Compass Surveying and Theodolite MCQ Quiz - Objective Question with Answer for Compass Surveying and Theodolite - Download Free PDF

Last updated on Jun 11, 2025

Latest Compass Surveying and Theodolite MCQ Objective Questions

Compass Surveying and Theodolite Question 1:

The value of the smallest division of the circle of a repeating theodolite is 10 minutes. what is the suitable vernier to read up to 10 seconds?

  1. 60
  2. 30
  3. 90
  4. 110
  5. 140

Answer (Detailed Solution Below)

Option 1 : 60

Compass Surveying and Theodolite Question 1 Detailed Solution

Concept: 

Least count = \(\frac{S}{n}\)

n → no. of divisions on vernier scale

s → smallest division of main scale

Calculation: 

s = 10’ = 10 minutes

L.C = 10” = \(\frac{{10'}}{{60}} = \frac{1}{{6}}\) minutes

\(\frac{1}{{6}} = \frac{{10}}{n}\)

n = 10 × 6

n = 60

Compass Surveying and Theodolite Question 2:

In which direction is the zero marked in the ring of the prism compass?

  1. West
  2. South
  3. North
  4. East
  5. None of the above

Answer (Detailed Solution Below)

Option 2 : South

Compass Surveying and Theodolite Question 2 Detailed Solution

Concept:

Prismatic compass:

  • The graduated ring is attached to the needle and does not rotate with the line of sight.
  • The graduations have 0 at S, 90° at W, 180° at N, and 270° at E.
  • Graduations are engraved inverted since the graduated ring is read through the prism.
  • The readings are taken with the help of a prism provided at the eye vane.
  • Sighting and reading can be done simultaneously.
  • The instrument can be held in hand also while making the observations.
  • The eye vane consists of a metal vane with large silt.

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Additional Information

  • The graduations have 0 at N and S, 90° at  East and West in the surveyor compass.

Compass Surveying and Theodolite Question 3:

When the magnetic bearing of the sun at noon is 185°20', the magnetic declination will be

  1. 5°20' North
  2. 5°20' South
  3. 5°20' West
  4. 5°20' East

Answer (Detailed Solution Below)

Option 3 : 5°20' West

Compass Surveying and Theodolite Question 3 Detailed Solution

Explanation:

Magnetic Declination and Magnetic Bearing of the Sun

Definition: Magnetic declination is the angle between the geographic north (true north) and the magnetic north at a specific location. It is an essential parameter in navigation and surveying as it helps correct compass readings. Magnetic declination can be either east or west depending on whether the magnetic north is to the east or west of true north. The magnetic bearing of the sun is the direction to the sun, measured clockwise from the magnetic north.

Given Scenario: In the problem, the magnetic bearing of the sun at noon is 185°20'. At noon, the sun is due south in the sky when viewed from the northern hemisphere. The magnetic declination is calculated by comparing the magnetic bearing of the sun with its true bearing (geographic direction).

Calculation:

At noon, the sun’s true bearing is 180° (due south). However, the magnetic bearing of the sun is given as 185°20'. This means the compass is reading a direction that is west of the true bearing.

To find the magnetic declination:

  • Magnetic Declination = Magnetic Bearing - True Bearing
  • Magnetic Declination = 185°20' - 180°
  • Magnetic Declination = 5°20' West

The declination is west because the magnetic bearing is greater than the true bearing, indicating that the magnetic north is west of true north.

Compass Surveying and Theodolite Question 4:

The whole circle bearing and the reduced bearing of a line will be the same when the line is in the ________ quadrant.

  1. north-west
  2. north-east
  3. south-east
  4. south-west

Answer (Detailed Solution Below)

Option 2 : north-east

Compass Surveying and Theodolite Question 4 Detailed Solution

Explanation:

  1. The whole circle bearing (WCB) and the reduced bearing (RB) of a line will be the same when the line lies in the north-east quadrant.
  2. This is because, in the north-east quadrant, both the WCB and RB are measured in a similar manner (0° to 90° from the north direction), so they will have the same value.

 Additional InformationWhole Circle Bearing (WCB):

  1. The Whole Circle Bearing is the angle measured in a clockwise direction from the north direction, ranging from 0° to 360°.

  2. It is called "whole circle" because it considers a full 360° rotation to describe the direction of a line.

  3. WCB is used in situations where you need a full circular measurement from the north, with values from 0° to 360°, irrespective of whether the line is heading towards the north, south, east, or west.

Reduced Circle Bearing (RCB):

  1. The Reduced Circle Bearing (also known as Quadrantal Bearing) is used to express the bearing relative to the nearest cardinal direction (north or south), and it uses a range of 0° to 90° for each quadrant (north-east, north-west, south-east, south-west).

  2. The direction is measured as an angle from either north or south, depending on which quadrant the line is in, and then it is written as a combination of cardinal direction and angle.

Compass Surveying and Theodolite Question 5:

Which of the following statements is/are correct about the variation of magnetic declination?

Statement I: Magnetic declination is more at magnetic poles and less at equator.

Statement II: Magnetic declination is more in the summer than in the winter.

Statement III: Magnetic declination is more at night and less in the day. 

  1. Statements I and II only
  2. Statement I only
  3. Statement II only
  4. Statements II and III only

Answer (Detailed Solution Below)

Option 1 : Statements I and II only

Compass Surveying and Theodolite Question 5 Detailed Solution

Explanation:

Statement I: Magnetic declination is more at magnetic poles and less at equator.

  • True.

  • Magnetic declination is the angle between true north and magnetic north.

  • Near the magnetic poles, this angle becomes large and erratic.

  • Near the magnetic equator, the deviation is generally smaller and more stable.

Statement II: Magnetic declination is more in the summer than in the winter.

  • True

  • In summer, the Earth's ionosphere experiences more solar radiation, which increases magnetic activity.

  • As a result, there is more fluctuation in the magnetic field, leading to a slightly higher magnetic declination.

Statement III: Magnetic declination is more at night and less in the day.

  • False.

  • Daily (diurnal) variation is minor, and during daytime, solar radiation affects ionospheric currents, causing slightly more variation than at night—not the other way around.

Additional InformationMagnetic Declination

  • It's the angle between true north (geographic north) and magnetic north.

  • Measured east or west from true north.

  • Essential in navigation, surveying, and compass correction.

  • The Earth's magnetic field is not uniform.

  • It changes over time due to movement in the Earth's molten outer core (known as secular variation).

  • Declination maps (isogonic charts) are used to track local values.

  • Long-term (secular): Slowly changes over years/decades.

  • Short-term (diurnal): Slight daily shifts due to solar radiation, but typically <0.1°.

  • Sudden changes: Can happen during geomagnetic storms or strong solar activity.

Top Compass Surveying and Theodolite MCQ Objective Questions

The lines joining points of equal dip are called

  1. Aclinic lines
  2. Isogonic lines
  3. Agonic lines
  4. Isoclinic lines

Answer (Detailed Solution Below)

Option 4 : Isoclinic lines

Compass Surveying and Theodolite Question 6 Detailed Solution

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Concept:

Dip:

  • It is the inclination of the magnetic needle with the horizontal. The dip is zero at the equator and the needle will remain horizontal.
  • At a place near 70° north latitude and 96° west longitude, the dip will be 90°. This area is called the magnetic north pole. Similarly, near the south magnetic pole, the dip is 90°.


Declination: 

  • It is the angle between the magnetic and geographic meridians or the angle in the horizontal plane between magnetic north and true north.


Explanation:

Magnetic Lines 

Definition

Agonic Line

The line joining the places of zero declination.

Aclinic Line

The line joining the places of zero dip

Isoclinic Line

The line joining the places of the same dip

Isogonic lines

Isogonic are the lines joining points of equal declination at a time of observation.

If the bearing of the side AB of a regular hexagon traverse ABCDEFA shown in the figure is 36°45', the bearing of the adjacent side BC of the traverse is:

F1 AbhishekM Madhuri 27.11.2021 D3

  1. 83°15'
  2. 96°45'
  3. 156°45'
  4. 216°15'

Answer (Detailed Solution Below)

Option 2 : 96°45'

Compass Surveying and Theodolite Question 7 Detailed Solution

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Explanation:

The difference (degree) in the magnitude of the fore bearing and back bearing of any line is 180° or if the difference is exactly 180°, the two stations may be considered as not affected by local attraction.

For regular hexagon, Sum of interior angles = (n - 2)180° 

F1 AbhishekM Madhuri 27.11.2021 D4

Sum of interior angles = (6 - 2)180° = 720° 

Each interior angle = \(\frac{720}{6}\) = 120° 

Back bearing = 180° + Fore bearing = 180° + 36°45' = 216°45'

∴ Fore bearing of BC = 216°45' - 120° = 96°45'

The main plate of a theodolite is divided into 1440 equal divisions. 60 divisions of the Vernier coincide exactly with 59 divisions of the main scale. The least count of the theodolite is

  1. 5”
  2. 10”
  3. 15”
  4. 20”

Answer (Detailed Solution Below)

Option 3 : 15”

Compass Surveying and Theodolite Question 8 Detailed Solution

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The least count of a vernier is equal to the difference in length of one division of main scale and one division of vernier scale.

In a direct vernier (n-1) divisions of the main scale is equal to the ‘n’ divisions on the vernier scale.

Thus,

n 'v' = (n – 1) 's'

\(\Rightarrow {\rm{v}} = \frac{{\left( {{\rm{n}} - 1} \right){\rm{s}}}}{{\rm{n}}}\)

Thus the least count is given by,

L.C = s – v

\(\Rightarrow {\rm{L}}.{\rm{C}} = {\rm{s}} - \frac{{\left( {{\rm{n}} - 1} \right){\rm{s}}}}{{\rm{n}}}\)

L C = s/n

Given:

Total division on main scale = 1440

Thus,

Length of one division (s) = 360°/1440

n = 60

\(\Rightarrow {\rm{L}}.{\rm{C}} = \frac{{360^\circ /1440}}{{60}} \times {3600^{{\rm{''}}}} = {15^{{\rm{''}}}}\)

Important Points

A theodolite is an important instrument used to measure horizontal and vertical angles.

There are two types of theodolites based on the method of obtaining reading:

a) Vernier Theodolite:-

  • These theodolites use verniers to take readings and are most commonly used. The upper plate of a transit theodolite has two verniers which are diametrically opposite to each other. If this plate is unclamped the upper plate rotates and the reading of the vernier changes.

b) Precise optical theodolites:-

  • Mostly used for astronomical works.

The bearing of a line AB is 150°15' and the angle ABC between line AB and BC is 110°30' as shown in the given figure.

F1 Akhil 29-11-21 Savita D1

What is the bearing of line BC?

  1. 79°15'
  2. 80°45'
  3. 330°15'
  4. 440°45'

Answer (Detailed Solution Below)

Option 2 : 80°45'

Compass Surveying and Theodolite Question 9 Detailed Solution

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Concept:

We know the relationship between FB and BB 

Back bearing (BB) = Fore bearing (FB) ± 180°. 

+ve sign is used if FB is less than 180° and –ve sign is used if FB is more than 180°.

Included angle = Fore Bearing of next line - Back Bearing of the previous line

Calculation:

F1 Akhil 29-11-21 Savita D1

Fore Bearing of AB = 150°15'

Included Angle ABC = 110°30'

Back Bearing of AB = 150°15' + 180° = 330°15' 

Included angle ABC = F.BBC - B.BAB 

110°30' = F.B.BC - 330° 15'

F.B.BC = 440°45' 

F.B.BC = 440°45' - 360° = 80° 45'

Note: 

If the included angle is negative, then add 360°.

If the included angle is greater than 360° then deduct 360°.

Which of the following is TRUE for the limit of accuracy in a compass surveying?

  1. Should not more than 5 minutes
  2. Should not be less than 5 minutes
  3. Should not more than 10 minutes
  4. Should not be less than 10 minutes

Answer (Detailed Solution Below)

Option 1 : Should not more than 5 minutes

Compass Surveying and Theodolite Question 10 Detailed Solution

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Explanation:

Accuracy

The accuracy of a set of repeated observations is defined as the amount of closeness of their mean to the population or distribution mean, i.e., the closeness of the mean of observations to the true value.

Degree of accuracy

  • The degree of accuracy indicates the accuracy attained in the measurements.
  • It is usually expressed as the ratio of the error and the associated measured value.
  • For example, a degree of accuracy of 1 in 10,000 indicates that there is an error of 1 unit in 10,000 units of measured/observed value.

Note:

For linear measurement:

The degree of accuracy of linear measurement is usually expressed as the ratio of the probable error and the measured distance.

For example, if there is a probable error of ± 0.05 m in a measured distance of 584.65 m, the degree of accuracy is 1 in 11700 as explained below.

For angular measurement:

For angular measurements, the degree of accuracy is usually expressed as k × √N, where N = Number of angles measured

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The angular measurement taken in compass surveying has the error should not be more than 5 minutes. Thus, the limit of accuracy is not more than 5 minutes.

The following bearings were taken in a closed compass traverse.  

Line

Fore bearing

Back bearing

AB

80° 10'

259° 0'

BC

120° 20'

301° 50'

CD

170° 50'

350° 50'

DE

230° 10'

49° 30'

EA

310° 20'

130° 15'


Calculate the corrected fore bearing of line ‘DE’ by assuming that the observed bearing of line ‘CD’ is correct.  

  1. 229° 55'
  2. 230° 10'
  3. 230° 15'
  4. 230° 5'

Answer (Detailed Solution Below)

Option 4 : 230° 5'

Compass Surveying and Theodolite Question 11 Detailed Solution

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Explanation:

  • Fore-bearing (FB) is the direction of a line measured in the forward direction from a known point. The angle between the survey line and the north direction is measured clockwise.
  • Back-bearing (BB) is the direction of the same line but measured in the reverse or backward direction from the endpoint back to the starting point. It is in the opposite direction to the fore-bearing and is measured in the opposite direction (180 degrees different).
  • Relation between FB and BB:

BB = FB + 180°, if FB < 180°

BB = FB – 180°, if FB > 180°.​

Here there is no local attraction given, so we have to solve by the include-angle method.

Include angle: The horizontal angle measured between two consecutive survey lines or directions.

Include angle = Fore-bearing of next line - Backbearing of previous

The sum of Include angle in clockwise direction (i.e, excluded angle) = (2n+4)90 = (2x5+4)x90° = 1260°

Angle

 FB of next line

BB of previous line

Include-angle

Final include angle

A

80°10'

130°15'

-50°5' (+360°)

309°55'

B

120°  20'

259° 0'

-138° 40' (+360°)

221°20’

C

170° 50'

301° 50'

-131° (+360°)

229°

D

230° 10'

350° 50'

-120°40’ (+360°)

239°20’

E

310° 20'

49° 30'

260°50’

260°50’

      Sum  1260°25’

So, the error = 1260°25' - 1260° = 25' 

So, Corrected include angle D = 239°20' - (25'/5') = 239°15' 

Thus, Include angle D = FBDE - BBCD 

FBDE = Include angle D +BBCD = 239°15' - 350°50' = 590°05' (- 360°) = 230°5'

The magnetic bearing of the sun at noon is 178º. The magnetic declination at the place is

  1. 2° W
  2. 2º E
  3. 2º N
  4. 2º S

Answer (Detailed Solution Below)

Option 2 : 2º E

Compass Surveying and Theodolite Question 12 Detailed Solution

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Concept:

TB (True Bearing) = MB (Magnetic bearing) ± Declination

(Use + ve for eastern and – ve for western declination)

F2 N.M. N.J 30-07-2019 D7

Calculation:

  • At Noon, the sun is exactly on the geographical meridian.
  • Hence, the true bearing of the sun at noon is zero or 180° depending upon whether it is to the North of the place or to the South of the place.
  • Since the magnetic bearing of the sun is 178°, the true bearing will be 180 °.


True Bearing at Noon = 180°

Magnetic Bearing = 178°

Declination = True Bearing - Magnetic Bearing = 180° - 178° = + 2°

∴ Magnetic Declination = 2° East (+ve sign indicates East)

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  • Sometimes the direction of declination may not be mentioned in the question and in such cases, standard sign conventions used for declination must be considered.
  • Since declination was given a positive value in the above case we would assume is to be eastern declination for computing the value of true bearing.

Agonic line is the line joining points having declination-

  1. Minimum Declination
  2. Maximum Declination
  3. Same Declination
  4. Zero Declination

Answer (Detailed Solution Below)

Option 4 : Zero Declination

Compass Surveying and Theodolite Question 13 Detailed Solution

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Agonic lines:

 

F2 A.M Madhu 26.05.20 D1

A line having zero degree declination is known as Agonic line

True bearing and magnetic bearing both are equal for agonic lines.

Isogonic lines:

F2 A.M Madhu 26.05.20 D2

Isogonic lines are lines of same declination.

Agonic lines are always isogonic lines.


Additional Information

Isoclinic Line: Line connecting points of equal dip.

Aclinic Line: Line connecting points of zero dip.

Consider the following statements with respect to compass surveying and identify the correct answer.

Statement A: The direction of a survey line measured using a prismatic compass is called magnetic bearing.

Statement B: The direction of a survey line measured using a surveyor compass is called arbitrary bearing. 

  1. Statement A is correct and B is incorrect
  2. Both statements are incorrect
  3. Statement B is correct and A is incorrect
  4. Both statements are correct

Answer (Detailed Solution Below)

Option 1 : Statement A is correct and B is incorrect

Compass Surveying and Theodolite Question 14 Detailed Solution

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Important terms:

Arbitrary bearing: The horizontal angle made by the survey line with reference to arbitrary meridian passing through one of the extremities.

True Bearing: It is horizontal angle between the true meridian and the survey line measured in a clockwise direction.

Azimuth: it is the horizontal angle or direction of a compass bearing.

Arbitrary Meridian: Any convenient direction from a survey station to some well defined permanent object is known as arbitrary meridian. This is used for small area survey or to determine the relative directions of small traverse.

Grid Meridian: For survey of country, the true meridian passing through the central place is sometimes taken as a reference meridian for the whole country. Such a meridian is known as Grid meridian.

Which of the figures represents the correct graduation in a surveyor's compass?

  1. F1 Abhayraj.L 21-12-20 Savita D16
  2. F1 Abhayraj.L 21-12-20 Savita D17
  3. F1 Abhayraj.L 21-12-20 Savita D18
  4. F1 Chandra Madhu 24.02.21 D1

Answer (Detailed Solution Below)

Option 2 : F1 Abhayraj.L 21-12-20 Savita D17

Compass Surveying and Theodolite Question 15 Detailed Solution

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Concept:

Compass surveying:

Compass surveying is a type of surveying in which the directions of surveying lines are determined with a magnetic compass, and the length of the surveying lines are measured with a tape or chain or laser range finder. The compass is generally used to run a traverse line. There are mainly two types of compass are used:

  • Prismatic compass
  • Surveyor's compass

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F1 Chandra Madhu 24.02.21  D2

Explanation:

Surveyor's compass:

  • It can only be used on a tripod.
  • In the graduated card, The East and West are interchanged.
  • Gives bearing in the quadrantal bearing system
  • Range of angle measured 0-900.
  • The needle is of edge bar type. 
  • The diameter of the compass is 150mm. 
  • The least count is 15 minutes.
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