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Question 1
ప్రశ్న 1
A proposed access-road alignment requires two successive circular arcs of DIFFERENT radii, both bending in the same direction and meeting tangentially without an intervening straight. Which type of horizontal curve is formed?
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Explanation:
A compound circular curve consists of two or more circular arcs of different radii bending in the same direction. The component arcs meet tangentially at their junction. This junction is commonly called the point of compound curvature, or PCC. Each component arc has its own radius and central angle. Compound curves may be used where terrain or alignment restrictions make a single-radius curve unsuitable. The direct change in radius at the junction should also be examined for vehicle comfort and safety.
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Question 2
ప్రశ్న 2
Two circular arcs of radii R1 and R2, where R1 is not equal to R2, form a conventional COMPOUND curve and meet directly at point PCC. Which geometric condition is correct at PCC?
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Explanation:
The component arcs of a conventional compound curve join tangentially at PCC. Their tangent directions are therefore identical at the junction. The circle centres lie on the same normal line through PCC and on the same side of the common tangent. Curvature of a circular arc equals the reciprocal of its radius. Since the two radii differ, their curvature magnitudes also differ. Thus the tangent direction is continuous, but curvature changes abruptly at a direct compound-curve junction.
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Question 3
ప్రశ్న 3
Two circular arcs of radii 350 m and 200 m form a directly connected COMPOUND curve with a common tangent at PCC. Assuming both circle centres lie on the same side of the common tangent, what is the distance between their centres?
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Explanation:
The circle centres of a directly connected compound curve lie on the same normal through PCC. Each centre is separated from PCC by its corresponding radius. Because both centres are on the same side of the common tangent, their separation is the absolute difference between the radii. Therefore the centre-to-centre distance is 350 - 200 = 150 m. The sum of radii would apply to directly joined reverse circular arcs whose centres lie on opposite sides. The calculated distance is a geometric property of the specified compound junction.
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Question 4
ప్రశ్న 4
A right-hand COMPOUND circular curve consists of two successive arcs with central angles of 25 degrees and 35 degrees. Both arcs bend clockwise in the direction of travel. What is the total change in tangent direction across the compound curve?
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Explanation:
For a compound curve whose component arcs bend in the same direction, their directional changes are added. The first circular arc turns the alignment clockwise through 25 degrees. The second arc adds another clockwise turn of 35 degrees. The total direction change is therefore 25 + 35 = 60 degrees clockwise. This is the combined intersection or deflection angle for the two-arc alignment. Subtracting the angles would be appropriate for oppositely directed turns rather than the stated compound curve.
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Question 5
ప్రశ్న 5
A COMPOUND circular curve has a first arc of radius 200 m and central angle 30 degrees, followed tangentially by a second arc of radius 100 m and central angle 60 degrees in the SAME direction. What is the total circular arc length to three decimal places?
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Explanation:
The length of each circular arc is calculated separately using L = pi R Delta/180, with Delta in degrees. The first arc length is pi multiplied by 200 multiplied by 30 divided by 180, giving 104.719755 m. The second arc length is pi multiplied by 100 multiplied by 60 divided by 180, also giving 104.719755 m. Adding the two component lengths produces 209.439510 m. The total length is therefore 209.440 m to three decimal places. A single-radius arc-length formula should not be applied to the whole compound curve without accounting for its different radii.
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Question 6
ప్రశ్న 6
Which statement correctly defines a conventional REVERSE circular curve used in horizontal route alignment?
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Explanation:
A reverse circular curve consists of two successive circular arcs bending in opposite directions. At a direct junction, the arcs share a common tangent at the point of reverse curvature, or PRC. The resulting horizontal alignment is commonly described as S-shaped. The circle centres are located on opposite sides of the common tangent. Reverse curves may be useful for connecting offset route alignments under restricted conditions. For higher-speed applications, transitions and adequate superelevation reversal arrangements must be considered.
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Question 7
ప్రశ్న 7
Two directly joined circular arcs form a REVERSE curve with a common tangent at PRC. Their radii are 200 m and 120 m, and their centres lie on opposite sides of the common tangent along the same normal. What is the distance between the two centres?
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Explanation:
At the point of reverse curvature, the radii to the two circle centres are normal to the common tangent. For a reverse curve, the centres lie on opposite sides of this tangent. The line joining the centres therefore passes through PRC. Their separation equals the sum of the two radii. Substitution gives 200 + 120 = 320 m. This differs from the compound-curve case, where centres on the same side are separated by the difference of their radii.
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Question 8
ప్రశ్న 8
A reverse circular alignment first turns RIGHT through a central angle of 35 degrees and then turns LEFT through a central angle of 25 degrees. What is the NET change in horizontal travel direction?
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Explanation:
The component arcs of a reverse curve produce directional changes of opposite signs. Taking right turns as positive, the first arc contributes +35 degrees. The second arc contributes -25 degrees because it turns left. Their algebraic sum is +35 - 25 = +10 degrees. Thus the final tangent is directed 10 degrees clockwise relative to the initial tangent. Adding the magnitudes would incorrectly treat both arcs as turning in the same direction.
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Question 9
ప్రశ్న 9
Why is a DIRECT reverse circular curve, with no intervening transition arrangement, generally undesirable on a high-speed road?
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Explanation:
A direct reverse curve can have a continuous tangent direction at its junction. However, its signed curvature changes from one side of the alignment to the other. This creates an abrupt reversal in the required lateral acceleration at a given travelling speed. The direction of roadway superelevation may also need to be reversed between the two arcs. Appropriate transition arrangements and sufficient length for crossfall development can reduce these difficulties. The concern is vehicle dynamics and geometric design rather than an inability to establish a common tangent.
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Question 10
ప్రశ్న 10
For a high-speed road, which geometric arrangement is generally more suitable for connecting a STRAIGHT tangent to a constant-radius circular arc while introducing curvature progressively?
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Explanation:
A straight tangent has zero horizontal curvature. A circular curve of finite radius R has constant curvature equal to 1/R. Connecting them directly produces an abrupt change in curvature at the tangent point. A properly designed transition curve allows curvature to increase progressively from zero to 1/R. This produces a smoother development of lateral acceleration as the vehicle enters the circular portion. The transition also provides useful length for introducing roadway superelevation and, where necessary, additional pavement width.
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Question 11
ప్రశ్న 11
For a CLOTHOID or Euler spiral used as a transition between a straight tangent and a circular curve of radius R, which relationship correctly describes its curvature kappa at arc distance s from the spiral origin, when total spiral length is Ls?
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Explanation:
The defining property of a clothoid is that its curvature varies linearly with arc length. At its origin on the straight tangent, the curvature is zero. At the end of the transition, its curvature must equal 1/R to match the circular curve. Therefore the intermediate curvature is kappa(s) = s/(R Ls). The corresponding instantaneous radius decreases progressively from infinity toward R. This linear curvature relationship is also expressed using the clothoid parameter A, where A squared equals R multiplied by Ls.
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Question 12
ప్రశ్న 12
A clothoid transition curve has total arc length Ls = 75 m and joins a circular curve of radius R = 300 m. If its clothoid parameter A is defined by A^2 = R Ls, what is A?
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Explanation:
The clothoid parameter relates the transition length to the radius at its circular-curve junction. The defining relation is A squared = R multiplied by Ls. Substituting R = 300 m and Ls = 75 m gives A squared = 22500 m squared. Taking the positive square root gives A = 150 m. The parameter has units of length. It characterizes the variation in curvature along the specified clothoid.
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Question 13
ప్రశ్న 13
A clothoid of total length 60 m joins a circular curve of radius 300 m. At a point 20 m from the tangent-to-spiral origin, measured along the clothoid, what is its INSTANTANEOUS radius of curvature?
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Explanation:
For a clothoid, the curvature at arc distance s is s/(R Ls). The corresponding instantaneous radius r is therefore R Ls/s. The final circular radius is 300 m and the transition length is 60 m. At s = 20 m, r = (300 multiplied by 60)/20. This gives an instantaneous radius of 900 m. The radius decreases from infinity at the spiral origin to 300 m at its end.
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Question 14
ప్రశ్న 14
A clothoid transition has length Ls = 80 m and joins a circular curve of radius R = 200 m. What is the CHANGE IN TANGENT DIRECTION from the spiral origin to the point s = 40 m along the spiral? Use theta(s) = s^2/(2 R Ls) radians.
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Explanation:
The direction change along a clothoid is obtained by integrating its linearly increasing curvature. The specified expression is theta(s) = s squared divided by 2 R Ls. Substituting s = 40 m, R = 200 m and Ls = 80 m gives theta = 1600/(2 multiplied by 200 multiplied by 80). This simplifies to 1600/32000 = 0.050 rad. The value is approximately 2.865 degrees when expressed in angular degrees. This is the rotation of the local tangent, not the chord deflection from the initial tangent to the intermediate point.
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Question 15
ప్రశ్న 15
A clothoid has a total tangent-direction change theta_s from its beginning to its circular-curve junction. At HALF its total arc length, what fraction of theta_s has accumulated?
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Explanation:
In a clothoid, curvature increases linearly with arc distance from the origin. The accumulated change in tangent direction is proportional to the square of that distance. The relationship is theta(s)/theta_s = (s/Ls)^2. At half the transition length, s/Ls = 1/2. Squaring this ratio gives 1/4. Therefore only one-fourth of the total tangent-direction change has accumulated at the halfway point.
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Question 16
ప్రశ్న 16
A symmetrical spiral-circular-spiral alignment has a circular radius of 300 m and each transition length is 60 m. Using the conventional APPROXIMATE shift formula p = Ls^2/(24R), what is the shift of the circular curve?
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Explanation:
Introducing transition spirals requires the main circular arc to be displaced inward relative to the original simple circular alignment. The conventional approximate shift is p = Ls squared divided by 24R. The transition length is 60 m and the circular radius is 300 m. Substitution gives p = 60 squared divided by (24 multiplied by 300). This simplifies to 3600/7200 = 0.500 m. The formula is a small-angle approximation and should not be treated as an exact expression for arbitrarily long transitions.
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Question 17
ప్రశ్న 17
A SYMMETRICAL spiral-circular-spiral curve has circular radius R = 300 m, total intersection angle Delta = 60 degrees and transition length Ls = 60 m at EACH end. The approximate shift is p = 0.500 m. Using the specified approximation T = (R + p) tan(Delta/2) + Ls/2, what is the tangent length from PI to the beginning of the entry spiral, to three decimal places?
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Explanation:
The question supplies the conventional approximate tangent-length formula for a symmetrical transitioned curve. Substituting R = 300 m, p = 0.500 m and Delta/2 = 30 degrees gives T = 300.500 tan(30 degrees) + 30. The first term is approximately 173.493756 m. Adding half the transition length, 30 m, gives 203.493756 m. Therefore the approximate tangent length is 203.494 m. The formula accounts for both the shifted circular arc and the entry transition, unlike the simple-curve expression R tan(Delta/2).
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Question 18
ప్రశ్న 18
A symmetrical spiral-circular-spiral alignment has total intersection angle Delta = 60 degrees, circular radius R = 300 m and transition length Ls = 60 m at EACH end. For a clothoid, the tangent rotation through each transition is theta_s = Ls/(2R) radians. What is the CENTRAL ANGLE of the remaining circular arc, to three decimal degrees?
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Explanation:
The total change of alignment direction is 60 degrees. Each clothoid transition contributes a tangent rotation of Ls/(2R) radians. Substitution gives theta_s = 60/(600) = 0.100 radian, or approximately 5.729578 degrees. The two transitions together contribute approximately 11.459156 degrees. Subtracting this from 60 degrees gives the central angle of the circular arc as 48.540844 degrees. Rounded to three decimal degrees, the circular central angle is 48.541 degrees.
వివరణ:
Question 19
ప్రశ్న 19
A symmetrical spiral-circular-spiral alignment has total intersection angle Delta = 60 degrees, circular radius R = 300 m and transition length Ls = 60 m at EACH end. Assuming exact clothoid tangent rotations theta_s = Ls/(2R), what is the length of the remaining CONSTANT-RADIUS circular arc, to three decimal places?
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Explanation:
The total intersection angle in radians is pi/3. Each transition contributes a tangent rotation of Ls/(2R) = 0.100 radian. The remaining circular central angle is therefore pi/3 - 0.200 radian. Multiplying this by the circular radius gives Lc = 300(pi/3 - 0.200). This simplifies to 100 pi - 60 = 254.159265 m. The remaining circular arc length is consequently 254.159 m, excluding both transition lengths.
వివరణ:
Question 20
ప్రశ్న 20
A symmetrical spiral-circular-spiral curve has circular radius 300 m, total intersection angle 60 degrees and TWO transition spirals, each 60 m long. The chainage of TS (tangent-to-spiral) is 2+000.000 m. Using exact clothoid tangent-rotation geometry and measuring chainage along the complete alignment, what is the final ST (spiral-to-tangent) chainage, to three decimal places?
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Explanation:
The remaining constant-radius circular arc has a length of 254.159265 m. There are two transition spirals, each having an arc length of 60 m. The complete alignment length from TS to ST is therefore 60 + 254.159265 + 60 = 374.159265 m. The TS chainage is 2000.000 m. Adding the total alignment length gives ST chainage = 2374.159265 m. Rounded to three decimal places, the result is 2+374.159 m.
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Question 21
ప్రశ్న 21
What is the principal relationship between a properly designed horizontal TRANSITION curve and the introduction of SUPERELEVATION on a road?
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Explanation:
Superelevation raises the outer part of the roadway relative to the inner part to assist vehicles negotiating horizontal curvature. A transition curve provides a gradual change in horizontal curvature. Its length can also be used to develop the required pavement crossfall progressively. This helps avoid an abrupt change in pavement geometry at the beginning of the circular arc. The chosen transition length must satisfy the applicable geometric and superelevation-development requirements. The exact distribution of runoff depends on the adopted design arrangement and standards.
వివరణ:
Question 22
ప్రశ్న 22
For a CLOTHOID transition, assume constant vehicle speed v and the comfort criterion Ls = v^3/(C R), where v is in m/s, R is the final circular radius in metres and C is the permitted rate of change of lateral acceleration in m/s^3. If v = 20 m/s, R = 250 m and C = 0.40 m/s^3, what transition length is required?
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Explanation:
The stated comfort criterion limits the rate at which lateral acceleration develops as a vehicle traverses a clothoid. The specified expression is Ls = v cubed divided by C R. Substituting v = 20 m/s gives v cubed = 8000 m cubed per second cubed. The denominator is 0.40 multiplied by 250 = 100 in consistent units. Therefore Ls = 8000/100 = 80 m. This is the length required by the stated comfort criterion and must be compared with other applicable design requirements.
వివరణ:
Question 23
ప్రశ్న 23
Under the specified CLOTHOID comfort criterion Ls = v^3/(C R), the final circular radius R and permitted rate of change of lateral acceleration C remain unchanged. If the design speed DOUBLES, how does the required transition length change?
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Explanation:
The stated comfort-based transition length is directly proportional to the cube of vehicle speed. The circular radius and allowable acceleration-change rate are held constant. If speed increases from v to 2v, its cube increases from v cubed to 8v cubed. The required transition length consequently becomes eight times its original value. This demonstrates the strong influence of design speed on comfort-based transition requirements. The relationship applies specifically to the stated criterion and should not be confused with every other transition-length design condition.
వివరణ:
Question 24
ప్రశ్న 24
A roadway is to develop a final superelevation rate e = 0.06 by progressively raising one pavement edge relative to the selected rotation axis over an EFFECTIVE WIDTH of 7.0 m. Assume the entire edge elevation change is introduced uniformly along the transition, and the maximum permitted relative longitudinal gradient is 1 vertical in 150 horizontal. Using Ls = e W times 150, what is the minimum transition length required by this runoff criterion?
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Explanation:
The required edge elevation change relative to the chosen rotation axis is e multiplied by the effective width W. Substituting e = 0.06 and W = 7.0 m gives a rise of 0.420 m. The permissible relative longitudinal gradient is one vertical unit in 150 horizontal units. The minimum development length is therefore 0.420 multiplied by 150. This gives Ls = 63 m. The calculation uses the explicitly stated simplified runoff arrangement and does not include any additional crossfall-removal length or project-specific design allowance.
వివరణ:
Question 25
ప్రశ్న 25
A highway transition is being designed using TWO specified minimum-length criteria. The comfort criterion is Lc = v^3/(C R), with v = 20 m/s, C = 0.50 m/s^3 and R = 250 m. The superelevation-runoff criterion is Le = e W N, with e = 0.06, effective rotated width W = 8.0 m and limiting relative gradient 1 in N = 150. If the adopted length must satisfy BOTH criteria and no other limits govern, what is the MINIMUM permissible transition length?
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Explanation:
The comfort-based transition length is calculated using Lc = v cubed divided by C R. Substituting the data gives Lc = 8000/(0.50 multiplied by 250) = 64 m. The superelevation-runoff length is Le = e W N. Substitution gives Le = 0.06 multiplied by 8.0 multiplied by 150 = 72 m. Both criteria must be satisfied, so the greater of the two minimum lengths governs. Therefore the minimum permissible transition length under the stated assumptions is 72 m.
వివరణ:
Answer Key సమాధానాల పట్టిక
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Question 1 ప్రశ్న 1Answer: B. Compound circular curve. సమాధానం: B.
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Question 2 ప్రశ్న 2Answer: D. The arcs share a common tangent, but their curvature magnitudes differ because their radii differ. సమాధానం: D.
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Question 3 ప్రశ్న 3Answer: A. 150 m. సమాధానం: A.
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Question 4 ప్రశ్న 4Answer: C. 60 degrees clockwise. సమాధానం: C.
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Question 5 ప్రశ్న 5Answer: B. 209.440 m. సమాధానం: B.
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Question 6 ప్రశ్న 6Answer: A. It consists of successive circular arcs curving in opposite directions and joined tangentially, normally forming an S-shaped alignment. సమాధానం: A.
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Question 7 ప్రశ్న 7Answer: D. 320 m. సమాధానం: D.
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Question 8 ప్రశ్న 8Answer: C. 10 degrees right. సమాధానం: C.
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Question 9 ప్రశ్న 9Answer: B. Because the signed curvature reverses abruptly and the required crossfall or superelevation must also change direction. సమాధానం: B.
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Question 10 ప్రశ్న 10Answer: D. A transition curve that starts with zero curvature and reaches the circular curve's curvature at its end. సమాధానం: D.
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Question 11 ప్రశ్న 11Answer: A. kappa(s) = s/(R Ls), giving zero curvature at the origin and 1/R at the circular-curve junction. సమాధానం: A.
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Question 12 ప్రశ్న 12Answer: C. 150 m. సమాధానం: C.
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Question 13 ప్రశ్న 13Answer: B. 900 m. సమాధానం: B.
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Question 14 ప్రశ్న 14Answer: D. 0.050 rad. సమాధానం: D.
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Question 15 ప్రశ్న 15Answer: A. One-fourth. సమాధానం: A.
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Question 16 ప్రశ్న 16Answer: C. 0.500 m. సమాధానం: C.
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Question 17 ప్రశ్న 17Answer: B. 203.494 m. సమాధానం: B.
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Question 18 ప్రశ్న 18Answer: A. 48.541 degrees. సమాధానం: A.
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Question 19 ప్రశ్న 19Answer: D. 254.159 m. సమాధానం: D.
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Question 20 ప్రశ్న 20Answer: C. 2+374.159 m. సమాధానం: C.
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Question 21 ప్రశ్న 21Answer: B. The transition provides length over which roadway crossfall can be changed progressively toward the superelevation required on the circular curve. సమాధానం: B.
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Question 22 ప్రశ్న 22Answer: A. 80 m. సమాధానం: A.
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Question 23 ప్రశ్న 23Answer: D. It becomes eight times the original length. సమాధానం: D.
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Question 24 ప్రశ్న 24Answer: C. 63 m. సమాధానం: C.
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Question 25 ప్రశ్న 25Answer: B. 72 m. సమాధానం: B.