Q: Road design on hill slopes — if the actual road gradient deviates from the proposed contour gradient toward the uphill side, what earthwork is required along the centre line? Choose the most appropriate action.

Introduction / Context: On hill roads, the contour gradient represents the alignment maintaining a specified longitudinal slope. If the chosen alignment strays upward (towards higher ground), the designed grade line lies below the ground surface, necessitating specific earthwork to bring the roadway to grade. Given Data / Assumptions: Road on a hillside with a proposed contour gradient. Actual alignment deviates uphill relative to the proposed path. Decision needed on the nature of earthwork at the centre line. Concept / Approach: When the alignment shifts to higher ground, the natural surface is above the design grade. To achieve the desired grade, material must be removed along the centre line, i.e., excavation (cutting). Conversely, if the alignment deviates downhill, an embankment would be necessary to raise the formation. Step-by-Step Solution: Identify relative position: uphill deviation → ground level higher than design grade.Select earthwork: remove surplus material → cutting.Apply along centre line to set formation at the design gradient.Confirm that embankment would be used only for downhill deviation. Verification / Alternative check: Standard hill-road design practices illustrate that when the alignment moves into higher contours, cutting is unavoidable to maintain the target gradient. Why Other Options Are Wrong: Embankment: Applicable for downhill deviations where ground is lower than grade. Earthwork (unspecified): Vague; the correct specific action is cutting. None of these: Incorrect because cutting is required. Common Pitfalls: Misreading the phrase “uphill side” and prescribing fill instead of cut; always compare ground level with the designed grade line. Final Answer: Excavation (cutting) on the centre line

Question 1

Traverse adjustment – making algebraic sums of latitudes and departures zero In a closed traverse, the process of correcting the observations so that the algebraic sums of latitudes and departures are both zero is called what?

Accepted Answer

Introduction / Context: Closed traverses ideally return to the starting point, making the algebraic sums of departures (eastings) and latitudes (northings) equal to zero. In practice, small measurement errors cause misclosures that must be distributed among the traverse legs. This question asks for the name of the operation by which both sums are adjusted to zero. Given Data / Assumptions: A closed traverse with observed bearings/angles and lengths. Computed unadjusted departures and latitudes show small misclosures. A standard adjustment method (e.g., Bowditch or transit rule) will be applied. Concept / Approach: Balancing the traverse means distributing the linear misclosures so that the final, adjusted coordinates satisfy algebraic sum of departures = 0 and algebraic sum of latitudes = 0. The Bowditch (compass) rule distributes corrections proportional to length, while the transit rule distributes proportional to the absolute value of the departure/latitude. The result is a self-consistent set of coordinates suitable for plotting and further computations (areas, coordinates of detail points). Step-by-Step Solution: 1) Compute preliminary departures and latitudes for each side.2) Sum to find misclosures: ΣDep ≠ 0 and ΣLat ≠ 0.3) Choose an adjustment method (e.g., Bowditch).4) Apply corrections to each side; recompute so ΣDep = 0 and ΣLat = 0. Verification / Alternative check: After adjustment, coordinate loop should close, and area checks should be consistent. Independent checks (angular closure, distance closure) confirm the quality of the traverse. Why Other Options Are Wrong: Balancing latitudes/departures (alone): Corrects only one sum, not both. Balancing the sights: Non-standard term in traverse adjustment. Common Pitfalls: Forgetting to adjust both components; applying unequal sign conventions; neglecting to recompute coordinates after distributing corrections. Final Answer: Balancing the traverse

Question 2

Optics in surveying and engineering drawing: Which statements about the power of a lens and how powers combine for thin lenses in contact are correct?

Accepted Answer

Introduction / Context: Lenses appear in many civil and surveying instruments (levels, theodolites, total stations) and also in drafting aids and optical sights. Understanding “power” clarifies how focal length relates to instrument magnification and how compound eyepieces or lens groups behave when combined. This question checks three foundational facts: definition of power, its unit, and how powers add for thin lenses in contact. Given Data / Assumptions: Lenses are thin and coaxial so the “thin lens” approximations apply. Focal length f is measured in meters for power calculations. When thin lenses are placed in contact, spacing is negligible for first-order power addition. Concept / Approach: Lens power P quantifies refracting strength. By definition, P = 1 / f when f is in meters. The SI unit is diopter, written D or m^-1. For thin lenses placed in contact, the equivalent power is the sum of individual powers: P_total = P1 + P2 + …, which is widely used in designing eyepieces and objective–eyepiece combinations in surveying telescopes. Step-by-Step Solution: Define power: P = 1 / f (f in meters).Recognize the unit: diopter (1 diopter = 1 m^-1).Combine thin lenses: P_total = P1 + P2 + P3 … for lenses in contact.Therefore, all three statements are simultaneously true. Verification / Alternative check: Optics texts for engineering instruments adopt diopters for quick mental calculation: for example, a 0.25 m focal length lens has power 4 D. Stacking two 2 D thin lenses gives 4 D total (approximate) when in contact, matching P_total = P1 + P2. Why Other Options Are Wrong: If any one statement were false, modern optical design basics would be contradicted. Since all three are correct, the only complete answer is the inclusive option. Common Pitfalls: Using focal length in centimeters when calculating diopters; forgetting that power addition presumes thin lenses in contact (finite separations demand more detailed matrix methods); confusing magnification with power (they are related but not identical). Final Answer: All of the above

Question 3

Levelling practice (dumpy/auto level): Which statements correctly describe a back sight (BS) reading and how it is used to obtain the height of instrument (HI)?

Accepted Answer

Introduction / Context: In differential levelling, the first staff reading after setting up the level is usually a back sight (BS). Correctly identifying and calculating with BS ensures accurate transfer of elevations from a known benchmark to new points. The question verifies understanding of what a BS is, how it produces height of instrument (HI), and sign conventions for special cases like inverted staff readings. Given Data / Assumptions: Reduced level (RL) of a starting point or benchmark is known or can be computed. Line of sight is assumed horizontal after proper instrument leveling. Inverted staff readings occur under structures or when sighting to soffits; sign convention must be respected. Concept / Approach: A back sight establishes the height of the collimation (HI). If RL_known is the reduced level of the point and BS is the staff reading, then HI = RL_known + BS for a normal upright staff. For an inverted staff (held upside down), the reading represents a vertical offset below the line of sight and is algebraically negative in the levelling computation. Step-by-Step Solution: Identify BS: first reading on a known point (benchmark, change point) → establishes HI.Compute HI: HI = RL_known + BS (upright staff).Handle inverted staff: treat the reading as negative, so HI = RL_known + (−BS_magnitude).Use HI to compute fore sights (FS) to obtain RLs of new points: RL_new = HI − FS. Verification / Alternative check: Levelling field books consistently show BS in the BS column, added to the RL of the known point to get HI; any inverted-reading entries are specially marked and signed to avoid mistakes. Why Other Options Are Wrong: The only complete choice that captures definition, calculation, and sign convention is the inclusive option. Any single statement alone is incomplete. Common Pitfalls: Confusing BS and FS; forgetting to reverse the sign for inverted staff; mixing instrument change (IC) entries leading to incorrect HI carry-over; omitting arithmetic checks (sum of BS − sum of FS = last RL − first RL). Final Answer: All of the above

Question 4

Tacheometry (stadia method): In a stadia theodolite, which extra hairs are provided on the diaphragm for distance measurement?

Accepted Answer

Introduction / Context: Tacheometry allows rapid distance and elevation measurement using a theodolite or transit equipped with stadia hairs. Recognizing the diaphragm pattern is essential for reading intercepts on the staff and converting them into distances using the stadia constants. Given Data / Assumptions: A standard stadia theodolite has a central horizontal cross hair for line of sight. Two extra hairs are placed symmetrically above and below the central horizontal hair. The vertical hair remains single for ranging/centering. Concept / Approach: Distance D is computed from the staff intercept s between the upper and lower stadia hairs using D = k * s + c, where k is the multiplying constant and c is the additive constant (both instrument-specific). Thus, the diaphragm must provide two additional horizontal hairs to read s directly on the staff. Step-by-Step Solution: Identify required intercept: s = reading_upper − reading_lower on the staff.Relate to distance: D = k * s + c (slope distance or horizontal distance depending on method).Confirm diaphragm layout: one vertical hair (for alignment), three horizontal hairs (central + two stadia hairs).Therefore, the extra hairs are horizontal stadia hairs. Verification / Alternative check: Manufacturers’ manuals and surveying texts depict the stadia diaphragm with two additional horizontal hairs; vertical hair remains single for sighting the staff centerline. Why Other Options Are Wrong: Vertical extra hairs are not used for stadia measurement. Adding both horizontal and vertical extras is unnecessary and not standard for stadia work. “None of these” is false since the correct configuration is well known. Common Pitfalls: Reading the wrong pair of hairs; confusing stadia intercept with staff height difference; forgetting to apply the additive constant when required. Final Answer: Two additional horizontal hairs (stadia hairs) equidistant from the central horizontal hair

Question 5

Engineering graphics – diagonal scale: A properly constructed diagonal scale allows readings up to how many “dimensions” (orders of subdivision) on a single scale?

Accepted Answer

Introduction / Context: Diagonal scales are standard in engineering drawing for precise measurement without resorting to excessively long scales. They use geometric diagonals to subdivide the smallest main division, enabling fine readings directly on the scale. The question asks how many orders of subdivision are available on a typical diagonal scale. Given Data / Assumptions: The main scale provides whole units (e.g., meters). Secondary divisions provide tenths of the unit. Diagonal construction produces hundredths from the tenths. Concept / Approach: By drawing a rectangle subdivided horizontally into tenths and diagonally from the bottom-left to top-right corners of each small rectangle, the intercept of a diagonal with a vertical line provides hundredth-level interpolation. Thus, three “dimensions” (orders) can be read: units, tenths, and hundredths, greatly improving precision over a plain scale. Step-by-Step Solution: Read units on the main scale (e.g., whole meters).Read tenths on the secondary divisions to the left of zero.Read hundredths using the diagonal intersections inside the small rectangle.Combine the three readings to obtain the final value. Verification / Alternative check: Any standard text on engineering graphics shows construction enabling two successive subdivisions: first into tenths, then into hundredths using diagonals, confirming the “three dimensions” capability. Why Other Options Are Wrong: One or two dimensions underestimate the diagonal scale’s refinement. Four dimensions claim thousandths, which is beyond typical diagonal scale construction and impractical for drafting precision. Common Pitfalls: Misreading left-of-zero subdivisions; mixing up diagonal direction; forgetting that accuracy depends on careful drawing and line thickness control. Final Answer: Three dimensions (units, tenths, and hundredths)

Question 6

Surveying telescopes – cross hairs: Where are the cross hairs (reticle) fitted relative to the objective and the eyepiece so that both the staff image and the cross hairs appear simultaneously sharp?

Accepted Answer

Introduction / Context: Sharp coincidence of the cross hairs with the image is crucial for precise sighting in levels and theodolites. This is achieved by placing the reticle at a location where the image formed by the objective and the cross hairs themselves are both at the eyepiece’s focal plane. Given Data / Assumptions: The telescope is a Keplerian type used in surveying instruments. The objective forms a real, inverted image of the target at its focal plane. The eyepiece magnifies objects located at its focal plane without introducing parallax if the image and cross hairs are coincident. Concept / Approach: Place the cross hair diaphragm at the common focal plane of objective and eyepiece. Then, when the objective brings the staff image into that plane and the eyepiece is focused so the reticle is sharp, there is no relative motion (parallax) between image and cross hairs as the eye shifts, ensuring accurate readings. Step-by-Step Solution: Focus the eyepiece first until the cross hairs are razor-sharp (placing the reticle at the eyepiece’s focal plane).Aim at the staff and focus the objective to bring the image onto the same plane.Check for parallax by moving the eye slightly; absence of relative motion confirms correct placement.Thus, the correct location is the common focal plane (optical center of eyepiece). Verification / Alternative check: Instrument manuals specify the reticle location at the focal plane to eliminate parallax; any other placement produces observable image drift against the cross hairs when the eye moves. Why Other Options Are Wrong: Inside the objective or arbitrarily in front of the eyepiece, the image and reticle are not coplanar, causing parallax. “Center of the telescope” is a vague geometric location, not an optical plane. Common Pitfalls: Focusing the objective before the eyepiece; accepting slight parallax; dirty or misaligned reticle causing apparent focus issues. Final Answer: At the optical center (focal plane) of the eyepiece, i.e., the common focal plane of objective and eyepiece

Question 7

Optical design – Ramsden eyepiece (used in surveying telescopes): Which specifications correctly describe a Ramsden eyepiece construction and its focal relationships?

Accepted Answer

Introduction / Context: The Ramsden eyepiece is common in surveying instruments because it balances field of view, eye relief, and distortion. Recognizing its construction ensures proper interpretation of cross-hair placement and parallax behavior during focusing. Given Data / Assumptions: Each lens is plano-convex with equal focal length. Convex faces are oriented inward toward each other. Specified separations are approximate design ratios widely cited for Ramsden optics. Concept / Approach: A Ramsden eyepiece uses two equal plano-convex lenses with convex faces facing. Typical separation is about 2/3 f (f being the focal length of one lens). The diaphragm is placed near the eye lens side; with the chosen distances, rays emerging from a diaphragm point are approximately parallel after passing the eyepiece, aiding in clear viewing of the reticle and minimizing aberrations in the central field. Step-by-Step Solution: Confirm construction: two equal plano-convex lenses, convex faces inward (A and B true).Confirm separation: lens spacing ≈ (2/3) f of either lens (C true).Confirm diaphragm relation: diaphragm to front lens ≈ f/4 yielding near-parallel exit rays for points on the diaphragm (D true).Therefore, all listed statements are consistent with Ramsden design. Verification / Alternative check: Optical handbooks list two-lens eyepiece families (Huygens, Ramsden). Ramsden positions the diaphragm between lenses near the eye lens, providing a real image plane suitable for cross hairs and less chromatic aberration centrally. Why Other Options Are Wrong: Choosing any single statement would omit other necessary design descriptors; the Ramsden is characterized by the combination. Common Pitfalls: Confusing Ramsden with Huygens (which places the diaphragm outside and uses different lens spacing and orientation); misplacing the diaphragm leading to parallax or poor reticle illumination. Final Answer: All of the above

Question 8

Survey errors – classification: Systematic errors that persist in a regular pattern during a survey operation are primarily caused by which factor?

Accepted Answer

Introduction / Context: Error analysis in surveying separates random (accidental), personal, and systematic components. Correct classification guides prevention: random errors are controlled statistically, personal errors by training, and systematic errors by calibration and adjustment. This question asks for the main cause behind systematic, regularly repeating errors. Given Data / Assumptions: Observations show consistent bias in one direction over repeated measurements. Field conditions and procedure remain similar across observations. Instrument condition may influence readings in a predictable way. Concept / Approach: Systematic errors have magnitude and sign that follow a rule (e.g., index error, collimation error, tape length error, temperature/scale effects). These typically originate from faulty calibration, imperfect adjustment, or physical defects. In contrast, carelessness or inattention cause sporadic blunders or personal/random errors without a steady bias. Step-by-Step Solution: Identify regular pattern: same direction and similar magnitude → systematic.Trace to cause: instrument misadjustment (e.g., non-horizontal line of sight, index error) or scale error.Apply correction/calibration or re-adjust instrument to remove bias.Therefore, “faulty instrument” is the principal source among the options. Verification / Alternative check: Two-peg test for levels, collimation checks for theodolites, and tape standardization all target the detection and removal of systematic instrument errors. Why Other Options Are Wrong: Carelessness and inattention lead to random or gross blunders, not consistent, law-like biases. “None of these” is wrong because faulty instruments are a classic source of systematic error. Common Pitfalls: Attributing a persistent bias to “bad luck”; failing to re-run checks when suspecting instrument error; neglecting temperature or tension corrections for tapes and EDM calibration for distances. Final Answer: Faulty or imperfectly adjusted instrument

Question 9

Reciprocal levelling / two-peg test computation: A level set up over peg A has eye-piece height above A = 1.540 m and reads 0.705 m on staff held at peg B. Then set up over peg B with eye-piece height above B = 1.490 m and read 2.195 m on staff at A…

Accepted Answer

Introduction / Context: This is a classic reciprocal levelling (or two-peg test style) computation. By observing from each end, collimation and refraction effects are largely canceled, allowing determination of the true difference in level even if the line of sight has a small inclination error. Given Data / Assumptions: Height of eye (instrument axis above peg tops): h_A = 1.540 m at A, h_B = 1.490 m at B. Staff reading at B from A: r_B = 0.705 m (upright staff). Staff reading at A from B: r_A = 2.195 m (upright staff). Sight distances are the same line AB in opposite directions. Concept / Approach: Let RL_A and RL_B be elevations of pegs A and B. With the instrument set over A: HI_1 = RL_A + h_A and RL_B = HI_1 − r_B, so RL_B − RL_A = h_A − r_B. With the instrument set over B: HI_2 = RL_B + h_B and RL_A = HI_2 − r_A, so RL_B − RL_A = r_A − h_B. Small collimation/refraction errors make these two values differ slightly; the true difference is taken as their mean. Step-by-Step Solution: Compute from setup at A: RL_B − RL_A = h_A − r_B = 1.540 − 0.705 = 0.835 m.Compute from setup at B: RL_B − RL_A = r_A − h_B = 2.195 − 1.490 = 0.705 m.Average to remove line-of-sight bias: (0.835 + 0.705) / 2 = 0.770 m.Hence, B is 0.770 m higher than A in level difference magnitude. Verification / Alternative check: Check sums: h_A + h_B = 3.030 m, r_A + r_B = 2.900 m; the mismatch (0.130 m) indicates collimation/refraction effects, which averaging neutralizes in the final result. Why Other Options Are Wrong: 2.900 m and 3.030 m: these are sums (r_A + r_B) or (h_A + h_B), not a level difference. 0.785 m: incorrect rounding; precise mean is 0.770 m. 1.770 m: unrelated combination of numbers. Common Pitfalls: Subtracting in the wrong order; ignoring the need to average reciprocal values; mixing heights of instrument with staff readings without consistent sign convention. Final Answer: 0.770 m

Question 10

Plane geometry for surveying computations: Using only the base AC and its corresponding perpendicular height h, what is the correct expression for the area of triangle ABC?

Accepted Answer

Introduction / Context: Area relations are frequently needed in surveying for lot calculations, offsets, and coordinate methods. When a base and its perpendicular height are known, the area of a triangle reduces to a simple, universally known formula. The question deliberately restricts you to base AC and the perpendicular height h to ensure a unique correct expression. Given Data / Assumptions: AC is a known side of triangle ABC, chosen as the base. h is the perpendicular distance from the opposite vertex to base AC. No other sides or angles are required for this specific method. Concept / Approach: For any triangle, area = (1/2) * base * height when the height is perpendicular to the chosen base. Although there are other correct formulae (sine rule variants and Heron’s formula), this problem requires the version involving base AC and its perpendicular height only, leading uniquely to 0.5 * AC * h. Step-by-Step Solution: Identify the base: AC.Identify the height: the perpendicular from the opposite vertex to AC equals h.Apply area identity: Area = 0.5 * base * corresponding height.Hence, Area = 0.5 * AC * h. Verification / Alternative check: If other data were given, equivalent forms exist: Area = 0.5 * b * c * sin A, etc., or Heron’s formula using the semiperimeter S. However, because the problem restricts the inputs to AC and h only, those forms are intentionally out of scope. Why Other Options Are Wrong: AC * h: missing the 0.5 factor, so it doubles the true area. 0.5 * a * c * sin B: correct in general but requires sides a, c and angle B, which are not part of the stated method. sqrt( S * (S - a) * (S - b) * (S - c) ): Heron’s formula is correct but does not use AC and h as requested. Common Pitfalls: Using the wrong height (oblique distance rather than perpendicular); forgetting the 0.5 factor; mixing base symbols from different conventions. Final Answer: Area = 0.5 * AC * h

Question 11

Levelling terminology: A relatively fixed point whose elevation above a stated datum is known (or established) and used for transferring levels is called what?

Accepted Answer

Introduction / Context: Successful levelling needs reliable reference elevations. Surveyors therefore establish and maintain permanent points with known elevations. The question asks for the precise term used in field books and specifications for such points. Given Data / Assumptions: A known elevation is tied to a consistent datum (e.g., mean sea level or project datum). The point is physically stable and recoverable. It is intended for repeated use to start or check levelling runs. Concept / Approach: The correct term is “bench mark” (BM). A BM’s reduced level (RL) is known; the RL is a numerical value, not the point itself. “Datum” is the zero or reference level, not the mark. “Reference point” is generic and may lack a known elevation. Hence, “bench mark” uniquely identifies the object described. Step-by-Step Solution: Recognize that the object is a physical point, not a number → eliminates “reduced level.”Recognize that “datum” is the reference surface, not a field point.Recognize that “bench mark” is defined as a fixed point with known RL.Therefore, select “Bench mark.” Verification / Alternative check: Survey manuals classify BMs as GTS (Great Trigonometrical Survey), permanent BMs, arbitrary BMs, and temporary BMs, all serving the same purpose of carrying elevations. Why Other Options Are Wrong: Datum point: ambiguous and usually refers to the abstract reference level, not a field monument. Reduced level: the numeric elevation value, not the point. Reference point: may be geometric only; not necessarily with known elevation. Common Pitfalls: Writing “RL of BM” backward as “BM of RL”; failing to protect or describe BMs properly leading to loss; assuming a temporary mark’s stability without re-check. Final Answer: Bench mark

Question 12

Geodetic surveying — in which situations is geodetic (high-precision, large-area) surveying undertaken? Select the most comprehensive purpose from the list below.

Accepted Answer

Introduction / Context: Geodetic surveying extends beyond ordinary plane surveying by considering the curvature of the Earth and employing high-precision techniques. It establishes accurate control networks, supports national mapping, and underpins geodesy—the science of Earth measurement. This question checks whether you can recognize the full scope of geodetic work rather than a single, narrow outcome. Given Data / Assumptions: Large areas where Earth curvature cannot be neglected. High-precision instruments and observation procedures are used. Outputs include accurate mapping and a robust control framework. Concept / Approach: Geodetic surveys determine positions (latitude, longitude, and often ellipsoidal/orthometric heights) with stringent accuracy through triangulation, trilateration, GNSS, leveling, and gravity observations. They create primary control networks that feed into topographic, cadastral, and engineering surveys over wide regions. Step-by-Step Solution: Identify objectives: national/large-area mapping and scientific geodesy.Recognize methods: finest instruments, rigorous observation, and adjustments.Relate outcomes: accurate control points for subsequent surveys.Hence, all listed purposes apply to geodetic surveying. Verification / Alternative check: National mapping agencies (e.g., geodetic control networks) exemplify the “all-in” nature—control points, accurate maps, and scientific Earth measurements are all outputs of geodetic activity. Why Other Options Are Wrong: Each single-purpose option is true but incomplete. Only “All of the above” captures the complete mandate of geodetic surveying. Common Pitfalls: Confusing geodetic with plane surveying; ignoring curvature and control accuracy leads to cumulative errors over large extents. Final Answer: All of the above

Question 13

Levelling operations — interpreting consecutive staff readings taken from the same instrument position: Which statements correctly indicate a rise or a fall?

Accepted Answer

Introduction / Context: In differential levelling, staff readings are taken on successive points using the same height of instrument (HI). Understanding how the numerical values of staff readings translate into “rise” or “fall” is essential for correctly reducing levels and avoiding sign mistakes in field books. Given Data / Assumptions: Two consecutive staff readings are observed from one instrument setup. The height of instrument remains unchanged between the two readings. We interpret the trend (increase/decrease) to decide rise or fall. Concept / Approach: Staff reading increases when the point is lower (farther down from the line of collimation). Staff reading decreases when the point is higher. Therefore, comparing two consecutive readings: a decrease indicates a rise; an increase indicates a fall. Step-by-Step Solution: Let R1 be the first reading and R2 the second reading from the same HI.If R1 > R2, the second point is higher → a rise (option b).If R1 < R2, the second point is lower → a fall (option c).Therefore, options (b) and (c) together are correct. Verification / Alternative check: Rise/fall method: Rise = R1 − R2 when positive; Fall = R2 − R1 when positive. The signs confirm the above logic. Why Other Options Are Wrong: (a) and (d) reverse the meaning of increasing/decreasing readings. Any single option other than (e) is incomplete because both statements (b) and (c) are needed to fully describe the rule. Common Pitfalls: Mixing backsight/foresight conventions with rise/fall logic; always compare readings from the same HI to avoid confusion. Final Answer: Both (b) and (c)

Question 14

Two-peg test (collimation error) — A dumpy level was set at the midpoint between two pegs A and B, 50 m apart. Staff readings were A = 1.22 and B = 1.06. With the level set up near A, the readings were A = 1.55 and B = 1.37. Determine the collimatio…

Accepted Answer

Introduction / Context: The two-peg test is used to detect and quantify collimation error (line of sight not truly horizontal) in a level. By observing staff readings with the instrument at the midpoint and then near one peg, we can isolate the error and express it per unit sight length for practical adjustments and checks. Given Data / Assumptions: Peg spacing: 50 m. Midpoint setup readings: A = 1.22, B = 1.06. Near-A setup readings: A = 1.55, B = 1.37. Near reading at A has negligible error; far reading at B carries most of the collimation effect. Concept / Approach: At the midpoint, the true difference in elevation between A and B is obtained because equal sight lengths cancel the error. With the instrument near A, compare the observed difference with the true difference; the discrepancy arises mainly from the far sight on B. Scale the error to 100 m to report a standard figure and determine the sign (upward/downward inclination). Step-by-Step Solution: True difference from midpoint setup: Δtrue = A − B = 1.22 − 1.06 = 0.16 m (A lower than B by 0.16 m).Observed difference from near-A setup: Δobs = 1.55 − 1.37 = 0.18 m.Error on the far sight (≈50 m) = Δobs − Δtrue = 0.18 − 0.16 = 0.02 m.Per 100 m error = 0.02 * (100 / 50) = 0.04 m.Sign: Larger observed difference indicates the distant reading at B is too small, which occurs when the line of sight is inclined upward; hence “inclined upward.” Verification / Alternative check: A line of sight tilted upward reduces far staff readings. The computed increase of 0.02 m over 50 m aligns with this behavior, confirming the sign and magnitude. Why Other Options Are Wrong: 0.02 m inclined upwards: Magnitude per 100 m is incorrect (should be 0.04 m). 0.04 m inclined downwards: Wrong sign. None of these: Incorrect because option “0.04 m inclined upward” matches the calculation. Common Pitfalls: Forgetting to scale the error to 100 m; mixing up which staff reading carries the error when the instrument is near one peg. Final Answer: 0.04 m inclined upward

Question 15

Road design on hill slopes — if the actual road gradient deviates from the proposed contour gradient toward the uphill side, what earthwork is required along the centre line? Choose the most appropriate action.

Accepted Answer

Introduction / Context: On hill roads, the contour gradient represents the alignment maintaining a specified longitudinal slope. If the chosen alignment strays upward (towards higher ground), the designed grade line lies below the ground surface, necessitating specific earthwork to bring the roadway to grade. Given Data / Assumptions: Road on a hillside with a proposed contour gradient. Actual alignment deviates uphill relative to the proposed path. Decision needed on the nature of earthwork at the centre line. Concept / Approach: When the alignment shifts to higher ground, the natural surface is above the design grade. To achieve the desired grade, material must be removed along the centre line, i.e., excavation (cutting). Conversely, if the alignment deviates downhill, an embankment would be necessary to raise the formation. Step-by-Step Solution: Identify relative position: uphill deviation → ground level higher than design grade.Select earthwork: remove surplus material → cutting.Apply along centre line to set formation at the design gradient.Confirm that embankment would be used only for downhill deviation. Verification / Alternative check: Standard hill-road design practices illustrate that when the alignment moves into higher contours, cutting is unavoidable to maintain the target gradient. Why Other Options Are Wrong: Embankment: Applicable for downhill deviations where ground is lower than grade. Earthwork (unspecified): Vague; the correct specific action is cutting. None of these: Incorrect because cutting is required. Common Pitfalls: Misreading the phrase “uphill side” and prescribing fill instead of cut; always compare ground level with the designed grade line. Final Answer: Excavation (cutting) on the centre line

Question 16

Telescope optics in surveying — identify the correct statements about image formation and reference lines in common survey telescopes. Choose the most comprehensive option.

Accepted Answer

Introduction / Context: Survey telescopes (astronomical and Galileo types) differ in eyepiece construction and image formation. Understanding where the real image forms and how the line of sight and line of collimation are defined is foundational for precise sighting, focusing, and collimation adjustments in field instruments. Given Data / Assumptions: Astronomical telescope: convex eyepiece; real inverted image at the focal plane. Galileo telescope: concave eyepiece; erect image with no real intermediate focus. Cross-hairs are on a diaphragm at the focal plane for sighting. Concept / Approach: In the astronomical type, the objective forms a real image at its focal plane, which the eyepiece magnifies. In the Galileo type, the eyepiece intercepts the converging beam before a real image forms, yielding an erect image. The line of sight is the ideal line through the optical centers; the practical sighting reference through the cross-hair intersection defines the line of collimation. Step-by-Step Solution: Match image formation for each telescope type as described.Define line of sight (optical centers) and line of collimation (through cross-hair intersection).Confirm that each statement A–D represents a correct textbook definition.Hence, the combined option “All of the above” is correct. Verification / Alternative check: Standard surveying texts on optics and instrument adjustment present exactly these definitions and distinctions. Why Other Options Are Wrong: Any single-statement choice omits other true facts; only “All of the above” covers all correct descriptions. Common Pitfalls: Confusing “line of sight” with “line of collimation”; in practice, collimation error is the misalignment between these ideal lines. Final Answer: All of the above

Question 17

Contours — which is considered the best general method for interpolating contour positions between known points in practical mapping? Choose the most appropriate technique.

Accepted Answer

Introduction / Context: Contour interpolation converts spot levels into continuous contour lines representing equal elevations. In practical topographic drafting, speed and reasonable accuracy are both critical, so the choice of method directly affects productivity and quality. Given Data / Assumptions: We seek a generally preferred method in routine mapping. Trade-offs: speed vs accuracy vs resources. Techniques available: estimation, graphical, computation. Concept / Approach: Estimation is quick but subjective; computation is accurate but time-consuming. Graphical methods (e.g., proportional division along lines between known levels) balance accuracy and efficiency, making them the preferred general-purpose approach in manual/plan-based workflows. Step-by-Step Solution: Identify the objective: reliable, repeatable contour placement.Compare methods: estimation (fast but subjective), computation (accurate but slow), graphical (balanced).Select graphical methods as the best general solution.Apply proportional distances along lines between points to place contour points consistently. Verification / Alternative check: Survey drafting guides recommend graphical interpolation for routine mapping jobs due to its balanced accuracy and speed. Why Other Options Are Wrong: Estimation: Excessively subjective. Computation: Overly time-intensive for most mapping scales. All of these: Not precise—one method is generally preferred. Common Pitfalls: Over-reliance on estimation leading to uneven contours; ignoring proportional rules along breaklines and spot levels. Final Answer: Graphical methods (e.g., proportional interpolation on plan)

Question 18

Chaining — sag correction for a suspended tape: A tape of length l and weight W (kg per m) is supported at its ends under a pull P (kg). What is the sag correction to be applied to the measured length?

Accepted Answer

Introduction / Context: When a steel tape is supported only at its ends, it sags under its own weight, making the measured horizontal distance longer than the true straight-line distance. A sag correction must be subtracted to obtain the correct length. This question asks for the standard formula in consistent units. Given Data / Assumptions: Tape length = l (m). Tape weight per unit length = W (kg/m) representing weight units consistent with pull P. Pull (tension) applied at the ends = P (kg). Small-sag approximation and symmetric suspension are assumed. Concept / Approach: Under uniform weight, the tape assumes a catenary; for small sag, the correction is derived from catenary approximations and proportional to W^2 and l^3, and inversely proportional to P^2. The correction is always positive in value and is subtracted from the measured length (because sag makes the measured length too long). Step-by-Step Solution: Model sag with small-deflection catenary assumptions.Apply the standard result: c_sag = (w^2 * L^3) / (24 * T^2).Map variables: w → W, L → l, T → P (consistent units).Therefore, c_sag = (W^2 * l^3) / (24 * P^2), to be subtracted from the measured length. Verification / Alternative check: Surveying texts list this formula; note that increasing tension P or shortening span l lowers the correction rapidly (P^2 and l^3 dependence). Why Other Options Are Wrong: (a) and (d): Wrong dimensional dependence; do not match catenary-based form. (c): Inverted dependence on W and P; physically incorrect. Common Pitfalls: Forgetting that the sag correction is subtractive; mixing force/weight units—keep W and P consistent (both treated as kg-force units here). Final Answer: c_sag = (W^2 * l^3) / (24 * P^2)

Question 19

Surveying terminology — the branch of surveying that determines both horizontal and vertical positions of points by instrumental observations is called: Select the correct term.

Accepted Answer

Introduction / Context: In engineering surveying, rapid determination of positions often requires simultaneous horizontal distances and elevation differences from a single setup. The specialized method that accomplishes this with stadia or subtense principles is widely used for topographic detail and preliminary works. Given Data / Assumptions: The method relies on angular measurements and staff intercepts. Heights and distances are derived from instrument readings using fixed constants. Common spellings vary (tacheometry/tachymetry), but the meaning is the same. Concept / Approach: Tacheometry (also spelled tachymetry) uses a theodolite or tacheometer with stadia lines to compute horizontal distance and elevation from a single observation. Telemetry refers to remote measurement and data transmission and is not a surveying branch. Hence, the correct term in surveying is tacheometry. Step-by-Step Solution: Identify the surveying goal: determine both plan position and height quickly.Recognize technique: stadia intercepts and vertical angles yield distance and rise/fall.Associate the method name: tacheometry is the established term.Exclude unrelated terminology like telemetry. Verification / Alternative check: Surveying manuals define tacheometry/tachymetry as the method for rapid distance and height determination using optical readings. Why Other Options Are Wrong: tachemetry: A variant spelling sometimes used, but the standard in the options is “tacheometry.” telemetry: Remote sensing/data transmission; not surveying layout. all the above: Incorrect because telemetry does not fit. Common Pitfalls: Spelling confusion between tacheometry and tachymetry; focus on meaning rather than orthography. Final Answer: tacheometry

Question 20

Surveying – Latitude of a Traverse Leg (Reduced Bearing Method) In plane surveying with a closed traverse, the latitude (northing or southing) of a traverse leg is computed by multiplying the measured length of that leg by which trigonometric functi…

Accepted Answer

Introduction: Traverse computation converts field measurements (lengths and bearings) into rectangular components called latitude (north–south) and departure (east–west). This question checks whether you recall the exact trigonometric relation between a side's reduced bearing and its latitude component. Given Data / Assumptions: Each traverse leg has a measured length L and a reduced bearing θ (0°–90° within its quadrant). Latitude is the projection of L on the north–south axis; departure is the projection on the east–west axis. Plane surveying assumptions apply (small area, neglecting curvature). Concept / Approach: Resolve the traverse side into orthogonal components using basic trigonometry. The component along the meridian (latitude) equals L * cos θ, while the component along the perpendicular (departure) equals L * sin θ. Signs (N/S and E/W) come from the quadrant of the reduced bearing, not from the magnitude formula itself. Step-by-Step Solution: 1) Let L be the length and θ the reduced bearing measured from the north/south line.2) Latitude = L * cos θ; take it as positive for northings and negative for southings based on the quadrant.3) Departure = L * sin θ; take it as positive for eastings and negative for westings based on the quadrant.4) Use these to compute misclosure, corrections (e.g., Bowditch), and coordinates. Verification / Alternative check: Check a limiting case: if θ = 0° (bearing exactly north/south), cos θ = 1 so latitude = L and departure = 0, which is consistent with geometry. Why Other Options Are Wrong: Tangent/cosecant do not represent orthogonal projections; 'sign of bearing' is not a magnitude; sine corresponds to departure, not latitude. Common Pitfalls: Swapping sine and cosine for latitude/departure; forgetting to apply the correct algebraic sign from the quadrant. Final Answer: Cosine of its reduced bearing

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