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GATE CE 2023 Set 2

All 65 solved GATE CE 2023 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 18Medium 37Hard 10

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65 of 65 questions

General Aptitude (GA)

10
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    Question

    The line ran _______ the page, right through the centre, and divided the page into two.
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    Question

    Kind : ________ : : Often : Seldom
    (By word meaning)
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    Question

    In how many ways can cells in a 3×33 \times 3 grid be shaded, such that each row and each column have exactly one shaded cell? An example of one valid shading is shown.
    A 3x3 grid with one cell shaded in each row and column
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    Question

    There are 4 red, 5 green, and 6 blue balls inside a box. If NN number of balls are picked simultaneously, what is the smallest value of NN that guarantees there will be at least two balls of the same colour?
    One cannot see the colour of the balls until they are picked.
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    Question

    Consider a circle with its centre at the origin (O)(O), as shown. Two operations are allowed on the circle.
    Operation 1: Scale independently along the xx and yy axes.
    Operation 2: Rotation in any direction about the origin.
    Which figure among the options can be achieved through a combination of these two operations on the given circle?
    A circle centered at the origin on a Cartesian coordinate system
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    Question

    Elvesland is a country that has peculiar beliefs and practices. They express almost all their emotions by gifting flowers. For instance, if anyone gifts a white flower to someone, then it is always taken to be a declaration of one’s love for that person. In a similar manner, the gifting of a yellow flower to someone often means that one is angry with that person.
    Based only on the information provided above, which one of the following sets of statement(s) can be logically inferred with certainty?
    (i) In Elvesland, one always declares one’s love by gifting a white flower.
    (ii) In Elvesland, all emotions are declared by gifting flowers.
    (iii) In Elvesland, sometimes one expresses one’s anger by gifting a flower that is not yellow.
    (iv) In Elvesland, sometimes one expresses one’s love by gifting a white flower.
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    Question

    Three husband-wife pairs are to be seated at a circular table that has six identical chairs. Seating arrangements are defined only by the relative position of the people. How many seating arrangements are possible such that every husband sits next to his wife?
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    Question

    Based only on the following passage, which one of the options can be inferred with certainty?
    When the congregation sang together, Apenyo would also join, though her little screams were not quite audible because of the group singing. But whenever there was a special number, trouble would begin; Apenyo would try singing along, much to the embarrassment of her mother. After two or three such mortifying Sunday evenings, the mother stopped going to church altogether until Apenyo became older and learnt to behave.
    At home too, Apenyo never kept quiet; she hummed or made up silly songs to sing by herself, which annoyed her mother at times but most often made her become pensive. She was by now convinced that her daughter had inherited her love of singing from her father who had died unexpectedly away from home.
    [Excerpt from These Hills Called Home by Temsula Ao]
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    Question

    If xx satisfies the equation 48x=2564^{8^x} = 256, then xx is equal to ______.
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    Question

    Consider a spherical globe rotating about an axis passing through its poles. There are three points PP, QQ, and RR situated respectively on the equator, the north pole, and midway between the equator and the north pole in the northern hemisphere. Let PP, QQ, and RR move with speeds vPv_P, vQv_Q, and vRv_R, respectively.
    Which one of the following options is CORRECT?
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Civil Engineering (CE) Set 2

55
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    Question

    Let ϕ\phi be a scalar field, and u\mathbf{u} be a vector field. Which of the following identities is true for div(ϕu)\text{div}(\phi \mathbf{u})?
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    Question

    Which of the following probability distribution functions (PDFs) has the mean greater than the median?
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    Question

    A remote village has exactly 1000 vehicles with sequential registration numbers starting from 1000. Out of the total vehicles, 30% are without pollution clearance certificate. Further, even- and odd-numbered vehicles are operated on even- and odd-numbered dates, respectively.
    If 100 vehicles are chosen at random on an even-numbered date, the number of vehicles expected without pollution clearance certificate is ________.
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    Question

    A circular solid shaft of span L=5 mL = 5\text{ m} is fixed at one end and free at the other end. A torque T=100 kN.mT = 100\text{ kN.m} is applied at the free end. The shear modulus and polar moment of inertia of the section are denoted as GG and JJ, respectively. The torsional rigidity GJGJ is 50,000 kN.m2/rad50,000\text{ kN.m}^2/\text{rad}. The following are reported for this shaft:
    Statement i) The rotation at the free end is 0.01 rad0.01\text{ rad}
    Statement ii) The torsional strain energy is 1.0 kN.m1.0\text{ kN.m}With reference to the above statements, which of the following is true?
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    Question

    M20 concrete as per IS 456: 2000 refers to concrete with a design mix having _________________
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    Question

    When a simply-supported elastic beam of span LL and flexural rigidity EIEI (EE is the modulus of elasticity and II is the moment of inertia of the section) is loaded with a uniformly distributed load ww per unit length, the deflection at the mid-span is Δ0=5wL4384EI\Delta_0 = \frac{5 wL^4}{384 EI}. If the load on one half of the span is now removed, the mid-span deflection ________.
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    Question

    Muller-Breslau principle is used in analysis of structures for _______________.
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    Question

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

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

    Identify the cross-drainage work in the figure.
    Cross-drainage work diagram showing a drainage/natural stream passing over a canal
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    Question

    Which one of the following options provides the correct match of the terms listed in Column-1 and Column-2?
    Column-1Column-2
    P: Horton equationI: Precipitation
    Q: Muskingum methodII: Flood frequency
    R: Penman methodIII: Evapotranspiration
    IV: Infiltration
    V: Channel routing
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    Question

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

    Which of the following is equal to the stopping sight distance?
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    Question

    The magnetic bearing of the sun for a location at noon is 183∘30′183^\circ 30'. If the sun is exactly on the geographic meridian at noon, the magnetic declination of the location is ________.
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    Question

    For the matrix[A]=[1−10−12−10−11][A] = \begin{bmatrix} 1 & -1 & 0 \\ -1 & 2 & -1 \\ 0 & -1 & 1 \end{bmatrix}which of the following statements is/are TRUE?
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    Question

    In the frame shown in the figure (not to scale), all four members (AB, BC, CD, and AD) have the same length and same constant flexural rigidity. All the joints A, B, C, and D are rigid joints. The midpoints of AB, BC, CD, and AD, are denoted by E, F, G, and H, respectively. The frame is in unstable equilibrium under the shown forces of magnitude PP acting at E and G. Which of the following statements is/are TRUE?
    A square frame ABCD with midpoints E, F, G, H. Forces P act inwards at E and G.
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    Question

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

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

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

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

    The steady-state temperature distribution in a square plate ABCD is governed by the 2-dimensional Laplace equation. The side AB is kept at a temperature of 100 °C and the other three sides are kept at a temperature of 0 °C. Ignoring the effect of discontinuities in the boundary conditions at the corners, the steady-state temperature at the center of the plate is obtained as T0T_0 °C. Due to symmetry, the steady-state temperature at the center will be same (T0T_0 °C), when any one side of the square is kept at a temperature of 100 °C and the remaining three sides are kept at a temperature of 0 °C. Using the principle of superposition, the value of T0T_0 is _________________________ (rounded off to two decimal places).
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    Question

    An unconfined compression strength test was conducted on a cohesive soil. The test specimen failed at an axial stress of 76 kPa76\ \text{kPa}. The undrained cohesion (in kPa\text{kPa}, in integer) of the soil is _________________________.
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    Question

    The pressure in a pipe at X is to be measured by an open manometer as shown in figure. Fluid A is oil with a specific gravity of 0.8 and Fluid B is mercury with a specific gravity of 13.6. The absolute pressure at X is _________________________ kN/m2kN/m^2 (round off to one decimal place).
    [Assume density of water as 1000kg/m31000 kg/m^3 and acceleration due to gravity as 9.81m/s29.81 m/s^2 and atmospheric pressure as 101.3kN/m2101.3 kN/m^2]
    [Note: Figure is not to scale]
    Manometer diagram showing pipe X connected to a U-tube with Fluid A and Fluid B. Heights are 75 cm and 25 cm.
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    Question

    For the elevation and temperature data given in the table, the existing lapse rate in the environment is _________ ∘C/100 m^\circ\text{C}/100\text{ m} (round off to two decimal places).
    Elevation from ground level (m)Temperature (∘C^\circ\text{C})
    514.2
    32516.9
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    Question

    If the size of the ground area is 6extkmimes3extkm6 ext{ km} imes 3 ext{ km} and the corresponding photo size in the aerial photograph is 30extcmimes15extcm30 ext{ cm} imes 15 ext{ cm}, then the scale of the photograph is 1:1 : ________ (in integer).
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    Question

    The solution of the differential equationd3ydx3−5.5d2ydx2+9.5dydx−5y=0\frac{d^3y}{dx^3} - 5.5 \frac{d^2y}{dx^2} + 9.5 \frac{dy}{dx} - 5y = 0is expressed as y=C1e2.5x+C2eαx+C3eβxy = C_1 e^{2.5x} + C_2 e^{\alpha x} + C_3 e^{\beta x}, where C1,C2,C3,αC_1, C_2, C_3, \alpha, and β\beta are constants, with α\alpha and β\beta being distinct and not equal to 2.5. Which of the following options is correct for the values of α\alpha and β\beta?
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    Question

    Two vectors [2103]T[2 \quad 1 \quad 0 \quad 3]^T and [1012]T[1 \quad 0 \quad 1 \quad 2]^T belong to the null space of a 4×44 \times 4 matrix of rank 2. Which one of the following vectors also belongs to the null space?
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    Question

    Cholesky decomposition is carried out on the following square matrix [A][A].[A]=[8−5−5a22][A] = \begin{bmatrix} 8 & -5 \\ -5 & a_{22} \end{bmatrix}Let lijl_{ij} and aija_{ij} be the (i,j)th(i,j)^{th} elements of matrices [L][L] and [A][A], respectively. If the element l22l_{22} of the decomposed lower triangular matrix [L][L] is 1.968, what is the value (rounded off to the nearest integer) of the element a22a_{22}?
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    Question

    In a two-dimensional stress analysis, the state of stress at a point is shown in the figure. The values of length of PQPQ, QRQR, and RPRP are 4, 3, and 5 units, respectively. The principal stresses are ________. (round off to one decimal place)
    A triangular stress element PQR with normal stresses $\sigma_x$ and $\sigma_y$ on faces PQ and QR, and normal stress $\sigma = 120$ MPa and shear stress $\tau = 70$ MPa on the inclined face RP.
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    Question

    Two plates are connected by fillet welds of size 10 mm and subjected to tension, as shown in the figure. The thickness of each plate is 12 mm. The yield stress and the ultimate stress of steel under tension are 250 MPa and 410 MPa, respectively. The welding is done in the workshop (partial safety factor, γmw=1.25\gamma_{mw} = 1.25). As per the Limit State Method of IS 800: 2007, what is the minimum length (in mm, rounded off to the nearest higher multiple of 5 mm) required of each weld to transmit a factored force PP equal to 275 kN?
    A diagram showing two overlapping plates connected by fillet welds on the sides. The top plate has a width of 100 mm and a force P acting upwards. The bottom plate has a width of 150 mm and a force P acting downwards. Fillet welds are indicated on the vertical edges of the overlap.
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    Question

    In the given figure, Point O indicates the stress point of a soil element at initial non-hydrostatic stress condition. For the stress path (OP), which of the following loading conditions is correct?
    Stress path diagram showing q vs p with a line OP of slope 1
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    Question

    The figure shows a vertical retaining wall with backfill consisting of cohesive-frictional soil and a failure plane developed due to passive earth pressure. The forces acting on the failure wedge are: PP as the reaction force between the wall and the soil, RR as the reaction force on the failure plane, CC as the cohesive force along the failure plane and WW as the weight of the failure wedge. Assuming that there is no adhesion between the wall and the wedge, identify the most appropriate force polygon for the wedge.
    Retaining wall with failure plane and backfill
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    Question

    A compound symmetrical open channel section as shown in the figure has a maximum of ____________ critical depth(s).
    Compound symmetrical open channel section with main channel and flood plains
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    Question

    The critical flow condition in a channel is given by ________.
    [Note: α\alpha – kinetic energy correction factor; QQ – discharge; AcA_c – cross-sectional area of flow at critical flow condition; TcT_c – top width of flow at critical flow condition; gg – acceleration due to gravity]
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    Question

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

    A delivery agent is at a location R. To deliver the order, she is instructed to travel to location P along straight-line paths of RC, CA, AB and BP of 5 km each. The direction of each path is given in the table below as whole circle bearings. Assume that the latitude (L) and departure (D) of R is (0, 0) km. What is the latitude and departure of P (in km, rounded off to one decimal place)?
    PathsRCCAABBP
    Directions (in degrees)120090240
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    Question

    Which of the following statements is/are TRUE?
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    Question

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

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

    The figure presents the time-space diagram for when the traffic on a highway is suddenly stopped for a certain time and then released. Which of the following statements are true?
    Time-space diagram showing vehicle trajectories in a distance-time coordinate system with three distinct regions: P (initial flow), Q (stopped traffic), and R (released traffic).
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    Question

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

    A 5 cm long metal rod AB was initially at a uniform temperature of T0T_0 °C. Thereafter, temperature at both the ends are maintained at 0 °C. Neglecting the heat transfer from the lateral surface of the rod, the heat transfer in the rod is governed by the one-dimensional diffusion equation ∂T∂t=D∂2T∂x2\frac{\partial T}{\partial t} = D \frac{\partial^2 T}{\partial x^2}, where DD is the thermal diffusivity of the metal, given as 1.0 cm2^2/s.
    The temperature distribution in the rod is obtained asT(x,t)=∑n=1,3,5…∞Cnsin⁡nπx5e−βn2t,T(x,t) = \sum_{n=1,3,5\dots}^{\infty} C_n \sin \frac{n\pi x}{5} e^{-\beta n^2 t},where xx is in cm measured from A to B with x=0x = 0 at A, tt is in s, CnC_n are constants in °C, TT is in °C, and β\beta is in s−1^{-1}.
    The value of β\beta (in s−1^{-1}, rounded off to three decimal places) is _____________.
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    Question

    A beam is subjected to a system of coplanar forces as shown in the figure. The magnitude of vertical reaction at Support P is __________ N (round off to one decimal place).
    A simply supported beam PQ of length 6m is subjected to several forces. A force of 500N acts at 2m from P, inclined at 60 degrees. A vertical downward force of 200N acts at 3.5m from P. A horizontal force of 100N acts on a bracket of height 0.5m at 4.5m from P.
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    Question

    For the frame shown in the figure (not to scale), all members (AB, BC, CD, GB, and CH) have the same length, LL and flexural rigidity, EIEI. The joints at B and C are rigid joints, and the supports A and D are fixed supports. Beams GB and CH carry uniformly distributed loads of ww per unit length. The magnitude of the moment reaction at A is wL2/kwL^2/k. What is the value of kk (in integer)?
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    Question

    Consider the singly reinforced section of a cantilever concrete beam under bending, as shown in the figure (M25 grade concrete, Fe415 grade steel). The stress block parameters for the section at ultimate limit state, as per IS 456: 2000 notations, are given. The ultimate moment of resistance for the section by the Limit State Method is __________ kN.m (round off to one decimal place).
    [Note: Here, AsA_s is the total area of tension steel bars, b is the width of the section, d is the effective depth of the bars, fckf_{ck} is the characteristic compressive cube strength of concrete, fyf_y is the yield stress of steel, and xux_u is the depth of neutral axis.]
    Three diagrams showing the cross-section, stress distribution, and force distribution for a reinforced concrete beam.
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    A 2D thin plate with modulus of elasticity, E=1.0 N/m2E = 1.0 \text{ N/m}^2, and Poisson’s ratio, μ=0.5\mu = 0.5, is in plane stress condition. The displacement field in the plate is given by u=Cx2yu = Cx^2y and v=0v = 0, where uu and vv are displacements (in m) along the XX and YY directions, respectively, and CC is a constant (in m−2\text{m}^{-2}). The distances xx and yy along XX and YY, respectively, are in m. The stress in the XX direction is σXX=40xy N/m2\sigma_{XX} = 40xy \text{ N/m}^2, and the shear stress is τXY=αx2 N/m2\tau_{XY} = \alpha x^2 \text{ N/m}^2. What is the value of α\alpha (in N/m4\text{N/m}^4, in integer)?
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    Question

    An idealised frame supports a load as shown in the figure. The horizontal component of the force transferred from the horizontal member PQPQ to the vertical member RSRS at PP is _________ N (round off to one decimal place).
    Idealised frame with vertical member RS, horizontal member PQ, and strut TU supporting a 10 N load at Q
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    A square footing is to be designed to carry a column load of 500 kN500\text{ kN} which is resting on a soil stratum having the following average properties: bulk unit weight =19 kN/m3= 19\text{ kN/m}^3; angle of internal friction =0∘= 0^\circ and cohesion =25 kPa= 25\text{ kPa}. Considering the depth of the footing as 1 m1\text{ m} and adopting Meyerhof’s bearing capacity theory with a factor of safety of 33, the width of the footing (in m) is ___________________________ (round off to one decimal place)
    [Assume the applicable shape and depth factor values as unity; ground water level at greater depth.]
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    A circular pile of diameter 0.60.6 m and length 88 m was constructed in a cohesive soil stratum having the following properties: bulk unit weight =19= 19 kN/m3^3; angle of internal friction =0∘= 0^\circ and cohesion =25= 25 kPa.
    The allowable load the pile can carry with a factor of safety of 33 is _________________ kN (round off to one decimal place).
    [Adopt: Adhesion factor, α=1.0\alpha = 1.0 and Bearing capacity factor, Nc=9.0N_c = 9.0]
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    For the flow setup shown in the figure (not to scale), the hydraulic conductivities of the two soil samples, Soil 1 and Soil 2, are 1010 mm/s and 11 mm/s, respectively. Assume the unit weight of water as 1010 kN/m3^3 and ignore the velocity head. At steady state, what is the total head (in m, rounded off to two decimal places) at any point located at the junction of the two samples? ___________________________
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    A consolidated drained (CD) triaxial test was carried out on a sand sample with the known effective shear strength parameters, c′=0c' = 0 and ϕ′=30∘\phi' = 30^\circ. In the test, prior to the failure, when the sample was undergoing axial compression under constant cell pressure, the drainage valve was accidentally closed. At the failure, 360 kPa deviatoric stress was recorded along with 70 kPa pore water pressure. If the test is repeated without such error, and no back pressure is applied in either of the tests, what is the deviatoric stress (in kPa, in integer) at the failure?
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    A catchment may be idealized as a circle of radius 30 km. There are five rain gauges, one at the center of the catchment and four on the boundary (equi-spaced), as shown in the figure (not to scale).
    The annual rainfall recorded at these gauges in a particular year are given below.
    GaugeG1G_1G2G_2G3G_3G4G_4G5G_5
    Rainfall (mm)910930925895905
    Using the Thiessen polygon method, what is the average rainfall (in mm, rounded off to two decimal places) over the catchment in that year?
    Rain gauge locations in a circular catchment
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    The cross-section of a small river is sub-divided into seven segments of width 1.5 m each. The average depth, and velocity at different depths were measured during a field campaign at the middle of each segment width. The discharge computed by the velocity area method for the given data is _________ m3/sm^3/s (round off to one decimal place).
    SegmentAverage depth (D) (m)0.2D0.6D0.8D
    10.40--0.40--
    20.700.76--0.70
    31.201.19--1.13
    41.401.25--1.10
    51.101.13--1.09
    60.800.69--0.65
    70.45--0.42--
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    The theoretical aerobic oxidation of biomass (C5H7O2NC_5H_7O_2N) is given below:C5H7O2N+5O2→5CO2+NH3+2H2OC_5H_7O_2N + 5O_2 \rightarrow 5CO_2 + NH_3 + 2H_2OThe biochemical oxidation of biomass is assumed as a first-order reaction with a rate constant of 0.23/d0.23/d at 20∘C20^\circ C (logarithm to base ee). Neglecting the second-stage oxygen demand from its biochemical oxidation, the ratio of BOD5BOD_5 at 20∘C20^\circ C to total organic carbon (TOC) of biomass is _________________________ (round off to two decimal places).
    [Consider the atomic weights of C, H, O and N as 12 g/mol12\text{ g/mol}, 1 g/mol1\text{ g/mol}, 16 g/mol16\text{ g/mol} and 14 g/mol14\text{ g/mol}, respectively]
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    A system of seven river segments is shown in the schematic diagram. The RiR_i’s, QiQ_i’s, and CiC_i’s (i=1i = 1 to 77) are the river segments, their corresponding flow rates, and concentrations of a conservative pollutant, respectively. Assume complete mixing at the intersections, no additional water loss or gain in the system, and steady state condition. Given: Q1=5 m3/sQ_1 = 5\text{ m}^3/\text{s}; Q2=15 m3/sQ_2 = 15\text{ m}^3/\text{s}; Q4=3 m3/sQ_4 = 3\text{ m}^3/\text{s}; Q6=8 m3/sQ_6 = 8\text{ m}^3/\text{s}; C1=8 kg/m3C_1 = 8\text{ kg/m}^3; C2=12 kg/m3C_2 = 12\text{ kg/m}^3; C6=10 kg/m3C_6 = 10\text{ kg/m}^3. What is the steady state concentration (in kg/m3\text{kg/m}^3, rounded off to two decimal place) of the pollutant in the river segment 7 ?
    Schematic diagram of river segments R1 to R7
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