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GATE CE 2024 Set 1

All 65 solved GATE CE 2024 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 16Medium 38Hard 11

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65 of 65 questions

General Aptitude (GA)

10
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    Question

    If ‘→\rightarrow’ denotes increasing order of intensity, then the meaning of the words
    [simmer →\rightarrow seethe →\rightarrow smolder] is analogous to [break →\rightarrow raze →\rightarrow ________ ].
    Which one of the given options is appropriate to fill the blank?
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    Question

    In a locality, the houses are numbered in the following way:
    The house-numbers on one side of a road are consecutive odd integers starting from
    301, while the house-numbers on the other side of the road are consecutive even
    numbers starting from 302. The total number of houses is the same on both sides of
    the road.
    If the difference of the sum of the house-numbers between the two sides of the road
    is 27, then the number of houses on each side of the road is
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    Question

    For positive integers pp and qq, with pq≠1\frac{p}{q} \neq 1, (pq)pq=p(pq−1)(\frac{p}{q})^{\frac{p}{q}} = p^{(\frac{p}{q}-1)}. Then,
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    Question

    Which one of the given options is a possible value of xx in the following sequence?3,7,15,x,63,127,2553, 7, 15, x, 63, 127, 255
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    Question

    On a given day, how many times will the second-hand and the minute-hand of a clock cross each other during the clock time 12:05:00 hours to 12:55:00 hours?
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    Question

    In the given text, the blanks are numbered (i)−(iv). Select the best match for all the blanks.
    From the ancient Athenian arena to the modern Olympic stadiums, athletics
    (i)
    the potential for a spectacle. The crowd
    (ii)
    with bated
    breath as the Olympian artist twists his body, stretching the javelin behind him.
    Twelve strides in, he begins to cross-step. Six cross-steps
    (iii)
    in an abrupt
    stop on his left foot. As his body
    (iv)
    like a door turning on a hinge, the
    javelin is launched skyward at a precise angle.
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    Question

    Three distinct sets of indistinguishable twins are to be seated at a circular table that has 8 identical chairs. Unique seating arrangements are defined by the relative positions of the people.
    How many unique seating arrangements are possible such that each person is sitting next to their twin?
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    Question

    The chart given below compares the Installed Capacity (MW) of four power generation technologies, T1, T2, T3, and T4, and their Electricity Generation (MWh) in a time of 1000 hours (h).
    A dual-axis chart showing Installed Capacity (MW) as bars and Electricity Generation (MWh) as points for four technologies T1, T2, T3, and T4.
    The Capacity Factor of a power generation technology is:Capacity Factor=Electricity Generation (MWh)Installed Capacity (MW)×1000 (h)\text{Capacity Factor} = \frac{\text{Electricity Generation (MWh)}}{\text{Installed Capacity (MW)} \times 1000 \text{ (h)}}Which one of the given technologies has the highest Capacity Factor?
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    Question

    In the 4×44 \times 4 array shown below, each cell of the first three columns has either a cross (X) or a number, as per the given rule.
    A 4x4 grid where the first three columns contain numbers or crosses (X) and the fourth column is empty.
    Rule: The number in a cell represents the count of crosses around its immediate neighboring cells (left, right, top, bottom, diagonals).
    As per this rule, the maximum number of crosses possible in the empty column is
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    Question

    During a half-moon phase, the Earth-Moon-Sun form a right triangle. If the Moon-Earth-Sun angle at this half-moon phase is measured to be 89.85∘89.85^\circ, the ratio of the Earth-Sun and Earth-Moon distances is closest to
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Civil Engineering Set 1 (CE1)

55
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    Question

    The smallest positive root of the equationx5−5x4−10x3+50x2+9x−45=0x^5 - 5x^4 - 10x^3 + 50x^2 + 9x - 45 = 0lies in the range
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    Question

    The second-order differential equation in an unknown function u:u(x,y)u: u(x, y) is defined as∂2u∂x2=2\frac{\partial^2 u}{\partial x^2} = 2Assuming g:g(x)g: g(x), f:f(y)f: f(y), and h:h(y)h: h(y), the general solution of the above differential equation is
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    Question

    The probability that a student passes only in Mathematics is 13\frac{1}{3}. The probability that the student passes only in English is 49\frac{4}{9}. The probability that the student passes in both of these subjects is 16\frac{1}{6}. The probability that the student will pass in at least one of these two subjects is
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    Question

    The three-dimensional state of stress at a point is given byσ=(10000400000) MPa.\sigma = \begin{pmatrix} 10 & 0 & 0 \\ 0 & 40 & 0 \\ 0 & 0 & 0 \end{pmatrix} \text{ MPa.}The maximum shear stress at the point is
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    Question

    Concrete of characteristic strength 30 MPa is required. If 40 specimens of concrete cubes are to be tested, the minimum number of specimens having at least 30 MPa strength should be
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    Question

    Consider the statements PP and QQ.
    P: Client’s Preliminary Estimate is used for budgeting costs toward the end of planning and design phase.
    Q: Client’s Detailed Estimate is used for controlling costs during the execution of the project.
    Which one of the following options is CORRECT?
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    Question

    The following figure shows the arrangement of formwork for casting a cantilever RC beam.
    arrangement of formwork for casting a cantilever RC beam
    The correct sequence of removing the Shores/Props is
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    Question

    A 2 m2\text{ m} wide strip footing is founded at a depth of 1.5 m1.5\text{ m} below the ground level in a homogeneous pure clay bed. The clay bed has unit cohesion of 40 kPa40\text{ kPa}. Due to seasonal fluctuations of water table from peak summer to peak monsoon period, the net ultimate bearing capacity of the footing, as per Terzaghi’s theory, will
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    Question

    Consider the statements P and Q.
    P: Soil particles formed by mechanical weathering, and close to their origin are generally subrounded.
    Q: Activity of the clay physically signifies its swell potential.
    Which one of the following options is CORRECT?
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    Question

    The number of degrees of freedom for a natural open channel flow with a mobile bed is
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    Question

    The following table gives various components of Municipal Solid Waste (MSW) and a list of treatment/separation techniques.
    Component of MSWTreatment/separation technique
    P - Ferrous metalsi - Incineration
    Q - Aluminum and copperii - Rapid composting
    R - Food wasteiii - Eddy current separator
    S - Cardboardiv - Magnetic separator
    The CORRECT match is
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    Question

    A car is travelling at a speed of 60 km/hr60\text{ km/hr} on a section of a National Highway having a downward gradient of 2%2\%. The driver of the car suddenly observes a stopped vehicle on the car path at a distance 130 m130\text{ m} ahead, and applies brake. If the brake efficiency is 60%60\%, coefficient of friction is 0.70.7, driver’s reaction time is 2.5 s2.5\text{ s}, and acceleration due to gravity is 9.81 m/s29.81\text{ m/s}^2, the distance (in meters) required by the driver to bring the car to a safe stop lies in the range
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    Question

    As per the International Civil Aviation Organization (ICAO), the basic runway length is increased by x (%)x\ (\%) for every y (m)y\ (\text{m}) raise in elevation from the Mean Sea Level (MSL). The values of xx and yy, respectively, are
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    Question

    Which one of the following statements related to bitumen is FALSE?
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    Question

    If the number of sides resulting in a closed traverse is increased from three to four, the sum of the interior angles increases by
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    Question

    A surveyor observes a zenith angle of 93∘00′00′′93^\circ 00' 00'' during a theodolite survey. The corresponding vertical angle is
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    Question

    Among the following statements relating the fundamental lines of a transit theodolite, which one is CORRECT?
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    Question

    For the following partial differential equation,x∂2f∂x2+y∂2f∂y2=x2+y22x \frac{\partial^2 f}{\partial x^2} + y \frac{\partial^2 f}{\partial y^2} = \frac{x^2 + y^2}{2}which of the following option(s) is/are CORRECT?
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    Question

    The elements that DO NOT increase the strength of structural steel are
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    Question

    Consider a balanced doubly-reinforced concrete section. If the material and other sectional properties remain unchanged, for which of the following cases will the section becomes under-reinforced?
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    Question

    The primary air pollutant(s) is/are
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    Question

    Consider the data of f(x)f(x) given in the table.
    ii012
    xix_i123
    f(xi)f(x_i)00.30100.4771
    The value of f(1.5)f(1.5) estimated using second-order Newton’s interpolation formula is ______________ (rounded off to 2 decimal places).
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    Question

    The plane frame shown in the figure has fixed support at joint A, hinge support at joint F, and roller support at joint I. In the figure, A to I indicate joints of the frame.
    A plane frame with joints A through I, featuring a fixed support at A, a hinge support at F, and a roller support at I.
    If the axial deformations are neglected, the degree of kinematic indeterminacy is ________ (in integer).
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    Question

    An embankment is constructed with soil by maintaining the degree of saturation as 75%75\% during compaction. The specific gravity of soil is 2.682.68 and the moisture content is 17%17\% during compaction. Consider the unit weight of water as 10 kN/m310\text{ kN/m}^3. The dry unit weight (in kN/m3\text{kN/m}^3) of the compacted soil is ________________ (rounded off to 22 decimal places).
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    Question

    A 30 cm30\text{ cm} diameter well fully penetrates an unconfined aquifer of saturated thickness 20 m20\text{ m} with hydraulic conductivity of 10 m/day10\text{ m/day}. Under the steady pumping rate for a long time, the drawdowns in two observation wells located at 10 m10\text{ m} and 100 m100\text{ m} from the pumping well are 5 m5\text{ m} and 1 m1\text{ m}, respectively. The corresponding pumping rate (in m3/day\text{m}^3\text{/day}) from the well is _____________ (rounded off to 22 decimal places).
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    Question

    What are the eigenvalues of the matrix [211141112]\begin{bmatrix} 2 & 1 & 1 \\ 1 & 4 & 1 \\ 1 & 1 & 2 \end{bmatrix} ?
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    Question

    A vector field p⃗\vec{p} and a scalar field rr are given byp⃗=(2x2−3xy+z2)i^+(2y2−3yz+x2)j^+(2z2−3xz+x2)k^\vec{p} = ( 2x^2 - 3xy + z^2 ) \hat{i} + ( 2y^2 - 3yz + x^2 ) \hat{j} + (2z^2 - 3xz + x^2 ) \hat{k}r=6x2+4y2−z2−9xyz−2xy+3xz−yzr = 6x^2 + 4y^2 - z^2 - 9xyz - 2xy + 3xz - yzConsider the statements P and Q.
    P: Curl of the gradient of the scalar field rr is a null vector.
    Q: Divergence of curl of the vector field p⃗\vec{p} is zero.
    Which one of the following options is CORRECT?
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    Question

    Find the correct match between the plane stress states and the Mohr’s circles.
    Plane stress states P, Q, R, S and Mohr's circles I, II, III, IV
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    Question

    The beam shown in the figure is subjected to a uniformly distributed downward load of intensity qq between supports A and B.
    📷 Figure: Beam with supports A, B, C, an internal hinge, and UDL
    Considering the upward reactions as positive, the support reactions are
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    Question

    A homogeneous shaft PQRPQR with fixed supports at both ends is subjected to a torsional moment TT at point QQ, as shown in the figure. The polar moments of inertia of the portions PQPQ and QRQR of the shaft with circular cross-sections are J1J_1 and J2J_2, respectively. The torsional moment reactions at the supports PP and RR are TPT_P and TRT_R, respectively.
    Diagram of a shaft PQR fixed at both ends with a torsional moment T applied at point Q. The shaft has two segments: PQ with length L1 and polar moment of inertia J1, and QR with length L2 and polar moment of inertia J2.
    (Figure NOT to scale)
    If TP/TR=4T_P/T_R = 4 and J1/J2=2J_1/J_2 = 2, the ratio of the lengths L1/L2L_1/L_2 is
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    Question

    A vertical smooth rigid retaining wall is supporting horizontal ground with dry cohesionless backfill having a friction angle of 30∘30^\circ. The inclinations of failure planes with respect to the major principal plane for Rankine’s active and passive earth pressure conditions, respectively, are
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    Question

    A flow velocity field V⃗:V⃗(x,y)\vec{V}: \vec{V}(x, y) for a fluid is represented by V⃗=3i^+(5x)j^\vec{V} = 3 \hat{i} + (5x) \hat{j}In the context of the fluid and the flow, which one of the following statements is CORRECT?
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    Question

    For assessing the compliance with the emissions standards of incineration plants, a correction needs to be applied to the measured concentrations of air pollutants. The emission standard (based on 11% Oxygen) for HCl is 50 mg/Nm350\text{ mg/Nm}^3 and the measured concentrations of HCl and Oxygen in flue gas are 42 mg/Nm342\text{ mg/Nm}^3 and 13%, respectively.
    Assuming 21% Oxygen in air, the CORRECT statement is:
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    Question

    The free mean speed is 60 km/hr60\text{ km/hr} on a given road. The average space headway at jam density on this road is 8 m8\text{ m}. For a linear speed-density relationship, the maximum flow (in veh/hr/lane) expected on the road is
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    Question

    A map is prepared with a scale of 1: 1000 and a contour interval of 1 m. If the distance between two adjacent contours on the map is 10 mm, the slope of the ground between the adjacent contours is
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    Question

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

    The return period of a large earthquake for a given region is 200 years. Assuming that earthquake occurrence follows Poisson’s distribution, the probability that it will be exceeded at least once in 50 years is ________________ % (rounded off to the nearest integer).
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    Question

    A 2 m×2 m2\text{ m} \times 2\text{ m} tank of 3 m3\text{ m} height has inflow, outflow and stirring mechanisms. Initially, the tank was half-filled with fresh water. At t=0t = 0, an inflow of a salt solution of concentration 5 g/m35\text{ g/m}^3 at the rate of 2 litre/s2\text{ litre/s} and an outflow of the well stirred mixture at the rate of 1 litre/s1\text{ litre/s} are initiated. This process can be modelled using the following differential equation:dmdt+m6000+t=0.01\frac{dm}{dt} + \frac{m}{6000 + t} = 0.01where mm is the mass (grams) of the salt at time tt (seconds). The mass of the salt (in grams) in the tank at 75%75\% of its capacity is _____________ (rounded off to 2 decimal places).
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    Question

    The plane truss shown in the figure has 13 joints and 22 members. The truss is made of a homogeneous, prismatic, linearly elastic material. All members have identical axial rigidity. A to M indicate the joints of the truss. The truss has pin supports at joints A and L and roller support at joint K. The truss is subjected to a 10 kN10\text{ kN} vertically downward force at joint H and a 10 kN10\text{ kN} horizontal force in the rightward direction at joint B as shown.
    Plane truss with joints A-M and loads
    (Figure NOT to scale)
    The magnitude of the reaction (in kN) at the pin support L is _____________ (rounded off to 1 decimal place).
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    Question

    An inverted T-shaped concrete beam (B1) in the figure, with centroidal axis X−XX - X, is subjected to an effective prestressing force of 1000 kN1000\text{ kN} acting at the bottom kern point of the beam cross-section. Also consider an identical concrete beam (B2) with the same grade of concrete but without any prestressing force.
    Inverted T-beam cross section with dimensions and kern point
    (Figure NOT to scale)
    The additional cracking moment (in kN. m) that can be carried by beam B1 in comparison to beam B2 is ____________ (rounded off to the nearest integer).
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    Question

    The initial cost of an equipment is Rs. 1,00,000. Its salvage value at the end of accounting life of 5 years is Rs. 10,000. The difference in depreciation (in Rs.) computed using ‘double-declining balance method’ and ‘straight line method’ of depreciation in Year-2 is _____________ (in positive integer).
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    Question

    A slab panel with an effective depth of 250250 mm is reinforced with 0.2%0.2\% main reinforcement using 88 mm diameter steel bars. The uniform center-to-center spacing (in mm) at which the 88 mm diameter bars are placed in the slab panel is __________ (rounded off to the nearest integer).
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    Question

    The total primary consolidation settlement (ScS_c) of a building constructed on a 1010 m thick saturated clay layer is estimated to be 5050 mm. After 300300 days of the construction of the building, primary consolidation settlement was reported as 1010 mm. The additional time (in days) required to achieve 50%50\% of ScS_c will be ______________________ (rounded off to the nearest integer).
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    Question

    An infinite slope is made up of cohesionless soil with seepage parallel to and up to the sloping surface. The angle of slope is 30∘30^\circ with respect to horizontal ground surface. The unit weights of the saturated soil and water are 20 kN/m320\text{ kN/m}^3 and 10 kN/m310\text{ kN/m}^3, respectively. The minimum angle of shearing resistance of the soil (in degrees) for the critically stable condition of the slope is _____________ (rounded off to the nearest integer).
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    Question

    A soil sample was consolidated at a cell pressure of 20 kPa20\text{ kPa} and a back pressure of 10 kPa10\text{ kPa} for 24 hours during a consolidated undrained (CU) triaxial test. The cell pressure was increased to 30 kPa30\text{ kPa} on the next day and it resulted in the development of pore water pressure of 1 kPa1\text{ kPa}. The soil sample failed when the axial stress was gradually increased to 50 kPa50\text{ kPa}. The pore water pressure at failure was recorded as 21 kPa21\text{ kPa}. The value of Skempton’s pore pressure parameter BB for the soil sample is ______________ (rounded off to 2 decimal places).
    Your answer

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    Question

    The ordinates of a 1-hour unit hydrograph (UH) are given below.
    Time (hours)012345
    Ordinates of 1-hour UH (m3/sm^3/s)01350809585
    Time (hours)67891011
    Ordinates of 1-hour UH (m3/sm^3/s)5535151030
    These ordinates are used to derive a 3-hour UH. The peak discharge (in m3/sm^3/s) for the derived 3-hour UH is _____________ (rounded off to the nearest integer).
    Your answer

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    Question

    A standard round bottom triangular canal section as shown in the figure has a bed slope of 1 in 200. Consider the Chezy's coefficient as 150 m¹/²/s.
    A diagram of a triangular channel cross-section with a rounded bottom. The side slopes are indicated as 1.5 horizontal to 1 vertical. A 90-degree angle is shown at the bottom vertex. The depth of flow is labeled 'y'.
    The normal depth of flow, y (in meters) for carrying a discharge of 20 m³/s is __________ (rounded off to 2 decimal places).
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    Question

    A spillway has unit discharge of 7.5 m³/s/m. The flow depth at the downstream horizontal apron is 0.5 m. The tail water depth (in meters) required to form a hydraulic jump is __________ (rounded off to 2 decimal places).
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    Question

    A 5 m × 5 m closed tank of 10 m height contains water and oil, and is connected to an overhead water reservoir as shown in the figure. Use γw=10\gamma_w = 10 kN/m³ and Specific gravity of oil = 0.8.
    A diagram showing a closed tank on the right containing oil over water, connected by a pipe to an open overhead reservoir on the left containing water. The water surface in the reservoir is 8m above the tank top. The pipe connects 2m below the reservoir water surface to the top of the closed tank. The closed tank has 2m of oil on top of 4m of water. The side of the tank is labeled PQR.
    The total force (in kN) due to pressure on the side PQR of the tank is __________ (rounded off to the nearest integer).
    Your answer

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    Question

    Activated carbon is used to remove a pollutant from wastewater in a mixed batch reactor, which follows first-order reaction kinetics.
    At a reaction rate of 0.380.38 /day, the time (in days) required to remove the pollutant by 95%95\% is ______________ (rounded off to 11 decimal place).
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    Question

    A water treatment plant treats 25 MLD water with a natural alkalinity of 4.0 mg/L (as CaCO3CaCO_3). It is estimated that, during coagulation of this water, 450 kg/day of calcium bicarbonate (Ca(HCO3)2Ca(HCO_3)_2) is required based on the alum dosage.
    Consider the atomic weights as: Ca-40, H-1, C-12, O-16.
    The quantity of pure quick lime, CaO (in kg) required for this process per day is___________ (rounded off to 2 decimal places).
    Your answer

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    Question

    The number of trains and their corresponding speeds for a curved Broad Gauge section with 437 m radius, are
    • 20 trains travel at a speed of 40 km/hr
    • 15 trains travel at a speed of 50 km/hr
    • 12 trains travel at a speed of 60 km/hr
    • 8 trains travel at a speed of 70 km/hr
    • 3 trains travel at a speed of 80 km/hr
    If the gauge (center-to-center distance between the rail heads) is taken as 1750 mm, the required equilibrium cant (in mm) will be ______________ (rounded off to the nearest integer).
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    Question

    The figure presents the trajectories of six vehicles within a time-space domain. The number in the parentheses represents unique identification of each vehicle.
    (Figure NOT to scale)
    The mean speed (in km/hr) of the vehicles in the entire time-space domain is ______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________
    ```
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    Question

    The following data is obtained from an axle load survey at a site:
    Average rear axle load = 12000 kg12000\text{ kg}
    Number of commercial vehicles = 800 per day800\text{ per day}The pavement at this site would be reconstructed over a period of 5 years5\text{ years} from the date of survey. The design life of the reconstructed pavement is 15 years15\text{ years}. Use the standard axle load as 8160 kg8160\text{ kg} and the annual average vehicle growth rate as 4.0%4.0\%. Assume that Equivalent Wheel Load Factor (EWLF) and Vehicle Damage Factor (VDF) are equal.
    The cumulative standard axle (in msa) for the pavement design is ________________ (rounded off to 22 decimal places).
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    Question

    A bird is resting on a point P at a height of 88 m above the Mean Sea Level (MSL). Upon hearing a loud noise, the bird flies parallel to the ground surface and reaches a point Q which is located at a height of 33 m above MSL. The ground surface has a falling gradient of 11 in 22. Ignoring the effects of curvature and refraction, the horizontal distance (in meters) between points P and Q is _______________ (in integer).
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