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GATE CE 2021 Set 1

All 65 solved GATE CE 2021 Set 1 questions in exam order. Open a question, commit to an answer, and learn from the step-by-step solution. One question at a time.

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Questions

65

Paper marks

100

Question formats

3

MCQ · NAT · MSQ

Revision mode

Self-paced

No timer. Focus on understanding.

Difficulty mixEasy 22Medium 34Hard 9

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65 of 65 questions

General Aptitude (GA)

10
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    Question

    Getting to the top is ________ than staying on top.
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    Question

    📷 Figure: The word TRIANGLE shown in the first quadrant of a Cartesian coordinate system
    The mirror image of the above text about the x-axis is
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    Question

    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?
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    Question

    ⊕\oplus and ⊙\odot are two operators on numbers pp and qq such that
    p⊕q=p2+q2pqp \oplus q = \frac{p^2 + q^2}{pq} and p⊙q=p2qp \odot q = \frac{p^2}{q};
    If x⊕y=2⊙2x \oplus y = 2 \odot 2, then x=x =
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    Question

    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 seated to the right of Q. The number of distinct seating arrangements possible is:
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    Question

    Statement: Either P marries Q or X marries Y
    Among the options below, the logical NEGATION of the above statement is:
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    Question

    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 shape.
    Folding operation 2: The sheet is folded into half by joining the long edges of the current shape.
    Folding operation 1 is carried out on Sheet M three times.
    Folding operation 2 is carried out on Sheet N three times.
    The ratio of perimeters of the final folded shape of Sheet N to the final folded shape of Sheet M is ________.
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    Question

    Five line segments of equal lengths, PR, PS, QS, QT and RT are used to form a star as shown in the figure above.
    A five-pointed star with vertices labeled P, Q, R, S, T and an angle theta at vertex P
    The value of θ\theta, in degrees, is ________
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    Question

    A function, λ\lambda, is defined byλ(p,q)={(p−q)2,if p≥q,p+q,if p<q.\lambda(p, q) = \begin{cases} (p - q)^2, & \text{if } p \geq q, \\ p + q, & \text{if } p < q. \end{cases}The value of the expression λ(−(−3+2),(−2+3))(−(−2+1))\frac{\lambda(-(-3 + 2), (-2 + 3))}{(-(-2 + 1))} is:
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    Question

    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 is so important that we have different words to refer to its different flavors, such as imagination, invention and innovation.
    Based on the above passage, which one of the following is TRUE?
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Civil Engineering (CE, Set-1)

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    Question

    The rank of matrix [1223342556277829]\begin{bmatrix} 1 & 2 & 2 & 3 \\ 3 & 4 & 2 & 5 \\ 5 & 6 & 2 & 7 \\ 7 & 8 & 2 & 9 \end{bmatrix} is
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    Question

    If P=[1234]P = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} and Q=[0110]Q = \begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix} then QTPTQ^T P^T is
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    Question

    The shape of the cumulative distribution function of Gaussian distribution is
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    Question

    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 any section is also shown.
    Propped cantilever beam EF with unit moving load and sign convention for shear force
    The CORRECT qualitative nature of the influence line diagram for shear force at G is
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    Question

    Gypsum is typically added in cement to
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    Question

    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 (in ₹) of the contractor is
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    Question

    In an Oedometer apparatus, a specimen of fully saturated clay has been consolidated under a vertical pressure of 50 kN/m250\text{ kN/m}^2 and is presently at equilibrium. The effective stress and pore water pressure immediately on increasing the vertical stress to 150 kN/m2150\text{ kN/m}^2, respectively are
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    Question

    A partially-saturated soil sample has natural moisture content of 25%25\% and bulk unit weight of 18.5 kN/m318.5\text{ kN/m}^3. The specific gravity of soil solids is 2.652.65 and unit weight of water is 9.81 kN/m39.81\text{ kN/m}^3. The unit weight of the soil sample on full saturation is
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    Question

    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 of rectangular section is
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    Question

    'Kinematic viscosity' is dimensionally represented as
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    Question

    Which one of the following statements is correct?
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    Question

    Which one of the following is correct?
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    Question

    The liquid forms of particulate air pollutants are
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    Question

    The shape of the most commonly designed highway vertical curve is
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    Question

    A highway designed for 80 km/h80\text{ km/h} speed has a horizontal curve section with radius 250 m250\text{ m}. If the design lateral friction is assumed to develop fully, the required super elevation is
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    Question

    Which of the following is NOT a correct statement?
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    Question

    Which of the following is/are correct statement(s)?
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    Question

    Consider the limit:lim⁡x→1(1ln⁡x−1x−1)\lim_{x \to 1} \left( \frac{1}{\ln x} - \frac{1}{x - 1} \right)The limit (correct up to one decimal place) is ___________
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    Question

    The volume determined from ∭V8xyz dV\iiint_V 8 xyz \, dV for V=[2,3]×[1,2]×[0,1]V = [2, 3] \times [1, 2] \times [0, 1] will be (in integer) ________.
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    Question

    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 θ\theta, locating the X-axis, is assumed to be positive when measured from the x-axis in counter-clockwise direction.
    Stress transformation diagram showing x-y and X-Y coordinate systems with various stress components labeled: $\sigma_{XX} = 120$ MPa, $\sigma_{XY} = 50$ MPa, $\sigma_{xx} = 40$ MPa, $\sigma_{yy} = 35.6$ MPa, and an angle $\theta = 30^\circ$ between the x and X axes.
    The absolute magnitude of the shear stress component σxy\sigma_{xy} (in MPa, round off to one decimal place) in x-y coordinate system is ________.
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    Question

    The equation of deformation is derived to be y=x2−xLy = x^2 - xL for a beam shown in the figure.
    A simply supported beam of length $L$ with a pin support at the left end (origin of x-y system) and a roller support at the right end. The x-axis is along the beam, and the y-axis is vertical.
    The curvature of the beam at the mid-span (in units, in integer) will be ________.
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    Question

    A truss EFGH is shown in the figure, in which all the members have the same axial rigidity RR. In the figure, PP is the magnitude of external horizontal forces acting at joints F and G.
    A truss EFGH with horizontal forces P acting at joints F and G. The truss has a square base of side L and diagonal members.
    If R=500×103R = 500 \times 10^3 kN, P=150P = 150 kN and L=3L = 3 m, the magnitude of the horizontal displacement of joint G (in mm, round off to one decimal place) is __________.
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    Question

    The cohesion (cc), angle of internal friction (ϕ\phi) and unit weight (γ\gamma) of a soil are 15 kPa, 20∘20^\circ and 17.5 kN/m³, respectively. The maximum depth of unsupported excavation in the soil (in m, round off to two decimal places) is __________.
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    Question

    Two reservoirs are connected through a homogeneous and isotropic aquifer having hydraulic conductivity (KK) of 25 m/day and effective porosity (η\eta) of 0.3 as shown in the figure (not to scale). Ground water is flowing in the aquifer at the steady state.
    Diagram showing two reservoirs separated by an aquifer of length 2 km. Reservoir 1 has a water level of 30 m above datum, and Reservoir 2 has a water level of 10 m above datum. The aquifer is bounded by an aquiclude above and an aquifuge below.
    If water in Reservoir 1 is contaminated then the time (in days, round off to one decimal place) taken by the contaminated water to reach Reservoir 2 will be __________.
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    Question

    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 optimum cycle length using the Webster’s method (in seconds, round off to one decimal place) is ___________
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    The solution of the second-order differential equation d2ydx2+2dydx+y=0\frac{d^2y}{dx^2} + 2\frac{dy}{dx} + y = 0 with boundary conditions y(0)=1y(0) = 1 and y(1)=3y(1) = 3 is
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    Question

    The value of ∫01exdx\int_0^1 e^x dx using the trapezoidal rule with four equal subintervals is
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    Question

    A 50 mL50\text{ mL} sample of industrial wastewater is taken into a silica crucible. The empty weight of the crucible is 54.352 g54.352\text{ g}. The crucible with the sample is dried in a hot air oven at 104 ∘C104\text{ }^\circ\text{C} till a constant weight of 55.129 g55.129\text{ g}. Thereafter, the crucible with the dried sample is fired at 600 ∘C600\text{ }^\circ\text{C} for 1 h1\text{ h} in a muffle furnace, and the weight of the crucible along with residue is determined as 54.783 g54.783\text{ g}. The concentration of total volatile solids is ____________.
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    Question

    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 block are negligible compared to the forces P and Q. The coefficient of friction (μ\mu) along the inclined surface between the wedge and the block is 0.20.2. All other surfaces are frictionless. The wedge angle is 30∘30^\circ.
    A diagram showing a vertical block N and a triangular wedge M. Force Q acts vertically downwards on block N. Force P acts horizontally to the right on wedge M. Surface 1 is the horizontal base, Surface 2 is the inclined interface between M and N, and Surface 3 is the vertical wall against which block N rests.
    The limiting force P, in terms of Q, required for impending motion of block N to just move it in the upward direction is given as P=αQP = \alpha Q. The value of the coefficient 'α\alpha' (round off to one decimal place) is
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    Question

    Contractor X is developing his bidding strategy against Contractor Y. The ratio of Y**'s bid price to **X**'s cost for the 3030 previous bids in which Contractor **X has competed against Contractor Y is given in the Table
    Ratio of **Y**'s bid price to **X**'s costNumber of bids
    1.021.0266
    1.041.041212
    1.061.0633
    1.101.1066
    1.121.1233
    Based on the bidding behaviour of the Contractor Y, the probability of winning against Contractor Y at a mark up of 8%8\% for the next project is
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    Question

    Based on drained triaxial shear tests on sands and clays, the representative variations of volumetric strain (ΔV/V\Delta V/V) with the shear strain (γ\gamma) is shown in the figure.
    Graph showing volumetric strain vs shear strain with two curves, P and Q. Curve P shows initial compression followed by expansion (dilatancy). Curve Q shows continuous compression.
    Choose the CORRECT option regarding the representative behaviour exhibited by Curve PP and Curve QQ.
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    Question

    A fluid flowing steadily in a circular pipe of radius RR has a velocity that is everywhere parallel to the axis (centerline) of the pipe. The velocity distribution along the radial direction is Vr=U(1−r2R2)V_r = U \left( 1 - \frac{r^2}{R^2} \right), where rr is the radial distance as measured from the pipe axis and UU is the maximum velocity at r=0r = 0. The average velocity of the fluid in the pipe is
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    Question

    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)Number of positive results out of 5 tubesNumber of negative results out of 5 tubes
    0.0150
    0.00132
    0.000114
    The most probable number (MPN) of coliform organisms for the above results is to be obtained using the following MPN Index.
    MPN Index for Various Combinations of Positive Results when Five Tubes used per Dilution of 10.0 mL, 1.0 mL and 0.1 mL
    Combination of positive tubesMPN Index per 100 mL
    0 - 2 - 411
    1 - 3 - 519
    4 - 2 - 022
    5 - 3 - 1110
    The MPN of coliform organisms per 100 mL is
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    Question

    Ammonia nitrogen is present in a given wastewater sample as the ammonium ion (NH4+NH_4^+) and ammonia (NH3NH_3). If pH is the only deciding factor for the proportion of these two constituents, which of the following is a correct statement?
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    Question

    On a road, the speed – density relationship of a traffic stream is given by u=70−0.7ku = 70 - 0.7k (where speed, uu, is in km/h and density, kk, is in veh/km). At the capacity condition, the average time headway will be
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    Question

    The values of abscissa (xx) and ordinate (yy) of a curve are as follows:
    XXyy
    2.05.00
    2.57.25
    3.010.00
    3.513.25
    4.017.00
    By Simpson’s 1/3rd rule, the area under the curve (round off to two decimal places) is ___________
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    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 places) that at least 2 vehicles will arrive in any given 1-minute interval is __________
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    Question

    Refer the truss as shown in the figure (not to scale).
    A truss with joints P, Q, R, S, T. A downward load F is applied at joint T. Supports are at P and S. Member properties E, A and E, 2A are indicated.
    If load, F=103F = 10\sqrt{3} kN, moment of inertia, I=8.33×106I = 8.33 \times 10^6 mm4^4, area of cross-section, A=104A = 10^4 mm2^2, and length, L=2L = 2 m for all the members of the truss, the compressive stress (in kN/m2^2, in integer) carried by the member Q-R is __________
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    Question

    A prismatic cantilever prestressed concrete beam of span length, L=1.5L = 1.5 m has one straight tendon placed in the cross-section as shown in the following figure (not to scale). The total prestressing force of 5050 kN in the tendon is applied at dc=50d_c = 50 mm from the top in the cross-section of width, b=200b = 200 mm and depth, d=300d = 300 mm.
    A cantilever beam of length L with a point load P at the free end. A straight prestressing tendon is shown at distance $d_c$ from the top. The cross-section shows width b, depth d, and the tendon position.
    If the concentrated load, P=5P = 5 kN, the resultant stress (in MPa, in integer) experienced at point 'Q' will be __________
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    A column is subjected to a total load (PP) of 60 kN60\text{ kN} supported through a bracket connection, as shown in the figure (not to scale).
    Bracket connection with a column, a bracket plate, and 6 bolts. A load P = 60 kN is applied at a distance of 100 mm from the column face. Bolt spacing is 40 mm horizontally and 30 mm vertically.
    The resultant force in bolt R (in kN, round off to one decimal place) is ___________
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    Question

    Employ stiffness matrix approach for the simply supported beam as shown in the figure to calculate unknown displacements/rotations. Take length, L=8 mL = 8\text{ m}; modulus of elasticity, E=3×104 N/mm2E = 3 \times 10^4\text{ N/mm}^2; moment of inertia, I=225×106 mm4I = 225 \times 10^6\text{ mm}^4.
    Simply supported beam ABC of total length L. A point load P is applied at mid-span B. The left half AB has flexural rigidity E, 2I and the right half BC has flexural rigidity E, I.
    The mid-span deflection of the beam (in mm, round off to integer) under P=100 kNP = 100\text{ kN} in downward direction will be ___________
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    Question

    A square plate O-P-Q-R of a linear elastic material with sides 1.0 m1.0\text{ m} is loaded in a state of plane stress. Under a given stress condition, the plate deforms to a new configuration O-P'-Q'-R' as shown in the figure (not to scale). Under the given deformation, the edges of the plate remain straight.
    A square plate O-P-Q-R on x-y axes. O is at (0,0). P is at (1,0), Q at (1,1), R at (0,1). It deforms to O-P'-Q'-R'. Displacement markers show P moves 20 mm right and 10 mm up to P'. R moves 10 mm right and 10 mm up to R'. Dimensions are in meters, displacements in mm.
    The horizontal displacement of the point (0.5 m,0.5 m)(0.5\text{ m}, 0.5\text{ m}) in the plate O-P-Q-R (in mm, round off to one decimal place) is ___________
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    Question

    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.
    ActivityDuration (in weeks)Depends upon
    N2-
    P5N
    Q3N
    R4P
    S5Q
    T8R
    U7R, S
    V2U
    W3U
    X5T, V
    Y1W
    Z3X, Y
    The total float of the activity “V” (in weeks, in integer) is ________.
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    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 ground water table was as low as 10 m below the ground level in the past. Take unit weight of water, γw=9.81 kN/m3\gamma_w = 9.81\text{ kN/m}^3.
    Soil profile diagram showing sand and clay layers with present and past GWT levels
    The overconsolidation ratio (OCR) (round off to two decimal places) at the mid-point of the clay layer is __________.
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    A retaining wall of height 10 m10\text{ m} with clay backfill is shown in the figure (not to scale). Weight of the retaining wall is 5000 kN per m5000\text{ kN per m} acting at 3.3 m3.3\text{ m} from the toe of the retaining wall. The interface friction angle between base of the retaining wall and the base soil is 20∘20^\circ. The depth of clay in front of the retaining wall is 2.0 m2.0\text{ m}. The properties of the clay backfill and the clay placed in front of the retaining wall are the same. Assume that the tension crack is filled with water. Use Rankine's earth pressure theory. Take unit weight of water, γw=9.81 kN/m3\gamma_w = 9.81\text{ kN/m}^3.
    Retaining wall diagram showing dimensions, soil properties, and weight location
    The factor of safety (round off to two decimal places) against sliding failure of the retaining wall after ignoring the passive earth pressure will be ________.
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    A combined trapezoidal footing of length LL supports two identical square columns (P1P_1 and P2P_2) of size 0.5 m×0.5 m0.5\text{ m} \times 0.5\text{ m}, as shown in the figure. The columns P1P_1 and P2P_2 carry loads of 2000 kN2000\text{ kN} and 1500 kN1500\text{ kN}, respectively.
    Combined trapezoidal footing diagram
    If the stress beneath the footing is uniform, the length of the combined footing LL (in m, round off to two decimal places) is ___________
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    An unsupported slope of height 15 m15\text{ m} is shown in the figure (not to scale), in which the slope face makes an angle 50∘50^\circ with the horizontal. The slope material comprises purely cohesive soil having undrained cohesion 75 kPa75\text{ kPa}. A trial slip circle KLMKLM, with a radius 25 m25\text{ m}, passes through the crest and toe of the slope and it subtends an angle 60∘60^\circ at its center OO. The weight of the active soil mass (WW, bounded by KLMNKLMN) is 2500 kN/m2500\text{ kN/m}, which is acting at a horizontal distance of 10 m10\text{ m} from the toe of the slope. Consider the water table to be present at a very large depth from the ground surface.
    Slope stability diagram
    Considering the trial slip circle KLMKLM, the factor of safety against the failure of slope under undrained condition (round off to two decimal places) is ___________
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    An unlined canal under regime conditions along with a silt factor of 11 has a width of flow 71.25 m71.25\text{ m}. Assuming the unlined canal as a wide channel, the corresponding average depth of flow (in m, round off to two decimal places) in the canal will be ___________
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    A cylinder (2.0 m2.0\text{ m} diameter, 3.0 m3.0\text{ m} long and 25 kN25\text{ kN} weight) is acted upon by water on one side and oil (specific gravity =0.8= 0.8) on other side as shown in the figure.
    A diagram showing a cylinder of 2.0 m diameter and 3.0 m length. Water is on the left side with a free surface 1 m above the top of the cylinder. Oil with specific gravity 0.8 is on the right side with a free surface at the level of the top of the cylinder. Points P, Q, and R are marked on the cylinder surface.
    The absolute ratio of the net magnitude of vertical forces to the net magnitude of horizontal forces (round off to two decimal places) is _________
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    A tube-well of 20 cm20\text{ cm} diameter fully penetrates a horizontal, homogeneous, and isotropic confined aquifer of infinite horizontal extent. The aquifer is of 30 m30\text{ m} uniform thickness. A steady pumping at the rate of 40 litres/s40\text{ litres/s} from the well for a long time results in a steady drawdown of 4 m4\text{ m} at the well face. The subsurface flow to the well due to pumping is steady, horizontal and Darcian and the radius of influence of the well is 245 m245\text{ m}. The hydraulic conductivity of the aquifer (in m/day\text{m/day}, round off to integer) is _________
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    A baghouse filter has to treat 12 m3/s12\text{ m}^3/\text{s} of waste gas continuously. The baghouse is to be divided into 55 sections of equal cloth area such that one section can be shut down for cleaning and/or repairing, while the other 44 sections continue to operate. An air-to-cloth ratio of 6.0 m3/min-m26.0\text{ m}^3/\text{min-m}^2 cloth will provide sufficient treatment to the gas. The individual bags are of 32 cm32\text{ cm} in diameter and 5 m5\text{ m} in length. The total number of bags (in integer) required in the baghouse is _________
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    A secondary clarifier handles a total flow of 9600 m3/d9600\text{ m}^3/\text{d} from the aeration tank of a conventional activated-sludge treatment system. The concentration of solids in the flow from the aeration tank is 3000 mg/L3000\text{ mg/L}. The clarifier is required to thicken the solids to 12000 mg/L12000\text{ mg/L}, and hence it is to be designed for a solid flux of 3.2 kg/(m2⋅h)3.2\text{ kg}/(\text{m}^2\cdot\text{h}). The surface area of the designed clarifier for thickening (in m2\text{m}^2, in integer) is ________.
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    Spot speeds of vehicles observed at a point on a highway are 40,55,60,6540, 55, 60, 65 and 80 km/h80\text{ km/h}. The space-mean speed (in km/h\text{km/h}, round off to two decimal places) of the observed vehicles is ________.
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    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- 0.8
    1400 to 1700- 1.0
    The effective gradient of the runway (in %, round off to two decimal places) is ________.
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    Traversing is carried out for a closed traverse PQRS. The internal angles at vertices P, Q, R and S are measured as 92∘92^\circ, 68∘68^\circ, 123∘123^\circ, and 77∘77^\circ, respectively. If fore bearing of line PQ is 27∘27^\circ, fore bearing of line RS (in degrees, in integer) is _______.
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