GATE Technical: Civil Engineering (CE) Set 2 questions with solutions

Q1. Consider a spherical globe rotating about an axis passing through its poles. There are three points P, Q, and R situated respectively on the equator, the north pole, and midway between the equator and the north pole in the northern hemisphere. Let P, Q, and R move with speeds v_P, v_Q, and v_R respectively. Which one of the following options is CORRECT?

1. v_P < v_R < v_Q
2. v_P < v_Q < v_R
3. v_P > v_R > v_Q
4. v_P = v_R ≠ v_Q

Answer: v_P > v_R > v_Q

All points share the same angular velocity, so linear speed v = omega*R*cos(latitude). The equator (P) has the largest radius, the pole (Q) has zero, and the mid-latitude point (R) is in between, giving vP > vR > vQ, option index 2.

Q2. A circular solid shaft of span L = 5 m is fixed at one end and free at the other end. A torque T = 100 kN.m is applied at the free end. The shear modulus and polar moment of inertia of the section are denoted as G and J, respectively. The torsional rigidity GJ is 50,000 kN.m²/rad. The following are reported for this shaft: Statement i) The rotation at the free end is 0.01 rad Statement ii) The torsional strain energy is 1.0 kN.m With reference to the above statements, which of the following is true?

1. Both the statements are correct
2. Statement i) is correct, but Statement ii) is wrong
3. Statement i) is wrong, but Statement ii) is correct
4. Both the statements are wrong

Answer: Statement i) is correct, but Statement ii) is wrong

Statement i) is correct because the rotation at the free end can be calculated using the formula for torsion, which shows that a torque of 100 kN.m and a torsional rigidity of 50,000 kN.m²/rad results in a rotation of 0.01 rad. However, Statement ii) is incorrect as the torsional strain energy is calculated to be 2.5 kN.m, not 1.0 kN.m.

Q3. Muller-Breslau principle is used in analysis of structures for _____________.

1. drawing an influence line diagram for any force response in the structure
2. writing the virtual work expression to get the equilibrium equation
3. superposing the load effects to get the total force response in the structure
4. relating the deflection between two points in a member with the curvature diagram in-between

Answer: drawing an influence line diagram for any force response in the structure

The Muller-Breslau principle states that the influence line for a specific response in a structure can be derived by considering the effect of removing or altering the support or loading condition associated with that response, making it essential for drawing influence line diagrams.

Q4. A standard penetration test (SPT) was carried out at a location by using a manually operated hammer dropping system with 50% efficiency. The recorded SPT value at a particular depth is 28. If an automatic hammer dropping system with 70% efficiency is used at the same location, the recorded SPT value will be _______.

1. 28
2. 20
3. 40
4. 25

Answer: 20

SPT blow count scales inversely with delivered energy: N2 = N1*(E1/E2) = 28*(50/70) = 20. A higher-efficiency hammer delivers more energy per blow, so fewer blows are recorded; the answer is 20, not 25.

Q5. A vertical sheet pile wall is installed in an anisotropic soil having coefficient of horizontal permeability, k_H and coefficient of vertical permeability, k_V. In order to draw the flow net for the isotropic condition, the embedment depth of the wall should be scaled by a factor of ________, without changing the horizontal scale.

1. √(k_H/k_V)
2. √(k_V/k_H)
3. 1.0
4. k_H/k_V

Answer: √(k_V/k_H)

The correct option is √(k_V/k_H) because to achieve isotropic conditions, the vertical scale of the flow net must be adjusted to account for the differing permeabilities in the horizontal and vertical directions. This scaling ensures that the flow behavior represented in the net accurately reflects the anisotropic properties of the soil.

Q6. Which one of the following options provides the correct match of the terms listed in Column-1 and Column-2? Column-1 P: Horton equation Q: Muskingum method R: Penman method Column-2 I: Precipitation II: Flood frequency III: Evapotranspiration IV: Infiltration V: Channel routing

1. P-IV, Q-V, R-III
2. P-III, Q-IV, R-I
3. P-IV, Q-III, R-II
4. P-III, Q-I, R-IV

Answer: P-IV, Q-V, R-III

The Horton equation relates to infiltration (P-IV), the Muskingum method is used for channel routing (Q-V), and the Penman method is a widely accepted approach for estimating evapotranspiration (R-III), making option A the correct match.

Q7. In the context of Municipal Solid Waste Management, ‘Haul’ in ‘Hauled Container System operated in conventional mode’ includes the _________.

1. time spent by the transport truck at the disposal site
2. time spent by the transport truck in traveling between a pickup point and the disposal site with a loaded container
3. time spent by the transport truck in picking up a loaded container at a pickup point
4. time spent by the transport truck in driving from the depot to the first pickup point

Answer: time spent by the transport truck in traveling between a pickup point and the disposal site with a loaded container

The correct option accurately describes the specific phase of waste transport where the truck is actively moving a loaded container from the collection point to the disposal site, which is a critical part of the hauling process in waste management.

Q8. Which of the following is equal to the stopping sight distance?

1. (braking distance required to come to stop) + (distance travelled during the perception-reaction time)
2. (braking distance required to come to stop) - (distance travelled during the perception-reaction time)
3. (braking distance required to come to stop)
4. (distance travelled during the perception-reaction time)

Answer: (braking distance required to come to stop) + (distance travelled during the perception-reaction time)

The stopping sight distance is the total distance a driver needs to safely stop their vehicle, which includes both the distance traveled during the time it takes to perceive a hazard and react, as well as the distance required to brake to a complete stop.

Q9. The magnetic bearing of the sun for a location at noon is 183° 30'. If the sun is exactly on the geographic meridian at noon, the magnetic declination of the location is _________.

1. 3° 30' W
2. 3° 30' E
3. 93° 30' W
4. 93° 30' E

Answer: 3° 30' W

The magnetic declination is the difference between magnetic north and true north. Since the sun is on the geographic meridian at noon, and the magnetic bearing is 183° 30', this indicates that magnetic north is 3° 30' west of true north.

Q10. With regard to the shear design of RCC beams, which of the following statements is/are TRUE?

1. Excessive shear reinforcement can lead to compression failure in concrete
2. Beams without shear reinforcement, even if adequately designed for flexure, can have brittle failure
3. The main (longitudinal) reinforcement plays no role in the shear resistance of beam
4. As per IS456:2000, the nominal shear stress in the beams of varying depth depends on both the design shear force as well as the design bending moment

Answer: Beams without shear reinforcement, even if adequately designed for flexure, can have brittle failure

Beams that lack shear reinforcement are susceptible to brittle failure, regardless of their flexural design, because they may not adequately resist shear forces, leading to sudden and catastrophic failure.

Q11. The reason(s) of the nonuniform elastic settlement profile below a flexible footing, resting on a cohesionless soil while subjected to uniform loading, is/are:

1. Variation of friction angle along the width of the footing
2. Variation of soil stiffness along the width of the footing
3. Variation of friction angle along the depth of the footing
4. Variation of soil stiffness along the depth of the footing

Answer: Variation of soil stiffness along the depth of the footing

The correct option is right because the stiffness of the soil can change with depth due to factors like density and compaction, leading to different settlement responses under a uniform load. This variation affects how the footing distributes the load, resulting in a nonuniform settlement profile.

Q12. Which of the following is/are NOT active disinfectant(s) in water treatment?

1. OH (hydroxyl radical)
2. O3 (ozone)
3. OCl− (hypochlorite ion)
4. Cl− (chloride ion)

Answer: Cl− (chloride ion)

The chloride ion (Cl−) is not an active disinfectant because it does not possess the oxidative properties necessary to kill pathogens, unlike the other options which are effective in disinfection processes.

Q13. As per the Indian Roads Congress guidelines (IRC 86: 2018), extra widening depends on which of the following parameters?

1. Horizontal curve radius
2. Superelevation
3. Number of lanes
4. Longitudinal gradient

Answer: Horizontal curve radius

Extra widening is primarily influenced by the horizontal curve radius because sharper curves require additional road width to accommodate vehicles safely, reducing the risk of overturning and improving overall stability during turns.

Q14. The critical flow condition in a channel is given by ________. [Note: α – kinetic energy correction factor; Q – discharge; A_c – cross-sectional area of flow at critical flow condition; T_c – top width of flow at critical flow condition; g – acceleration due to gravity]

1. αQ²/g = A_c³/T_c
2. αQ/g = A_c³/T_c²
3. αQ²/g = A_c³/T_c²
4. αQ/g = A_c³/T_c

Answer: αQ²/g = A_c³/T_c

At critical flow the Froude number is unity, giving the condition alpha*Q^2/g = A_c^3/T_c (equivalently alpha*Q^2*T_c/(g*A_c^3) = 1). The exponents on A and the single power of T_c distinguish the correct form.

Q15. Match the following air pollutants with the most appropriate adverse health effects: Air pollutant (P) Aromatic hydrocarbons (Q) Carbon monoxide (R) Sulfur oxides (S) Ozone Health effect to human and/or test animal (I) Reduce the capability of the blood to carry oxygen (II) Bronchitis and pulmonary emphysema (III) Damage of chromosomes (IV) Carcinogenic effect

1. (P) – (II), (Q) – (I), (R) – (IV), (S) – (III)
2. (P) – (IV), (Q) – (I), (R) – (III), (S) – (II)
3. (P) – (III), (Q) – (I), (R) – (II), (S) – (IV)
4. (P) – (IV), (Q) – (I), (R) – (II), (S) – (III)

Answer: (P) – (IV), (Q) – (I), (R) – (II), (S) – (III)

Aromatic hydrocarbons are known to have carcinogenic effects, carbon monoxide reduces the blood's oxygen-carrying capacity, sulfur oxides can lead to bronchitis and pulmonary emphysema, and ozone is associated with chromosome damage, making this option correctly match each pollutant with its respective health effect.

Q16. Which of the following statements is/are TRUE ?

1. The thickness of a turbulent boundary layer on a flat plate kept parallel to the flow direction is proportional to the square root of the distance from the leading edge
2. If the streamlines and equipotential lines of a source are interchanged with each other, the resulting flow will be a sink
3. For a curved surface immersed in a stationary liquid, the vertical component of the force on the curved surface is equal to the weight of the liquid above it
4. For flow through circular pipes, the momentum correction factor for laminar flow is larger than that for turbulent flow

Answer: For flow through circular pipes, the momentum correction factor for laminar flow is larger than that for turbulent flow

In laminar flow, the velocity profile is parabolic, leading to a greater momentum correction factor compared to turbulent flow, which has a flatter profile. This results in a more uniform velocity distribution in turbulent flow, thus requiring a smaller correction factor.

Q17. In the context of water and wastewater treatments, the correct statements are:

1. particulate matter may shield microorganisms during disinfection
2. ammonia decreases chlorine demand
3. phosphorus stimulates algal and aquatic growth
4. calcium and magnesium increase hardness and total dissolved solids

Answer: particulate matter may shield microorganisms during disinfection

Particulate matter can create a physical barrier that protects microorganisms from the effects of disinfectants, reducing the effectiveness of the disinfection process.

Q18. Which of the following statements is/are TRUE for the aerobic composting of sewage sludge?

1. Bulking agent is added during the composting process to reduce the porosity of the solid mixture
2. Leachate can be generated during composting
3. Actinomycetes are involved in the process
4. In-vessel composting systems cannot be operated in the plug-flow mode

Answer: Actinomycetes are involved in the process

Actinomycetes are a group of bacteria that play a crucial role in the decomposition of organic matter during aerobic composting, helping to break down complex compounds and contributing to the overall microbial activity essential for effective composting.

Q19. Consider the Marshall method of mix design for bituminous mix. With the increase in bitumen content, which of the following statements is/are TRUE?

1. the Stability decreases initially and then increases
2. the Flow increases monotonically
3. the air voids (VA) increases initially and then decreases
4. the voids filled with bitumen (VFB) increases monotonically

Answer: the voids filled with bitumen (VFB) increases monotonically

As bitumen content increases, the amount of voids filled with bitumen (VFB) also increases consistently, leading to better binding and stability of the mix. This relationship is direct and does not exhibit fluctuations, making it a reliable trend in mix design.