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GATE CE 2025 Set 2

All 65 solved GATE CE 2025 Set 2 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 19Medium 37Hard 9

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65 of 65 questions

General Aptitude (GA)

10
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    Question

    Even though I had planned to go skiing with my friends, I had to __________ at the last moment because of an injury.
    Select the most appropriate option to complete the above sentence.
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    Question

    The President, along with the Council of Ministers, ___________ to visit India next week.
    Select the most appropriate option to complete the above sentence.
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    Question

    An electricity utility company charges ₹ 7 per kWh (kilo watt-hour). If a 40-watt desk light is left on for 10 hours each night for 180 days, what would be the cost of energy consumption? If the desk light is on for 2 more hours each night for the 180 days, what would be the percentage-increase in the cost of energy consumption?
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    Question

    In the context of the given figure, which one of the following options correctly represents the entries in the blocks labelled (i), (ii), (iii), and (iv), respectively?
    NUF(i)
    211496
    HL(ii)O
    12(iv)15(iii)
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    Question

    A bag contains Violet (V), Yellow (Y), Red (R), and Green (G) balls. On counting them, the following results are obtained:
    (i) The sum of Yellow balls and twice the number of Violet balls is 50.
    (ii) The sum of Violet and Green balls is 50.
    (iii) The sum of Yellow and Red balls is 50.
    (iv) The sum of Violet and twice the number of Red balls is 50.
    Which one of the following Pie charts correctly represents the balls in the bag?
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    Question

    “His life was divided between the books, his friends, and long walks. A solitary man, he worked at all hours without much method, and probably courted his fatal illness in this way. To his own name there is not much to show; but such was his liberality that he was continually helping others, and fruits of his erudition are widely scattered, and have gone to increase many a comparative stranger’s reputation.”
    (From E.V. Lucas’s “A Funeral”)
    Based only on the information provided in the above passage, which one of the following statements is true?
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    Question

    For the clock shown in the figure, if
    O∗=OQSZPRTO^* = O Q S Z P R T, and
    X∗=XZPWYOQX^* = X Z P W Y O Q,
    then which one among the given options is most appropriate for P∗P^*?
    A clock face with letters O, P, Q, R, S, T, U, V, W, X, Y, Z at positions 12, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 respectively.
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    Question

    Consider a five-digit number PQRSTPQRST that has distinct digits P,Q,R,SP, Q, R, S, and TT, and satisfies the following conditions:
    P<QP < Q
    S>P>TS > P > T
    R<TR < T
    If integers 1 through 5 are used to construct such a number, the value of PP is:
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    Question

    A business person buys potatoes of two different varieties P and Q, mixes them in a certain ratio and sells them at ₹ 192 per kg.
    The cost of the variety P is ₹ 800 for 5 kg.
    The cost of the variety Q is ₹ 800 for 4 kg.
    If the person gets 8% profit, what is the P:Q ratio (by weight)?
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    Question

    Three villages P, Q, and R are located in such a way that the distance PQ = 13 km, QR = 14 km, and RP = 15 km, as shown in the figure. A straight road joins Q and R. It is proposed to connect P to this road QR by constructing another road. What is the minimum possible length (in km) of this connecting road?
    Note: The figure shown is representative.
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Civil Engineering (CE2)

55
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    Question

    For the matrix [A][A] given below, the transpose is ______.[A]=[234145432][A] = \begin{bmatrix} 2 & 3 & 4 \\ 1 & 4 & 5 \\ 4 & 3 & 2 \end{bmatrix}
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    Question

    Integration of ln⁡(x)\ln(x) with xx i.e.,∫ln⁡(x)dx=______.\int \ln(x) dx = \_\_\_\_\_\_.
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    Question

    Consider the following statements (P) and (Q):
    (P): Fly ash and ground granulated blast furnace slag can be used as mineral admixtures in concrete.
    (Q): As per IS 456:2000, the minimum moist curing period becomes higher when a mineral admixture is added to concrete.
    Identify the CORRECT option from choices given below.
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    Question

    Consider the pin-jointed truss shown in the figure. Influence line is drawn for the axial force in the member G-I, when a unit load travels on the bottom chord of the truss. Identify the CORRECT influence line from the following options:
    Note: Positive value corresponds to tension and negative value corresponds to compression in the member.
    A pin-jointed truss with a span of 36 m (6 panels of 6 m each) and a total height of 6 m. Joints are labeled A through P.
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    Question

    The most suitable test for measuring the permeability of clayey soils in the laboratory is ______.
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    Question

    A hydraulic jump occurs in an open channel when the slope of the channel changes from ______.
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    Question

    The bacteria mainly responsible for crown corrosion in a sewer is ______.
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    Question

    The recommended minimum traffic growth rate and design period considered for structural design of flexible pavements for national highways in India as per IRC 37:2018 is ____ percentage and ____ years, respectively.
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    Question

    After applying the correction for elevation and temperature, the runway length is 700700 m. The corrected runway length (in m) for an effective gradient of 1%1\% is ______ (round off to the nearest integer).
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    Question

    The point where the road alignment changes from a tangent to a curve is known as ______.
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    Question

    Consider a velocity vector, V⃗\vec{V} in (x,y,z)(x, y, z) coordinates given below. Pick one or more CORRECT statements(s) from the choices given below.V⃗=ux⃗+vy⃗\vec{V} = u\vec{x} + v\vec{y}
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    Question

    Given that AA and BB are not null sets, which of the following statements regarding probability is/are CORRECT?
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    Question

    In the context of construction materials, which of the following statements is/are CORRECT?
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    Question

    Which of the following statements is/are INCORRECT?
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    Question

    Pick one or more CORRECT statement(s) from the choices given below, in the context of upstream and downstream cut-offs provided below the concrete apron of weirs / barrages constructed across alluvial rivers.
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    Question

    In the context of the effect of drainage density on the run-off generation and the hydrograph at the catchment outlet, all other factors remaining the same, pick one or more CORRECT statement(s) from the choices given below.
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    Question

    Identify the treatment technology/technologies NOT recommended for highly biodegradable organic solid wastes.
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    Question

    Which of the following statements is/are INCORRECT?
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    Question

    The “order” of the following ordinary differential equation is ______.d3ydx3+(d2ydx2)6+(dydx)4+y=0\frac{d^3y}{dx^3} + \left(\frac{d^2y}{dx^2}\right)^6 + \left(\frac{dy}{dx}\right)^4 + y = 0
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    Question

    The design shear strength of a reinforced concrete rectangular beam with a width of 250 mm250\text{ mm} and an effective depth of 500 mm500\text{ mm}, is 0.3 MPa0.3\text{ MPa}. The torsional moment capacity of the section (in kN.m\text{kN.m}) under pure torsion, as per IS 456:2000, is ______ (round off to one decimal place).
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    Question

    From a flow-net diagram drawn under a concrete dam, following information are obtained: (i) The head difference between upstream and downstream side of the dam is 9 m9\text{ m}. (ii) The total number of equipotential drops between upstream and downstream side of the dam is 1010. (iii) The length of the field nearest to the toe of the dam in the downstream side is 1 m1\text{ m}.
    If the soil below the dam is having a saturated unit weight of 21 kN/m321\text{ kN/m}^3 and unit weight of water is 9.81 kN/m39.81\text{ kN/m}^3, then the factor of safety against the quick condition will be ______ (round off to two decimal places).
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    Question

    A 6 m thick clay stratum has drainage at both its top and bottom surface due to the presence of sand strata. The time to complete 50% consolidation is 2 years. The coefficient of volume change (mvm_v) is 1.51×10−3 m2/kN1.51 \times 10^{-3} \text{ m}^2/\text{kN} and unit weight of water is 9.81 kN/m39.81 \text{ kN/m}^3.
    The coefficient of permeability (in m/year) is ______ (round off to three decimal places).
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    Question

    Consider steady flow of water in the series pipe system shown below, with specified discharge. The diameters of Pipes A and B are 2 m and 1 m, respectively. The lengths of pipes A and B are 100 m and 200 m, respectively. Assume the Darcy-Weisbach friction coefficient, ff as 0.01 for both the pipes.
    The ratio of head loss in Pipe-B to the head loss in Pipe-A is ______ (round off to the nearest integer).
    A series pipe system showing water level in a tank connected to Pipe-A (Diameter = 2 m, Length = 100 m, f = 0.01) which is then connected to Pipe-B (Diameter = 1 m, Length = 200 m, f = 0.01).
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    Question

    Free residual chlorine concentration in water was measured to be 2 mg/l2 \text{ mg/l} (as Cl2Cl_2). The pHpH of water is 8.58.5. By using the chemical equation given below, the HOClHOCl concentration (in μmoles/l\mu\text{moles/l}) in water is ________________ (round off to one decimal place).HOCl⇌H++OCl−,pK=7.50HOCl \rightleftharpoons H^+ + OCl^-, \quad pK = 7.50Atomic weight: Cl(35.5)Cl(35.5)
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    Question

    A surveyor measured the distance between two points on the plan drawn to a scale of 1 cm=40 m1\text{ cm} = 40\text{ m} and the result was 468 m468\text{ m}. Later, it was discovered that the scale used was 1 cm=20 m1\text{ cm} = 20\text{ m}.
    The true distance between the points (in m) is ______ (round off to the nearest integer).
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    Question

    Pick the CORRECT solution for the following differential equationdydx=ex−y\frac{dy}{dx} = e^{x-y}
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    Question

    A circular tube of thickness 10 mm10\text{ mm} and diameter 250 mm250\text{ mm} is welded to a flat plate using 5 mm5\text{ mm} fillet weld along the circumference. Assume Fe410 steel and shop welding.
    As per IS 800:2007, the torque that can be resisted by the weld (in kN.m) is ______ (round off to one decimal place).
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    Question

    The figure shows a propped cantilever with uniform flexural rigidity EIEI (in N.m2^2) and subjected to a moment MM (in N.m). Consider forces and displacements in the upward direction as positive.
    Find the upward reaction at the propped support B (in N) when this support settles by (−Δ)(-\Delta), given in metres.
    A propped cantilever beam of length $L$ with a fixed support at A and a propped support at B. A clockwise moment $M$ is applied at end B.
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    Question

    Let the state of stress at a point in a body be the difference of two plane states of stress shown in the figure. Consider all the possible planes perpendicular to the x-y plane and passing through that point. The magnitude of the maximum compressive stress on any such plane is kσ0k\sigma_0, where kk is equal to _____ (round off to one decimal place).
    Two stress states. State 1 shows uniaxial tension $3\sigma_0$ along the x-axis. State 2 shows uniaxial tension $3\sigma_0$ along an axis rotated $45^\circ$ counter-clockwise from the x-axis.
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    Question

    Consider a reinforced concrete beam section of 350 mm width and 600 mm depth. The beam is reinforced with the tension steel of 800 mm2^2 area at an effective cover of 40 mm. Consider M20 concrete and Fe415 steel. Let the stress block considered for concrete in IS 456:2000 be replaced by an equivalent rectangular stress block, with no change in (a) the area of the stress block, (b) the design strength of concrete (at the strain of 0.0035), and (c) the location of neutral axis at flexural collapse. The ultimate moment of resistance of the beam (in kN.m) is __________________ (round off to the nearest integer).
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    Question

    For a partially saturated soil deposit at a construction site, water content (ww) is 15%, degree of saturation (SS) is 67%, void ratio (ee) is 0.6 and specific gravity of solids in the soil (GsG_s) is 2.67. Consider unit weight of water as 9.81 kN/m39.81\text{ kN/m}^3.
    To fully saturate 5 m35\text{ m}^3 of this soil, the required weight of water (in kN) will be ______ (round off to the nearest integer).
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    Question

    Consider flow in a long and very wide rectangular open channel. Width of the channel can be considered as infinity compared to the depth of flow. Uniform flow depth is 1.0 m1.0\text{ m}. The bed slope of the channel is 0.00010.0001. The Manning roughness coefficient value is 0.020.02. Acceleration due to gravity, gg can be taken as 9.81 m/s29.81\text{ m/s}^2.
    The critical depth (in m) corresponding to the flow rate resulting from the above conditions is ______ (round off to one decimal place).
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    Question

    Match the following in Column I with Column II.
    Column IColumn II
    (1) Vehicle Damage FactorA. Stability of subgrade soil
    (2) Passenger Car UnitB. Capacity of a roadway
    (3) Perception Reaction TimeC. Design rigid pavement
    (4) California Bearing RatioD. Design flexible pavement
    E. Stopping sight distance
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    Question

    Consider the function given below and pick one or more CORRECT statement(s) from the following choices.f(x)=x3−152x2+18x+20f(x) = x^3 - \frac{15}{2}x^2 + 18x + 20
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    Question

    Pick the CORRECT eigen value(s) of the matrix [A][A] from the following choices.[A]=[6842][A] = \begin{bmatrix} 6 & 8 \\ 4 & 2 \end{bmatrix}
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    Question

    In the pin-jointed truss shown in the figure, the members that carry zero force are identified. Which of the following options is/are zero-force members?
    A pin-jointed truss with joints labeled A through M, featuring a 60 kN vertical load at joint B and supports at joints L and M.
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    Question

    In the context of shear strength of soil, which of the following statements is/are CORRECT?
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    Question

    The drag force, FDF_D on a sphere due to a fluid flowing past the sphere is a function of viscosity, μ\mu, the mass density, ρ\rho, the velocity of flow, VV, and the diameter of the sphere, DD.
    Pick the relevant (one or more) non-dimensional parameter(s) pertaining to the above process from the following list.
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    Question

    A compound has a general formula CaHbOcNdC_aH_bO_cN_d and molecular weight 187. A 935 mg/l solution of the compound is prepared in distilled deionized water. The Total Organic Carbon (TOC) is measured as 360 mg/l (as C). The Chemical Oxygen Demand (COD) and the Total Kjeldahl Nitrogen (TKN) are determined as 600 mg/l (as O2O_2) and 140 mg/l (as N), respectively (as per the chemical equation given below). Which of the following options is/are CORRECT?CaHbOcNd+(4a+b−2c−3d)4O2→aCO2+b−3d2H2O+dNH3C_aH_bO_cN_d + \frac{(4a + b - 2c - 3d)}{4} O_2 \to aCO_2 + \frac{b - 3d}{2} H_2O + dNH_3Atomic weight: C(12), H(1), O(16), N(14)
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    Question

    The free flow speed of a highway is 100 km/h100\text{ km/h} and its capacity is 4000 vehicle/h4000\text{ vehicle/h}. Assume speed density relation is linear.
    For a traffic volume of 2000 vehicle/h2000\text{ vehicle/h}, choose all the possible speeds (in km/h) from the options given below (round off to two decimal places).
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    Question

    Consider a discrete random variable XX whose probabilities are given below. The standard deviation of the random variable is ______ (round off to one decimal place).
    xix_i1248
    P(X=xi)P(X = x_i)0.30.10.30.3
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    Question

    A steel beam supported by three parallel pin-jointed steel rods is shown in the figure. The moment of inertia of the beam is 8×107 mm48 \times 10^7 \text{ mm}^4. Take modulus of elasticity of steel as 210 GPa210 \text{ GPa}. The beam is subjected to uniformly distributed load of 6.25 kN/m6.25 \text{ kN/m}, including its self-weight. The axial force (in kN) in the centre rod CD is ______ (round off to one decimal place).
    A steel beam supported by three parallel pin-jointed steel rods AB, CD, and EF. Rods AB and EF have a diameter of 12 mm, while rod CD has a diameter of 30 mm. The beam is 4 m long, divided into two 2 m segments. A uniformly distributed load of 6.25 kN/m is applied across the beam.
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    Question

    The figure shows a network diagram for a construction project. The activities A, B, C, D, E, and F are represented by arrows and their durations are in the figure.
    The total float available for the activity E in day(s) is equal to _____ (round off to the nearest integer).
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    Question

    A reinforced concrete beam has a support section with width of 300300 mm and effective depth of 500500 mm. The support section is reinforced with 33 bars of 2020 mm diameter at the tension side. Two-legged vertical stirrups of 1010 mm diameter and Fe415 steel at a spacing of 100100 mm are provided as shear reinforcement. Assume that there is no possibility of diagonal compression failure at the section.
    As per IS 456:2000, the maximum shear resisted by the vertical stirrups (in kN), as per limit state design, is ___________ (round off to one decimal place).
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    Question

    The bank of a canal has the profile shown in the figure. The material is a homogeneous clay with a bulk unit weight of 2020 kN/m3^3, undrained cohesion of 3030 kPa and it is fully saturated (ϕu=0\phi_u = 0). For the trial slip circle shown, the area ABCDEA is 150150 m2^2 and the centroid is at P. A tension crack (DE) of 2.52.5 m deep was also observed. Assume unit weight of water is 9.819.81 kN/m3^3 and consider 11 m run of the bank for the analysis.
    Considering the canal is empty and tension crack is completely filled with water, the factor of safety against slope failure of the bank is ______ (round off to two decimal places).
    Profile of a canal bank with a trial slip circle, showing dimensions and centroid P
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    A designer used plate load test to obtain the value of the bearing capacity factor NγN_\gamma. A circular plate of 1 m diameter was placed on the surface of a dry sand layer extending very deep beneath the ground. The unit weight of the sand is 16.66 kN/m3^3. The plate is loaded to failure at a pressure of 1500 kPa.
    Considering Terzaghi’s bearing capacity theory, the bearing capacity factor NγN_\gamma is ______ (round off to the nearest integer).
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    Question

    A 4×44 \times 4 group pile, with each pile 20 m long and 500 mm in diameter, is installed in a square pattern in a clayey soil, as shown in the figure. The average unconfined compressive strength of the soil is 100 kN/m2^2, and the adhesion factor is 0.8. Neglect the bearing at the tip of the piles. For a group efficiency factor of 1.0, the centre to centre spacing (ss) of the piles (in m) would be ________ (round off to two decimal places).
    Diagram showing a 4x4 group pile in clay soil with dimensions and plan view
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    A 60 cm diameter well completely penetrates a confined aquifer of permeability 5×10−45 \times 10^{-4} m/s. The length of the strainer (spanning the entire thickness of the aquifer) is 10 m. The drawdown at the well under steady state pumping is 1.0 m. Assume that the radius of influence for this pumping is 300 m. The discharge from the well (in litres per minute) is ______ (round off to the nearest integer).
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    The peak of flood hydrograph due to a 3-hour duration storm in a catchment is 180 m3/s180\text{ m}^3/\text{s}. The total rainfall depth is 6.6 cm6.6\text{ cm}. It can be assumed that the average infiltration loss is 0.2 cm/h0.2\text{ cm/h}. There are no other losses. The base flow is constant at a value of 30 m3/s30\text{ m}^3/\text{s}.
    The peak value of the 3-hour unit hydrograph for this catchment (in m3/s\text{m}^3/\text{s}) is ______ (round off to the nearest integer).
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    Question

    The shaft of a 6 m wide gate in the figure will fail at a moment of 3924 kN.m about the hinge P. The maximum value of water depth hh (in m) that the gate can hold is ________________ (round off to the nearest integer).
    Note:
    Density of water = 1000 kg/m3^3
    Acceleration due to gravity = 9.81 m/s2^2
    A diagram showing a gate hinged at point P. The gate has an inclined section with a vertical height of 4 m and a horizontal width of 3 m. Water is on the left side of the gate, and the depth from the water surface to the hinge P is labeled as $h$.
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    Question

    The analyses results of a water sample are given below. The non-carbonate hardness of the water (in mg/L\text{mg/L}) as CaCO3\text{CaCO}_3 is ______ (in integer).
    IonConcentration (mg/L\text{mg/L} as CaCO3\text{CaCO}_3)
    Ca2+\text{Ca}^{2+}150150
    Mg2+\text{Mg}^{2+}4040
    Fe2+\text{Fe}^{2+}1010
    Na+\text{Na}^{+}5050
    K+\text{K}^{+}1010
    CO32−\text{CO}_3^{2-}120120
    HCO3−\text{HCO}_3^{-}3030
    Cl−\text{Cl}^{-}5050
    Other anions were not analysed.
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    A community generates 1 million litres/day (MLD) of wastewater. This wastewater is treated using activated sludge process (ASP). The working volume of the aeration tank of the ASP is 250 m3250\text{ m}^3, and the biomass concentration in the tank is 3000 mg/L3000\text{ mg/L}. Analyses results showed that a biomass concentration of 10 mg/L10\text{ mg/L} is present in the treated effluent from the secondary sedimentation tank of the ASP. Sludge wastage from the system is at a rate of 5000 L/day5000\text{ L/day} with a biomass concentration of 10000 mg/L10000\text{ mg/L}. The system is in steady state condition.
    The biological sludge residence time (BSRT) of the system (in days) is______ (round off to one decimal place).
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    A settling chamber is used for the removal of discrete particulate matter from air with following conditions. Horizontal velocity of air =0.2 m/s= 0.2\text{ m/s}; Temperature of air stream =77∘C= 77^\circ\text{C}; Specific gravity of particle to be removed =2.65= 2.65; Chamber length =12 m= 12\text{ m}; Chamber height =2 m= 2\text{ m}; Viscosity of air at 77∘C=2.1×10−5 kg/m.s77^\circ\text{C} = 2.1 \times 10^{-5}\text{ kg/m.s}; Acceleration due to gravity (g)=9.81 m/s2(g) = 9.81\text{ m/s}^2; Density of air at 77∘C=1.0 kg/m377^\circ\text{C} = 1.0\text{ kg/m}^3; Assume the density of water as 1000 kg/m31000\text{ kg/m}^3 and Laminar condition exists in the chamber.
    The minimum size of particle that will be removed with 100% efficiency in the settling chamber (in μm\mu\text{m}) is ______ (round off to one decimal place).
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    On a two-lane highway, a horizontal curve of radius 300 m300\text{ m} is provided. The design speed is 80 km/h80\text{ km/h}.
    If the longest wheelbase of vehicle expected on this highway is 7 m7\text{ m}, then the extra widening required (in m) is ______ (round off to two decimal places).
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    If the Fore Bearing of the lines AB and BC are 60∘60^\circ and 122∘122^\circ, respectively, then the interior angle ∠ABC\angle ABC (in degrees) is ______ (round off to the nearest integer).
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