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Question 1
ప్రశ్న 1
A theodolite is set up at station O to measure the horizontal angle between survey lines OA and OB. Which statement correctly describes the horizontal angle AOB?
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Explanation:
A horizontal angle is the angle between the horizontal projections of two sight directions. The theodolite measures this angle through its graduated horizontal circle. Its standing axis must be properly levelled to establish the intended vertical axis of rotation. The telescope may sight targets at different elevations while their horizontal directions are compared. A vertical angle instead describes the inclination of a sight line relative to a horizontal reference. Horizontal angle measurements are fundamental to traversing, triangulation and construction setting out.
వివరణ:
Question 2
ప్రశ్న 2
Which sequence correctly describes the ORDINARY method of measuring the clockwise horizontal angle AOB with a conventional vernier transit theodolite?
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Explanation:
The ordinary method measures a horizontal angle through successive sightings of its two defining directions. The instrument is first centred and levelled over the angular station O. A reference circle reading is established while accurately bisecting A. The upper motion then permits the telescope to turn horizontally toward B while the lower plate remains fixed. The reading difference gives the required clockwise angle, with circle wraparound accounted for if necessary. Repeating the observation on the opposite face provides an additional check and can reduce certain instrumental errors.
వివరణ:
Question 3
ప్రశ్న 3
During ordinary horizontal-angle measurement, a theodolite gives a circle reading of 38°24'30" when sighting A and 127°18'10" when subsequently sighting B clockwise, without disturbing the circle setting. What is the angle AOB?
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Explanation:
The clockwise horizontal angle is obtained by subtracting the initial circle reading from the final reading. The initial reading is 38°24'30" and the final reading is 127°18'10". Subtracting the seconds requires borrowing one minute because 10 seconds is less than 30 seconds. The resulting difference is 88°53'40". The readings belong to the same continuous horizontal-circle setting, so no revolution correction is required. This result is the observed clockwise angle between directions OA and OB.
వివరణ:
Question 4
ప్రశ్న 4
In an ordinary clockwise horizontal-angle observation, the initial circle reading is 335°42'20" and the final reading after sighting the second target is 24°17'50". The instrument has crossed the 360° graduation once. What angle was measured?
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Explanation:
The final circle reading is numerically smaller because the telescope has crossed the zero graduation. One complete revolution of 360° must therefore be added to the final reading before subtraction. The unwrapped final reading becomes 384°17'50". Subtracting 335°42'20" gives 48°35'30". Direct subtraction without allowing for circle wraparound would incorrectly produce a negative value for the specified clockwise movement. The correct measured horizontal angle is 48°35'30".
వివరణ:
Question 5
ప్రశ్న 5
The horizontal angle AOB is measured as 64°20'40" with the theodolite in FACE LEFT and 64°21'20" in FACE RIGHT. Assuming the observations have equal reliability, what is the mean horizontal angle?
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Explanation:
Face-left and face-right observations provide two independent determinations of the same horizontal angle under reversed telescope conditions. Their average is appropriate when both observations have equal reliability and have been reduced to the same angular convention. Converting the readings into seconds or averaging their seconds after accounting for minutes gives the same result. The mean of 64°20'40" and 64°21'20" is 64°21'00". The observations differ by 40 seconds, placing the mean 20 seconds from either value. Averaging the two faces can reduce certain instrumental errors but does not guarantee freedom from every field error.
వివరణ:
Question 6
ప్రశ్న 6
In the ordinary method, the horizontal circle was initially set to 0° at vernier A and 180° at vernier B while sighting the first target. On sighting the second target, vernier A indicates 73°42' and vernier B indicates 253°44'. What is the mean horizontal angle obtained from the two verniers?
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Explanation:
The two verniers are positioned approximately 180 degrees apart on the graduated horizontal circle. The value indicated by vernier A is 73°42'. The corresponding angular value from vernier B is obtained by subtracting 180° from 253°44', giving 73°44'. The mean of these equivalent angle values is 73°43'. Averaging appropriately reduced readings from opposite verniers helps reduce the effect of certain eccentricity errors. The raw values of 73°42' and 253°44' must not be averaged without first accounting for their 180-degree separation.
వివరణ:
Question 7
ప్రశ్న 7
Which statement best describes the REPETITION method of measuring a horizontal angle with a conventional transit theodolite?
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Explanation:
The repetition method measures one selected horizontal angle several times in succession. The instrument's upper and lower horizontal motions permit the angle to be accumulated mechanically on the circle. After the prescribed repetitions, the accumulated angular displacement is divided by the number of repetitions. This can improve the precision of the resulting angle compared with relying on one circle reading. Observations may also be made on both instrument faces to reduce certain systematic errors. The procedure is particularly useful when precise measurement of a limited number of angles is required.
వివరణ:
Question 8
ప్రశ్న 8
In the REPETITION method, after the first measurement of horizontal angle AOB, the telescope is pointing toward B and the circle shows the first accumulated angle. What is the correct procedure for accumulating the same angle a second time on a conventional vernier theodolite?
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Explanation:
The repetition method depends on preserving the accumulated circle reading between successive angular turns. After the first sighting of B, the lower motion allows the telescope to return to A while the upper and lower plates remain coupled. The accumulated reading is thereby preserved. The upper motion is then used to turn from A to B again, adding another measurement of the same angle. After two repetitions, the unwrapped circle displacement is approximately twice the required angle. Resetting the horizontal circle to zero between repetitions would defeat the mechanical accumulation procedure.
వివరణ:
Question 9
ప్రశ్న 9
A horizontal angle is measured by the repetition method three times, beginning with a circle reading of 0°00'00". The final accumulated reading after the third repetition is 224°17'30", and no complete revolution occurred. What is the mean angle?
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Explanation:
The repetition method gives the mean angle by dividing the total accumulated angular displacement by the number of repetitions. The initial reading is zero, so the accumulated displacement is 224°17'30". Converting to seconds gives 224 multiplied by 3600 plus 17 multiplied by 60 plus 30, or 807450 seconds. Dividing by three gives 269150 seconds. Converting this result back to degrees, minutes and seconds gives 74°45'50". Since no complete circle revolution occurred, no multiple of 360° needs to be added.
వివరణ:
Question 10
ప్రశ్న 10
During four clockwise repetitions of a horizontal angle, the initial circle reading is 28°15'00" and the final accumulated circle reading is 338°17'40". No complete revolution of the circle occurred. What is the mean observed angle?
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Explanation:
The accumulated angular displacement is the final reading minus the initial reading. Subtracting 28°15'00" from 338°17'40" gives 310°02'40". This accumulated displacement represents four measurements of the same horizontal angle. Dividing 310°02'40" by four gives 77°30'40". A direct check confirms that four times 77°30'40" equals 310°02'40". The initial circle reading must be subtracted because the repetition sequence did not begin at zero.
వివరణ:
Question 11
ప్రశ్న 11
A surveyor measures a horizontal angle by three clockwise repetitions, starting from 0°00'00". The accumulated angular displacement passes through one complete revolution, and the final displayed circle reading is 66°42'00". What is the mean horizontal angle?
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Explanation:
The circle display has passed through one complete revolution during the three repetitions. Therefore 360° must be added to the displayed final reading of 66°42'00". The total accumulated displacement is 426°42'00". Dividing this displacement by three gives 142°14'00". Multiplying the calculated angle by three independently reproduces 426°42'00". Ignoring the completed revolution would incorrectly produce an angle of only 22°14'00".
వివరణ:
Question 12
ప్రశ్న 12
Three clockwise repetitions of the same horizontal angle give an accumulated angle of 195°24'30" in FACE LEFT. Three further repetitions, with the circle accumulation restarted from zero, give 195°25'30" in FACE RIGHT. Assuming equal reliability, what is the final mean angle?
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Explanation:
The face-left mean angle is obtained by dividing 195°24'30" by three, giving 65°08'10". The face-right mean is 195°25'30" divided by three, giving 65°08'30". The two face means are based on the same number of repetitions and have equal stated reliability. Their arithmetic mean is therefore 65°08'20". The two face results differ by 20 seconds, so their mean lies 10 seconds from either result. Averaging the reversed-face observations helps reduce instrumental effects that change sign between faces.
వివరణ:
Question 13
ప్రశ్న 13
At a theodolite station, the horizontal directions of five well-distributed survey targets must be observed accurately. Which method is especially suitable, and what is its defining feature?
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Explanation:
The reiteration method is also called the direction method or method of series. It is particularly suitable when several horizontal directions must be measured from one station. The telescope is turned successively toward the selected targets around the horizon. Finally, the reference direction is sighted again to provide an angular closure check. Ideally the angles around the station sum to 360 degrees. The observations may be repeated on the opposite face to obtain improved mean angular values.
వివరణ:
Question 14
ప్రశ్న 14
In a reiteration observation at station O, the successive clockwise circle readings for targets A, B, C and D are 0°00'00", 78°35'20", 196°10'50" and 281°42'10" respectively. The horizon closes at 360°00'00" on A. What is the horizontal angle COD measured clockwise from C to D?
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Explanation:
In reiteration, the angle between successive target directions is obtained from their horizontal-circle readings. The reading on C is 196°10'50" and that on D is 281°42'10". Subtracting the former from the latter gives 85°31'20". The other successive angles are 78°35'20", 117°35'30" and 78°17'50" for the final return from D to A. Adding all four sector angles gives exactly 360°00'00". This confirms the arithmetic closure of the stated direction readings.
వివరణ:
Question 15
ప్రశ్న 15
In a reiteration survey, three consecutive clockwise angles around a station are 88°15'00", 101°20'00" and 94°40'00". If the horizontal circle closes exactly after one full revolution, what is the remaining fourth angle?
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Explanation:
A complete set of consecutive horizontal angles around a station should sum to 360 degrees. The three given angles are 88°15', 101°20' and 94°40'. Their sum is 284°15'00". Subtracting this total from 360°00'00" gives 75°45'00". Adding the fourth angle back to 284°15'00" reproduces exactly 360°00'00". This calculation illustrates the horizon-closure condition used in the reiteration method.
వివరణ:
Question 16
ప్రశ్న 16
A reiteration set contains four consecutive angles of equal assumed precision whose observed sum is 360°00'40". If the angular closing error is distributed equally among the four angles, what correction should be applied to EACH observed angle?
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Explanation:
The theoretical sum of consecutive angles completing the horizon is 360°00'00". The observed sum exceeds this value by 40 seconds. Therefore the angular closing error is positive 40 seconds. To obtain the theoretical total, the corrections must sum to negative 40 seconds. Under the explicitly stated equal-precision assumption, each of the four angles receives a correction of -40/4 = -10 seconds. Equal distribution is not automatically suitable when the angular observations have significantly different precisions.
వివరణ:
Question 17
ప్రశ్న 17
Which statement correctly distinguishes a DIRECT clockwise horizontal angle at a traverse station from a DEFLECTION angle?
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Explanation:
A direct or angle-to-the-right observation may be measured clockwise from the backsight direction to the next traverse direction. A deflection angle instead uses the forward extension of the preceding traverse line as its reference. Deflection angles are designated right or left according to the direction of turning. The distinction is important because the backsight direction is opposite to the forward prolongation of the preceding line. Consequently the two angular values need not be equal. Deflection-angle observations are particularly useful for route surveys such as roads, railways and pipelines.
వివరణ:
Question 18
ప్రశ్న 18
At traverse station B, the smaller included angle ABC between the backsight BA and the forward line BC is 132°15'00". The route is known to turn RIGHT from the forward prolongation of AB toward BC. What is the corresponding right deflection angle?
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Explanation:
A deflection angle is measured from the forward prolongation of the preceding traverse line to the succeeding line. The backsight BA points in the opposite direction to the prolongation of AB. Therefore the magnitude of the deflection angle is the supplement of the smaller included angle at B. Subtracting 132°15'00" from 180°00'00" gives 47°45'00". The question explicitly states that the traverse turns right, so the deflection is designated 47°45'00" R. The right or left designation must be retained because the magnitude alone does not fully describe the change in direction.
వివరణ:
Question 19
ప్రశ్న 19
The whole-circle bearing of traverse line AB is 72°40'00", measured clockwise from north. At B, the succeeding line BC makes a RIGHT deflection angle of 23°30'00" from the forward prolongation of AB. What is the whole-circle bearing of BC?
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Explanation:
A right deflection corresponds to a clockwise change in traverse direction. The forward prolongation of AB at B has the same whole-circle bearing as AB. Therefore the bearing of BC is obtained by adding the right deflection to the bearing of AB. The required sum is 72°40'00" + 23°30'00" = 96°10'00". Since the result is less than 360 degrees, no circle-wrap adjustment is required. A left deflection would instead require subtraction of the angular magnitude.
వివరణ:
Question 20
ప్రశ్న 20
Which statement correctly distinguishes an ANGLE OF ELEVATION from an ANGLE OF DEPRESSION measured using a theodolite?
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Explanation:
A vertical angle describes the inclination of the telescope line of sight relative to a horizontal reference. When the target lies above the horizontal line through the instrument, the observation is an angle of elevation. When it lies below that horizontal line, the observation is an angle of depression. A conventional signed vertical-angle system often assigns positive values to elevation and negative values to depression. The numerical display of a vertical circle depends on whether the instrument uses vertical angles or zenith angles. The reference convention must therefore be identified before interpreting raw circle readings.
వివరణ:
Question 21
ప్రశ్న 21
Which statement correctly relates the ZENITH angle to the signed vertical angle of a target, assuming the conventional face-left zenith-circle system in which a horizontal sight reads 90°?
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Explanation:
The zenith angle is measured downward from the upward vertical or zenith direction. In the stated face-left convention, a horizontal sight has a zenith-circle reading of 90 degrees. A target above the horizontal consequently has a zenith angle smaller than 90 degrees. A target below the horizontal has a zenith angle greater than 90 degrees. The signed vertical angle is therefore calculated as 90 degrees minus the zenith angle. This relationship applies to the specified circle convention and should not be imposed on instruments using different vertical-circle graduations.
వివరణ:
Question 22
ప్రశ్న 22
A theodolite uses a FACE-LEFT zenith-circle convention in which a horizontal sight reads 90°00'00". The observed zenith-circle reading to a target is 83°24'20". Assuming no vertical-circle index error, what is the vertical angle?
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Explanation:
For the stated face-left zenith-circle convention, the vertical angle is 90 degrees minus the observed zenith angle. The observed value is 83°24'20". Subtracting it from 90°00'00" gives 6°35'40". The resulting vertical angle is positive because the zenith angle is less than 90 degrees. Therefore the target lies above the horizontal line through the instrument. The assumption of zero index error allows the observed zenith reading to be used without an additional correction.
వివరణ:
Question 23
ప్రశ్న 23
A theodolite with conventional zenith-circle readings observes the SAME target in both faces. The FACE-LEFT reading is 83°24'20" and the FACE-RIGHT reading is 276°36'40". For this instrument, vertical angle from face left equals 90° minus the face-left reading, while vertical angle from face right equals the face-right reading minus 270°. What is the mean vertical angle?
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Explanation:
The face-left vertical angle is 90°00'00" - 83°24'20" = +6°35'40". The face-right vertical angle is 276°36'40" - 270°00'00" = +6°36'40". Both results are positive and therefore indicate elevation. The arithmetic mean of these two angles is +6°36'10". The face-left and face-right readings sum to 360°01'00", indicating a vertical-circle index discrepancy under the conventional model. Averaging the reduced angles from both faces compensates for the common index error when the instrument condition remains stable.
వివరణ:
Question 24
ప్రశ్న 24
A theodolite uses a conventional zenith-circle system in which, for the SAME fixed target and in the absence of index error, face-left and face-right zenith readings sum to 360°. The observed face-left reading is 96°12'40" and the face-right reading is 263°49'00". If the index error is defined as one-half of the observed sum minus 360°, what is the index error?
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Explanation:
Under the given zenith-circle convention, the ideal sum of the two face readings is 360°00'00". Adding 96°12'40" and 263°49'00" gives 360°01'40". The observed sum therefore exceeds the ideal sum by 1 minute 40 seconds, equivalent to 100 seconds. The specified index-error definition requires dividing that excess by two. Hence the index error is positive 50 seconds, or +0°00'50". The corresponding index correction applied to either raw zenith-circle reading would have the opposite sign under the stated common-index-error model.
వివరణ:
Question 25
ప్రశ్న 25
A surveyor observes a horizontal angle repeatedly in both face-left and face-right positions, but the theodolite standing axis is not truly vertical because the instrument was inadequately levelled. Which statement about error reduction is MOST CORRECT?
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Explanation:
Observing on both faces changes the sign of some instrumental error contributions. This permits compensation for certain collimation and horizontal-axis adjustment errors when the observations are properly paired. Repetition and averaging can also reduce the influence of some random pointing and reading errors. However, an inclined standing axis can produce errors that are not reliably removed merely by face reversal. Accurate levelling must therefore be carried out before angular observations are accepted. Incorrect centering, disturbed signals, instrument movement and other field errors also require separate precautions and checks.
వివరణ:
Answer Key సమాధానాల పట్టిక
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Question 1 ప్రశ్న 1Answer: C. The angle between the horizontal projections of OA and OB, measured about the vertical axis. సమాధానం: C.
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Question 2 ప్రశ్న 2Answer: A. Set up and level at O, establish a circle reading while accurately sighting A, release the upper clamp, turn clockwise to B, bisect B and determine the difference between the readings. సమాధానం: A.
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Question 3 ప్రశ్న 3Answer: B. 88°53'40". సమాధానం: B.
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Question 4 ప్రశ్న 4Answer: D. 48°35'30". సమాధానం: D.
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Question 5 ప్రశ్న 5Answer: C. 64°21'00". సమాధానం: C.
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Question 6 ప్రశ్న 6Answer: A. 73°43'00". సమాధానం: A.
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Question 7 ప్రశ్న 7Answer: D. The same horizontal angle is accumulated through successive measurements, and the total accumulated angle is divided by the number of repetitions. సమాధానం: D.
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Question 8 ప్రశ్న 8Answer: B. Release the lower clamp and return to A without changing the accumulated circle reading; then use the upper motion to sight B again and add another angular turn. సమాధానం: B.
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Question 9 ప్రశ్న 9Answer: C. 74°45'50". సమాధానం: C.
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Question 10 ప్రశ్న 10Answer: A. 77°30'40". సమాధానం: A.
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Question 11 ప్రశ్న 11Answer: D. 142°14'00". సమాధానం: D.
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Question 12 ప్రశ్న 12Answer: B. 65°08'20". సమాధానం: B.
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Question 13 ప్రశ్న 13Answer: C. Reiteration method, because several successive horizontal angles are observed around the station and the horizon is closed. సమాధానం: C.
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Question 14 ప్రశ్న 14Answer: A. 85°31'20". సమాధానం: A.
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Question 15 ప్రశ్న 15Answer: D. 75°45'00". సమాధానం: D.
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Question 16 ప్రశ్న 16Answer: B. -10 seconds. సమాధానం: B.
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Question 17 ప్రశ్న 17Answer: C. A direct angle may be measured clockwise from the backsight direction to the foresight, whereas a deflection angle is measured from the forward prolongation of the preceding traverse line to the succeeding line. సమాధానం: C.
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Question 18 ప్రశ్న 18Answer: D. 47°45'00" right. సమాధానం: D.
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Question 19 ప్రశ్న 19Answer: B. 96°10'00". సమాధానం: B.
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Question 20 ప్రశ్న 20Answer: A. An angle of elevation is measured above the horizontal, whereas an angle of depression is measured below the horizontal. సమాధానం: A.
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Question 21 ప్రశ్న 21Answer: C. The signed vertical angle equals 90° minus the face-left zenith angle. సమాధానం: C.
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Question 22 ప్రశ్న 22Answer: D. 6°35'40" elevation. సమాధానం: D.
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Question 23 ప్రశ్న 23Answer: B. 6°36'10" elevation. సమాధానం: B.
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Question 24 ప్రశ్న 24Answer: A. +0°00'50". సమాధానం: A.
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Question 25 ప్రశ్న 25Answer: C. Face reversal can reduce certain collimation and trunnion-axis errors, but it does not reliably eliminate the effect of an improperly levelled standing axis. సమాధానం: C.