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GATE CE 2018 Set 1

All 65 solved GATE CE 2018 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

2

MCQ · NAT

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Difficulty mixEasy 25Medium 36Hard 4

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65 of 65 questions

General Aptitude (GA)

10
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    Question

    “The driver applied the _____ as soon as she approached the hotel where she wanted to take a ______.”
    The words that best fill the blanks in the above sentence are
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    Question

    “It is no surprise that every society has had codes of behaviour; however, the nature of these codes is often _________.”
    The word that best fills the blank in the above sentence is
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    Question

    Hema’s age is 5 years more than twice Hari’s age. Suresh’s age is 13 years less than 10 times Hari’s age. If Suresh is 3 times as old as Hema, how old is Hema?
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    Question

    Tower A is 9090 m tall and tower B is 140140 m tall. They are 100100 m apart. A horizontal skywalk connects the floors at 7070 m in both the towers. If a taut rope connects the top of tower A to the bottom of tower B, at what distance (in meters) from tower A will the rope intersect the skywalk?
    1. A.
      22.22
    2. B.
      50
    3. C.
      57.87
    4. D.
      77.78

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    Question

    The temperature TT in a room varies as a function of the outside temperature T0T_0 and the number of persons in the room pp, according to the relation T=K(Θp+T0)T = K (\Theta p + T_0), where Θ\Theta and KK are constants. What would be the value of Θ\Theta given the following data?
    T0T_0ppTT
    25232.4
    30542.0
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    Question

    A fruit seller sold a basket of fruits at 12.5% loss. Had he sold it for Rs. 108 more, he would have made a 10% gain. What is the loss in Rupees incurred by the fruit seller?
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    Question

    The price of a wire made of a superalloy material is proportional to the square of its length. The price of 10 m length of the wire is Rs. 1600. What would be the total price (in Rs.) of two wires of lengths 4 m and 6m?
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    Question

    Which of the following function(s) is an accurate description of the graph for the range(s) indicated?
    Piecewise linear and absolute value function graph
    (i) y=2x+4y = 2x + 4 for −3≤x≤−1-3 \leq x \leq -1
    (ii) y=∣x−1∣y = |x - 1| for −1≤x≤2-1 \leq x \leq 2
    (iii) y=∣∣x∣−1∣y = ||x| - 1| for −1≤x≤2-1 \leq x \leq 2
    (iv) y=1y = 1 for 2≤x≤32 \leq x \leq 3
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    Question

    Consider a sequence of numbers a1,a2,a3,…,ana_1, a_2, a_3, \dots, a_n where an=1n−1n+2a_n = \frac{1}{n} - \frac{1}{n+2}, for each integer n>0n > 0. What is the sum of the first 50 terms?
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    Question

    Each of the letters arranged as below represents a unique integer from 1 to 9. The letters are positioned in the figure such that (A×B×C)(A \times B \times C), (B×G×E)(B \times G \times E) and (D×E×F)(D \times E \times F) are equal.
    Which integer among the following choices cannot be represented by the letters A, B, C, D, E, F or G?
    A grid-like arrangement of letters: A and D on top, B, G, E in the middle, C and F at the bottom.
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Civil Engineering (Set 1)

55
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    Question

    Which one of the following matrices is singular?
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    Question

    For the given orthogonal matrix QQ,Q=[3/72/76/7−6/73/72/72/76/7−3/7]Q = \begin{bmatrix} 3/7 & 2/7 & 6/7 \\ -6/7 & 3/7 & 2/7 \\ 2/7 & 6/7 & -3/7 \end{bmatrix}The inverse is
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    Question

    At the point x=0x = 0, the function f(x)=x3f(x) = x^3 has
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    Question

    A column of height hh with a rectangular cross-section of size a×2aa \times 2a has a buckling load of PP. If the cross-section is changed to 0.5a×3a0.5a \times 3a and its height changed to 1.5h1.5h, the buckling load of the redesigned column will be
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    Question

    A steel column of ISHB 350 @72.4 kg/m is subjected to a factored axial compressive load of 2000 kN. The load is transferred to a concrete pedestal of grade M20 through a square base plate. Consider bearing strength of concrete as 0.45fck0.45f_{ck}, where fckf_{ck} is the characteristic strength of concrete. Using limit state method and neglecting the self weight of base plate and steel column, the length of a side of the base plate to be provided is
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    Question

    The Le Chatelier apparatus is used to determine
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    Question

    The deformation in concrete due to sustained loading is
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    Question

    A solid circular beam with radius of 0.25 m0.25\text{ m} and length of 2 m2\text{ m} is subjected to a twisting moment of 20 kNm20\text{ kNm} about the z-axis at the free end, which is the only load acting as shown in the figure. The shear stress component τxy\tau_{xy} at Point ‘M’ in the cross-section of the beam at a distance of 1 m1\text{ m} from the fixed end is
    Schematic of a cantilever beam under torsion and its circular cross-section showing point M at the top
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    Question

    Two rectangular under-reinforced concrete beam sections XX and YY are similar in all aspects except that the longitudinal compression reinforcement in section YY is 10% more. Which one of the following is the correct statement?
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    Question

    The percent reduction in the bearing capacity of a strip footing resting on sand under flooding condition (water level at the base of the footing) when compared to the situation where the water level is at a depth much greater than the width of footing, is approximately
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    Question

    The width of a square footing and the diameter of a circular footing are equal. If both the footings are placed on the surface of sandy soil, the ratio of the ultimate bearing capacity of circular footing to that of square footing will be
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    Question

    Bernoulli’s equation is applicable for
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    Question

    There are 20,000 vehicles operating in a city with an average annual travel of 12,000 km per vehicle. The NOxNO_x emission rate is 2.0 g/km per vehicle. The total annual release of NOxNO_x will be
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    Question

    A bitumen sample has been graded as VG30 as per IS : 73-2013. The ‘30’ in the grade means that
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    Question

    The speed-density relationship for a road section is shown in the figure.
    speed-density relationship graph
    The shape of the flow-density relationship is
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    Question

    A well-designed signalized intersection is one in which the
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    Question

    A flow field is given by u=y2u = y^2, v=−xyv = -xy, w=0w = 0. Value of the z-component of the angular velocity (in radians per unit time, up to two decimal places) at the point (0,−1,1)(0, -1, 1) is ______
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    Question

    The frequency distribution of the compressive strength of 20 concrete cube specimens is given in the table.
    f (MPa)Number of specimens with compressive strength equal to f
    234
    282
    22.55
    315
    294
    If μ\mu is the mean strength of the specimens and σ\sigma is the standard deviation, the number of specimens (out of 20) with compressive strength less than μ−3σ\mu - 3\sigma is ______
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    Question

    In a fillet weld, the direct shear stress and bending tensile stress are 50 MPa50\text{ MPa} and 150 MPa150\text{ MPa}, respectively. As per IS 800: 2007, the equivalent stress (in MPa, up to two decimal places) will be ______
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    Question

    In a shrinkage limit test, the volume and mass of a dry soil pat are found to be 50 cm350\text{ cm}^3 and 88 g88\text{ g}, respectively. The specific gravity of the soil solids is 2.712.71 and the density of water is 1 g/cc1\text{ g/cc}. The shrinkage limit (in %, up to two decimal places) is ______
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    Question

    A core cutter of 130 mm130\text{ mm} height has inner and outer diameters of 100 mm100\text{ mm} and 106 mm106\text{ mm}, respectively. The area ratio of the core cutter (in %, up to two decimal places) is ______
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    Question

    A 1:50 model of a spillway is to be tested in the laboratory. The discharge in the prototype spillway is 1000 m3/s1000\text{ m}^3/\text{s}. The corresponding discharge (in m3/s\text{m}^3/\text{s}, up to two decimal places) to be maintained in the model, neglecting variation in acceleration due to gravity, is ______
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    Question

    A 10 m10\text{ m} wide rectangular channel carries a discharge of 20 m3/s20\text{ m}^3/\text{s} under critical condition. Using g=9.81 m/s2g = 9.81\text{ m}/\text{s}^2, the specific energy (in m, up to two decimal places) is ______
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    Question

    For routing of flood in a given channel using the Muskingum method, two of the routing coefficients are estimated as C0=−0.25C_0 = -0.25 and C1=0.55C_1 = 0.55. The value of the third coefficient C2C_2 would be ______
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    Question

    A city generates 40×10640 \times 10^6 kg of municipal solid waste (MSW) per year, out of which only 10% is recovered/recycled and the rest goes to landfill. The landfill has a single lift of 3 m height and is compacted to a density of 550550 kg/m3^3. If 80% of the landfill is assumed to be MSW, the landfill area (in m2^2, up to one decimal place) required would be ______
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    Question

    The value of the integral ∫0πxcos⁡2x dx\int_{0}^{\pi} x \cos^2 x \, dx is
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    Question

    A cantilever beam of length 2 m with a square section of side length 0.1 m is loaded vertically at the free end. The vertical displacement at the free end is 5 mm. The beam is made of steel with Young’s modulus of 2.0×1011 N/m22.0 \times 10^{11} \text{ N/m}^2. The maximum bending stress at the fixed end of the cantilever is
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    Question

    A cylinder of radius 250 mm250\text{ mm} and weight, W=10 kNW = 10\text{ kN} is rolled up an obstacle of height 50 mm50\text{ mm} by applying a horizontal force PP at its centre as shown in the figure.
    A cylinder of radius 250 mm and weight W being rolled up a 50 mm obstacle by a horizontal force P.
    All interfaces are assumed frictionless. The minimum value of PP is
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    Question

    A plate in equilibrium is subjected to uniform stresses along its edges with magnitude σxx=30 MPa\sigma_{xx} = 30\text{ MPa} and σyy=50 MPa\sigma_{yy} = 50\text{ MPa} as shown in the figure.
    A square plate with uniform tensile stresses sigma_xx and sigma_yy applied to its edges.
    The Young’s modulus of the material is 2×1011 N/m22 \times 10^{11}\text{ N/m}^2 and the Poisson’s ratio is 0.30.3. If σzz\sigma_{zz} is negligibly small and assumed to be zero, then the strain εzz\varepsilon_{zz} is
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    Question

    The figure shows a simply supported beam PQPQ of uniform flexural rigidity EIEI carrying two moments MM and 2M2M.
    A simply supported beam PQ of length L with two moments M and 2M applied at L/3 and 2L/3 from support P respectively.
    The slope at PP will be
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    Question

    A 0.5 m×0.5 m0.5\text{ m} \times 0.5\text{ m} square concrete pile is to be driven in a homogeneous clayey soil having undrained shear strength, cu=50 kPac_u = 50\text{ kPa} and unit weight, γ=18.0 kN/m3\gamma = 18.0\text{ kN/m}^3. The design capacity of the pile is 500 kN500\text{ kN}. The adhesion factor α\alpha is given as 0.750.75. The length of the pile required for the above design load with a factor of safety of 2.02.0 is
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    Question

    A closed tank contains 0.5 m0.5\text{ m} thick layer of mercury (specific gravity =13.6= 13.6) at the bottom. A 2.0 m2.0\text{ m} thick layer of water lies above the mercury layer. A 3.0 m3.0\text{ m} thick layer of oil (specific gravity =0.6= 0.6) lies above the water layer. The space above the oil layer contains air under pressure. The gauge pressure at the bottom of the tank is 196.2 kN/m2196.2\text{ kN/m}^2. The density of water is 1000 kg/m31000\text{ kg/m}^3 and the acceleration due to gravity is 9.81 m/s29.81\text{ m/s}^2. The value of pressure in the air space is
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    Question

    A rapid sand filter comprising a number of filter beds is required to produce 99 MLD99\text{ MLD} of potable water. Consider water loss during backwashing as 5%5\%, rate of filtration as 6.0 m/h6.0\text{ m/h} and length to width ratio of filter bed as 1.351.35. The width of each filter bed is to be kept equal to 5.2 m5.2\text{ m}. One additional filter bed is to be provided to take care of break-down, repair and maintenance. The total number of filter beds required will be
    1. A.
      1919
    2. B.
      2020
    3. C.
      2121
    4. D.
      2222

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    Question

    A priority intersection has a single-lane one-way traffic road crossing an undivided two-lane two-way traffic road. The traffic stream speed on the single-lane road is 20 kmph and the speed on the two-lane road is 50 kmph. The perception-reaction time is 2.5 s, coefficient of longitudinal friction is 0.38 and acceleration due to gravity is 9.81 m/s29.81\text{ m/s}^2. A clear sight triangle has to be ensured at this intersection. The minimum lengths of the sides of the sight triangle along the two-lane road and the single-lane road, respectively will be
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    Question

    The following details refer to a closed traverse:
    LineNorthing (m)Southing (m)Easting (m)Westing (m)
    PQ----437173----
    QR101----558----
    RS419--------96
    SP----83----634
    The length and direction (whole circle bearing) of closure, respectively are
    1. A.
      1 m and 90∘90^\circ
    2. B.
      2 m and 90∘90^\circ
    3. C.
      1 m and 270∘270^\circ
    4. D.
      2 m and 270∘270^\circ

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    Question

    A square area (on the surface of the earth) with side 100 m and uniform height, appears as 1 cm2^2 on a vertical aerial photograph. The topographic map shows that a contour of 650 m passes through the area. If focal length of the camera lens is 150 mm, the height from which the aerial photograph was taken, is
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    Question

    The solution at x=1,t=1x = 1, t = 1 of the partial differential equation ∂2u∂x2=25∂2u∂t2\frac{\partial^2 u}{\partial x^2} = 25 \frac{\partial^2 u}{\partial t^2} subject to initial conditions of u(0)=3xu(0) = 3x and ∂u∂t(0)=3\frac{\partial u}{\partial t}(0) = 3 is ______
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    Question

    The solution (up to three decimal places) at x=1x = 1 of the differential equation d2ydx2+2dydx+y=0\frac{d^2 y}{dx^2} + 2 \frac{dy}{dx} + y = 0 subject to boundary conditions y(0)=1y(0) = 1 and dydx(0)=−1\frac{dy}{dx}(0) = -1 is ______
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    Question

    Variation of water depth (yy) in a gradually varied open channel flow is given by the first order differential equationdydx=1−e−103ln⁡(y)250−45e−3ln⁡(y)\frac{dy}{dx} = \frac{1 - e^{-\frac{10}{3}\ln(y)}}{250 - 45e^{-3\ln(y)}}Given initial condition: y(x=0)=0.8 my(x = 0) = 0.8\text{ m}. The depth (in m, up to three decimal places) of flow at a downstream section at x=1 mx = 1\text{ m} from one calculation step of Single Step Euler Method is ______
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    Question

    An RCC short column (with lateral ties) of rectangular cross section of 250 mm×300 mm250\text{ mm} \times 300\text{ mm} is reinforced with four numbers of 16 mm16\text{ mm} diameter longitudinal bars. The grades of steel and concrete are Fe415 and M20, respectively. Neglect eccentricity effect. Considering limit state of collapse in compression (IS 456 : 2000), the axial load carrying capacity of the column (in kN, up to one decimal place), is ______
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    Question

    An RCC beam of rectangular cross section has factored shear of 200 kN at its critical section. Its width bb is 250 mm and effective depth dd is 350 mm. Assume design shear strength τc\tau_c of concrete as 0.62 N/mm2^2 and maximum allowable shear stress τc,max\tau_{c,max} in concrete as 2.8 N/mm2^2. If two legged 10 mm diameter vertical stirrups of Fe250 grade steel are used, then the required spacing (in cm, up to one decimal place) as per limit state method will be ______
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    Question

    The dimensions of a symmetrical welded I-section are shown in the figure.
    Symmetrical welded I-section with dimensions: flange width 140 mm, flange thickness 9 mm, web height 200 mm, web thickness 6.1 mm
    The plastic section modulus about the weaker axis (in cm3^3, up to one decimal place) is ______
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    Question

    Consider the deformable pin-jointed truss with loading, geometry and section properties as shown in the figure.
    A pin-jointed truss with three members: horizontal AB, vertical BC, and diagonal AC. Joint C is at the top, A is at the bottom-left with a roller support, and B is at the bottom-right with a pin support. Loads at C are P horizontal to the right and 2P vertical downwards. Member properties: AC is 2AE, BC is AE, AB is AE. Lengths: AB is L, BC is L.
    Given that E=2×1011 N/m2E = 2 \times 10^{11} \text{ N/m}^2, A=10 mm2A = 10 \text{ mm}^2, L=1 mL = 1 \text{ m} and P=1 kNP = 1 \text{ kN}. The horizontal displacement of Joint C (in mm, up to one decimal place) is ______
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    At a construction site, a contractor plans to make an excavation as shown in the figure.
    Cross-section of an excavation site. A clay layer exists from elevation 0 to 20 m. A highly pervious sand layer is below elevation 0. A river is adjacent with water level at elevation +20 m. The proposed excavation removes clay from elevation 30 m down to elevation 10 m, leaving a 10 m thick clay layer above the sand.
    The water level in the adjacent river is at an elevation of +20.0 m+20.0 \text{ m}. Unit weight of water is 10 kN/m310 \text{ kN/m}^3. The factor of safety (up to two decimal places) against sand boiling for the proposed excavation is ______
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    A conventional drained triaxial compression test was conducted on a normally consolidated clay sample under an effective confining pressure of 200 kPa200 \text{ kPa}. The deviator stress at failure was found to be 400 kPa400 \text{ kPa}. An identical specimen of the same clay sample is isotropically consolidated to a confining pressure of 200 kPa200 \text{ kPa} and subjected to standard undrained triaxial compression test. If the deviator stress at failure is 150 kPa150 \text{ kPa}, the pore pressure developed (in kPa, up to one decimal place) is ______
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    The void ratio of a soil is 0.550.55 at an effective normal stress of 140140 kPa. The compression index of the soil is 0.250.25. In order to reduce the void ratio to 0.40.4, an increase in the magnitude of effective normal stress (in kPa, up to one decimal place) should be ______
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    A rigid smooth retaining wall of height 77 m with vertical backface retains saturated clay as backfill. The saturated unit weight and undrained cohesion of the backfill are 17.217.2 kN/m3^3 and 2020 kPa, respectively. The difference in the active lateral forces on the wall (in kN per meter length of wall, up to two decimal places), before and after the occurrence of tension cracks is ______
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    Rainfall depth over a watershed is monitored through six number of well distributed rain gauges. Gauged data are given below
    Rain Gauge Number123456
    Rainfall Depth (mm)470465435525480510
    Area of Thiessen Polygon (×104\times 10^4 m2^2)9510098808592
    The Thiessen mean value (in mm, up to one decimal place) of the rainfall is ______
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    The infiltration rate ff in a basin under ponding condition is given by f=30+10e−2tf = 30 + 10e^{-2t}, where, ff is in mm/h and tt is time in hour. Total depth of infiltration (in mm, up to one decimal place) during the last 20 minutes of a storm of 30 minutes duration is ______
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    In a laboratory, a flow experiment is performed over a hydraulic structure. The measured values of discharge and velocity are 0.05 m3/s0.05\text{ m}^3\text{/s} and 0.25 m/s0.25\text{ m/s}, respectively. If the full scale structure (30 times bigger) is subjected to a discharge of 270 m3/s270\text{ m}^3\text{/s}, then the time scale (model to full scale) value (up to two decimal places) is ______
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    A water sample analysis data is given below.
    IonConcentration, mg/LAtomic Weight
    Ca2+\text{Ca}^{2+}6040
    Mg2+\text{Mg}^{2+}3024.31
    HCO3−\text{HCO}_3^-40061
    The carbonate hardness (expressed as mg/L of CaCO3\text{CaCO}_3, up to one decimal place) for the water sample is ______
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    The ultimate BOD (L0L_0) of a wastewater sample is estimated as 87% of COD. The COD of this wastewater is 300 mg/L. Considering first order BOD reaction rate constant k (use natural log) = 0.23 per day and temperature coefficient θ=1.047\theta = 1.047, the BOD value (in mg/L, up to one decimal place) after three days of incubation at 27∘C27^\circ\text{C} for this wastewater will be ______
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    A waste activated sludge (WAS) is to be blended with green waste (GW). The carbon (C) and nitrogen (N) contents, per kg of WAS and GW, on dry basis are given in the table.
    ParameterWASGW
    Carbon (g)54360
    Nitrogen (g)106
    The ratio of WAS to GW required (up to two decimal places) to achieve a blended C:N ratio of 20:1 on dry basis is ______
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    Given the following data: design life n=15n = 15 years, lane distribution factor D=0.75D = 0.75, annual rate of growth of commercial vehicles r=6%r = 6\%, vehicle damage factor F=4F = 4 and initial traffic in the year of completion of construction =3000= 3000 Commercial Vehicles Per Day (CVPD). As per IRC:37-2012, the design traffic in terms of cumulative number of standard axles (in million standard axles, up to two decimal places) is ______
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    An aircraft approaches the threshold of a runway strip at a speed of 200 km/h. The pilot decelerates the aircraft at a rate of 1.697 m/s2^2 and takes 18 s to exit the runway strip. If the deceleration after exiting the runway is 1 m/s2^2, then the distance (in m, up to one decimal place) of the gate position from the location of exit on the runway is ______
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