Survey Engineering Question and Mock Test Set- 1 (0 to 100 question)

Formula:

Probable error of the mean=Probable error of a single observationn\text{Probable error of the mean} = \frac{\text{Probable error of a single observation}}{\sqrt{n}}Probable error of the mean=n​Probable error of a single observation​

Where:

• $n$ = number of observations

• Probable error of a single observation = ±0.04 m

• Probable error of the mean = ±0.01 m

🧮 Step-by-Step Calculation:

0.01=0.04n0.01 = \frac{0.04}{\sqrt{n}}0.01=n​0.04​

Multiply both sides by n\sqrt{n}n​:

0.01n=0.040.01 \sqrt{n} = 0.040.01n​=0.04

Divide both sides by 0.01:

n=0.040.01=4\sqrt{n} = \frac{0.04}{0.01} = 4n​=0.010.04​=4

Now square both sides:

n=42=16n = 4^2 = 16n=42=16

✅ Final Answer:

16\boxed{16}16​

Explanation:

In triangulation (used in surveying), a well-conditioned triangle is one in which the angles are such that errors in angle measurement cause minimal distortion in the calculated sides.

• If any angle is too small, small errors in angle measurement can lead to large errors in side lengths due to the nature of trigonometric functions.

• Therefore, to ensure good accuracy and numerical stability, it is generally recommended that:

  • No angle should be less than 30°

  • No angle should be more than 120°

✅ Final Answer:

30∘\boxed{30^\circ}30∘​

Explanation:

In chaining:

• A chain is typically 20 meters.

• 10 arrows are used to count each full chain laid.

• After completing 1 chain (20 m), the leader drops an arrow, and the follower picks it up.

• So, the number of arrows with the follower indicates how many chains have been completed from the starting point up to the follower.

Given:

• Follower has 6 arrows ⇒ 6 chains completed ⇒ follower is at 6 chains from start.

• Leader has 4 arrows ⇒ He’s currently chaining the 7th to 10th chains.

🚶 Position Breakdown:

• Follower is always at the point where the last arrow was picked up.

• Therefore, if he has 6 arrows, he’s at 6 chains from the starting point.

✅ Final Answer:

6 chains\boxed{6 \text{ chains}}6 chains​

(This is correct — not 120 m, unless the question specifically asks for the distance in meters.)

Explanation:

• In a metric chain, each link is 0.2 meters (20 cm) long.

• To find the number of links:

Number of Links=Total Length of ChainLength of One Link=300.2=150\text{Number of Links} = \frac{\text{Total Length of Chain}}{\text{Length of One Link}} = \frac{30}{0.2} = \boxed{150}Number of Links=Length of One LinkTotal Length of Chain​=0.230​=150​

So, a 30-meter metric chain has 150 links.

Explanation:

• Invar is a specialized alloy primarily used in precision instruments like tapes, wires, and rods used for high-accuracy surveying.

• It is known for its very low coefficient of thermal expansion, making it highly stable with temperature changes.

🔬 Composition of Invar:

• Nickel: 36%

• Steel (Iron): 64%

This specific ratio (around 36% nickel) gives Invar its unique property of thermal stability, ideal for precise linear measurements in geodetic surveying.

Explanation:

• In plane surveying, the Earth is assumed to be flat — the curvature is neglected. This works well for small areas (usually < 250 km²), where curvature effects are minimal.

• In geodetic surveying, the Earth’s curvature is considered, as it deals with large areas or high-precision measurements (like national or global-level mapping, GPS control networks).

Why other options are incorrect:

• Large difference of elevations: That can happen in both types of surveying and is not a defining factor.

• Coverage of large area: True for geodetic, but the reason for the difference is the curvature, not just area.

• Undulations of topography: These exist in both types and are handled by leveling or contouring methods, not by switching surveying types.

Explanation:

• Residual Error (also simply called residual) is:

  The difference between the observed value and the most probable (adjusted) value of a measurement.

$$\text{Residual}=\text{Observed Value}-\text{Most Probable Value}$$

It reflects the deviation of an individual observation after adjustments (like in least squares method).

📌 What About "True Error"?

• True Error = Observed value − True (actual, unknown) value

• But in practice, true value is never known, so residuals are used instead (based on computed most probable value).

✅ Summary of Terms:

🟢 Final Answer:

Residual Error\boxed{\text{Residual Error}}Residual Error​

📋 Given Table:

🧠 Concept:

• Local attraction is suspected at a station when the difference between the fore bearing and back bearing is not exactly 180°.

• Ideally:

  $$\text{B.B.}=\text{F.B.}\pm 180°$$

🔍 Step-by-Step Check:

🔹 Line AB:

• F.B. = 104°30′

• B.B. = 284°30′

• Difference = 284°30′ − 104°30′ = 180° ✅

🔹 Line BC:

• F.B. = 48°15′

• B.B. = 226°00′

• Difference = 226°00′ − 48°15′ = 177°45′ ❌

👉 Error = 2°15′ → Local attraction likely at B or C

🔹 Line CD:

• F.B. = 290°30′

• B.B. = 115°15′

• Difference = 290°30′ − 115°15′ = 175°15′ ❌

👉 Error = 4°45′ → Local attraction likely at C or D

🔹 Line DA:

• F.B. = 180°15′

• B.B. = 357°15′

• Difference = 357°15′ − 180°15′ = 177°00′ ❌

👉 Error = 3° → Local attraction likely at D or A

🧾 Summary of Errors:

🔍 Stations that appear in multiple errors:

• C (in both BC and CD)

• D (in both CD and DA)

✅ Final Answer:

c) C and D\boxed{\text{c) C and D}}c) C and D​

(i) Are inverted — Correct

• In a prismatic compass, the graduations on the aluminium ring (attached to the magnetic needle) are inverted, so they appear upright when viewed through the prism.

• This is done intentionally for proper reading via the prism.

❌ (ii) Are upright — Incorrect

• The actual graduations are printed inverted on the ring, so this statement is not true.

❌ (iii) Run clockwise having 0° at south — Incorrect

• That’s true for surveyors’ compass, not prismatic compass.

• Surveyor’s compass has 0° at South and increases clockwise.

✅ (iv) Run clockwise having 0° at north — Correct

• In a prismatic compass, the graduations:

  • Run clockwise

  • Have 0° at North

  • 90° at East, 180° at South, 270° at West

✅ Final Answer:

(i) and (iv)\boxed{(i) \text{ and } (iv)}(i) and (iv)​

Explanation:

• Magnetic declination is the angle between the true meridian (geographic north) and the magnetic meridian (magnetic north).

• Declination can be:

  • Positive (East declination): Magnetic meridian is east of true meridian.

  • Negative (West declination): Magnetic meridian is west of true meridian.

📌 So:

• Negative declination ⇒ Magnetic North is west of True North

✅ Final Answer:

b) western side of the true meridian\boxed{\text{b) western side of the true meridian}}b) western side of the true meridian​

Explanation:

To find the included angle between two lines AB and BC, we follow these steps:

🔹 Step 1: Compute back bearing (BB) of AB

Since forebearing of AB = 35°, the back bearing is:

BBAB=35°+180°=215°BB_{AB} = 35° + 180° = 215°BBAB​=35°+180°=215°

🔹 Step 2: Find the angle between BB of AB and FB of BC

Now we compute the angle between:

• Back bearing of AB = 215°

• Forebearing of BC = 15°

Included Angle=FBBC−BBAB=15°−215°=−200°\text{Included Angle} = FB_{BC} - BB_{AB} = 15° - 215° = -200°Included Angle=FBBC​−BBAB​=15°−215°=−200°

Since angle cannot be negative, we add 360°:

360°−200°=160°360° - 200° = \boxed{160°}360°−200°=160°​

Wait! This is the exterior angle. The included angle is the interior angle, and it's the smaller angle between the two bearings.

So now we take:

\text{Included Angle} = 360° - 160° = \boxed{200°} ❌ Not in options But this seems off — let's double-check: --- ### ✅ Proper Method (Clockwise Angle from AB to BC): We can use the formula for included angle between two **forebearings**: \[ \text{Included Angle} = FB_{BC} - FB_{AB} = 15° - 35° = -20°

Now, convert negative to positive by adding 360°:

$$360°-20°=340°\Rightarrow \text{Exterior Angle}$$

So, included angle (interior) =

360° - 340° = \boxed{20°} \] ❌ Not matching the correct logic. --- Let’s try the most accurate approach: --- ### 🔁 **Correct way:** \[ \text{Included Angle} = FB_{BC} - BB_{AB} = 15° - 215° = -200° \Rightarrow 360° - 200° = \boxed{160°}

That matches option c)

✅ Final Answer:

c) 160°\boxed{\text{c) 160°}}c) 160°​

Explanation:

• In surveying:

  • Forebearing (FB) of line AB = Bearing from point A to B

  • Back bearing (BB) of line AB = Bearing from point B to A

Since these are in opposite directions, they always differ by 180°.

🔁 Formula:

BB=FB±180∘\text{BB} = \text{FB} \pm 180^\circBB=FB±180∘

• Add or subtract depending on whether the FB is less than or greater than 180°, to keep it within 0°–360°.

📌 Example:

• If FB of AB = 60°, then:

  $$\text{BB of AB}=60°+180°=240°$$

• If FB = 210°, then:

  $$\text{BB}=210°-180°=30°$$

✅ Conclusion:

The forebearing and back bearing of the same line always differ by 180° — Correct!\boxed{\text{The forebearing and back bearing of the same line always differ by 180° — Correct!}}The forebearing and back bearing of the same line always differ by 180° — Correct!​

a) "The true meridians at different places are parallel to each other." ❌

• Incorrect Statement

• True meridians are lines that point toward the geographic North Pole.

• On the Earth's curved surface, true meridians converge as you move toward the poles.

• Therefore, they are not parallel.

🔹 b) "The true meridian at any place is not variable." ✅

• True meridian at a point is fixed, because it always points toward the geographic North Pole.

🔹 c) "The true meridians converge to a point in northern and southern hemispheres." ✅

• Correct — all true meridians converge at the poles, both North and Sout

Explanation:

Offset methods are used in chain surveying to locate details (like boundaries, fences, roads) from a survey line. Let's review each option:

🔹 a) Method of Perpendicular Offsets ✅

• Offsets are taken at right angles to the survey line.

• It's the simplest and most efficient method.

• Requires less measurement because:

  • The offsets are direct and easy to measure with a cross staff or optical square.

  • No need to measure long slant lines or complex geometry.

🔹 b) Method of Oblique Offsets

• Offsets are taken at an angle other than 90°.

• Requires measurement of the angle and the oblique length, which adds effort and potential for error.

🔹 c) Method of Ties

• Used when a point is located by measuring distances to two known points.

• Involves two ground measurements per point, hence more effort.

🔹 d) All involve equal measurement on the ground

• ❌ Incorrect — clearly not true based on the differences in technique and effort.

✅ Final Answer:

Method of perpendicular offsets\boxed{\text{Method of perpendicular offsets}}Method of perpendicular offsets​