( )
2𝐷02

(D) 𝐷2 (𝑢, 𝑣)
1 − exp ( )
2𝐷02

Q.77 Consider an imaging system with 128 128 pixels that produces a noiseless,
distortion-free digital image. It is used to digitize checkerboard patterns where all
squares of the pattern are in the field of view. Using this imaging system, if a
checkerboard pattern with 128 128 squares is digitized, each square will be
11 pixel in size. What is the size of the checkerboard square in the generated
digital image for which spatial aliasing is observed (measured in pixels of the
imaging system)?

(A) 1

(B) 2

(C) 0.9

(D) 2.5

Page 45 of 49

Q.78 For the correlation matrix of a 4-band satellite image as shown below, which of the
following statements is/are correct?

(A) Band 3 provides some unique information not found in other bands

(B) There is high redundancy in band 2 and 4

(C) The standard deviation of all the bands is equal

(D) Image cannot be classified using bands 1 and 3 only

Page 46 of 49

Q.79 The histogram of a red band in a 3-bit satellite image is shown below. Which of
the following statements is/are correct?

(A) There are more darker pixels in the image

(B) There are more brighter pixels in the image

(C) The mean digital number of the image is 1250

(D) It may be predicted that approximately 40% of area in the image is covered by
material with low spectral albedo in red band

Q.80 Which of the following statements is/are correct regarding across-track scanning
sensor of an airborne optical imaging system?

(A) The relief displacement will be along the direction of the flight line

(B) There is no relief displacement along the direction of the flight line

(C) The greater is the distance of the ground object from nadir, the lesser is the image
scale compression

(D) Linear features have sigmoidal distortion

Page 47 of 49

Q.81 In case of normalized difference vegetation index (NDVI), which of the following
statements is/are correct?

(A) It is functionally equivalent to a simple ratio of red to near infra-red reflectance

(B) It reduces many forms of multiplicative noise

(C) It reduces additive noise

(D) It is sensitive to canopy background variations

Q.82 The hue, intensity and saturation values for a pixel are 𝐻 = 0.5 rad, 𝑆 = 0.5 and
𝐼 = 0.3, respectively. If the pixel is converted to RGB color model, then the value
of the green pixel would be _____ (rounded off to 2 decimal places).

Q.83 The brightness values of four pixels in the input image are shown in the table below.
The image is rectified using nearest neighbor intensity interpolation, and the pixel
at location (5, 4) in the output image is to be filled with the value from coordinate
(5.3, 3.7) in the input image. The brightness value of the pixel at location (5, 4) in
the rectified output image is ______ (Answer in integer).

Page 48 of 49

Q.84 The error matrix resulting from randomly selected test pixels for a classified image
is given below. The Producer’s accuracy of class 1 is ___________% (rounded off
to 1 decimal place).

Page 49 of 49

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