GATE 2021 Civil Engineering
130 questions across 2 sessions
Set 1
The rank of matrix $\begin{bmatrix} 1 & 2 & 2 & 3 \\ 3 & 4 & 2 & 5 \\ 5 & 6 & 2 & 7 \\ 7 & 8 & 2 & 9 \end{bmatrix}$ is
Getting to the top is ___________ than staying on top.
If $P = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}$ and $Q = \begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix}$ then $Q^T P^T$ is
The mirror image of the above text about the x-axis is
In a company, 35% of the employees drink coffee, 40% of the employees drink tea and 10% of the employees drink both tea and coffee. What % of employees drink neither tea nor coffee...
The shape of the cumulative distribution function of Gaussian distribution is
A propped cantilever beam EF is subjected to a unit moving load as shown in the figure (not to scale). The sign convention for positive shear force at the left and right sides of a...
⊕ and ⊙ are two operators on numbers p and q such that p ⊕ q = p^2 + q^2 / pq and p ⊙ q = p^2 / q; If x ⊕ y = 2 ⊙ 2, then x =
Four persons P, Q, R and S are to be seated in a row, all facing the same direction, but not necessarily in the same order. P and R cannot sit adjacent to each other. S should be s...
Gypsum is typically added in cement to
The direct and indirect costs estimated by a contractor for bidding a project is ₹160000 and ₹20000 respectively. If the mark up applied is 10% of the bid price, the quoted price (...
Statement: Either P marries Q or X marries Y Among the options below, the logical NEGATION of the above statement is:
Consider two rectangular sheets, Sheet M and Sheet N of dimensions 6 cm x 4 cm each. Folding operation 1: The sheet is folded into half by joining the short edges of the current sh...
In an Oedometer apparatus, a specimen of fully saturated clay has been consolidated under a vertical pressure of 50 kN/m² and is presently at equilibrium. The effective stress and...
A partially-saturated soil sample has natural moisture content of 25% and bulk unit weight of 18.5 kN/m³. The specific gravity of soil solids is 2.65 and unit weight of water is 9....
Five line segments of equal lengths, PR, PS, QS, QT and RT are used to form a star as shown in the figure above. The value of θ, in degrees, is _________
A function, λ, is defined by λ(p,q) = { (p-q)², if p≥q, { p+q, if p <q. The value of the expression λ(-(-3+2),(-2+3)) / λ(-(-2+1)) is:
If water is flowing at the same depth in most hydraulically efficient triangular and rectangular channel sections then the ratio of hydraulic radius of triangular section to that o...
'Kinematic viscosity' is dimensionally represented as
Humans have the ability to construct worlds entirely in their minds, which don't exist in the physical world. So far as we know, no other species possesses this ability. This skill...
Which one of the following statements is correct?
Which one of the following is correct?
The liquid forms of particulate air pollutants are
The shape of the most commonly designed highway vertical curve is
A highway designed for 80 km/h speed has a horizontal curve section with radius 250 m. If the design lateral friction is assumed to develop fully, the required super elevation is
Which of the following is NOT a correct statement?
Which of the following is/are correct statement(s)?
Consider the limit: $\lim_{x\to 1} \left(\frac{1}{\ln x} - \frac{1}{x-1}\right)$ The limit (correct up to one decimal place) is _________
The volume determined from $\iiint_V 8 xyz \, dV$ for $V = [2, 3]\times [1, 2] \times [0,1]$ will be (in integer) _________
The state of stress in a deformable body is shown in the figure. Consider transformation of the stress from the x-y coordinate system to the X-Y coordinate system. The angle $\thet...
The equation of deformation is derived to be y = x² - xL for a beam shown in the figure. The curvature of the beam at the mid-span (in units, in integer) will be ________
A truss EFGH is shown in the figure, in which all the members have the same axial rigidity R. In the figure, P is the magnitude of external horizontal forces acting at joints F and...
The cohesion (c), angle of internal friction (φ) and unit weight (γ) of a soil are 15 kPa, 20° and 17.5 kN/m³, respectively. The maximum depth of unsupported excavation in the soil...
Two reservoirs are connected through a homogeneous and isotropic aquifer having hydraulic conductivity (K) of 25 m/day and effective porosity (η) of 0.3 as shown in the figure (not...
A signalized intersection operates in two phases. The lost time is 3 seconds per phase. The maximum ratios of approach flow to saturation flow for the two phases are 0.37 and 0.40....
The solution of the second-order differential equation $\frac{d^2y}{dx^2} + 2\frac{dy}{dx} + y = 0$ with boundary conditions $y(0) = 1$ and $y(1) = 3$ is
The value of $\int_0^1 e^x dx$ using the trapezoidal rule with four equal subintervals is
A 50 mL sample of industrial wastewater is taken into a silica crucible. The empty weight of the crucible is 54.352 g. The crucible with the sample is dried in a hot air oven at 10...
A wedge M and a block N are subjected to forces P and Q as shown in the figure. If force P is sufficiently large, then the block N can be raised. The weights of the wedge and the b...
Contractor X is developing his bidding strategy against Contractor Y. The ratio of Y's bid price to X's cost for the 30 previous bids in which Contractor X has competed against Con...
Based on drained triaxial shear tests on sands and clays, the representative variations of volumetric strain (ΔV/V) with the shear strain (γ) is shown in the figure. Choose the COR...
A fluid flowing steadily in a circular pipe of radius R has a velocity that is everywhere parallel to the axis (centerline) of the pipe. The velocity distribution along the radial...
A water sample is analyzed for coliform organisms by the multiple-tube fermentation method. The results of confirmed test are as follows: Sample size (mL) 0.01 0.001 0.0001 Number...
Ammonia nitrogen is present in a given wastewater sample as the ammonium ion (NH4+) and ammonia (NH3). If pH is the only deciding factor for the proportion of these two constituent...
On a road, the speed - density relationship of a traffic stream is given by u=70-0.7k (where speed, u, is in km/h and density, k, is in veh/km). At the capacity condition, the aver...
The values of abscissa (x) and ordinate (y) of a curve are as follows: X y 2.0 5.00 2.5 7.25 3.0 10.00 3.5 13.25 4.0 17.00 By Simpson's 1/3rd rule, the area under the curve (round...
Vehicular arrival at an isolated intersection follows the Poisson distribution. The mean vehicular arrival rate is 2 vehicle per minute. The probability (round off to two decimal p...
Refer the truss as shown in the figure (not to scale). If load, F = 10√3 kN, moment of inertia, I = 8.33 × 10^6 mm^4, area of cross-section, A = 10^4 mm^2, and length, L = 2 m for...
A prismatic cantilever prestressed concrete beam of span length, L = 1.5 m has one straight tendon placed in the cross-section as shown in the following figure (not to scale). The...
A column is subjected to a total load (P) of 60 kN supported through a bracket connection, as shown in the figure (not to scale). The resultant force in bolt R (in kN, round off to...
Employ stiffness matrix approach for the simply supported beam as shown in the figure to calculate unknown displacements/rotations. Take length, L = 8 m; modulus of elasticity, E =...
A square plate O-P-Q-R of a linear elastic material with sides 1.0 m is loaded in a state of plane stress. Under a given stress condition, the plate deforms to a new configuration...
A small project has 12 activities – N, P, Q, R, S, T, U, V, W, X, Y, and Z. The relationship among these activities and the duration of these activities are given in the Table. Act...
The soil profile at a construction site is shown in the figure (not to scale). Ground water table (GWT) is at 5 m below the ground level at present. An old well data shows that the...
A retaining wall of height 10 m with clay backfill is shown in the figure (not to scale). Weight of the retaining wall is 5000 kN per m acting at 3.3 m from the toe of the retainin...
A combined trapezoidal footing of length L supports two identical square columns (P1 and P2) of size 0.5 m × 0.5 m, as shown in the figure. The columns P1 and P2 carry loads of 200...
An unsupported slope of height 15 m is shown in the figure (not to scale), in which the slope face makes an angle 50° with the horizontal. The slope material comprises purely cohes...
An unlined canal under regime conditions along with a silt factor of 1 has a width of flow 71.25 m. Assuming the unlined canal as a wide channel, the corresponding average depth of...
A cylinder (2.0 m diameter, 3.0 m long and 25 kN weight) is acted upon by water on one side and oil (specific gravity = 0.8) on other side as shown in the figure. The absolute rati...
A tube-well of 20 cm diameter fully penetrates a horizontal, homogeneous and isotropic confined aquifer of infinite horizontal extent. The aquifer is of 30 m uniform thickness. A s...
A baghouse filter has to treat 12 m³/s of waste gas continuously. The baghouse is to be divided into 5 sections of equal cloth area such that one section can be shut down for clean...
A secondary clarifier handles a total flow of 9600 m³/d from the aeration tank of a conventional activated-sludge treatment system. The concentration of solids in the flow from the...
Spot speeds of vehicles observed at a point on a highway are 40, 55, 60, 65 and 80 km/h. The space-mean speed (in km/h, round off to two decimal places) of the observed vehicles is...
The longitudinal section of a runway provides the following data: End-to-end runway (m) | Gradient (%) ---|--- 0 to 300 | + 1.2 300 to 600 | - 0.7 600 to 1100 | + 0.6 1100 to 1400...
Traversing is carried out for a closed traverse PQRS. The internal angles at vertices P, Q, R and S are measured as 92°, 68°, 123°, and 77°, respectively. If fore bearing of line P...
Set 2
Which of the above sentences are grammatically CORRECT? (i) Arun and Aparna are here. (ii) Arun and Aparna is here. (iii) Arun's families is here. (iv) Arun's family is here.
The value of $\lim_{x\to\infty} \frac{x \ln(x)}{1+x^2}$ is
The rank of the matrix $\begin{bmatrix} 5 & 0 & -5 & 0 \\ 0 & 2 & 0 & 1 \\ -5 & 0 & 5 & 0 \\ 0 & 1 & 0 & 2 \end{bmatrix}$ is
The mirror image of the above text about the x-axis is
Two identical cube shaped dice each with faces numbered 1 to 6 are rolled simultaneously. The probability that an even number is rolled out on each dice is:
The unit normal vector to the surface X²+Y²+Z²-48=0 at the point (4, 4, 4) is
If A is a square matrix then orthogonality property mandates
$\odot$ and $\oplus$ are two operators on numbers p and q such that p $\odot$ q = p - q, and p $\oplus$ q = p $\times$ q Then, (9 $\odot$ (6 $\oplus$ 7)) $\odot$ (7 $\oplus$ (6 $\o...
Four persons P, Q, R and S are to be seated in a row. R should not be seated at the second position from the left end of the row. The number of distinct seating arrangements possib...
In general, the CORRECT sequence of surveying operations is
Strain hardening of structural steel means
On a planar field, you travelled 3 units East from a point O. Next you travelled 4 units South to arrive at point P. Then you travelled from P in the North-East direction such that...
The author said, "Musicians rehearse before their concerts. Actors rehearse their roles before the opening of a new play. On the other hand, I find it strange that many public spea...
A single story building model is shown in the figure. The rigid bar of mass 'm' is supported by three massless elastic columns whose ends are fixed against rotation. For each of th...
Seasoning of timber for use in construction is done essentially to
1. Some football players play cricket. 2. All cricket players play hockey. Among the options given below, the statement that logically follows from the two statements 1 and 2 above...
In the figure shown above, PQRS is a square. The shaded portion is formed by the intersection of sectors of circles with radius equal to the side of the square and centers at S and...
In case of bids in Two-Envelop System, the correct option is
The most appropriate triaxial test to assess the long-term stability of an excavated clay slope is
In an equilateral triangle PQR, side PQ is divided into four equal parts, side QR is divided into six equal parts and side PR is divided into eight equal parts. The length of each...
As per the Unified Soil Classification System (USCS), the type of soil represented by 'MH' is
The ratio of the momentum correction factor to the energy correction factor for a laminar flow in a pipe is
Relationship between traffic speed and density is described using a negatively sloped straight line. If v_f is the free-flow speed then the speed at which the maximum flow occurs i...
Determine the correctness or otherwise of the following Assertion [a] and the Reason [r]. Assertion [a]: One of the best ways to reduce the amount of solid wastes is to reduce the...
The hardness of a water sample is measured directly by titration with 0.01 M solution of ethylenediamine tetraacetic acid (EDTA) using eriochrome black T (EBT) as an indicator. The...
The softening point of bitumen has the same unit as that of
Which of the following statement(s) is/are correct?
The value (round off to one decimal place) of $\int_{-1}^{1} x e^{|x|} dx$ is
A solid circular torsional member OPQ is subjected to torsional moments as shown in the figure (not to scale). The yield shear strength of the constituent material is 160 MPa. The...
A propped cantilever beam XY, with an internal hinge at the middle, is carrying a uniformly distributed load of 10 kN/m, as shown in the figure. The vertical reaction at support X...
The internal ($d_i$) and external ($d_o$) diameters of a Shelby sampler are 48 mm and 52 mm, respectively. The area ratio ($A_r$) of the sampler (in %, round off to two decimal pla...
A 12-hour unit hydrograph (of 1 cm excess rainfall) of a catchment is of a triangular shape with a base width of 144 hour and a peak discharge of 23 m³/s. The area of the catchment...
A lake has a maximum depth of 60 m. If the mean atmospheric pressure in the lake region is 91 kPa and the unit weight of the lake water is 9790 N/m³, the absolute pressure (in kPa,...
In a three-phase signal system design for a four-leg intersection, the critical flow ratios for each phase are 0.18, 0.32, and 0.22. The total loss time in each of the phases is 2...
A horizontal angle θ is measured by four different surveyors multiple times and the values reported are given below. Surveyor | Angle θ | Number of observations ---|---|--- 1 | 36°...
If k is a constant, the general solution of dy/dx - y/x = 1 will be in the form of
The smallest eigenvalue and the corresponding eigenvector of the matrix [[2, -2], [-1, 6]], respectively, are
A prismatic steel beam is shown in the figure. The plastic moment, M_p calculated for the collapse mechanism using static method and kinematic method is
A frame EFG is shown in the figure. All members are prismatic and have equal flexural rigidity. The member FG carries a uniformly distributed load w per unit length. Axial deformat...
A clay layer of thickness H has a preconsolidation pressure $p_c$ and an initial void ratio $e_0$. The initial effective overburden stress at the mid-height of the layer is $p_0$....
A rectangular open channel of 6 m width is carrying a discharge of 20 m³/s. Consider the acceleration due to gravity as 9.81 m/s² and assume water as incompressible and inviscid. T...
Read the statements given below. (i) Value of the wind profile exponent for the 'very unstable' atmosphere is smaller than the wind profile exponent for the 'neutral' atmosphere. (...
A water filtration unit is made of uniform-size sand particles of 0.4 mm diameter with a shape factor of 0.84 and specific gravity of 2.55. The depth of the filter bed is 0.70 m an...
For a given traverse, latitudes and departures are calculated and it is found that sum of latitudes is equal to +2.1 m and the sum of departures is equal to -2.8 m. The length and...
From laboratory investigations, the liquid limit, plastic limit, natural moisture content and flow index of a soil specimen are obtained as 60%, 27%, 32% and 27, respectively. The...
A function is defined in Cartesian coordinate system as $f(x, y) = xe^y$. The value of the directional derivative of the function (in integer) at the point (2, 0) along the directi...
An elevated cylindrical water storage tank is shown in the figure. The tank has inner diameter of 1.5 m. It is supported on a solid steel circular column of diameter 75 mm and tota...
A prismatic fixed-fixed beam, modelled with a total lumped-mass of 10 kg as a single degree of freedom (SDOF) system is shown in the figure. If the flexural stiffness of the beam i...
A perfectly flexible and inextensible cable is shown in the figure (not to scale). The external loads at F and G are acting vertically. The magnitude of tension in the cable segmen...
A fire hose nozzle directs a steady stream of water of velocity 50 m/s at an angle of 45° above the horizontal. The stream rises initially but then eventually falls to the ground....
A rectangular cross-section of a reinforced concrete beam is shown in the figure. The diameter of each reinforcing bar is 16 mm. The values of modulus of elasticity of concrete and...
The activity details for a small project are given in the Table. Activity | Duration (days) | Depends on A | 6 | - B | 10 | A C | 14 | A D | 8 | B E | 12 | C F | 8 | C G | 16 | D,...
An equipment has been purchased at an initial cost of ₹160000 and has an estimated salvage value of ₹10000. The equipment has an estimated life of 5 years. The difference between t...
A rectangular footing of size 2.8 m x 3.5 m is embedded in a clay layer and a vertical load is placed with an eccentricity of 0.8 m as shown in the figure (not to scale). Take Bear...
The soil profile at a road construction site is as shown in figure (not to scale). A large embankment is to be constructed at the site. The ground water table (GWT) is located at t...
Numerically integrate, $f(x) = 10x - 20x^2$ from lower limit $a = 0$ to upper limit $b = 0.5$. Use Trapezoidal rule with five equal subdivisions. The value (in units, round off to...
The void ratio of a clay soil sample M decreased from 0.575 to 0.510 when the applied pressure is increased from 120 kPa to 180 kPa. For the same increment in pressure, the void ra...
The hyetograph in the figure corresponds to a rainfall event of 3 cm. If the rainfall event has produced a direct runoff of 1.6 cm, the φ-index of the event (in mm/hour, round off...
A venturimeter as shown in the figure (not to scale) is connected to measure the flow of water in a vertical pipe of 20 cm diameter. Assume g = 9.8 m/s². When the deflection in the...
A reservoir with a live storage of 300 million cubic metre irrigates 40000 hectares (1 hectare = 10⁴ m²) of a crop with two fillings of the reservoir. If the base period of the cro...
An activated sludge process (ASP) is designed for secondary treatment of 7500 m³/day of municipal wastewater. After primary clarifier, the ultimate BOD of the influent, which enter...
A grit chamber of rectangular cross-section is to be designed to remove particles with diameter of 0.25 mm and specific gravity of 2.70. The terminal settling velocity of the parti...
In an aggregate mix, the proportions of coarse aggregate, fine aggregate and mineral filler are 55%, 40% and 5%, respectively. The values of bulk specific gravity of the coarse agg...
The stopping sight distance (SSD) for a level highway is 140 m for the design speed of 90 km/h. The acceleration due to gravity and deceleration rate are 9.81 m/s² and 3.5 m/s², re...
For a 2º curve on a high speed Broad Gauge (BG) rail section, the maximum sanctioned speed is 100 km/h and the equilibrium speed is 80 km/h. Consider dynamic gauge of BG rail as 17...