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The observed angles are given with their probable errors, and we need to correct them. The correction is generally made by adjusting the measured values by the probable errors. Step 1: Understand the observation and correction.
The angles are observed with an error margin indicated by ± for each value. For instance, P = 40° 30' 01'' ± 02'' means that the observed value of P could vary by ±2 seconds. So, to get the corrected angle, we need to subtract the error from the observed value. - Angle P: The error for P is ±02'', so we subtract 0.2 from 40° 30' 01'' to get 40° 29' 59.9''.
- Angle Q: The error for Q is ±03'', so we subtract 0.3 from 60° 00' 02'' to get 59° 59' 59.7''. This rounds to 59° 59' 59.5''.
- Angle R: The error for R is ±04'', so we subtract 0.4 from 79° 30' 05'' to get 79° 30' 0.6''.
Step 2: Comparison with options.
By comparing the corrected values with the options, we find that option (C) matches the corrected values exactly. Thus, the correct answer is (C) P = 40° 29' 59.9'', Q = 59° 59' 59.5'', R = 79° 30' 0.6''.

DGPS (Differential GPS) positioning is a method used to improve the accuracy of GPS measurements by using a reference station to correct errors in the GPS signal. DGPS primarily helps in correcting errors caused by atmospheric conditions, such as ionospheric and tropospheric delays, which can distort the GPS signal. Step 1: Understanding the errors in GPS positioning. - Atmospheric error is caused by the ionosphere and troposphere affecting the GPS signal. DGPS corrects these errors by using a reference station and applying the necessary adjustments. - Multi-path error occurs when the GPS signal bounces off nearby objects, leading to inaccurate measurements. While DGPS improves accuracy, it doesn't directly mitigate multi-path errors. - Cycle-slip error occurs due to sudden changes in phase in the signal, often caused by satellite signal loss or interference. DGPS does not specifically address cycle-slip errors. - Topographic error is related to the terrain and obstacles that may obstruct the GPS signal, but DGPS doesn't directly mitigate topographic errors. Step 2: Conclusion. DGPS effectively mitigates atmospheric errors, making option (A) the correct answer. Thus, the correct answer is (A).

The Global Positioning System (GPS) works by sending signals from satellites to receivers on the Earth. The GPS signal includes different components that help the receiver determine its position. The primary components of the GPS signal are the Coarse-Acquisition (C/A) code, Precision code, and the P(Y) code.
- Coarse-Acquisition (C/A) code: The C/A code is a civilian-use component of the GPS signal that is used by all GPS receivers. This code is transmitted by all GPS satellites and is used by the receiver to decode the signal and calculate the position. It has a 1,023-bit length and repeats every millisecond.
- Precision code: This code is encrypted and primarily used by military GPS receivers. It is not available to all civilian receivers. The Precision code offers a more accurate signal than the C/A code but requires specialized military equipment to decode.
- Link-1 and Link-2C frequencies: These are the frequencies at which the GPS satellites communicate with the receiver. While the Link-1 and Link-2 frequencies are part of the GPS signal structure, they are not directly related to the component that all GPS receivers can decipher. These are used for more advanced, military-based applications.
Since the Coarse-Acquisition (C/A) code is the only component accessible by all GPS receivers (civilian or military), the correct answer is (A).

The Global Navigation Satellite System (GNSS) is used for positioning, navigation, and timing (PNT) information. GNSS systems such as GPS provide three-dimensional positioning, which requires both horizontal (latitude, longitude) and vertical (altitude) information.
For 2D positioning, which only requires horizontal information (latitude and longitude), a minimum of three satellites are needed. This is because, with three satellites, a GPS receiver can perform trilateration to calculate the position in two dimensions.
However, for 3D positioning, which includes the vertical dimension (altitude), a minimum of four satellites are required. Here's why:
- With three satellites, the GPS receiver can determine the position on a flat plane, but it does not have enough information to calculate the altitude (height above the Earth's surface).
- The fourth satellite is needed to provide the necessary information to calculate the altitude. Additionally, the fourth satellite helps in compensating for timing errors in the receiver's clock.
The reason a fourth satellite is needed is because the GPS receiver’s clock is not perfectly synchronized with the satellite clocks, and the fourth satellite allows the receiver to correct for this time discrepancy.
Thus, to perform 3D positioning, a minimum of four satellites are required. This ensures that the receiver can calculate not only the horizontal position but also the altitude accurately.
Final Answer:
The correct answer is (B) 4 satellites, as they are required for accurate 3D positioning.

NAVSTAR GPS (Global Positioning System) is a satellite-based navigation system. Its primary objective is to provide three key services: positioning, navigation, and timing. Step 1: Understanding the services of GPS
- Positioning: GPS determines the precise position (latitude, longitude, and altitude) of an object on Earth by using signals from multiple satellites. This is the fundamental service provided by GPS.
- Navigation: GPS helps users navigate by providing directions and guiding them from one location to another. This is especially useful for navigation in unfamiliar areas.
- Timing: GPS also provides accurate time synchronization. The system has highly precise atomic clocks on each satellite, which help provide accurate time across the globe. Step 2: Analysis of the options
- Option (A): Positioning, Velocity and Timing. While velocity is important in GPS systems, it is not the primary service provided by NAVSTAR GPS. Hence, this option is incorrect.
- Option (B): Positioning, Navigation and Timing. This is the correct answer, as these are the three main services provided by NAVSTAR GPS.
- Option (C): Velocity, Navigation and Timing. This is not correct, as velocity is not a primary service of GPS.
- Option (D): Positioning, Velocity and Navigation. This option is incorrect because velocity is not one of the core services of GPS. Thus, the correct answer is (B) Positioning, Navigation and Timing.

In the case of a tilted photograph, the scale is not uniform throughout its extent. The scale varies depending on the distance from the nadir (the point directly below the camera). As the tilt increases, the scale distortion increases, with the scale being smaller near the edges of the photograph and larger near the nadir.
Step 1: Understanding the Concepts
- Option (A) is incorrect because the scale in a tilted photograph is not uniform. It changes depending on the position relative to the nadir.
- Option (B) is correct as the relief displacement, which is the apparent shift in position of a point on a photograph due to tilt, is indeed radial from the nadir point.
- Option (C) is correct since the bisector of the angle of tilt does intersect the tilted photograph at the isocentre, which is the point where the scale is uniform.
- Option (D) is correct as the line perpendicular to the principal line and passing through the isocentre is known as the axis of tilt. Step 2: Conclusion
Therefore, the correct answer is (A), as the scale of a tilted photograph is not uniform.

In surveying, the closing error in a traverse is the difference between the starting and ending points of the traverse. To calculate the closing error, we use the sum of the latitudes (north-south components) and the sum of the departures (east-west components). The closing error can be expressed in terms of its length and its direction (bearing).
Step 1: Calculate the Closing Error Length
The length of the closing error can be calculated using the Pythagorean theorem: Given: Substituting the values: Thus, the length of the closing error is approximately 2.57 m.
Step 2: Calculate the Whole Circle Bearing
The Whole Circle Bearing (WCB) of the closing error is the angle between the sum of the latitudes and the sum of the departures, which can be found using the formula: Substituting the given values: Thus, the Whole Circle Bearing of the closing error is approximately 57°.
Therefore, the correct answer is (B), Length = 2.57 m and Whole Circle Bearing = 57°.

- Option (A): Latitude ranges from 0° at the Equator to 90° North or South at the poles. Longitude ranges from 0° at the Prime Meridian to 180° East or West. This statement is correct.
- Option (B): This statement incorrectly describes the ranges of latitude and longitude. Latitude does not range from 0° to 180°, and longitude does not range from 0° to 90° North or South. Thus, this statement is incorrect.
- Option (C): Longitude is the angular distance measured east or west from the Prime Meridian. It is calculated as the angle between the Greenwich Meridian and the meridian passing through the given point. This statement is correct.
- Option (D): The latitude and longitude of a place are fixed coordinates based on the Earth's reference system. While slight changes can occur due to tectonic activity, they do not typically change with time. This statement is incorrect.
Thus, the correct answers are (A) and (C).

In surveying, the main principle is to start from the whole and move towards the part. This ensures accuracy and efficiency in measuring and mapping, especially when conducting land surveys. Step 1: Understanding the principle. The principle of working from the whole to part means that surveyors first establish the large-scale features or reference points, which then guide the measurement of smaller, more detailed features. This method helps in minimizing errors as the survey progresses. Step 2: Analyzing the options. - Option (A) is correct because it correctly states that surveying starts from the whole (large-scale) and moves towards the part (smaller details). - Option (B) is incorrect because working from part to whole would be inefficient and prone to errors as small-scale measurements would be based on incomplete data. - Option (C) and Option (D) are incorrect because the elevation order (higher to lower or vice versa) is not related to the main surveying principle; it focuses on the logical measurement progression. Thus, the correct answer is (A).

A cadastral survey is the type of survey conducted to define the boundaries of land for the purpose of land property transactions. This survey helps in determining the ownership and boundaries of a parcel of land, and is critical for legal purposes such as buying, selling, and registering land. Step 1: Understanding the types of surveys. - A cadastral survey is specifically concerned with mapping land boundaries, ownership, and property lines, making it the most appropriate term for land transactions.
- A city survey is typically focused on urban planning and development but not on defining property boundaries for legal purposes.
- A municipality survey involves mapping and planning for local governance, and is also unrelated to property boundary definitions.
- A geodetic survey is concerned with large-scale measurements of the Earth's surface and curvature, not specific land boundaries.
Step 2: Conclusion. Therefore, the correct answer is (B) because it directly refers to surveys that define land property boundaries. Thus, the correct answer is (B).

In surveying, the departure of a line is calculated by multiplying its length by the sine of the reduced bearing of the line. This is because the departure corresponds to the east-west component of the line, which can be determined using the sine function.
Step 1: Understanding Departure
The departure is the horizontal distance that a line covers in the east-west direction, and it is given by: Thus, the correct answer is (A) Sine.

The multiplying constant in a Tacheometer is given by the ratio of the focal length to the distance between the stadia hairs . This constant is used to calculate distances based on the observed readings in Tacheometry.
Step 1: Formula for Multiplying Constant
The multiplying constant is calculated using the formula: where is the focal length and is the distance between the stadia hairs.
Thus, the correct answer is (C) .

Step 1: Understanding the Concept:
Global Positioning System (GPS) positioning is based on the principle of trilateration, which involves measuring the distance (range) from the receiver to multiple satellites.
Step 2: Detailed Explanation:
To determine a position in three-dimensional space, we have four unknowns:
1. Latitude ( )
2. Longitude ( )
3. Altitude or Elevation ( )
4. Receiver Clock Bias ( )
While mathematically, three spheres (from 3 satellites) intersect at two points (one of which can usually be discarded as being in space), a fourth satellite is absolutely necessary to synchronize the receiver's clock with the atomic clocks on the satellites. Without this time synchronization, distance measurements would be highly inaccurate.
Step 3: Final Answer:
Therefore, a minimum of 4 satellites is required to solve for the four variables ( ) and provide a 3D position fix.