Your Answer : (Not Answered)

Correct Answer : B

The sum is (N−2)×180°.

Any closed polygon with N sides can be divided into N − 2 triangles from one vertex, each with angles adding to 180°. So the interior angles of a closed traverse must total (N − 2) × 180°, which is the angular check applied in the field.

For a quadrilateral, N = 4 gives 360°, as it should. (N − 4) × 180° would give zero for the same figure, and (N − 1) or (2N − 1) give 540° and 1260°, too large. The same rule is often written in right angles as (2N − 4) × 90°.

Your Answer : (Not Answered)

Correct Answer : D

The correct length of AB is 347.4 m.

A tape that is too short reads more than the true distance, because each 'tape length' laid down actually covers only 19.95 m:

\[ \begin{aligned} L &= \frac{L'}{L_n} \times l' = 348.28 \times \frac{19.95}{20} \\ &= 347.41\ \text{m} \end{aligned} \]

So the true length is a little less than the measured one. The other options are far from 348.28 m, while a 0.05 m error per 20 m can change the length by less than 1 m, so none of them can be right.

Your Answer : (Not Answered)

Correct Answer : C

The angle is called the dip.

A freely suspended magnetic needle aligns with the Earth's magnetic field, which is inclined to the horizontal everywhere except at the magnetic equator. The vertical angle between the needle and the horizontal is the dip or inclination; it is zero at the magnetic equator and 90° at the magnetic poles. Compass needles carry a small rider to counteract it.

Declination is the horizontal angle between the magnetic and true meridians. Azimuth and bearing are horizontal directions of a line, not vertical angles.

Your Answer : (Not Answered)

Correct Answer : D

The true bearing is 130° 15′.

With a westerly declination, magnetic north lies west of true north, so magnetic bearings are larger than true ones. True bearing = magnetic bearing minus the west declination.

\[ 135^\circ 30' - 5^\circ 15' = 130^\circ 15' \]

140° 45′ adds the declination, which would be correct for an easterly declination. 130° 45′ is a slip in the minutes, and 135° 30′ ignores declination.

Your Answer : (Not Answered)

Correct Answer : C

The sensitivity is \(\frac{1}{500}\) radians.

The sensitivity of a bubble tube is the angle through which the axis turns when the bubble moves one division. For a small angle that is the length of a division divided by the radius of the tube, in the same units:

\[ \begin{aligned} \theta &= \frac{2\ \text{mm}}{1000\ \text{mm}} \\ &= \frac{1}{500}\ \text{rad} \end{aligned} \]

That is about 412 seconds of arc. The other options are out by a factor of 4, 10 or 100, the kind of error that mixing millimetres with centimetres or metres produces.

Your Answer : (Not Answered)

Correct Answer : A

The arithmetic check applies to back sights, intermediate sights and fore sights.

In the rise and fall method every reading, including each intermediate sight, is compared with the one before it to give a rise or a fall, and every reduced level is worked out from those rises and falls. The check

sum of B.S. − sum of F.S. = sum of rises − sum of falls = last R.L. − first R.L.

therefore tests the reduction of all the reduced levels, intermediate ones included. This is its advantage over the height of collimation method, whose usual check does not cover intermediate sights. Options that leave out the intermediate sights, or the fore sights, are incomplete.

Your Answer : (Not Answered)

Correct Answer : C

They represent a depression.

Contours are lines of equal elevation. If closed contours carry lower values the closer they are to the centre, the ground falls towards the middle, which is a depression, a pit or a basin.

A hill shows the opposite: closed contours with values rising towards the centre. A river bed or valley gives V-shaped contours pointing upstream, and a saddle or pass shows two sets of closed high contours on either side of a low gap.

Your Answer : (Not Answered)

Correct Answer : D

The error in the staff reading is e = 0.073 m.

The bubble is off by 2.5 divisions of 30'' each, so the line of sight is tilted by 75''. Converting to radians and multiplying by the distance:

\[ \begin{aligned} \alpha &= 75'' = \frac{75}{206265} = 3.636 \times 10^{-4} \\ e &= \alpha D = 3.636 \times 10^{-4} \times 200 \\ &= 0.0727\ \text{m} \end{aligned} \]

The 2 mm division length is not needed because the sensitivity is already given as an angle per division. Using one division (30'') would give 0.029 m, and the other options match no consistent step.

Your Answer : (Not Answered)

Correct Answer : A

A passometer measures the number of paces in a given distance.

The passometer counts each step automatically as the surveyor walks. Multiplying the count by the average length of the surveyor's pace gives a rough distance, which is good enough for reconnaissance and small-scale surveys.

It does not measure steps in a vertical plane, nor count obstacles. Counting the revolutions of a wheel over a distance is the job of an odometer or a perambulator (measuring wheel), not a passometer.

Your Answer : (Not Answered)

Correct Answer : A

The scale 1/1000 is 1cm=10m.

A representative fraction of 1/1000 means one unit on the map stands for 1000 of the same units on the ground. So 1 cm on paper represents 1000 cm, and

\[ 1000 \text{ cm} = 10 \text{ m} \]

giving 1 cm = 10 m.

1 cm = 100 m is the scale 1/10000. 1 cm = 100 mm is 1/10, and 1 cm = 100 cm is 1/100. Each is out by a power of ten, a common slip when converting between centimetres and metres.

Your Answer : (Not Answered)

Correct Answer : A

The longest line in chain triangulation is the base line.

In chain surveying the area is divided into triangles. The base line is the longest of the main survey lines, usually running through the middle of the area, and the whole framework is built on it, so it is measured with the most care.

Check lines (proof lines) join points on the sides of triangles to check their accuracy. Tie lines join points on the main lines to locate details. Both are shorter than the base line.

Your Answer : (Not Answered)

Correct Answer : C

The whole circle bearing is about 152 degrees.

A positive departure means the line runs east and a negative latitude means it runs south, so it lies in the south-east quadrant. The reduced bearing is measured from south towards east:

\[ \begin{aligned} \theta &= \tan^{-1}\frac{70}{130} = 28.3^{\circ} \\ WCB &= 180^{\circ} - 28.3^{\circ} = 151.7^{\circ} \approx 152^{\circ} \end{aligned} \]

28 is the reduced bearing S 28 E, not the whole circle bearing measured clockwise from north. 62 is the angle measured from the east-west line instead, and 208 puts the line in the south-west quadrant, which would need a negative departure.

Your Answer : (Not Answered)

Correct Answer : C

A staff reading on a point whose elevation is to be determined is a fore sight.

The fore sight (FS) is the last staff reading taken from a setting of the level, on a point whose reduced level is unknown, often a change point or the end of the line. Its RL is the height of instrument minus the fore sight: RL = HI − FS.

A back sight is taken on a point of known level. A back bearing belongs to compass traversing and is a direction, not a staff reading. A bench mark is a point of known level, not a reading.

Your Answer : (Not Answered)

Correct Answer : B

A staff reading taken on a point of known elevation is a back sight.

A back sight (BS) is the first reading taken after setting up the level, on a bench mark or a point whose reduced level is already known. Adding it to that RL gives the height of instrument: HI = RL + BS.

A fore sight is the last reading before moving the instrument, taken on a point whose level is to be found. 'Plane of sight' (line of collimation) is the horizontal line through the instrument, not a reading.

Your Answer : (Not Answered)

Correct Answer : A

The vertical distance of a point above or below the datum is its reduced level.

The reduced level (RL) of a point is its height relative to a chosen datum, usually mean sea level. Points above the datum have positive RLs and points below it negative ones. In levelling, the staff readings are 'reduced' to these levels, which is where the name comes from.

A bench mark is a reference point whose RL is known, not the distance itself. The height of instrument is the RL of the line of collimation of the level, a property of the instrument setting rather than of a point on the ground.

Your Answer : (Not Answered)

Correct Answer : A

A fixed reference point of known elevation is a bench mark.

A bench mark (BM) is a permanent point whose reduced level is known, used as the starting or closing point in levelling. The Survey of India's great trigonometrical survey bench marks (GTS BMs) are the national ones; temporary bench marks are set up on a project for convenience.

A change point (also called a turning point) is a temporary point where both a fore sight and a back sight are taken while moving the instrument; its level is worked out, not known in advance. A reduced level is the elevation of a point, a value rather than a reference point.

Your Answer : (Not Answered)

Correct Answer : A

Straight, parallel and equally spaced contours represent a plane surface.

Contour spacing shows slope: equal spacing means a uniform slope, and straight parallel lines mean the surface does not bend. Together they describe an inclined plane, a surface of uniform gradient. (Contours on a level plane would not appear at all within it, since every point has the same elevation.)

A hill top shows as closed contours with higher values inside, and a depression as closed contours with lower values inside. Neither gives straight, parallel lines, so those options do not fit.

Your Answer : (Not Answered)

Correct Answer : C

The method is the rise and fall method.

In the rise and fall method, the difference between each staff reading and the one before it is worked out. If the new reading is smaller, the ground has risen by the difference; if larger, it has fallen. Each rise or fall is added to or subtracted from the previous reduced level (RL). The arithmetic check, sum of back sights minus sum of fore sights equals sum of rises minus sum of falls equals last RL minus first RL, checks every intermediate reading.

The height of instrument method finds each RL by subtracting the staff reading from the height of the line of collimation, not from differences between readings. 'Contour method' is not a method of reducing levels.

Your Answer : (Not Answered)

Correct Answer : B

The error of closure is 0.04 m.

The reduced level of a point is the starting level plus all back sights minus all fore sights, with the reading on the point itself counted as its final sight:

\[ \begin{aligned} RL &= 53.85 + 50.28 - 16.30 - 2.42 \\ &= 85.41\ \text{m} \end{aligned} \]

The bench mark's known elevation is 85.45 m, so the survey closes with an error of \(85.41 - 85.45 = -0.04\) m, a closing error of 0.04 m (the levels run 0.04 m low).

Leaving out the 2.42 m sight would give a nonsensical error of over 2 m, and 0.02, 0.06 and 0.08 m do not follow from the given sums.

Your Answer : (Not Answered)

Correct Answer : C

The difference is exactly 180°.

The fore bearing of a line AB is its direction measured at A, looking towards B. The back bearing is the direction of the same line measured at B, looking back towards A. Since these are two opposite directions along one straight line, their whole circle bearings differ by exactly 180°: BB = FB ± 180°.

If the observed difference is not 180°, that signals local attraction at one of the stations or an observation error, and the bearings must be corrected. A difference of 90°, or anything less or more than 180°, never holds for a correctly observed line.