Surveying Curves MCQ Quiz – 50 Questions for Sub Engineer

Welcome to the comprehensive Surveying – Curves Practice Quiz tailored specifically for the MP Sub Engineer (Civil) competitive examination. Curves are an indispensable component of highway and railway alignment design, making this topic high-yield for engineering entrance and recruitment exams.

Quiz Structure & Rules:

• Total Questions: 50 MCQs (Includes 20+ precise numerical calculation questions).
• Difficulty Level: 20% Easy, 50% Moderate, and 30% Difficult (As per Sub Engineer pattern).
• Marking Scheme: Correct Answer = +1 Mark, Wrong Answer = −0.25 Mark, Unattempted = 0 Mark.
• Immediate Feedback: Click 'Check Answer' on any question to instantly verify your choice and view step-by-step solutions.

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Q1. The angle of deflection ($\Delta$) of a simple circular curve is equal to which of the following angles at the center of the curve?

• A) Half of the central angle
• B) Central angle subtended by the curve
• C) Double the central angle
• D) One-fourth of the central angle

Q2. Calculate the tangent length ($T$) for a simple circular curve of radius $300\text{ m}$ having a deflection angle of $40^\circ$.

• A) $109.19\text{ m}$
• B) $218.38\text{ m}$
• C) $102.61\text{ m}$
• D) $118.52\text{ m}$

Q3. According to the $30\text{ m}$ arc definition, the degree of curve ($D$) and radius ($R$) are related by which exact expression?

• A) $R = \frac{1146}{D}$
• B) $R = \frac{1718.9}{D}$
• C) $R = \frac{573}{D}$
• D) $R = \frac{2000}{D}$

Q4. Determine the length of long chord ($LC$) for a curve having a radius of $250\text{ m}$ and a central angle of $60^\circ$.

• A) $125.00\text{ m}$
• B) $216.51\text{ m}$
• C) $250.00\text{ m}$
• D) $433.01\text{ m}$

Q5. Mid-ordinate ($M$) of a simple circular curve of radius $R$ and deflection angle $\Delta$ is given by the formula:

• A) $M = R \left[1 - \cos\left(\frac{\Delta}{2}\right)\right]$
• B) $M = R \left[\sec\left(\frac{\Delta}{2}\right) - 1\right]$
• C) $M = R \tan\left(\frac{\Delta}{2}\right)$
• D) $M = R \sin\left(\frac{\Delta}{2}\right)$

Q6. Find the external distance ($E$) for a circular curve with $R = 400\text{ m}$ and deflection angle $\Delta = 30^\circ$.

• A) $13.63\text{ m}$
• B) $14.12\text{ m}$
• C) $28.25\text{ m}$
• D) $107.18\text{ m}$

Q7. If the chainage of the Point of Intersection (PI) is $1250.00\text{ m}$ and the tangent length is $145.20\text{ m}$, what is the chainage of the Point of Curve (PC)?

• A) $1395.20\text{ m}$
• B) $1104.80\text{ m}$
• C) $1250.00\text{ m}$
• D) $959.60\text{ m}$

Q8. Calculate the length of a curve ($L$) having a radius of $350\text{ m}$ and deflection angle of $45^\circ$.

• A) $274.89\text{ m}$
• B) $144.97\text{ m}$
• C) $549.78\text{ m}$
• D) $267.81\text{ m}$

Q9. Rankine's method of deflection angles for setting out circular curves relies on which basic instrument combination?

• A) Two chain/tapes only
• B) One theodolite and one tape
• C) Two theodolites only
• D) Total station with prism pole

Q10. Calculate the tangential angle $\delta$ (in minutes) for a chord length of $20\text{ m}$ and radius of $200\text{ m}$ using Rankine's formula.

• A) $85.94\text{ minutes}$
• B) $171.89\text{ minutes}$
• C) $343.78\text{ minutes}$
• D) $120.00\text{ minutes}$

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Q11. A reverse curve consists of two circular arcs bending in opposite directions. What is the main operational disadvantage of a reverse curve on high-speed highways?

• A) Excessive cost of construction
• B) Sudden change of superelevation and centrifugal force
• C) Inability to join non-parallel tangents
• D) Requirement of zero tangent lengths

Q12. What ideal geometric curve shape is most widely used as a transition curve in highway engineering in India?

• A) Cubic Parabola
• B) Bernoulli's Lemniscate
• C) Spiral or Clothoid
• D) Hyperbola

Q13. For an ideal transition curve, the radius of curvature at any point is:

• A) Directly proportional to the distance from the beginning of the transition curve
• B) Inversely proportional to the length from the beginning of the transition curve
• C) Constant throughout its length
• D) Equal to infinity at the junction with the circular curve

Q14. Compute the shift ($S$) of a circular curve of radius $300\text{ m}$ if a transition curve of length $60\text{ m}$ is introduced.

• A) $0.50\text{ m}$
• B) $1.00\text{ m}$
• C) $0.25\text{ m}$
• D) $2.00\text{ m}$

Q15. Calculate the degree of curve ($D$) for a radius of $573\text{ m}$ according to $20\text{ m}$ arc definition.

• A) $1^\circ$
• B) $2^\circ$
• C) $3^\circ$
• D) $0.5^\circ$

Q16. A compound curve consists of two circular arcs of radii $R_1 = 300\text{ m}$ and $R_2 = 500\text{ m}$. The deflection angles for the respective arcs are $\Delta_1 = 30^\circ$ and $\Delta_2 = 40^\circ$. Calculate the total length of the compound curve.

• A) $506.15\text{ m}$
• B) $488.69\text{ m}$
• C) $523.60\text{ m}$
• D) $366.52\text{ m}$

Q17. In setting out a curve by the method of offsets from long chord, the maximum offset ($x_0$) occurs at:

• A) Point of Curve (PC)
• B) Point of Tangency (PT)
• C) Mid-point of the long chord
• D) Point of Intersection (PI)

Q18. If the radius of a curve is $200\text{ m}$ and length of long chord is $160\text{ m}$, calculate the mid-ordinate offset ($O_0$) using the exact formula $O_0 = R - \sqrt{R^2 - (L/2)^2}$.

• A) $16.72\text{ m}$
• B) $18.35\text{ m}$
• C) $16.00\text{ m}$
• D) $20.00\text{ m}$

Q19. Calculate the length of a transition curve required for a design speed $v = 65\text{ km/h}$ on a curve of radius $R = 220\text{ m}$, assuming rate of change of centrifugal acceleration $C = 0.6\text{ m/s}^3$.

• A) $44.38\text{ m}$
• B) $32.15\text{ m}$
• C) $52.70\text{ m}$
• D) $159.78\text{ m}$

Q20. In two-theodolite method of curve setting, what is the main field operation advantage?

• A) Linear measurements with tape are entirely eliminated
• B) Angular measurements are eliminated
• C) Only one person is required to perform the survey
• D) It can be set out without establishing PC and PT

Q21. A $4^\circ$ curve is specified using standard $30\text{ m}$ arc definition. What is the radius of this curve?

• A) $429.73\text{ m}$
• B) $286.48\text{ m}$
• C) $572.96\text{ m}$
• D) $143.24\text{ m}$

Q22. In the chord deflection method (offsets from chords produced), the offset $O_1$ for the first sub-chord of length $c_1$ on a curve of radius $R$ is:

• A) $O_1 = \frac{c_1^2}{2R}$
• B) $O_1 = \frac{c_1^2}{R}$
• C) $O_1 = \frac{c_1(c_1 + c_2)}{2R}$
• D) $O_1 = \frac{c_1^2}{4R}$

Q23. Compute the first offset ($O_1$) in chord deflection method if the initial sub-chord is $10\text{ m}$ and curve radius is $250\text{ m}$.

• A) $0.40\text{ m}$
• B) $0.20\text{ m}$
• C) $0.80\text{ m}$
• D) $0.10\text{ m}$

Q24. If the chainage of PC is $1000.00\text{ m}$ and curve length is $235.62\text{ m}$, what is the chainage of PT?

• A) $1235.62\text{ m}$
• B) $764.38\text{ m}$
• C) $1117.81\text{ m}$
• D) $1471.24\text{ m}$

Q25. In highway survey, the point where a straight line (tangent) meets the circular curve is formally termed as:

• A) Point of Tangency (PT)
• B) Point of Curve (PC) or Tangent Curve Point (TC)
• C) Point of Intersection (PI)
• D) Apex Point

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Q26. Compute the radial offset ($O_x$) at a distance $x = 20\text{ m}$ from the PC along the tangent, for a curve radius $R = 200\text{ m}$ (use exact expression $O_x = \sqrt{R^2 + x^2} - R$).

• A) $1.00\text{ m}$
• B) $0.998\text{ m}$
• C) $2.00\text{ m}$
• D) $0.50\text{ m}$

Q27. Using the approximate formula for radial offset ($O_x \approx \frac{x^2}{2R}$), compute the offset at distance $x = 30\text{ m}$ for $R = 300\text{ m}$.

• A) $1.50\text{ m}$
• B) $3.00\text{ m}$
• C) $0.75\text{ m}$
• D) $2.25\text{ m}$

Q28. A curve whose radius varies continuously from infinity at the tangent point to a finite value $R$ at the circular curve is called a:

• A) Simple curve
• B) Compound curve
• C) Transition curve
• D) Reverse curve

Q29. Calculate the deflection angle $\Delta$ of a curve if the tangent length is equal to the radius of the curve ($T = R$).

• A) $45^\circ$
• B) $60^\circ$
• C) $90^\circ$
• D) $30^\circ$

Q30. A vertical curve is provided on highways to join two intersecting gradients. What geometric shape is generally adopted for vertical curves?

• A) Circular arc
• B) Simple Parabola
• C) Spiral
• D) Ellipse

Q31. Calculate the length of a transition curve ($L_s$) required to introduce a full superelevation $e = 0.07$ on a $7\text{ m}$ wide road, if the rate of introduction of superelevation is 1 in 150 (outer edge raised relative to inner edge).

• A) $73.50\text{ m}$
• B) $105.00\text{ m}$
• C) $52.50\text{ m}$
• D) $36.75\text{ m}$

Q32. If the central angle of a circular curve is $90^\circ$, what is the ratio of its long chord length to its radius ($LC / R$)?

• A) $1.000$
• B) $1.414$
• C) $1.732$
• D) $2.000$

Q33. What is the apex distance (external distance $E$) of a curve when $R = 250\text{ m}$ and deflection angle $\Delta = 60^\circ$?

• A) $38.68\text{ m}$
• B) $133.97\text{ m}$
• C) $33.49\text{ m}$
• D) $66.98\text{ m}$

Q34. The total angle of deflection for setting out the $n$-th point on a curve using Rankine's method is $\Delta_n$. How is $\Delta_n$ related to individual tangential angles ($\delta_1, \delta_2, ... \delta_n$)?

• A) $\Delta_n = \delta_n$
• B) $\Delta_n = \Delta_{n-1} + \delta_n$
• C) $\Delta_n = 2 \times \delta_n$
• D) $\Delta_n = \frac{\delta_1 + \delta_2 + ... + \delta_n}{n}$

Q35. Calculate the mid-ordinate ($M$) of a simple circular curve with radius $300\text{ m}$ and central angle $60^\circ$.

• A) $40.19\text{ m}$
• B) $25.20\text{ m}$
• C) $50.40\text{ m}$
• D) $13.40\text{ m}$

Q36. Where are reverse curves mostly preferred and permitted in civil engineering practice?

• A) High-speed National Highways
• B) Main railway trunk routes
• C) Railway marshalling yards and hilly road bends at low speeds
• D) Expressways with multi-lane traffic

Q37. Find the chainage of PI if chainage of PC is $1450.00\text{ m}$ and tangent length is $125.50\text{ m}$.

• A) $1324.50\text{ m}$
• B) $1575.50\text{ m}$
• C) $1701.00\text{ m}$
• D) $1450.00\text{ m}$

Q38. A spiral transition curve has a length $L_s = 80\text{ m}$ and radius of circular arc $R = 200\text{ m}$. Calculate the total spiral angle ($\phi_s$) in radians.

• A) $0.20\text{ rad}$
• B) $0.40\text{ rad}$
• C) $0.10\text{ rad}$
• D) $0.80\text{ rad}$

Q39. Convert the spiral angle $\phi_s = 0.20\text{ rad}$ into degrees.

• A) $11.46^\circ$
• B) $22.92^\circ$
• C) $5.73^\circ$
• D) $15.00^\circ$

Q40. What is the relationship between the angle of deflection ($\alpha$) of a transition curve and its spiral angle ($\phi_s$)?

• A) $\alpha = \frac{\phi_s}{3}$
• B) $\alpha = \frac{\phi_s}{2}$
• C) $\alpha = \phi_s$
• D) $\alpha = 2 \phi_s$

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Q41. Calculate the perpendicular offset from tangent to a circular curve of radius $R = 400\text{ m}$ at distance $x = 40\text{ m}$ using approximation $O_x = \frac{x^2}{2R}$.

• A) $2.00\text{ m}$
• B) $1.00\text{ m}$
• C) $4.00\text{ m}$
• D) $0.50\text{ m}$

Q42. The point of intersection of two tangents is called PI. If the back azimuth of initial tangent is $45^\circ$ and forward azimuth of next tangent is $105^\circ$, what is the deflection angle $\Delta$?

• A) $60^\circ\text{ Right}$
• B) $150^\circ\text{ Right}$
• C) $60^\circ\text{ Left}$
• D) $30^\circ\text{ Right}$

Q43. In the chord deflection method, the second offset $O_2$ for a normal chord $c_2$ following a sub-chord $c_1$ on a curve of radius $R$ is given by:

• A) $O_2 = \frac{c_2(c_1 + c_2)}{2R}$
• B) $O_2 = \frac{c_2^2}{2R}$
• C) $O_2 = \frac{c_1 + c_2}{R}$
• D) $O_2 = \frac{c_2^2}{R}$

Q44. Calculate $O_2$ if $c_1 = 10\text{ m}$, $c_2 = 20\text{ m}$, and $R = 200\text{ m}$.

• A) $1.50\text{ m}$
• B) $1.00\text{ m}$
• C) $2.00\text{ m}$
• D) $3.00\text{ m}$

Q45. Bernoulli's Lemniscate transition curve is particularly suited for roads when the deflection angle is:

• A) Very small ($< 10^\circ$)
• B) Large (up to $180^\circ$ or sharp turns)
• C) Zero
• D) Exactly $90^\circ$ only

Q46. What is the fundamental purpose of providing superelevation (cant) along circular curves?

• A) To counteract centrifugal force acting outwards on the vehicle
• B) To increase speed above design limit
• C) To drain off rainwater towards the center
• D) To increase sight distance at night

Q47. If the radius of a curve is reduced to half its original value while keeping speed constant, how does the centrifugal force change?

• A) Halved
• B) Doubled
• C) Quadrupled
• D) Unchanged

Q48. Calculate the length of long chord for a curve having $R = 150\text{ m}$ and deflection angle $\Delta = 90^\circ$.

• A) $212.13\text{ m}$
• B) $150.00\text{ m}$
• C) $300.00\text{ m}$
• D) $235.62\text{ m}$

Q49. In a simple circular curve, the angle subtended by a sub-chord of $15\text{ m}$ length at the center for $R = 300\text{ m}$ is:

• A) $2.865^\circ$
• B) $5.730^\circ$
• C) $1.432^\circ$
• D) $0.050^\circ$

Q50. The total length of a curve is $314.16\text{ m}$ and its radius is $200\text{ m}$. Calculate its central deflection angle $\Delta$ in degrees.

• A) $90^\circ$
• B) $60^\circ$
• C) $45^\circ$
• D) $120^\circ$

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Important Surveying Curve Formulas

Keep these standard formulas handy for quick calculations in Civil Engineering competitive exams:

Element	Standard Formula	Key Notations
Tangent Length ($T$)	$T = R \tan\left(\frac{\Delta}{2}\right)$	$R$ = Radius, $\Delta$ = Deflection Angle
Length of Curve ($L$)	$L = \frac{\pi R \Delta}{180^\circ}$	$\Delta$ in degrees
Long Chord ($LC$)	$LC = 2R \sin\left(\frac{\Delta}{2}\right)$	Distance between PC and PT
External Distance ($E$)	$E = R \left[\sec\left(\frac{\Delta}{2}\right) - 1\right]$	Apex distance from PI to curve
Mid-Ordinate ($M$)	$M = R \left[1 - \cos\left(\frac{\Delta}{2}\right)\right]$	Distance from mid-point of chord to curve
Degree of Curve ($D$)	$R = \frac{1718.9}{D}$ ($30\text{ m}$ arc) $R = \frac{1146}{D}$ ($20\text{ m}$ arc)	$D$ in degrees, $R$ in meters
Shift of Transition Curve ($S$)	$S = \frac{L_s^2}{24 R}$	$L_s$ = Length of transition curve
Rankine's Tangential Angle ($\delta$)	$\delta = 1718.9 \times \frac{c}{R} \text{ (minutes)}$	$c$ = chord length, $R$ = curve radius

Frequently Asked Questions (FAQs)

Q1. What is a Simple Circular Curve?

A simple circular curve consists of a single arc of constant radius connecting two straight tangents to provide a gradual change in direction.

Q2. What is Tangent Length in curve surveying?

Tangent length ($T$) is the distance from the Point of Intersection (PI) to the Point of Curve (PC) or Point of Tangency (PT). Calculated as $T = R \tan(\Delta/2)$.

Q3. What is the difference between Long Chord and Short Chord?

Long chord is the straight line joining the point of curve (PC) to the point of tangency (PT). Short chords (or sub-chords) are shorter line segments measured along the curve between individual pegs during layout.

Q4. Why is a Transition Curve provided on highways and railways?

Transition curves are provided to gradually introduce centrifugal force, superelevation (cant), and extra widening, preventing sudden shocks to vehicles and improving passenger comfort.

Q5. What is a Reverse Curve and where is it used?

A reverse curve consists of two circular arcs bending in opposite directions with a common tangent. It is primarily used in railway yards, sidings, and low-speed hilly roads where space is constrained.

Q6. How does negative marking work in this online quiz?

For every correct answer, +1 Mark is awarded. For every incorrect answer, 0.25 Mark is deducted. Unattempted questions carry zero penalty.