Mathematical problems with solutions, and continue until we reach 100
questions: 100 Mathematical Multiple Choice Questions on
Development of Autonomous Aircraft Systems
1. An autonomous aircraft uses a LIDAR system that emits laser pulses at a rate of 100,000 pulses per
second. If each pulse takes 2 microseconds to return from an object, what is the maximum range the
LIDAR can detect, assuming the speed of light is 3 × 10^8 m/s?
a) 150 m
b) 300 m
c) 450 m
d) 600 m
Answer: b) 300 m
Solution:
Time for round trip = 2 × 10^-6 s
Distance = (Speed × Time) / 2
Distance = (3 × 10^8 × 2 × 10^-6) / 2 = 300 m
2. An autonomous drone is flying at a constant speed of 20 m/s. Its onboard computer processes
sensor data every 0.1 seconds. What is the distance traveled by the drone between two consecutive
sensor readings?
a) 1 m
b) 2 m
c) 3 m
d) 4 m
Answer: b) 2 m
Solution:
Distance = Speed × Time
Distance = 20 m/s × 0.1 s = 2 m
3. A radar system on an autonomous aircraft operates at a frequency of 10 GHz. What is the
wavelength of the radar signals?
a) 0.03 m
b) 0.05 m
c) 0.07 m
d) 0.09 m
Answer: a) 0.03 m
Solution:
Wavelength = Speed of light / Frequency
Wavelength = 3 × 10^8 m/s / (10 × 10^9 Hz) = 0.03 m
4. An autonomous aircraft's obstacle avoidance system detects an object 500 meters away. If the
aircraft is traveling at 100 m/s, how long does it have to initiate evasive maneuvers?
a) 3 seconds
b) 4 seconds
c) 5 seconds
d) 6 seconds
Answer: c) 5 seconds
Solution:
Time = Distance / Speed
Time = 500 m / 100 m/s = 5 seconds
5. The battery of an autonomous drone has a capacity of 5000 mAh. If the drone's average current
draw is 2.5 A, how long can the drone operate on a single charge?
a) 1 hour
b) 1.5 hours
c) 2 hours
d) 2.5 hours
Answer: c) 2 hours
Solution:
Operation time = Battery capacity / Current draw
Operation time = 5000 mAh / 2500 mA = 2 hours
6. An autonomous aircraft's GPS system has a position accuracy of ±5 meters. If the aircraft needs to
land on a circular pad with a radius of 10 meters, what is the probability that the GPS reading will
place the aircraft within the landing pad?
a) 25%
b) 50%
c) 75%
d) 100%
Answer: c) 75%
Solution:
Area of landing pad = π × r^2 = π × 10^2 = 314 m^2
Area of possible GPS readings = π × (r + accuracy)^2 = π × 15^2 = 707 m^2
Probability = Area of landing pad / Area of possible GPS readings = 314 / 707 ≈ 0.75 or 75%
7. An autonomous drone uses a stereo vision system with two cameras separated by 10 cm. If an
object is detected at a pixel disparity of 20 pixels, and each camera has a focal length of 5 mm with a
pixel size of 5 μm, what is the distance to the object?
a) 1.25 m
b) 2.5 m
c) 3.75 m
d) 5 m
Answer: b) 2.5 m
Solution:
Distance = (Baseline × Focal length) / (Pixel size × Disparity)
Distance = (0.1 m × 0.005 m) / (5 × 10^-6 m × 20) = 2.5 m
8. An autonomous aircraft's collision avoidance system predicts the trajectory of another aircraft. If
the other aircraft is 10 km away and approaching at 200 m/s, how long will it take for the two aircraft
to collide if no evasive action is taken?
a) 40 seconds
b) 45 seconds
c) 50 seconds
d) 55 seconds
Answer: c) 50 seconds
Solution:
Time to collision = Distance / Speed
Time to collision = 10,000 m / 200 m/s = 50 seconds
9. An autonomous drone's path planning algorithm calculates a route that is 5 km long. If the drone's
average speed is 15 m/s, how long will it take to complete the route?
a) 5 minutes 33 seconds
b) 5 minutes 44 seconds
c) 5 minutes 55 seconds
d) 6 minutes 6 seconds
Answer: a) 5 minutes 33 seconds
Solution:
Time = Distance / Speed
Time = 5,000 m / 15 m/s = 333.33 seconds ≈ 5 minutes 33 seconds
10. The control system of an autonomous aircraft operates at 100 Hz. What is the time interval
between two consecutive control loop iterations?
a) 0.001 seconds
b) 0.005 seconds
c) 0.01 seconds
d) 0.1 seconds
Answer: c) 0.01 seconds
Solution:
Time interval = 1 / Frequency
Time interval = 1 / 100 Hz = 0.01 seconds
11. An autonomous drone uses a magnetometer to measure the Earth's magnetic field. If the
magnetometer has a sensitivity of 0.1 μT (microtesla) and the Earth's magnetic field strength is
typically around 50 μT, what is the minimum angular resolution the drone can achieve in detecting its
orientation?
a) 0.1°
b) 0.2°
c) 0.3°
d) 0.4°
Answer: a) 0.1°
Solution:
Angular resolution = arcsin(Sensitivity / Field strength)
Angular resolution = arcsin(0.1 / 50) ≈ 0.1°
12. An autonomous aircraft's machine learning model for object detection has 10 million parameters.
If each parameter is stored as a 32-bit floating-point number, how much memory does the model
require?
a) 20 MB
b) 30 MB
c) 40 MB
d) 50 MB
Answer: c) 40 MB
Solution:
Memory = Number of parameters × Bits per parameter / 8 bits per byte
Memory = 10,000,000 × 32 / 8 = 40,000,000 bytes = 40 MB
13. An autonomous drone's propulsion system consumes 500 W of power. If the drone's battery has
a capacity of 10,000 mAh and operates at 11.1 V, how long can the drone fly?
a) 22 minutes
b) 33 minutes
c) 44 minutes
d) 55 minutes
Answer: b) 33 minutes
Solution:
Battery energy = 10,000 mAh × 11.1 V = 111,000 mWh = 111 Wh
Flight time = Battery energy / Power consumption
Flight time = 111 Wh / 500 W = 0.222 hours ≈ 33 minutes
14. An autonomous aircraft's navigation system uses a Kalman filter to estimate its position. If the
initial position uncertainty is 10 m and the measurement uncertainty is 2 m, what is the estimated
position uncertainty after one update?
a) 1.67 m
b) 1.82 m
c) 1.98 m
d) 2.14 m
Answer: a) 1.67 m
Solution:
Updated uncertainty = (Initial uncertainty × Measurement uncertainty) / (Initial uncertainty +
Measurement uncertainty)
Updated uncertainty = (10 × 2) / (10 + 2) = 1.67 m
15. An autonomous drone's obstacle detection system has a false positive rate of 1% and a true
positive rate of 99%. If the drone encounters 1000 non-obstacle situations and 10 real obstacles
during a flight, how many total obstacle detections will it make?
a) 10
b) 20
c) 30
d) 40
Answer: b) 20
Solution:
False positives = 1% of 1000 = 10
True positives = 99% of 10 = 9.9 ≈ 10
Total detections = False positives + True positives = 10 + 10 = 20
16. An autonomous aircraft's wind estimation algorithm calculates a headwind of 15 m/s. If the
aircraft's airspeed is 100 m/s, what is its ground speed?
a) 75 m/s
b) 85 m/s
c) 95 m/s
d) 105 m/s
Answer: b) 85 m/s
Solution:
Ground speed = Airspeed - Headwind
Ground speed = 100 m/s - 15 m/s = 85 m/s
17. An autonomous drone uses a PID controller for altitude control. If the proportional gain is 2, the
integral gain is 0.1, and the derivative gain is 0.5, what is the control output for an error of 5 meters,
an integral of error of 10 meter-seconds, and a rate of change of error of -2 meters per second?
a) 8.5
b) 9.5
c) 10.5
d) 11.5
Answer: c) 10.5
Solution:
Output = P + I + D
Output = (2 × 5) + (0.1 × 10) + (0.5 × -2)
Output = 10 + 1 - 0.5 = 10.5
18. An autonomous aircraft's path planning algorithm uses A* search. If the heuristic function
consistently underestimates the true cost by 20%, how much longer will the calculated path be
compared to the optimal path, in the worst case?
a) 10%
b) 20%
c) 30%
d) 40%
Answer: b) 20%
Solution:
Worst-case path length = Optimal path length × (1 / (1 - Underestimation))
Worst-case path length = Optimal path length × (1 / (1 - 0.2)) = Optimal path length × 1.25
Percentage increase = (1.25 - 1) × 100% = 25%
19. An autonomous drone's battery management system estimates that the battery has 30% charge
remaining. If the drone consumes 100 W of power and the battery capacity is 10,000 mAh at 11.1 V,
how much longer can the drone fly?
a) 10 minutes
b) 15 minutes
c) 20 minutes
d) 25 minutes
Answer: c) 20 minutes
Solution:
Remaining energy = 30% × 10,000 mAh × 11.1 V = 33,300 mWh = 33.3 Wh
Flight time = Remaining energy / Power consumption
Flight time = 33.3 Wh / 100 W = 0.333 hours = 20 minutes
20. An autonomous aircraft's SLAM (Simultaneous Localization and Mapping) algorithm processes
point cloud data with 1 million points. If each point is represented by 3 floating-point numbers (x, y, z
coordinates) and each floating-point number is 4 bytes, how much memory is required to store the
point cloud?
a) 8 MB
b) 12 MB
c) 16 MB
d) 20 MB
Answer: b) 12 MB
Solution:
Memory = Number of points × Coordinates per point × Bytes per coordinate
Memory = 1,000,000 × 3 × 4 bytes = 12,000,000 bytes = 12 MB
21. An autonomous drone's object tracking algorithm predicts that an object will be at position (10,
5) in 2 seconds. If the object's current position is (2, 1), what is its estimated velocity vector?
a) (3, 1.5) m/s
b) (4, 2) m/s
c) (5, 2.5) m/s
d) (6, 3) m/s
Answer: b) (4, 2) m/s
Solution:
Velocity = (Change in position) / Time
Velocity_x = (10 - 2) / 2 = 4 m/s
Velocity_y = (5 - 1) / 2 = 2 m/s
Velocity vector = (4, 2) m/s
22. An autonomous aircraft's navigation system uses a GPS receiver with a position dilution of
precision (PDOP) of 2.5. If the GPS has a user equivalent range error (UERE) of 5 meters, what is the
expected position accuracy?
a) 10.5 meters
b) 12.5 meters
c) 14.5 meters
d) 16.5 meters
Answer: b) 12.5 meters
Solution:
Position accuracy = PDOP × UERE
Position accuracy = 2.5 × 5 meters = 12.5 meters
23. An autonomous drone's collision avoidance system detects an obstacle 50 meters away,
approaching at a relative velocity of 10 m/s. If the drone's maximum deceleration is 2 m/s^2, what is
the minimum distance at which it must start decelerating to avoid a collision?
a) 12.5 meters
b) 25 meters
c) 37.5 meters
d) 50 meters
Answer: b) 25 meters
Solution:
Using the equation of motion: v^2 = u^2 + 2as
0 = 10^2 + 2(-2)s
s = 100 / 4 = 25 meters
24. An autonomous aircraft's machine learning model for weather prediction has an accuracy of 85%
for predicting clear weather and 75% for predicting stormy weather. If clear weather occurs 70% of
the time, what is the overall accuracy of the model?
a) 80%
b) 82%
c) 84%
d) 86%
Answer: b) 82%
Solution:
Overall accuracy = (Accuracy_clear × Probability_clear) + (Accuracy_stormy × Probability_stormy)
Overall accuracy = (0.85 × 0.7) + (0.75 × 0.3) = 0.595 + 0.225 = 0.82 or 82%
. An autonomous aircraft's obstacle avoidance system detects an object 500 meters away. If the
aircraft is traveling at 100 m/s, how long does it have to initiate evasive maneuvers?
a) 3 seconds
b) 4 seconds
c) 5 seconds
d) 6 seconds
Answer: c) 5 seconds
Solution:
Time = Distance / Speed
Time = 500 m / 100 m/s = 5 seconds
5. The battery of an autonomous drone has a capacity of 5000 mAh. If the drone's average current
draw is 2.5 A, how long can the drone operate on a single charge?
a) 1 hour
b) 1.5 hours
c) 2 hours
d) 2.5 hours
Answer: c) 2 hours
Solution:
Operation time = Battery capacity / Current draw
Operation time = 5000 mAh / 2500 mA = 2 hours
6. An autonomous aircraft's GPS system has a position accuracy of ±5 meters. If the aircraft needs to
land on a circular pad with a radius of 10 meters, what is the probability that the GPS reading will
place the aircraft within the landing pad?
a) 25%
b) 50%
c) 75%
d) 100%
Answer: c) 75%
Solution:
Area of landing pad = π × r^2 = π × 10^2 = 314 m^2
Area of possible GPS readings = π × (r + accuracy)^2 = π × 15^2 = 707 m^2
Probability = Area of landing pad / Area of possible GPS readings = 314 / 707 ≈ 0.75 or 75%
7. An autonomous drone uses a stereo vision system with two cameras separated by 10 cm. If an
object is detected at a pixel disparity of 20 pixels, and each camera has a focal length of 5 mm with a
pixel size of 5 μm, what is the distance to the object?
a) 1.25 m
b) 2.5 m
c) 3.75 m
d) 5 m
Answer: b) 2.5 m
Solution:
Distance = (Baseline × Focal length) / (Pixel size × Disparity)
Distance = (0.1 m × 0.005 m) / (5 × 10^-6 m × 20) = 2.5 m
8. An autonomous aircraft's collision avoidance system predicts the trajectory of another aircraft. If
the other aircraft is 10 km away and approaching at 200 m/s, how long will it take for the two aircraft
to collide if no evasive action is taken?
a) 40 seconds
b) 45 seconds
c) 50 seconds
d) 55 seconds
Answer: c) 50 seconds
Solution:
Time to collision = Distance / Speed
Time to collision = 10,000 m / 200 m/s = 50 seconds
9. An autonomous drone's path planning algorithm calculates a route that is 5 km long. If the drone's
average speed is 15 m/s, how long will it take to complete the route?
a) 5 minutes 33 seconds
b) 5 minutes 44 seconds
c) 5 minutes 55 seconds
d) 6 minutes 6 seconds
Answer: a) 5 minutes 33 seconds
Solution:
Time = Distance / Speed
Time = 5,000 m / 15 m/s = 333.33 seconds ≈ 5 minutes 33 seconds
10. The control system of an autonomous aircraft operates at 100 Hz. What is the time interval
between two consecutive control loop iterations?
a) 0.001 seconds
b) 0.005 seconds
c) 0.01 seconds
d) 0.1 seconds
Answer: c) 0.01 seconds
Solution:
Time interval = 1 / Frequency
Time interval = 1 / 100 Hz = 0.01 seconds
11. An autonomous drone uses a magnetometer to measure the Earth's magnetic field. If the
magnetometer has a sensitivity of 0.1 μT (microtesla) and the Earth's magnetic field strength is
typically around 50 μT, what is the minimum angular resolution the drone can achieve in detecting its
orientation?
a) 0.1°
b) 0.2°
c) 0.3°
d) 0.4°
Answer: a) 0.1°
Solution:
Angular resolution = arcsin(Sensitivity / Field strength)
Angular resolution = arcsin(0.1 / 50) ≈ 0.1°
12. An autonomous aircraft's machine learning model for object detection has 10 million parameters.
If each parameter is stored as a 32-bit floating-point number, how much memory does the model
require?
a) 20 MB
b) 30 MB
c) 40 MB
d) 50 MB
Answer: c) 40 MB
Solution:
Memory = Number of parameters × Bits per parameter / 8 bits per byte
Memory = 10,000,000 × 32 / 8 = 40,000,000 bytes = 40 MB
13. An autonomous drone's propulsion system consumes 500 W of power. If the drone's battery has
a capacity of 10,000 mAh and operates at 11.1 V, how long can the drone fly?
a) 22 minutes
b) 33 minutes
c) 44 minutes
d) 55 minutes
Answer: b) 33 minutes
Solution:
Battery energy = 10,000 mAh × 11.1 V = 111,000 mWh = 111 Wh
Flight time = Battery energy / Power consumption
Flight time = 111 Wh / 500 W = 0.222 hours ≈ 33 minutes
14. An autonomous aircraft's navigation system uses a Kalman filter to estimate its position. If the
initial position uncertainty is 10 m and the measurement uncertainty is 2 m, what is the estimated
position uncertainty after one update?
a) 1.67 m
b) 1.82 m
c) 1.98 m
d) 2.14 m
Answer: a) 1.67 m
Solution:
Updated uncertainty = (Initial uncertainty × Measurement uncertainty) / (Initial uncertainty +
Measurement uncertainty)
Updated uncertainty = (10 × 2) / (10 + 2) = 1.67 m
15. An autonomous drone's obstacle detection system has a false positive rate of 1% and a true
positive rate of 99%. If the drone encounters 1000 non-obstacle situations and 10 real obstacles
during a flight, how many total obstacle detections will it make?
a) 10
b) 20
c) 30
d) 40
Answer: b) 20
Solution:
False positives = 1% of 1000 = 10
True positives = 99% of 10 = 9.9 ≈ 10
Total detections = False positives + True positives = 10 + 10 = 20
16. An autonomous aircraft's wind estimation algorithm calculates a headwind of 15 m/s. If the
aircraft's airspeed is 100 m/s, what is its ground speed?
a) 75 m/s
b) 85 m/s
c) 95 m/s
d) 105 m/s
Answer: b) 85 m/s
Solution:
Ground speed = Airspeed - Headwind
Ground speed = 100 m/s - 15 m/s = 85 m/s
17. An autonomous drone uses a PID controller for altitude control. If the proportional gain is 2, the
integral gain is 0.1, and the derivative gain is 0.5, what is the control output for an error of 5 meters,
an integral of error of 10 meter-seconds, and a rate of change of error of -2 meters per second?
a) 8.5
b) 9.5
c) 10.5
d) 11.5
Answer: c) 10.5
Solution:
Output = P + I + D
Output = (2 × 5) + (0.1 × 10) + (0.5 × -2)
Output = 10 + 1 - 0.5 = 10.5
18. An autonomous aircraft's path planning algorithm uses A* search. If the heuristic function
consistently underestimates the true cost by 20%, how much longer will the calculated path be
compared to the optimal path, in the worst case?
a) 10%
b) 20%
c) 30%
d) 40%
Answer: b) 20%
Solution:
Worst-case path length = Optimal path length × (1 / (1 - Underestimation))
Worst-case path length = Optimal path length × (1 / (1 - 0.2)) = Optimal path length × 1.25
Percentage increase = (1.25 - 1) × 100% = 25%
19. An autonomous drone's battery management system estimates that the battery has 30% charge
remaining. If the drone consumes 100 W of power and the battery capacity is 10,000 mAh at 11.1 V,
how much longer can the drone fly?
a) 10 minutes
b) 15 minutes
c) 20 minutes
d) 25 minutes
Answer: c) 20 minutes
Solution:
Remaining energy = 30% × 10,000 mAh × 11.1 V = 33,300 mWh = 33.3 Wh
Flight time = Remaining energy / Power consumption
Flight time = 33.3 Wh / 100 W = 0.333 hours = 20 minutes
20. An autonomous aircraft's SLAM (Simultaneous Localization and Mapping) algorithm processes
point cloud data with 1 million points. If each point is represented by 3 floating-point numbers (x, y, z
coordinates) and each floating-point number is 4 bytes, how much memory is required to store the
point cloud?
a) 8 MB
b) 12 MB
c) 16 MB
d) 20 MB
Answer: b) 12 MB
Solution:
Memory = Number of points × Coordinates per point × Bytes per coordinate
Memory = 1,000,000 × 3 × 4 bytes = 12,000,000 bytes = 12 MB
21. An autonomous drone's object tracking algorithm predicts that an object will be at position (10,
5) in 2 seconds. If the object's current position is (2, 1), what is its estimated velocity vector?
a) (3, 1.5) m/s
b) (4, 2) m/s
c) (5, 2.5) m/s
d) (6, 3) m/s
Answer: b) (4, 2) m/s
Solution:
Velocity = (Change in position) / Time
Velocity_x = (10 - 2) / 2 = 4 m/s
Velocity_y = (5 - 1) / 2 = 2 m/s
Velocity vector = (4, 2) m/s
22. An autonomous aircraft's navigation system uses a GPS receiver with a position dilution of
precision (PDOP) of 2.5. If the GPS has a user equivalent range error (UERE) of 5 meters, what is the
expected position accuracy?
a) 10.5 meters
b) 12.5 meters
c) 14.5 meters
d) 16.5 meters
Answer: b) 12.5 meters
Solution:
Position accuracy = PDOP × UERE
Position accuracy = 2.5 × 5 meters = 12.5 meters
23. An autonomous drone's collision avoidance system detects an obstacle 50 meters away,
approaching at a relative velocity of 10 m/s. If the drone's maximum deceleration is 2 m/s^2, what is
the minimum distance at which it must start decelerating to avoid a collision?
a) 12.5 meters
b) 25 meters
c) 37.5 meters
d) 50 meters
Answer: b) 25 meters
Solution:
Using the equation of motion: v^2 = u^2 + 2as
0 = 10^2 + 2(-2)s
s = 100 / 4 = 25 meters
24. An autonomous aircraft's machine learning model for weather prediction has an accuracy of 85%
for predicting clear weather and 75% for predicting stormy weather. If clear weather occurs 70% of
the time, what is the overall accuracy of the model?
a) 80%
b) 82%
c) 84%
d) 86%
Answer: b) 82%
Solution:
Overall accuracy = (Accuracy_clear × Probability_clear) + (Accuracy_stormy × Probability_stormy)
Overall accuracy = (0.85 × 0.7) + (0.75 × 0.3) = 0.595 + 0.225 = 0.82 or 82%
. An autonomous aircraft's obstacle avoidance system detects an object 500 meters away. If the
aircraft is traveling at 100 m/s, how long does it have to initiate evasive maneuvers?
a) 3 seconds
b) 4 seconds
c) 5 seconds
d) 6 seconds
Answer: c) 5 seconds
Solution:
Time = Distance / Speed
Time = 500 m / 100 m/s = 5 seconds
5. The battery of an autonomous drone has a capacity of 5000 mAh. If the drone's average current
draw is 2.5 A, how long can the drone operate on a single charge?
a) 1 hour
b) 1.5 hours
c) 2 hours
d) 2.5 hours
Answer: c) 2 hours
Solution:
Operation time = Battery capacity / Current draw
Operation time = 5000 mAh / 2500 mA = 2 hours
6. An autonomous aircraft's GPS system has a position accuracy of ±5 meters. If the aircraft needs to
land on a circular pad with a radius of 10 meters, what is the probability that the GPS reading will
place the aircraft within the landing pad?
a) 25%
b) 50%
c) 75%
d) 100%
Answer: c) 75%
Solution:
Area of landing pad = π × r^2 = π × 10^2 = 314 m^2
Area of possible GPS readings = π × (r + accuracy)^2 = π × 15^2 = 707 m^2
Probability = Area of landing pad / Area of possible GPS readings = 314 / 707 ≈ 0.75 or 75%
7. An autonomous drone uses a stereo vision system with two cameras separated by 10 cm. If an
object is detected at a pixel disparity of 20 pixels, and each camera has a focal length of 5 mm with a
pixel size of 5 μm, what is the distance to the object?
a) 1.25 m
b) 2.5 m
c) 3.75 m
d) 5 m
Answer: b) 2.5 m
Solution:
Distance = (Baseline × Focal length) / (Pixel size × Disparity)
Distance = (0.1 m × 0.005 m) / (5 × 10^-6 m × 20) = 2.5 m
8. An autonomous aircraft's collision avoidance system predicts the trajectory of another aircraft. If
the other aircraft is 10 km away and approaching at 200 m/s, how long will it take for the two aircraft
to collide if no evasive action is taken?
a) 40 seconds
b) 45 seconds
c) 50 seconds
d) 55 seconds
Answer: c) 50 seconds
Solution:
Time to collision = Distance / Speed
Time to collision = 10,000 m / 200 m/s = 50 seconds
9. An autonomous drone's path planning algorithm calculates a route that is 5 km long. If the drone's
average speed is 15 m/s, how long will it take to complete the route?
a) 5 minutes 33 seconds
b) 5 minutes 44 seconds
c) 5 minutes 55 seconds
d) 6 minutes 6 seconds
Answer: a) 5 minutes 33 seconds
Solution:
Time = Distance / Speed
Time = 5,000 m / 15 m/s = 333.33 seconds ≈ 5 minutes 33 seconds
10. The control system of an autonomous aircraft operates at 100 Hz. What is the time interval
between two consecutive control loop iterations?
a) 0.001 seconds
b) 0.005 seconds
c) 0.01 seconds
d) 0.1 seconds
Answer: c) 0.01 seconds
Solution:
Time interval = 1 / Frequency
Time interval = 1 / 100 Hz = 0.01 seconds
11. An autonomous drone uses a magnetometer to measure the Earth's magnetic field. If the
magnetometer has a sensitivity of 0.1 μT (microtesla) and the Earth's magnetic field strength is
typically around 50 μT, what is the minimum angular resolution the drone can achieve in detecting its
orientation?
a) 0.1°
b) 0.2°
c) 0.3°
d) 0.4°
Answer: a) 0.1°
Solution:
Angular resolution = arcsin(Sensitivity / Field strength)
Angular resolution = arcsin(0.1 / 50) ≈ 0.1°
12. An autonomous aircraft's machine learning model for object detection has 10 million parameters.
If each parameter is stored as a 32-bit floating-point number, how much memory does the model
require?
a) 20 MB
b) 30 MB
c) 40 MB
d) 50 MB
Answer: c) 40 MB
Solution:
Memory = Number of parameters × Bits per parameter / 8 bits per byte
Memory = 10,000,000 × 32 / 8 = 40,000,000 bytes = 40 MB
13. An autonomous drone's propulsion system consumes 500 W of power. If the drone's battery has
a capacity of 10,000 mAh and operates at 11.1 V, how long can the drone fly?
a) 22 minutes
b) 33 minutes
c) 44 minutes
d) 55 minutes
Answer: b) 33 minutes
Solution:
Battery energy = 10,000 mAh × 11.1 V = 111,000 mWh = 111 Wh
Flight time = Battery energy / Power consumption
Flight time = 111 Wh / 500 W = 0.222 hours ≈ 33 minutes
14. An autonomous aircraft's navigation system uses a Kalman filter to estimate its position. If the
initial position uncertainty is 10 m and the measurement uncertainty is 2 m, what is the estimated
position uncertainty after one update?
a) 1.67 m
b) 1.82 m
c) 1.98 m
d) 2.14 m
Answer: a) 1.67 m
Solution:
Updated uncertainty = (Initial uncertainty × Measurement uncertainty) / (Initial uncertainty +
Measurement uncertainty)
Updated uncertainty = (10 × 2) / (10 + 2) = 1.67 m
15. An autonomous drone's obstacle detection system has a false positive rate of 1% and a true
positive rate of 99%. If the drone encounters 1000 non-obstacle situations and 10 real obstacles
during a flight, how many total obstacle detections will it make?
a) 10
b) 20
c) 30
d) 40
Answer: b) 20
Solution:
False positives = 1% of 1000 = 10
True positives = 99% of 10 = 9.9 ≈ 10
Total detections = False positives + True positives = 10 + 10 = 20
16. An autonomous aircraft's wind estimation algorithm calculates a headwind of 15 m/s. If the
aircraft's airspeed is 100 m/s, what is its ground speed?
a) 75 m/s
b) 85 m/s
c) 95 m/s
d) 105 m/s
Answer: b) 85 m/s
Solution:
Ground speed = Airspeed - Headwind
Ground speed = 100 m/s - 15 m/s = 85 m/s
17. An autonomous drone uses a PID controller for altitude control. If the proportional gain is 2, the
integral gain is 0.1, and the derivative gain is 0.5, what is the control output for an error of 5 meters,
an integral of error of 10 meter-seconds, and a rate of change of error of -2 meters per second?
a) 8.5
b) 9.5
c) 10.5
d) 11.5
Answer: c) 10.5
Solution:
Output = P + I + D
Output = (2 × 5) + (0.1 × 10) + (0.5 × -2)
Output = 10 + 1 - 0.5 = 10.5
18. An autonomous aircraft's path planning algorithm uses A* search. If the heuristic function
consistently underestimates the true cost by 20%, how much longer will the calculated path be
compared to the optimal path, in the worst case?
a) 10%
b) 20%
c) 30%
d) 40%
Answer: b) 20%
Solution:
Worst-case path length = Optimal path length × (1 / (1 - Underestimation))
Worst-case path length = Optimal path length × (1 / (1 - 0.2)) = Optimal path length × 1.25
Percentage increase = (1.25 - 1) × 100% = 25%
19. An autonomous drone's battery management system estimates that the battery has 30% charge
remaining. If the drone consumes 100 W of power and the battery capacity is 10,000 mAh at 11.1 V,
how much longer can the drone fly?
a) 10 minutes
b) 15 minutes
c) 20 minutes
d) 25 minutes
Answer: c) 20 minutes
Solution:
Remaining energy = 30% × 10,000 mAh × 11.1 V = 33,300 mWh = 33.3 Wh
Flight time = Remaining energy / Power consumption
Flight time = 33.3 Wh / 100 W = 0.333 hours = 20 minutes
20. An autonomous aircraft's SLAM (Simultaneous Localization and Mapping) algorithm processes
point cloud data with 1 million points. If each point is represented by 3 floating-point numbers (x, y, z
coordinates) and each floating-point number is 4 bytes, how much memory is required to store the
point cloud?
a) 8 MB
b) 12 MB
c) 16 MB
d) 20 MB
Answer: b) 12 MB
Solution:
Memory = Number of points × Coordinates per point × Bytes per coordinate
Memory = 1,000,000 × 3 × 4 bytes = 12,000,000 bytes = 12 MB
21. An autonomous drone's object tracking algorithm predicts that an object will be at position (10,
5) in 2 seconds. If the object's current position is (2, 1), what is its estimated velocity vector?
a) (3, 1.5) m/s
b) (4, 2) m/s
c) (5, 2.5) m/s
d) (6, 3) m/s
Answer: b) (4, 2) m/s
Solution:
Velocity = (Change in position) / Time
Velocity_x = (10 - 2) / 2 = 4 m/s
Velocity_y = (5 - 1) / 2 = 2 m/s
Velocity vector = (4, 2) m/s
22. An autonomous aircraft's navigation system uses a GPS receiver with a position dilution of
precision (PDOP) of 2.5. If the GPS has a user equivalent range error (UERE) of 5 meters, what is the
expected position accuracy?
a) 10.5 meters
b) 12.5 meters
c) 14.5 meters
d) 16.5 meters
Answer: b) 12.5 meters
Solution:
Position accuracy = PDOP × UERE
Position accuracy = 2.5 × 5 meters = 12.5 meters
23. An autonomous drone's collision avoidance system detects an obstacle 50 meters away,
approaching at a relative velocity of 10 m/s. If the drone's maximum deceleration is 2 m/s^2, what is
the minimum distance at which it must start decelerating to avoid a collision?
a) 12.5 meters
b) 25 meters
c) 37.5 meters
d) 50 meters
Answer: b) 25 meters
Solution:
Using the equation of motion: v^2 = u^2 + 2as
0 = 10^2 + 2(-2)s
s = 100 / 4 = 25 meters
24. An autonomous aircraft's machine learning model for weather prediction has an accuracy of 85%
for predicting clear weather and 75% for predicting stormy weather. If clear weather occurs 70% of
the time, what is the overall accuracy of the model?
a) 80%
b) 82%
c) 84%
d) 86%
Answer: b) 82%
Solution:
Overall accuracy = (Accuracy_clear × Probability_clear) + (Accuracy_stormy × Probability_stormy)
Overall accuracy = (0.85 × 0.7) + (0.75 × 0.3) = 0.595 + 0.225 = 0.82 or 82%
. An autonomous aircraft's obstacle avoidance system detects an object 500 meters away. If the
aircraft is traveling at 100 m/s, how long does it have to initiate evasive maneuvers?
a) 3 seconds
b) 4 seconds
c) 5 seconds
d) 6 seconds
Answer: c) 5 seconds
Solution:
Time = Distance / Speed
Time = 500 m / 100 m/s = 5 seconds
5. The battery of an autonomous drone has a capacity of 5000 mAh. If the drone's average current
draw is 2.5 A, how long can the drone operate on a single charge?
a) 1 hour
b) 1.5 hours
c) 2 hours
d) 2.5 hours
Answer: c) 2 hours
Solution:
Operation time = Battery capacity / Current draw
Operation time = 5000 mAh / 2500 mA = 2 hours
6. An autonomous aircraft's GPS system has a position accuracy of ±5 meters. If the aircraft needs to
land on a circular pad with a radius of 10 meters, what is the probability that the GPS reading will
place the aircraft within the landing pad?
a) 25%
b) 50%
c) 75%
d) 100%
Answer: c) 75%
Solution:
Area of landing pad = π × r^2 = π × 10^2 = 314 m^2
Area of possible GPS readings = π × (r + accuracy)^2 = π × 15^2 = 707 m^2
Probability = Area of landing pad / Area of possible GPS readings = 314 / 707 ≈ 0.75 or 75%
7. An autonomous drone uses a stereo vision system with two cameras separated by 10 cm. If an
object is detected at a pixel disparity of 20 pixels, and each camera has a focal length of 5 mm with a
pixel size of 5 μm, what is the distance to the object?
a) 1.25 m
b) 2.5 m
c) 3.75 m
d) 5 m
Answer: b) 2.5 m
Solution:
Distance = (Baseline × Focal length) / (Pixel size × Disparity)
Distance = (0.1 m × 0.005 m) / (5 × 10^-6 m × 20) = 2.5 m
8. An autonomous aircraft's collision avoidance system predicts the trajectory of another aircraft. If
the other aircraft is 10 km away and approaching at 200 m/s, how long will it take for the two aircraft
to collide if no evasive action is taken?
a) 40 seconds
b) 45 seconds
c) 50 seconds
d) 55 seconds
Answer: c) 50 seconds
Solution:
Time to collision = Distance / Speed
Time to collision = 10,000 m / 200 m/s = 50 seconds
9. An autonomous drone's path planning algorithm calculates a route that is 5 km long. If the drone's
average speed is 15 m/s, how long will it take to complete the route?
a) 5 minutes 33 seconds
b) 5 minutes 44 seconds
c) 5 minutes 55 seconds
d) 6 minutes 6 seconds
Answer: a) 5 minutes 33 seconds
Solution:
Time = Distance / Speed
Time = 5,000 m / 15 m/s = 333.33 seconds ≈ 5 minutes 33 seconds
10. The control system of an autonomous aircraft operates at 100 Hz. What is the time interval
between two consecutive control loop iterations?
a) 0.001 seconds
b) 0.005 seconds
c) 0.01 seconds
d) 0.1 seconds
Answer: c) 0.01 seconds
Solution:
Time interval = 1 / Frequency
Time interval = 1 / 100 Hz = 0.01 seconds
11. An autonomous drone uses a magnetometer to measure the Earth's magnetic field. If the
magnetometer has a sensitivity of 0.1 μT (microtesla) and the Earth's magnetic field strength is
typically around 50 μT, what is the minimum angular resolution the drone can achieve in detecting its
orientation?
a) 0.1°
b) 0.2°
c) 0.3°
d) 0.4°
Answer: a) 0.1°
Solution:
Angular resolution = arcsin(Sensitivity / Field strength)
Angular resolution = arcsin(0.1 / 50) ≈ 0.1°
12. An autonomous aircraft's machine learning model for object detection has 10 million parameters.
If each parameter is stored as a 32-bit floating-point number, how much memory does the model
require?
a) 20 MB
b) 30 MB
c) 40 MB
d) 50 MB
Answer: c) 40 MB
Solution:
Memory = Number of parameters × Bits per parameter / 8 bits per byte
Memory = 10,000,000 × 32 / 8 = 40,000,000 bytes = 40 MB
13. An autonomous drone's propulsion system consumes 500 W of power. If the drone's battery has
a capacity of 10,000 mAh and operates at 11.1 V, how long can the drone fly?
a) 22 minutes
b) 33 minutes
c) 44 minutes
d) 55 minutes
Answer: b) 33 minutes
Solution:
Battery energy = 10,000 mAh × 11.1 V = 111,000 mWh = 111 Wh
Flight time = Battery energy / Power consumption
Flight time = 111 Wh / 500 W = 0.222 hours ≈ 33 minutes
14. An autonomous aircraft's navigation system uses a Kalman filter to estimate its position. If the
initial position uncertainty is 10 m and the measurement uncertainty is 2 m, what is the estimated
position uncertainty after one update?
a) 1.67 m
b) 1.82 m
c) 1.98 m
d) 2.14 m
Answer: a) 1.67 m
Solution:
Updated uncertainty = (Initial uncertainty × Measurement uncertainty) / (Initial uncertainty +
Measurement uncertainty)
Updated uncertainty = (10 × 2) / (10 + 2) = 1.67 m
15. An autonomous drone's obstacle detection system has a false positive rate of 1% and a true
positive rate of 99%. If the drone encounters 1000 non-obstacle situations and 10 real obstacles
during a flight, how many total obstacle detections will it make?
a) 10
b) 20
c) 30
d) 40
Answer: b) 20
Solution:
False positives = 1% of 1000 = 10
True positives = 99% of 10 = 9.9 ≈ 10
Total detections = False positives + True positives = 10 + 10 = 20
16. An autonomous aircraft's wind estimation algorithm calculates a headwind of 15 m/s. If the
aircraft's airspeed is 100 m/s, what is its ground speed?
a) 75 m/s
b) 85 m/s
c) 95 m/s
d) 105 m/s
Answer: b) 85 m/s
Solution:
Ground speed = Airspeed - Headwind
Ground speed = 100 m/s - 15 m/s = 85 m/s
17. An autonomous drone uses a PID controller for altitude control. If the proportional gain is 2, the
integral gain is 0.1, and the derivative gain is 0.5, what is the control output for an error of 5 meters,
an integral of error of 10 meter-seconds, and a rate of change of error of -2 meters per second?
a) 8.5
b) 9.5
c) 10.5
d) 11.5
Answer: c) 10.5
Solution:
Output = P + I + D
Output = (2 × 5) + (0.1 × 10) + (0.5 × -2)
Output = 10 + 1 - 0.5 = 10.5
18. An autonomous aircraft's path planning algorithm uses A* search. If the heuristic function
consistently underestimates the true cost by 20%, how much longer will the calculated path be
compared to the optimal path, in the worst case?
a) 10%
b) 20%
c) 30%
d) 40%
Answer: b) 20%
Solution:
Worst-case path length = Optimal path length × (1 / (1 - Underestimation))
Worst-case path length = Optimal path length × (1 / (1 - 0.2)) = Optimal path length × 1.25
Percentage increase = (1.25 - 1) × 100% = 25%
19. An autonomous drone's battery management system estimates that the battery has 30% charge
remaining. If the drone consumes 100 W of power and the battery capacity is 10,000 mAh at 11.1 V,
how much longer can the drone fly?
a) 10 minutes
b) 15 minutes
c) 20 minutes
d) 25 minutes
Answer: c) 20 minutes
Solution:
Remaining energy = 30% × 10,000 mAh × 11.1 V = 33,300 mWh = 33.3 Wh
Flight time = Remaining energy / Power consumption
Flight time = 33.3 Wh / 100 W = 0.333 hours = 20 minutes
20. An autonomous aircraft's SLAM (Simultaneous Localization and Mapping) algorithm processes
point cloud data with 1 million points. If each point is represented by 3 floating-point numbers (x, y, z
coordinates) and each floating-point number is 4 bytes, how much memory is required to store the
point cloud?
a) 8 MB
b) 12 MB
c) 16 MB
d) 20 MB
Answer: b) 12 MB
Solution:
Memory = Number of points × Coordinates per point × Bytes per coordinate
Memory = 1,000,000 × 3 × 4 bytes = 12,000,000 bytes = 12 MB
21. An autonomous drone's object tracking algorithm predicts that an object will be at position (10,
5) in 2 seconds. If the object's current position is (2, 1), what is its estimated velocity vector?
a) (3, 1.5) m/s
b) (4, 2) m/s
c) (5, 2.5) m/s
d) (6, 3) m/s
Answer: b) (4, 2) m/s
Solution:
Velocity = (Change in position) / Time
Velocity_x = (10 - 2) / 2 = 4 m/s
Velocity_y = (5 - 1) / 2 = 2 m/s
Velocity vector = (4, 2) m/s
22. An autonomous aircraft's navigation system uses a GPS receiver with a position dilution of
precision (PDOP) of 2.5. If the GPS has a user equivalent range error (UERE) of 5 meters, what is the
expected position accuracy?
a) 10.5 meters
b) 12.5 meters
c) 14.5 meters
d) 16.5 meters
Answer: b) 12.5 meters
Solution:
Position accuracy = PDOP × UERE
Position accuracy = 2.5 × 5 meters = 12.5 meters
23. An autonomous drone's collision avoidance system detects an obstacle 50 meters away,
approaching at a relative velocity of 10 m/s. If the drone's maximum deceleration is 2 m/s^2, what is
the minimum distance at which it must start decelerating to avoid a collision?
a) 12.5 meters
b) 25 meters
c) 37.5 meters
d) 50 meters
Answer: b) 25 meters
Solution:
Using the equation of motion: v^2 = u^2 + 2as
0 = 10^2 + 2(-2)s
s = 100 / 4 = 25 meters
24. An autonomous aircraft's machine learning model for weather prediction has an accuracy of 85%
for predicting clear weather and 75% for predicting stormy weather. If clear weather occurs 70% of
the time, what is the overall accuracy of the model?
a) 80%
b) 82%
c) 84%
d) 86%
Answer: b) 82%
Solution:
Overall accuracy = (Accuracy_clear × Probability_clear) + (Accuracy_stormy × Probability_stormy)
Overall accuracy = (0.85 × 0.7) + (0.75 × 0.3) = 0.595 + 0.225 = 0.82 or 82%
. An autonomous aircraft's obstacle avoidance system detects an object 500 meters away. If the
aircraft is traveling at 100 m/s, how long does it have to initiate evasive maneuvers?
a) 3 seconds
b) 4 seconds
c) 5 seconds
d) 6 seconds
Answer: c) 5 seconds
Solution:
Time = Distance / Speed
Time = 500 m / 100 m/s = 5 seconds
5. The battery of an autonomous drone has a capacity of 5000 mAh. If the drone's average current
draw is 2.5 A, how long can the drone operate on a single charge?
a) 1 hour
b) 1.5 hours
c) 2 hours
d) 2.5 hours
Answer: c) 2 hours
Solution:
Operation time = Battery capacity / Current draw
Operation time = 5000 mAh / 2500 mA = 2 hours
6. An autonomous aircraft's GPS system has a position accuracy of ±5 meters. If the aircraft needs to
land on a circular pad with a radius of 10 meters, what is the probability that the GPS reading will
place the aircraft within the landing pad?
a) 25%
b) 50%
c) 75%
d) 100%
Answer: c) 75%
Solution:
Area of landing pad = π × r^2 = π × 10^2 = 314 m^2
Area of possible GPS readings = π × (r + accuracy)^2 = π × 15^2 = 707 m^2
Probability = Area of landing pad / Area of possible GPS readings = 314 / 707 ≈ 0.75 or 75%
7. An autonomous drone uses a stereo vision system with two cameras separated by 10 cm. If an
object is detected at a pixel disparity of 20 pixels, and each camera has a focal length of 5 mm with a
pixel size of 5 μm, what is the distance to the object?
a) 1.25 m
b) 2.5 m
c) 3.75 m
d) 5 m
Answer: b) 2.5 m
Solution:
Distance = (Baseline × Focal length) / (Pixel size × Disparity)
Distance = (0.1 m × 0.005 m) / (5 × 10^-6 m × 20) = 2.5 m
8. An autonomous aircraft's collision avoidance system predicts the trajectory of another aircraft. If
the other aircraft is 10 km away and approaching at 200 m/s, how long will it take for the two aircraft
to collide if no evasive action is taken?
a) 40 seconds
b) 45 seconds
c) 50 seconds
d) 55 seconds
Answer: c) 50 seconds
Solution:
Time to collision = Distance / Speed
Time to collision = 10,000 m / 200 m/s = 50 seconds
9. An autonomous drone's path planning algorithm calculates a route that is 5 km long. If the drone's
average speed is 15 m/s, how long will it take to complete the route?
a) 5 minutes 33 seconds
b) 5 minutes 44 seconds
c) 5 minutes 55 seconds
d) 6 minutes 6 seconds
Answer: a) 5 minutes 33 seconds
Solution:
Time = Distance / Speed
Time = 5,000 m / 15 m/s = 333.33 seconds ≈ 5 minutes 33 seconds
10. The control system of an autonomous aircraft operates at 100 Hz. What is the time interval
between two consecutive control loop iterations?
a) 0.001 seconds
b) 0.005 seconds
c) 0.01 seconds
d) 0.1 seconds
Answer: c) 0.01 seconds
Solution:
Time interval = 1 / Frequency
Time interval = 1 / 100 Hz = 0.01 seconds
11. An autonomous drone uses a magnetometer to measure the Earth's magnetic field. If the
magnetometer has a sensitivity of 0.1 μT (microtesla) and the Earth's magnetic field strength is
typically around 50 μT, what is the minimum angular resolution the drone can achieve in detecting its
orientation?
a) 0.1°
b) 0.2°
c) 0.3°
d) 0.4°
Answer: a) 0.1°
Solution:
Angular resolution = arcsin(Sensitivity / Field strength)
Angular resolution = arcsin(0.1 / 50) ≈ 0.1°
12. An autonomous aircraft's machine learning model for object detection has 10 million parameters.
If each parameter is stored as a 32-bit floating-point number, how much memory does the model
require?
a) 20 MB
b) 30 MB
c) 40 MB
d) 50 MB
Answer: c) 40 MB
Solution:
Memory = Number of parameters × Bits per parameter / 8 bits per byte
Memory = 10,000,000 × 32 / 8 = 40,000,000 bytes = 40 MB
13. An autonomous drone's propulsion system consumes 500 W of power. If the drone's battery has
a capacity of 10,000 mAh and operates at 11.1 V, how long can the drone fly?
a) 22 minutes
b) 33 minutes
c) 44 minutes
d) 55 minutes
Answer: b) 33 minutes
Solution:
Battery energy = 10,000 mAh × 11.1 V = 111,000 mWh = 111 Wh
Flight time = Battery energy / Power consumption
Flight time = 111 Wh / 500 W = 0.222 hours ≈ 33 minutes
14. An autonomous aircraft's navigation system uses a Kalman filter to estimate its position. If the
initial position uncertainty is 10 m and the measurement uncertainty is 2 m, what is the estimated
position uncertainty after one update?
a) 1.67 m
b) 1.82 m
c) 1.98 m
d) 2.14 m
Answer: a) 1.67 m
Solution:
Updated uncertainty = (Initial uncertainty × Measurement uncertainty) / (Initial uncertainty +
Measurement uncertainty)
Updated uncertainty = (10 × 2) / (10 + 2) = 1.67 m
15. An autonomous drone's obstacle detection system has a false positive rate of 1% and a true
positive rate of 99%. If the drone encounters 1000 non-obstacle situations and 10 real obstacles
during a flight, how many total obstacle detections will it make?
a) 10
b) 20
c) 30
d) 40
Answer: b) 20
Solution:
False positives = 1% of 1000 = 10
True positives = 99% of 10 = 9.9 ≈ 10
Total detections = False positives + True positives = 10 + 10 = 20
16. An autonomous aircraft's wind estimation algorithm calculates a headwind of 15 m/s. If the
aircraft's airspeed is 100 m/s, what is its ground speed?
a) 75 m/s
b) 85 m/s
c) 95 m/s
d) 105 m/s
Answer: b) 85 m/s
Solution:
Ground speed = Airspeed - Headwind
Ground speed = 100 m/s - 15 m/s = 85 m/s
17. An autonomous drone uses a PID controller for altitude control. If the proportional gain is 2, the
integral gain is 0.1, and the derivative gain is 0.5, what is the control output for an error of 5 meters,
an integral of error of 10 meter-seconds, and a rate of change of error of -2 meters per second?
a) 8.5
b) 9.5
c) 10.5
d) 11.5
Answer: c) 10.5
Solution:
Output = P + I + D
Output = (2 × 5) + (0.1 × 10) + (0.5 × -2)
Output = 10 + 1 - 0.5 = 10.5
18. An autonomous aircraft's path planning algorithm uses A* search. If the heuristic function
consistently underestimates the true cost by 20%, how much longer will the calculated path be
compared to the optimal path, in the worst case?
a) 10%
b) 20%
c) 30%
d) 40%
Answer: b) 20%
Solution:
Worst-case path length = Optimal path length × (1 / (1 - Underestimation))
Worst-case path length = Optimal path length × (1 / (1 - 0.2)) = Optimal path length × 1.25
Percentage increase = (1.25 - 1) × 100% = 25%
19. An autonomous drone's battery management system estimates that the battery has 30% charge
remaining. If the drone consumes 100 W of power and the battery capacity is 10,000 mAh at 11.1 V,
how much longer can the drone fly?
a) 10 minutes
b) 15 minutes
c) 20 minutes
d) 25 minutes
Answer: c) 20 minutes
Solution:
Remaining energy = 30% × 10,000 mAh × 11.1 V = 33,300 mWh = 33.3 Wh
Flight time = Remaining energy / Power consumption
Flight time = 33.3 Wh / 100 W = 0.333 hours = 20 minutes
20. An autonomous aircraft's SLAM (Simultaneous Localization and Mapping) algorithm processes
point cloud data with 1 million points. If each point is represented by 3 floating-point numbers (x, y, z
coordinates) and each floating-point number is 4 bytes, how much memory is required to store the
point cloud?
a) 8 MB
b) 12 MB
c) 16 MB
d) 20 MB
Answer: b) 12 MB
Solution:
Memory = Number of points × Coordinates per point × Bytes per coordinate
Memory = 1,000,000 × 3 × 4 bytes = 12,000,000 bytes = 12 MB
21. An autonomous drone's object tracking algorithm predicts that an object will be at position (10,
5) in 2 seconds. If the object's current position is (2, 1), what is its estimated velocity vector?
a) (3, 1.5) m/s
b) (4, 2) m/s
c) (5, 2.5) m/s
d) (6, 3) m/s
Answer: b) (4, 2) m/s
Solution:
Velocity = (Change in position) / Time
Velocity_x = (10 - 2) / 2 = 4 m/s
Velocity_y = (5 - 1) / 2 = 2 m/s
Velocity vector = (4, 2) m/s
22. An autonomous aircraft's navigation system uses a GPS receiver with a position dilution of
precision (PDOP) of 2.5. If the GPS has a user equivalent range error (UERE) of 5 meters, what is the
expected position accuracy?
a) 10.5 meters
b) 12.5 meters
c) 14.5 meters
d) 16.5 meters
Answer: b) 12.5 meters
Solution:
Position accuracy = PDOP × UERE
Position accuracy = 2.5 × 5 meters = 12.5 meters
23. An autonomous drone's collision avoidance system detects an obstacle 50 meters away,
approaching at a relative velocity of 10 m/s. If the drone's maximum deceleration is 2 m/s^2, what is
the minimum distance at which it must start decelerating to avoid a collision?
a) 12.5 meters
b) 25 meters
c) 37.5 meters
d) 50 meters
Answer: b) 25 meters
Solution:
Using the equation of motion: v^2 = u^2 + 2as
0 = 10^2 + 2(-2)s
s = 100 / 4 = 25 meters
24. An autonomous aircraft's machine learning model for weather prediction has an accuracy of 85%
for predicting clear weather and 75% for predicting stormy weather. If clear weather occurs 70% of
the time, what is the overall accuracy of the model?
a) 80%
b) 82%
c) 84%
d) 86%
Answer: b) 82%
Solution:
Overall accuracy = (Accuracy_clear × Probability_clear) + (Accuracy_stormy × Probability_stormy)
Overall accuracy = (0.85 × 0.7) + (0.75 × 0.3) = 0.595 + 0.225 = 0.82 or 82%
. An autonomous aircraft's obstacle avoidance system detects an object 500 meters away. If the
aircraft is traveling at 100 m/s, how long does it have to initiate evasive maneuvers?
a) 3 seconds
b) 4 seconds
c) 5 seconds
d) 6 seconds
Answer: c) 5 seconds
Solution:
Time = Distance / Speed
Time = 500 m / 100 m/s = 5 seconds
5. The battery of an autonomous drone has a capacity of 5000 mAh. If the drone's average current
draw is 2.5 A, how long can the drone operate on a single charge?
a) 1 hour
b) 1.5 hours
c) 2 hours
d) 2.5 hours
Answer: c) 2 hours
Solution:
Operation time = Battery capacity / Current draw
Operation time = 5000 mAh / 2500 mA = 2 hours
6. An autonomous aircraft's GPS system has a position accuracy of ±5 meters. If the aircraft needs to
land on a circular pad with a radius of 10 meters, what is the probability that the GPS reading will
place the aircraft within the landing pad?
a) 25%
b) 50%
c) 75%
d) 100%
Answer: c) 75%
Solution:
Area of landing pad = π × r^2 = π × 10^2 = 314 m^2
Area of possible GPS readings = π × (r + accuracy)^2 = π × 15^2 = 707 m^2
Probability = Area of landing pad / Area of possible GPS readings = 314 / 707 ≈ 0.75 or 75%
7. An autonomous drone uses a stereo vision system with two cameras separated by 10 cm. If an
object is detected at a pixel disparity of 20 pixels, and each camera has a focal length of 5 mm with a
pixel size of 5 μm, what is the distance to the object?
a) 1.25 m
b) 2.5 m
c) 3.75 m
d) 5 m
Answer: b) 2.5 m
Solution:
Distance = (Baseline × Focal length) / (Pixel size × Disparity)
Distance = (0.1 m × 0.005 m) / (5 × 10^-6 m × 20) = 2.5 m
8. An autonomous aircraft's collision avoidance system predicts the trajectory of another aircraft. If
the other aircraft is 10 km away and approaching at 200 m/s, how long will it take for the two aircraft
to collide if no evasive action is taken?
a) 40 seconds
b) 45 seconds
c) 50 seconds
d) 55 seconds
Answer: c) 50 seconds
Solution:
Time to collision = Distance / Speed
Time to collision = 10,000 m / 200 m/s = 50 seconds
9. An autonomous drone's path planning algorithm calculates a route that is 5 km long. If the drone's
average speed is 15 m/s, how long will it take to complete the route?
a) 5 minutes 33 seconds
b) 5 minutes 44 seconds
c) 5 minutes 55 seconds
d) 6 minutes 6 seconds
Answer: a) 5 minutes 33 seconds
Solution:
Time = Distance / Speed
Time = 5,000 m / 15 m/s = 333.33 seconds ≈ 5 minutes 33 seconds
10. The control system of an autonomous aircraft operates at 100 Hz. What is the time interval
between two consecutive control loop iterations?
a) 0.001 seconds
b) 0.005 seconds
c) 0.01 seconds
d) 0.1 seconds
Answer: c) 0.01 seconds
Solution:
Time interval = 1 / Frequency
Time interval = 1 / 100 Hz = 0.01 seconds
11. An autonomous drone uses a magnetometer to measure the Earth's magnetic field. If the
magnetometer has a sensitivity of 0.1 μT (microtesla) and the Earth's magnetic field strength is
typically around 50 μT, what is the minimum angular resolution the drone can achieve in detecting its
orientation?
a) 0.1°
b) 0.2°
c) 0.3°
d) 0.4°
Answer: a) 0.1°
Solution:
Angular resolution = arcsin(Sensitivity / Field strength)
Angular resolution = arcsin(0.1 / 50) ≈ 0.1°
12. An autonomous aircraft's machine learning model for object detection has 10 million parameters.
If each parameter is stored as a 32-bit floating-point number, how much memory does the model
require?
a) 20 MB
b) 30 MB
c) 40 MB
d) 50 MB
Answer: c) 40 MB
Solution:
Memory = Number of parameters × Bits per parameter / 8 bits per byte
Memory = 10,000,000 × 32 / 8 = 40,000,000 bytes = 40 MB
13. An autonomous drone's propulsion system consumes 500 W of power. If the drone's battery has
a capacity of 10,000 mAh and operates at 11.1 V, how long can the drone fly?
a) 22 minutes
b) 33 minutes
c) 44 minutes
d) 55 minutes
Answer: b) 33 minutes
Solution:
Battery energy = 10,000 mAh × 11.1 V = 111,000 mWh = 111 Wh
Flight time = Battery energy / Power consumption
Flight time = 111 Wh / 500 W = 0.222 hours ≈ 33 minutes
14. An autonomous aircraft's navigation system uses a Kalman filter to estimate its position. If the
initial position uncertainty is 10 m and the measurement uncertainty is 2 m, what is the estimated
position uncertainty after one update?
a) 1.67 m
b) 1.82 m
c) 1.98 m
d) 2.14 m
Answer: a) 1.67 m
Solution:
Updated uncertainty = (Initial uncertainty × Measurement uncertainty) / (Initial uncertainty +
Measurement uncertainty)
Updated uncertainty = (10 × 2) / (10 + 2) = 1.67 m
15. An autonomous drone's obstacle detection system has a false positive rate of 1% and a true
positive rate of 99%. If the drone encounters 1000 non-obstacle situations and 10 real obstacles
during a flight, how many total obstacle detections will it make?
a) 10
b) 20
c) 30
d) 40
Answer: b) 20
Solution:
False positives = 1% of 1000 = 10
True positives = 99% of 10 = 9.9 ≈ 10
Total detections = False positives + True positives = 10 + 10 = 20
16. An autonomous aircraft's wind estimation algorithm calculates a headwind of 15 m/s. If the
aircraft's airspeed is 100 m/s, what is its ground speed?
a) 75 m/s
b) 85 m/s
c) 95 m/s
d) 105 m/s
Answer: b) 85 m/s
Solution:
Ground speed = Airspeed - Headwind
Ground speed = 100 m/s - 15 m/s = 85 m/s
17. An autonomous drone uses a PID controller for altitude control. If the proportional gain is 2, the
integral gain is 0.1, and the derivative gain is 0.5, what is the control output for an error of 5 meters,
an integral of error of 10 meter-seconds, and a rate of change of error of -2 meters per second?
a) 8.5
b) 9.5
c) 10.5
d) 11.5
Answer: c) 10.5
Solution:
Output = P + I + D
Output = (2 × 5) + (0.1 × 10) + (0.5 × -2)
Output = 10 + 1 - 0.5 = 10.5
18. An autonomous aircraft's path planning algorithm uses A* search. If the heuristic function
consistently underestimates the true cost by 20%, how much longer will the calculated path be
compared to the optimal path, in the worst case?
a) 10%
b) 20%
c) 30%
d) 40%
Answer: b) 20%
Solution:
Worst-case path length = Optimal path length × (1 / (1 - Underestimation))
Worst-case path length = Optimal path length × (1 / (1 - 0.2)) = Optimal path length × 1.25
Percentage increase = (1.25 - 1) × 100% = 25%
19. An autonomous drone's battery management system estimates that the battery has 30% charge
remaining. If the drone consumes 100 W of power and the battery capacity is 10,000 mAh at 11.1 V,
how much longer can the drone fly?
a) 10 minutes
b) 15 minutes
c) 20 minutes
d) 25 minutes
Answer: c) 20 minutes
Solution:
Remaining energy = 30% × 10,000 mAh × 11.1 V = 33,300 mWh = 33.3 Wh
Flight time = Remaining energy / Power consumption
Flight time = 33.3 Wh / 100 W = 0.333 hours = 20 minutes
20. An autonomous aircraft's SLAM (Simultaneous Localization and Mapping) algorithm processes
point cloud data with 1 million points. If each point is represented by 3 floating-point numbers (x, y, z
coordinates) and each floating-point number is 4 bytes, how much memory is required to store the
point cloud?
a) 8 MB
b) 12 MB
c) 16 MB
d) 20 MB
Answer: b) 12 MB
Solution:
Memory = Number of points × Coordinates per point × Bytes per coordinate
Memory = 1,000,000 × 3 × 4 bytes = 12,000,000 bytes = 12 MB
21. An autonomous drone's object tracking algorithm predicts that an object will be at position (10,
5) in 2 seconds. If the object's current position is (2, 1), what is its estimated velocity vector?
a) (3, 1.5) m/s
b) (4, 2) m/s
c) (5, 2.5) m/s
d) (6, 3) m/s
Answer: b) (4, 2) m/s
Solution:
Velocity = (Change in position) / Time
Velocity_x = (10 - 2) / 2 = 4 m/s
Velocity_y = (5 - 1) / 2 = 2 m/s
Velocity vector = (4, 2) m/s
22. An autonomous aircraft's navigation system uses a GPS receiver with a position dilution of
precision (PDOP) of 2.5. If the GPS has a user equivalent range error (UERE) of 5 meters, what is the
expected position accuracy?
a) 10.5 meters
b) 12.5 meters
c) 14.5 meters
d) 16.5 meters
Answer: b) 12.5 meters
Solution:
Position accuracy = PDOP × UERE
Position accuracy = 2.5 × 5 meters = 12.5 meters
23. An autonomous drone's collision avoidance system detects an obstacle 50 meters away,
approaching at a relative velocity of 10 m/s. If the drone's maximum deceleration is 2 m/s^2, what is
the minimum distance at which it must start decelerating to avoid a collision?
a) 12.5 meters
b) 25 meters
c) 37.5 meters
d) 50 meters
Answer: b) 25 meters
Solution:
Using the equation of motion: v^2 = u^2 + 2as
0 = 10^2 + 2(-2)s
s = 100 / 4 = 25 meters
24. An autonomous aircraft's machine learning model for weather prediction has an accuracy of 85%
for predicting clear weather and 75% for predicting stormy weather. If clear weather occurs 70% of
the time, what is the overall accuracy of the model?
a) 80%
b) 82%
c) 84%
d) 86%
Answer: b) 82%
Solution:
Overall accuracy = (Accuracy_clear × Probability_clear) + (Accuracy_stormy × Probability_stormy)
Overall accuracy = (0.85 × 0.7) + (0.75 × 0.3) = 0.595 + 0.225 = 0.82 or 82%
. An autonomous aircraft's obstacle avoidance system detects an object 500 meters away. If the
aircraft is traveling at 100 m/s, how long does it have to initiate evasive maneuvers?
a) 3 seconds
b) 4 seconds
c) 5 seconds
d) 6 seconds
Answer: c) 5 seconds
Solution:
Time = Distance / Speed
Time = 500 m / 100 m/s = 5 seconds
5. The battery of an autonomous drone has a capacity of 5000 mAh. If the drone's average current
draw is 2.5 A, how long can the drone operate on a single charge?
a) 1 hour
b) 1.5 hours
c) 2 hours
d) 2.5 hours
Answer: c) 2 hours
Solution:
Operation time = Battery capacity / Current draw
Operation time = 5000 mAh / 2500 mA = 2 hours
6. An autonomous aircraft's GPS system has a position accuracy of ±5 meters. If the aircraft needs to
land on a circular pad with a radius of 10 meters, what is the probability that the GPS reading will
place the aircraft within the landing pad?
a) 25%
b) 50%
c) 75%
d) 100%
Answer: c) 75%
Solution:
Area of landing pad = π × r^2 = π × 10^2 = 314 m^2
Area of possible GPS readings = π × (r + accuracy)^2 = π × 15^2 = 707 m^2
Probability = Area of landing pad / Area of possible GPS readings = 314 / 707 ≈ 0.75 or 75%
7. An autonomous drone uses a stereo vision system with two cameras separated by 10 cm. If an
object is detected at a pixel disparity of 20 pixels, and each camera has a focal length of 5 mm with a
pixel size of 5 μm, what is the distance to the object?
a) 1.25 m
b) 2.5 m
c) 3.75 m
d) 5 m
Answer: b) 2.5 m
Solution:
Distance = (Baseline × Focal length) / (Pixel size × Disparity)
Distance = (0.1 m × 0.005 m) / (5 × 10^-6 m × 20) = 2.5 m
8. An autonomous aircraft's collision avoidance system predicts the trajectory of another aircraft. If
the other aircraft is 10 km away and approaching at 200 m/s, how long will it take for the two aircraft
to collide if no evasive action is taken?
a) 40 seconds
b) 45 seconds
c) 50 seconds
d) 55 seconds
Answer: c) 50 seconds
Solution:
Time to collision = Distance / Speed
Time to collision = 10,000 m / 200 m/s = 50 seconds
9. An autonomous drone's path planning algorithm calculates a route that is 5 km long. If the drone's
average speed is 15 m/s, how long will it take to complete the route?
a) 5 minutes 33 seconds
b) 5 minutes 44 seconds
c) 5 minutes 55 seconds
d) 6 minutes 6 seconds
Answer: a) 5 minutes 33 seconds
Solution:
Time = Distance / Speed
Time = 5,000 m / 15 m/s = 333.33 seconds ≈ 5 minutes 33 seconds
10. The control system of an autonomous aircraft operates at 100 Hz. What is the time interval
between two consecutive control loop iterations?
a) 0.001 seconds
b) 0.005 seconds
c) 0.01 seconds
d) 0.1 seconds
Answer: c) 0.01 seconds
Solution:
Time interval = 1 / Frequency
Time interval = 1 / 100 Hz = 0.01 seconds
11. An autonomous drone uses a magnetometer to measure the Earth's magnetic field. If the
magnetometer has a sensitivity of 0.1 μT (microtesla) and the Earth's magnetic field strength is
typically around 50 μT, what is the minimum angular resolution the drone can achieve in detecting its
orientation?
a) 0.1°
b) 0.2°
c) 0.3°
d) 0.4°
Answer: a) 0.1°
Solution:
Angular resolution = arcsin(Sensitivity / Field strength)
Angular resolution = arcsin(0.1 / 50) ≈ 0.1°
12. An autonomous aircraft's machine learning model for object detection has 10 million parameters.
If each parameter is stored as a 32-bit floating-point number, how much memory does the model
require?
a) 20 MB
b) 30 MB
c) 40 MB
d) 50 MB
Answer: c) 40 MB
Solution:
Memory = Number of parameters × Bits per parameter / 8 bits per byte
Memory = 10,000,000 × 32 / 8 = 40,000,000 bytes = 40 MB
13. An autonomous drone's propulsion system consumes 500 W of power. If the drone's battery has
a capacity of 10,000 mAh and operates at 11.1 V, how long can the drone fly?
a) 22 minutes
b) 33 minutes
c) 44 minutes
d) 55 minutes
Answer: b) 33 minutes
Solution:
Battery energy = 10,000 mAh × 11.1 V = 111,000 mWh = 111 Wh
Flight time = Battery energy / Power consumption
Flight time = 111 Wh / 500 W = 0.222 hours ≈ 33 minutes
14. An autonomous aircraft's navigation system uses a Kalman filter to estimate its position. If the
initial position uncertainty is 10 m and the measurement uncertainty is 2 m, what is the estimated
position uncertainty after one update?
a) 1.67 m
b) 1.82 m
c) 1.98 m
d) 2.14 m
Answer: a) 1.67 m
Solution:
Updated uncertainty = (Initial uncertainty × Measurement uncertainty) / (Initial uncertainty +
Measurement uncertainty)
Updated uncertainty = (10 × 2) / (10 + 2) = 1.67 m
15. An autonomous drone's obstacle detection system has a false positive rate of 1% and a true
positive rate of 99%. If the drone encounters 1000 non-obstacle situations and 10 real obstacles
during a flight, how many total obstacle detections will it make?
a) 10
b) 20
c) 30
d) 40
Answer: b) 20
Solution:
False positives = 1% of 1000 = 10
True positives = 99% of 10 = 9.9 ≈ 10
Total detections = False positives + True positives = 10 + 10 = 20
16. An autonomous aircraft's wind estimation algorithm calculates a headwind of 15 m/s. If the
aircraft's airspeed is 100 m/s, what is its ground speed?
a) 75 m/s
b) 85 m/s
c) 95 m/s
d) 105 m/s
Answer: b) 85 m/s
Solution:
Ground speed = Airspeed - Headwind
Ground speed = 100 m/s - 15 m/s = 85 m/s
17. An autonomous drone uses a PID controller for altitude control. If the proportional gain is 2, the
integral gain is 0.1, and the derivative gain is 0.5, what is the control output for an error of 5 meters,
an integral of error of 10 meter-seconds, and a rate of change of error of -2 meters per second?
a) 8.5
b) 9.5
c) 10.5
d) 11.5
Answer: c) 10.5
Solution:
Output = P + I + D
Output = (2 × 5) + (0.1 × 10) + (0.5 × -2)
Output = 10 + 1 - 0.5 = 10.5
18. An autonomous aircraft's path planning algorithm uses A* search. If the heuristic function
consistently underestimates the true cost by 20%, how much longer will the calculated path be
compared to the optimal path, in the worst case?
a) 10%
b) 20%
c) 30%
d) 40%
Answer: b) 20%
Solution:
Worst-case path length = Optimal path length × (1 / (1 - Underestimation))
Worst-case path length = Optimal path length × (1 / (1 - 0.2)) = Optimal path length × 1.25
Percentage increase = (1.25 - 1) × 100% = 25%
19. An autonomous drone's battery management system estimates that the battery has 30% charge
remaining. If the drone consumes 100 W of power and the battery capacity is 10,000 mAh at 11.1 V,
how much longer can the drone fly?
a) 10 minutes
b) 15 minutes
c) 20 minutes
d) 25 minutes
Answer: c) 20 minutes
Solution:
Remaining energy = 30% × 10,000 mAh × 11.1 V = 33,300 mWh = 33.3 Wh
Flight time = Remaining energy / Power consumption
Flight time = 33.3 Wh / 100 W = 0.333 hours = 20 minutes
20. An autonomous aircraft's SLAM (Simultaneous Localization and Mapping) algorithm processes
point cloud data with 1 million points. If each point is represented by 3 floating-point numbers (x, y, z
coordinates) and each floating-point number is 4 bytes, how much memory is required to store the
point cloud?
a) 8 MB
b) 12 MB
c) 16 MB
d) 20 MB
Answer: b) 12 MB
Solution:
Memory = Number of points × Coordinates per point × Bytes per coordinate
Memory = 1,000,000 × 3 × 4 bytes = 12,000,000 bytes = 12 MB
21. An autonomous drone's object tracking algorithm predicts that an object will be at position (10,
5) in 2 seconds. If the object's current position is (2, 1), what is its estimated velocity vector?
a) (3, 1.5) m/s
b) (4, 2) m/s
c) (5, 2.5) m/s
d) (6, 3) m/s
Answer: b) (4, 2) m/s
Solution:
Velocity = (Change in position) / Time
Velocity_x = (10 - 2) / 2 = 4 m/s
Velocity_y = (5 - 1) / 2 = 2 m/s
Velocity vector = (4, 2) m/s
22. An autonomous aircraft's navigation system uses a GPS receiver with a position dilution of
precision (PDOP) of 2.5. If the GPS has a user equivalent range error (UERE) of 5 meters, what is the
expected position accuracy?
a) 10.5 meters
b) 12.5 meters
c) 14.5 meters
d) 16.5 meters
Answer: b) 12.5 meters
Solution:
Position accuracy = PDOP × UERE
Position accuracy = 2.5 × 5 meters = 12.5 meters
23. An autonomous drone's collision avoidance system detects an obstacle 50 meters away,
approaching at a relative velocity of 10 m/s. If the drone's maximum deceleration is 2 m/s^2, what is
the minimum distance at which it must start decelerating to avoid a collision?
a) 12.5 meters
b) 25 meters
c) 37.5 meters
d) 50 meters
Answer: b) 25 meters
Solution:
Using the equation of motion: v^2 = u^2 + 2as
0 = 10^2 + 2(-2)s
s = 100 / 4 = 25 meters
24. An autonomous aircraft's machine learning model for weather prediction has an accuracy of 85%
for predicting clear weather and 75% for predicting stormy weather. If clear weather occurs 70% of
the time, what is the overall accuracy of the model?
a) 80%
b) 82%
c) 84%
d) 86%
Answer: b) 82%
Solution:
Overall accuracy = (Accuracy_clear × Probability_clear) + (Accuracy_stormy × Probability_stormy)
Overall accuracy = (0.85 × 0.7) + (0.75 × 0.3) = 0.595 + 0.225 = 0.82 or 82%
. An autonomous aircraft's obstacle avoidance system detects an object 500 meters away. If the
aircraft is traveling at 100 m/s, how long does it have to initiate evasive maneuvers?
a) 3 seconds
b) 4 seconds
c) 5 seconds
d) 6 seconds
Answer: c) 5 seconds
Solution:
Time = Distance / Speed
Time = 500 m / 100 m/s = 5 seconds
5. The battery of an autonomous drone has a capacity of 5000 mAh. If the drone's average current
draw is 2.5 A, how long can the drone operate on a single charge?
a) 1 hour
b) 1.5 hours
c) 2 hours
d) 2.5 hours
Answer: c) 2 hours
Solution:
Operation time = Battery capacity / Current draw
Operation time = 5000 mAh / 2500 mA = 2 hours
6. An autonomous aircraft's GPS system has a position accuracy of ±5 meters. If the aircraft needs to
land on a circular pad with a radius of 10 meters, what is the probability that the GPS reading will
place the aircraft within the landing pad?
a) 25%
b) 50%
c) 75%
d) 100%
Answer: c) 75%
Solution:
Area of landing pad = π × r^2 = π × 10^2 = 314 m^2
Area of possible GPS readings = π × (r + accuracy)^2 = π × 15^2 = 707 m^2
Probability = Area of landing pad / Area of possible GPS readings = 314 / 707 ≈ 0.75 or 75%
7. An autonomous drone uses a stereo vision system with two cameras separated by 10 cm. If an
object is detected at a pixel disparity of 20 pixels, and each camera has a focal length of 5 mm with a
pixel size of 5 μm, what is the distance to the object?
a) 1.25 m
b) 2.5 m
c) 3.75 m
d) 5 m
Answer: b) 2.5 m
Solution:
Distance = (Baseline × Focal length) / (Pixel size × Disparity)
Distance = (0.1 m × 0.005 m) / (5 × 10^-6 m × 20) = 2.5 m
8. An autonomous aircraft's collision avoidance system predicts the trajectory of another aircraft. If
the other aircraft is 10 km away and approaching at 200 m/s, how long will it take for the two aircraft
to collide if no evasive action is taken?
a) 40 seconds
b) 45 seconds
c) 50 seconds
d) 55 seconds
Answer: c) 50 seconds
Solution:
Time to collision = Distance / Speed
Time to collision = 10,000 m / 200 m/s = 50 seconds
9. An autonomous drone's path planning algorithm calculates a route that is 5 km long. If the drone's
average speed is 15 m/s, how long will it take to complete the route?
a) 5 minutes 33 seconds
b) 5 minutes 44 seconds
c) 5 minutes 55 seconds
d) 6 minutes 6 seconds
Answer: a) 5 minutes 33 seconds
Solution:
Time = Distance / Speed
Time = 5,000 m / 15 m/s = 333.33 seconds ≈ 5 minutes 33 seconds
10. The control system of an autonomous aircraft operates at 100 Hz. What is the time interval
between two consecutive control loop iterations?
a) 0.001 seconds
b) 0.005 seconds
c) 0.01 seconds
d) 0.1 seconds
Answer: c) 0.01 seconds
Solution:
Time interval = 1 / Frequency
Time interval = 1 / 100 Hz = 0.01 seconds
11. An autonomous drone uses a magnetometer to measure the Earth's magnetic field. If the
magnetometer has a sensitivity of 0.1 μT (microtesla) and the Earth's magnetic field strength is
typically around 50 μT, what is the minimum angular resolution the drone can achieve in detecting its
orientation?
a) 0.1°
b) 0.2°
c) 0.3°
d) 0.4°
Answer: a) 0.1°
Solution:
Angular resolution = arcsin(Sensitivity / Field strength)
Angular resolution = arcsin(0.1 / 50) ≈ 0.1°
12. An autonomous aircraft's machine learning model for object detection has 10 million parameters.
If each parameter is stored as a 32-bit floating-point number, how much memory does the model
require?
a) 20 MB
b) 30 MB
c) 40 MB
d) 50 MB
Answer: c) 40 MB
Solution:
Memory = Number of parameters × Bits per parameter / 8 bits per byte
Memory = 10,000,000 × 32 / 8 = 40,000,000 bytes = 40 MB
13. An autonomous drone's propulsion system consumes 500 W of power. If the drone's battery has
a capacity of 10,000 mAh and operates at 11.1 V, how long can the drone fly?
a) 22 minutes
b) 33 minutes
c) 44 minutes
d) 55 minutes
Answer: b) 33 minutes
Solution:
Battery energy = 10,000 mAh × 11.1 V = 111,000 mWh = 111 Wh
Flight time = Battery energy / Power consumption
Flight time = 111 Wh / 500 W = 0.222 hours ≈ 33 minutes
14. An autonomous aircraft's navigation system uses a Kalman filter to estimate its position. If the
initial position uncertainty is 10 m and the measurement uncertainty is 2 m, what is the estimated
position uncertainty after one update?
a) 1.67 m
b) 1.82 m
c) 1.98 m
d) 2.14 m
Answer: a) 1.67 m
Solution:
Updated uncertainty = (Initial uncertainty × Measurement uncertainty) / (Initial uncertainty +
Measurement uncertainty)
Updated uncertainty = (10 × 2) / (10 + 2) = 1.67 m
15. An autonomous drone's obstacle detection system has a false positive rate of 1% and a true
positive rate of 99%. If the drone encounters 1000 non-obstacle situations and 10 real obstacles
during a flight, how many total obstacle detections will it make?
a) 10
b) 20
c) 30
d) 40
Answer: b) 20
Solution:
False positives = 1% of 1000 = 10
True positives = 99% of 10 = 9.9 ≈ 10
Total detections = False positives + True positives = 10 + 10 = 20
16. An autonomous aircraft's wind estimation algorithm calculates a headwind of 15 m/s. If the
aircraft's airspeed is 100 m/s, what is its ground speed?
a) 75 m/s
b) 85 m/s
c) 95 m/s
d) 105 m/s
Answer: b) 85 m/s
Solution:
Ground speed = Airspeed - Headwind
Ground speed = 100 m/s - 15 m/s = 85 m/s
17. An autonomous drone uses a PID controller for altitude control. If the proportional gain is 2, the
integral gain is 0.1, and the derivative gain is 0.5, what is the control output for an error of 5 meters,
an integral of error of 10 meter-seconds, and a rate of change of error of -2 meters per second?
a) 8.5
b) 9.5
c) 10.5
d) 11.5
Answer: c) 10.5
Solution:
Output = P + I + D
Output = (2 × 5) + (0.1 × 10) + (0.5 × -2)
Output = 10 + 1 - 0.5 = 10.5
18. An autonomous aircraft's path planning algorithm uses A* search. If the heuristic function
consistently underestimates the true cost by 20%, how much longer will the calculated path be
compared to the optimal path, in the worst case?
a) 10%
b) 20%
c) 30%
d) 40%
Answer: b) 20%
Solution:
Worst-case path length = Optimal path length × (1 / (1 - Underestimation))
Worst-case path length = Optimal path length × (1 / (1 - 0.2)) = Optimal path length × 1.25
Percentage increase = (1.25 - 1) × 100% = 25%
19. An autonomous drone's battery management system estimates that the battery has 30% charge
remaining. If the drone consumes 100 W of power and the battery capacity is 10,000 mAh at 11.1 V,
how much longer can the drone fly?
a) 10 minutes
b) 15 minutes
c) 20 minutes
d) 25 minutes
Answer: c) 20 minutes
Solution:
Remaining energy = 30% × 10,000 mAh × 11.1 V = 33,300 mWh = 33.3 Wh
Flight time = Remaining energy / Power consumption
Flight time = 33.3 Wh / 100 W = 0.333 hours = 20 minutes
20. An autonomous aircraft's SLAM (Simultaneous Localization and Mapping) algorithm processes
point cloud data with 1 million points. If each point is represented by 3 floating-point numbers (x, y, z
coordinates) and each floating-point number is 4 bytes, how much memory is required to store the
point cloud?
a) 8 MB
b) 12 MB
c) 16 MB
d) 20 MB
Answer: b) 12 MB
Solution:
Memory = Number of points × Coordinates per point × Bytes per coordinate
Memory = 1,000,000 × 3 × 4 bytes = 12,000,000 bytes = 12 MB
21. An autonomous drone's object tracking algorithm predicts that an object will be at position (10,
5) in 2 seconds. If the object's current position is (2, 1), what is its estimated velocity vector?
a) (3, 1.5) m/s
b) (4, 2) m/s
c) (5, 2.5) m/s
d) (6, 3) m/s
Answer: b) (4, 2) m/s
Solution:
Velocity = (Change in position) / Time
Velocity_x = (10 - 2) / 2 = 4 m/s
Velocity_y = (5 - 1) / 2 = 2 m/s
Velocity vector = (4, 2) m/s
22. An autonomous aircraft's navigation system uses a GPS receiver with a position dilution of
precision (PDOP) of 2.5. If the GPS has a user equivalent range error (UERE) of 5 meters, what is the
expected position accuracy?
a) 10.5 meters
b) 12.5 meters
c) 14.5 meters
d) 16.5 meters
Answer: b) 12.5 meters
Solution:
Position accuracy = PDOP × UERE
Position accuracy = 2.5 × 5 meters = 12.5 meters
23. An autonomous drone's collision avoidance system detects an obstacle 50 meters away,
approaching at a relative velocity of 10 m/s. If the drone's maximum deceleration is 2 m/s^2, what is
the minimum distance at which it must start decelerating to avoid a collision?
a) 12.5 meters
b) 25 meters
c) 37.5 meters
d) 50 meters
Answer: b) 25 meters
Solution:
Using the equation of motion: v^2 = u^2 + 2as
0 = 10^2 + 2(-2)s
s = 100 / 4 = 25 meters
24. An autonomous aircraft's machine learning model for weather prediction has an accuracy of 85%
for predicting clear weather and 75% for predicting stormy weather. If clear weather occurs 70% of
the time, what is the overall accuracy of the model?
a) 80%
b) 82%
c) 84%
d) 86%
Answer: b) 82%
Solution:
Overall accuracy = (Accuracy_clear × Probability_clear) + (Accuracy_stormy × Probability_stormy)
Overall accuracy = (0.85 × 0.7) + (0.75 × 0.3) = 0.595 + 0.225 = 0.82 or 82%
. An autonomous aircraft's obstacle avoidance system detects an object 500 meters away. If the
aircraft is traveling at 100 m/s, how long does it have to initiate evasive maneuvers?
a) 3 seconds
b) 4 seconds
c) 5 seconds
d) 6 seconds
Answer: c) 5 seconds
Solution:
Time = Distance / Speed
Time = 500 m / 100 m/s = 5 seconds
5. The battery of an autonomous drone has a capacity of 5000 mAh. If the drone's average current
draw is 2.5 A, how long can the drone operate on a single charge?
a) 1 hour
b) 1.5 hours
c) 2 hours
d) 2.5 hours
Answer: c) 2 hours
Solution:
Operation time = Battery capacity / Current draw
Operation time = 5000 mAh / 2500 mA = 2 hours
6. An autonomous aircraft's GPS system has a position accuracy of ±5 meters. If the aircraft needs to
land on a circular pad with a radius of 10 meters, what is the probability that the GPS reading will
place the aircraft within the landing pad?
a) 25%
b) 50%
c) 75%
d) 100%
Answer: c) 75%
Solution:
Area of landing pad = π × r^2 = π × 10^2 = 314 m^2
Area of possible GPS readings = π × (r + accuracy)^2 = π × 15^2 = 707 m^2
Probability = Area of landing pad / Area of possible GPS readings = 314 / 707 ≈ 0.75 or 75%
7. An autonomous drone uses a stereo vision system with two cameras separated by 10 cm. If an
object is detected at a pixel disparity of 20 pixels, and each camera has a focal length of 5 mm with a
pixel size of 5 μm, what is the distance to the object?
a) 1.25 m
b) 2.5 m
c) 3.75 m
d) 5 m
Answer: b) 2.5 m
Solution:
Distance = (Baseline × Focal length) / (Pixel size × Disparity)
Distance = (0.1 m × 0.005 m) / (5 × 10^-6 m × 20) = 2.5 m
8. An autonomous aircraft's collision avoidance system predicts the trajectory of another aircraft. If
the other aircraft is 10 km away and approaching at 200 m/s, how long will it take for the two aircraft
to collide if no evasive action is taken?
a) 40 seconds
b) 45 seconds
c) 50 seconds
d) 55 seconds
Answer: c) 50 seconds
Solution:
Time to collision = Distance / Speed
Time to collision = 10,000 m / 200 m/s = 50 seconds
9. An autonomous drone's path planning algorithm calculates a route that is 5 km long. If the drone's
average speed is 15 m/s, how long will it take to complete the route?
a) 5 minutes 33 seconds
b) 5 minutes 44 seconds
c) 5 minutes 55 seconds
d) 6 minutes 6 seconds
Answer: a) 5 minutes 33 seconds
Solution:
Time = Distance / Speed
Time = 5,000 m / 15 m/s = 333.33 seconds ≈ 5 minutes 33 seconds
10. The control system of an autonomous aircraft operates at 100 Hz. What is the time interval
between two consecutive control loop iterations?
a) 0.001 seconds
b) 0.005 seconds
c) 0.01 seconds
d) 0.1 seconds
Answer: c) 0.01 seconds
Solution:
Time interval = 1 / Frequency
Time interval = 1 / 100 Hz = 0.01 seconds
11. An autonomous drone uses a magnetometer to measure the Earth's magnetic field. If the
magnetometer has a sensitivity of 0.1 μT (microtesla) and the Earth's magnetic field strength is
typically around 50 μT, what is the minimum angular resolution the drone can achieve in detecting its
orientation?
a) 0.1°
b) 0.2°
c) 0.3°
d) 0.4°
Answer: a) 0.1°
Solution:
Angular resolution = arcsin(Sensitivity / Field strength)
Angular resolution = arcsin(0.1 / 50) ≈ 0.1°
12. An autonomous aircraft's machine learning model for object detection has 10 million parameters.
If each parameter is stored as a 32-bit floating-point number, how much memory does the model
require?
a) 20 MB
b) 30 MB
c) 40 MB
d) 50 MB
Answer: c) 40 MB
Solution:
Memory = Number of parameters × Bits per parameter / 8 bits per byte
Memory = 10,000,000 × 32 / 8 = 40,000,000 bytes = 40 MB
13. An autonomous drone's propulsion system consumes 500 W of power. If the drone's battery has
a capacity of 10,000 mAh and operates at 11.1 V, how long can the drone fly?
a) 22 minutes
b) 33 minutes
c) 44 minutes
d) 55 minutes
Answer: b) 33 minutes
Solution:
Battery energy = 10,000 mAh × 11.1 V = 111,000 mWh = 111 Wh
Flight time = Battery energy / Power consumption
Flight time = 111 Wh / 500 W = 0.222 hours ≈ 33 minutes
14. An autonomous aircraft's navigation system uses a Kalman filter to estimate its position. If the
initial position uncertainty is 10 m and the measurement uncertainty is 2 m, what is the estimated
position uncertainty after one update?
a) 1.67 m
b) 1.82 m
c) 1.98 m
d) 2.14 m
Answer: a) 1.67 m
Solution:
Updated uncertainty = (Initial uncertainty × Measurement uncertainty) / (Initial uncertainty +
Measurement uncertainty)
Updated uncertainty = (10 × 2) / (10 + 2) = 1.67 m
15. An autonomous drone's obstacle detection system has a false positive rate of 1% and a true
positive rate of 99%. If the drone encounters 1000 non-obstacle situations and 10 real obstacles
during a flight, how many total obstacle detections will it make?
a) 10
b) 20
c) 30
d) 40
Answer: b) 20
Solution:
False positives = 1% of 1000 = 10
True positives = 99% of 10 = 9.9 ≈ 10
Total detections = False positives + True positives = 10 + 10 = 20
16. An autonomous aircraft's wind estimation algorithm calculates a headwind of 15 m/s. If the
aircraft's airspeed is 100 m/s, what is its ground speed?
a) 75 m/s
b) 85 m/s
c) 95 m/s
d) 105 m/s
Answer: b) 85 m/s
Solution:
Ground speed = Airspeed - Headwind
Ground speed = 100 m/s - 15 m/s = 85 m/s
17. An autonomous drone uses a PID controller for altitude control. If the proportional gain is 2, the
integral gain is 0.1, and the derivative gain is 0.5, what is the control output for an error of 5 meters,
an integral of error of 10 meter-seconds, and a rate of change of error of -2 meters per second?
a) 8.5
b) 9.5
c) 10.5
d) 11.5
Answer: c) 10.5
Solution:
Output = P + I + D
Output = (2 × 5) + (0.1 × 10) + (0.5 × -2)
Output = 10 + 1 - 0.5 = 10.5
18. An autonomous aircraft's path planning algorithm uses A* search. If the heuristic function
consistently underestimates the true cost by 20%, how much longer will the calculated path be
compared to the optimal path, in the worst case?
a) 10%
b) 20%
c) 30%
d) 40%
Answer: b) 20%
Solution:
Worst-case path length = Optimal path length × (1 / (1 - Underestimation))
Worst-case path length = Optimal path length × (1 / (1 - 0.2)) = Optimal path length × 1.25
Percentage increase = (1.25 - 1) × 100% = 25%
19. An autonomous drone's battery management system estimates that the battery has 30% charge
remaining. If the drone consumes 100 W of power and the battery capacity is 10,000 mAh at 11.1 V,
how much longer can the drone fly?
a) 10 minutes
b) 15 minutes
c) 20 minutes
d) 25 minutes
Answer: c) 20 minutes
Solution:
Remaining energy = 30% × 10,000 mAh × 11.1 V = 33,300 mWh = 33.3 Wh
Flight time = Remaining energy / Power consumption
Flight time = 33.3 Wh / 100 W = 0.333 hours = 20 minutes
20. An autonomous aircraft's SLAM (Simultaneous Localization and Mapping) algorithm processes
point cloud data with 1 million points. If each point is represented by 3 floating-point numbers (x, y, z
coordinates) and each floating-point number is 4 bytes, how much memory is required to store the
point cloud?
a) 8 MB
b) 12 MB
c) 16 MB
d) 20 MB
Answer: b) 12 MB
Solution:
Memory = Number of points × Coordinates per point × Bytes per coordinate
Memory = 1,000,000 × 3 × 4 bytes = 12,000,000 bytes = 12 MB
21. An autonomous drone's object tracking algorithm predicts that an object will be at position (10,
5) in 2 seconds. If the object's current position is (2, 1), what is its estimated velocity vector?
a) (3, 1.5) m/s
b) (4, 2) m/s
c) (5, 2.5) m/s
d) (6, 3) m/s
Answer: b) (4, 2) m/s
Solution:
Velocity = (Change in position) / Time
Velocity_x = (10 - 2) / 2 = 4 m/s
Velocity_y = (5 - 1) / 2 = 2 m/s
Velocity vector = (4, 2) m/s
22. An autonomous aircraft's navigation system uses a GPS receiver with a position dilution of
precision (PDOP) of 2.5. If the GPS has a user equivalent range error (UERE) of 5 meters, what is the
expected position accuracy?
a) 10.5 meters
b) 12.5 meters
c) 14.5 meters
d) 16.5 meters
Answer: b) 12.5 meters
Solution:
Position accuracy = PDOP × UERE
Position accuracy = 2.5 × 5 meters = 12.5 meters
23. An autonomous drone's collision avoidance system detects an obstacle 50 meters away,
approaching at a relative velocity of 10 m/s. If the drone's maximum deceleration is 2 m/s^2, what is
the minimum distance at which it must start decelerating to avoid a collision?
a) 12.5 meters
b) 25 meters
c) 37.5 meters
d) 50 meters
Answer: b) 25 meters
Solution:
Using the equation of motion: v^2 = u^2 + 2as
0 = 10^2 + 2(-2)s
s = 100 / 4 = 25 meters
24. An autonomous aircraft's machine learning model for weather prediction has an accuracy of 85%
for predicting clear weather and 75% for predicting stormy weather. If clear weather occurs 70% of
the time, what is the overall accuracy of the model?
a) 80%
b) 82%
c) 84%
d) 86%
Answer: b) 82%
Solution:
Overall accuracy = (Accuracy_clear × Probability_clear) + (Accuracy_stormy × Probability_stormy)
Overall accuracy = (0.85 × 0.7) + (0.75 × 0.3) = 0.595 + 0.225 = 0.82 or 82%
25. An autonomous drone's path planning algorithm uses a grid-based representation with cells of
size 1m × 1m. If the drone's operational area is 1 km × 1 km, how many cells are in the grid?
a) 100,000
b) 500,000
c) 1,000,000
