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GATE CE 2019 Set 2

All 65 solved GATE CE 2019 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

2

MCQ · NAT

Revision mode

Self-paced

No timer. Focus on understanding.

Difficulty mixEasy 27Medium 34Hard 4

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65 of 65 questions

General Aptitude (GA)

10
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    Question

    Daytime temperatures in Delhi can ______ 40∘C40^\circ\text{C}.
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    Question

    The growth rate of ABC Motors in 2017 was the same ______ XYZ Motors in 2016.
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    Question

    Suresh wanted to lay a new carpet in his new mansion with an area of 70×5570 \times 55 sq. mts. However an area of 550 sq. mts. had to be left out for flower pots. If the cost of carpet is Rs. 50 per sq. mts., how much money (in Rs.) will be spent by Suresh for the carpet now?
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    Question

    A retaining wall with measurements 30 m×12 m×6 m30\text{ m} \times 12\text{ m} \times 6\text{ m} was constructed with bricks of dimensions 8 cm×6 cm×6 cm8\text{ cm} \times 6\text{ cm} \times 6\text{ cm}. If 60%60\% of the wall consists of bricks, the number of bricks used for the construction is ______ lakhs.
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    Question

    Hima Das was ____ only Indian athlete to win ____ gold for India.
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    Question

    Mohan, the manager, wants his four workers to work in pairs. No pair should work for more than 5 hours. Ram and John have worked together for 5 hours. Krishna and Amir have worked as a team for 2 hours. Krishna does not want to work with Ram. Whom should Mohan allot to work with John, if he wants all the workers to continue working?
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    Question

    Population of state X increased by x% and the population of state Y increased by y% from 2001 to 2011. Assume that x is greater than y. Let P be the ratio of the population of state X to state Y in a given year. The percentage increase in P from 2001 to 2011 is __________.
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    Question

    The Newspaper reports that over 500 hectares of tribal land spread across 28 tribal settlements in Mohinitampuram forest division have already been "alienated". A top forest official said, "First the tribals are duped out of their land holdings. Second, the families thus rendered landless are often forced to encroach further into the forests".
    On the basis of the information available in the paragraph, __________ is/are responsible for duping the tribals.
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    Question

    An oil tank can be filled by pipe X in 5 hours and pipe Y in 4 hours, each pump working on its own. When the oil tank is full and the drainage hole is open, the oil is drained in 20 hours. If initially the tank was empty and someone started the two pumps together but left the drainage hole open, how many hours will it take for the tank to be filled? (Assume that the rate of drainage is independent of the Head)
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    Question

    “Popular Hindi fiction, despite – or perhaps because of – its wide reach, often does not appear in our cinema. As ideals that viewers are meant to look up to rather than identify with, Hindi film protagonists usually read books of aspirational value: textbooks, English books, or high value literature.”
    Which one of the following CANNOT be inferred from the paragraph above?
    1. A.
      Though popular Hindi fiction has wide reach, it often does not appear in the movies
    2. B.
      Protagonists in Hindi movies, being ideals for viewers, read only books of aspirational value
    3. C.
      Textbooks, English books or high literature have aspirational value, but not popular Hindi fiction
    4. D.
      People do not look up to writers of textbooks, English books or high value literature

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CE (Set No 3) Stage 2

55
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    Question

    Euclidean norm (length) of the vector [4−2−6]T[4 \quad -2 \quad -6]^T is
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    Question

    The Laplace transform of sinh⁡(at)\sinh(at) is
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    Question

    The following inequality is true for all xx close to 0.2−x23<xsin⁡x1−cos⁡x<22 - \frac{x^2}{3} < \frac{x \sin x}{1 - \cos x} < 2What is the value of lim⁡x→0xsin⁡x1−cos⁡x\lim_{x \to 0} \frac{x \sin x}{1 - \cos x}?
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    Question

    What is curl of the vector field 2x2yi+5z2j−4yzk2x^2y\mathbf{i} + 5z^2\mathbf{j} - 4yz\mathbf{k}?
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    Question

    A closed thin-walled tube has thickness, tt, mean enclosed area within the boundary of the centerline of tube's thickness, AmA_m, and shear stress, τ\tau. Torsional moment of resistance, TT, of the section would be
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    Question

    A steel column is restrained against both translation and rotation at one end and is restrained only against rotation but free to translate at the other end. Theoretical and design (IS:800- 2007) values, respectively, of effective length factor of the column are
    1. A.
      1.01.0 and 1.01.0
    2. B.
      1.21.2 and 1.01.0
    3. C.
      1.21.2 and 1.21.2
    4. D.
      1.01.0 and 1.21.2

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    Question

    If the fineness modulus of a sample of fine aggregates is 4.3, the mean size of the particles in the sample is between
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    Question

    For a channel section subjected to a downward vertical shear force at its centroid, which one of the following represents the correct distribution of shear stress in flange and web?
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    Question

    Which one of the following options contains ONLY primary air pollutants?
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    Question

    Analysis of a water sample revealed that the sample contains the following species.
    CO32−,Na+,H+,PO43−,Al3+,H2CO3,Cl−,Ca2+,Mg2+,HCO3−,Fe2+,OH−CO_3^{2-}, Na^+, H^+, PO_4^{3-}, Al^{3+}, H_2CO_3, Cl^-, Ca^{2+}, Mg^{2+}, HCO_3^-, Fe^{2+}, OH^-
    Concentrations of which of the species will be required to compute alkalinity?
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    Question

    Structural failures considered in the mechanistic method of bituminous pavement design are
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    Question

    A solid sphere of radius, rr, and made of material with density, ρs\rho_s, is moving through the atmosphere (constant pressure, pp) with a velocity, vv. The net force ONLY due to atmospheric pressure (FpF_p) acting on the sphere at any time, tt, is
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    Question

    The velocity field in a flow system is given by v=2i+(x+y)j+(xyz)kv = 2\mathbf{i} + (x + y)\mathbf{j} + (xyz)\mathbf{k}. The acceleration of the fluid at (1,1,2)(1, 1, 2) is
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    Question

    An inflow hydrograph is routed through a reservoir to produce an outflow hydrograph. The peak flow of the inflow hydrograph is PIP_I and the time of occurrence of the peak is tIt_I. The peak flow of the outflow hydrograph is POP_O and the time of occurrence of the peak is tOt_O. Which one of the following statements is correct?
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    Question

    An earthen dam of height HH is made of cohesive soil whose cohesion and unit weight are cc and γ\gamma, respectively. If the factor of safety against cohesion is FcF_c, the Taylor's stability number (SnS_n) is
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    Question

    The notation "SC" as per Indian Standard Soil Classification System refers to
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    Question

    An anisotropic soil deposit has coefficient of permeability in vertical and horizontal directions as kzk_z and kxk_x, respectively. For constructing a flow net, the horizontal dimension of the problem's geometry is transformed by a multiplying factor of
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    Question

    The value of the function f(x)f(x) is given at nn distinct values of xx and its value is to be interpolated at the point x∗x^*, using all the nn points. The estimate is obtained first by the Lagrange polynomial, denoted by ILI_L, and then by the Newton polynomial, denoted by INI_N. Which one of the following statements is correct?
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    Question

    The speed-density relationship in a mid-block section of a highway follows the Greenshield's model. If the free flow speed is vfv_f and the jam density is kjk_j, the maximum flow observed on this section is
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    Question

    The degree of static indeterminacy of the plane frame as shown in the figure is _______
    A plane frame with three columns and three horizontal beams, including the support level. It has one fixed support and two hinged supports. An internal hinge is located on the first-floor beam near the first column.
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    Question

    The characteristic compressive strength of concrete required in a project is 25 MPa25\text{ MPa} and the standard deviation in the observed compressive strength expected at site is 4 MPa4\text{ MPa}. The average compressive strength of cubes tested at different water-cement (w/cw/c) ratios using the same material as is used for the project is given in the table.
    w/cw/c (%)45505560
    Average compressive strength of cubes (MPaMPa)35252015
    The water-cement ratio (in percent, round off to the lower integer) to be used in the mix is _______
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    Question

    The data from a closed traverse survey PQRS (run in the clockwise direction) are given in the table
    LineIncluded angle (in degrees)
    PQ88
    QR92
    RS94
    SP89
    The closing error for the traverse PQRS (in degrees) is ___________
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    Question

    A vehicle is moving on a road of grade +4%+4\% at a speed of 20 m/s20\text{ m/s}. Consider the coefficient of rolling friction as 0.460.46 and acceleration due to gravity as 10 m/s210\text{ m/s}^2. On applying brakes to reach a speed of 10 m/s10\text{ m/s}, the required braking distance (in mm, round off to nearest integer) along the horizontal, is ___________
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    Question

    The command area of a canal grows only one crop, i.e., wheat. The base period of wheat is 120 days and its total water requirement, Δ\Delta, is 40 cm40\text{ cm}. If the canal discharge is 2 m3/s2\text{ m}^3/\text{s}, the area, in hectares, rounded off to the nearest integer, which could be irrigated (neglecting all losses) is ________
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    Question

    Construction of a new building founded on a clayey soil was completed in January 2010. In January 2014, the average consolidation settlement of the foundation in clay was recorded as 10 mm. The ultimate consolidation settlement was estimated in design as 40 mm. Considering double drainage to occur at the clayey soil site, the expected consolidation settlement in January 2019 (in mm, round off to the nearest integer) will be
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    Question

    The probability density function of a continuous random variable distributed uniformly between xx and yy (for y>xy > x) is
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    Question

    Consider the hemi-spherical tank of radius 13 m as shown in the figure (not drawn to scale). What is the volume of water (in m³) when the depth of water at the centre of the tank is 6 m?
    A cross-section of a hemispherical tank with water, showing the radius of the hemisphere as 13m and the depth of water as 6m.
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    Question

    An ordinary differential equation is given below.(dydx)(xln⁡x)=y\left(\frac{dy}{dx}\right)(x \ln x) = yThe solution for the above equation is
    (Note: KK denotes a constant in the options)
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    Question

    For a plane stress problem, the state of stress at a point P is represented by the stress element as shown in figure.
    stress element at point P showing normal stresses of 80 MPa tension and 20 MPa compression, and shear stress of 25 MPa
    By how much angle (θ\theta) in degrees the stress element should be rotated in order to get the planes of maximum shear stress?
    rotated stress element showing counter-clockwise rotation angle theta
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    Question

    The critical bending compressive stress in the extreme fibre of a structural steel section is 10001000 MPa. It is given that the yield strength of the steel is 250250 MPa, width of flange is 250250 mm and thickness of flange is 1515 mm. As per the provisions of IS:800-2007, the non-dimensional slenderness ratio of the steel cross-section is
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    Question

    In the context of provisions relating to durability of concrete, consider the following assertions:
    Assertion (1): As per IS 456-2000, air entrainment to the extent of 3% to 6% is required for concrete exposed to marine environment.
    Assertion (2): The equivalent alkali content (in terms of Na2ONa_2O equivalent) for a cement containing 1% and 0.6% of Na2ONa_2O and K2OK_2O, respectively, is approximately 1.4% (rounded to 1 decimal place).
    Which one of the following statements is CORRECT?
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    Question

    Chlorine is used as the disinfectant in a municipal water treatment plant. It achieves 50 percent of disinfection efficiency measured in terms of killing the indicator microorganisms (E-Coli) in 3 minutes. The minimum time required to achieve 99 percent disinfection efficiency would be
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    Question

    A camera with a focal length of 20 cm20\text{ cm} fitted in an aircraft is used for taking vertical aerial photographs of a terrain. The average elevation of the terrain is 1200 m1200\text{ m} above mean sea level (MSL). What is the height above MSL at which an aircraft must fly in order to get the aerial photographs at a scale of 1:8000?
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    Question

    A flexible pavement has the following class of loads during a particular hour of the day.
    i. 80 buses with 2-axles (each axle load of 40 kN40\text{ kN});
    ii. 160 trucks with 2-axles (front and rear axle loads of 40 kN40\text{ kN} and 80 kN80\text{ kN}, respectively)
    The equivalent standard axle load repetitions for this vehicle combination as per IRC:37-2012 would be
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    Question

    The inverse of the matrix [234431124]\begin{bmatrix} 2 & 3 & 4 \\ 4 & 3 & 1 \\ 1 & 2 & 4 \end{bmatrix} is
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    Question

    A long uniformly distributed load of 10 kN/m10\text{ kN/m} and a concentrated load of 60 kN60\text{ kN} are moving together on the beam ABCD shown in the figure (not drawn to scale). The relative positions of the two loads are not fixed. The maximum shear force (in kN\text{kN}, round off to the nearest integer) caused at the internal hinge B due to the two loads is ______
    Beam ABCD with internal hinge at B and supports at A, C, D
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    Question

    A plane frame shown in the figure (not to scale) has linear elastic springs at node H. The spring constants are kx=ky=5×105 kN/mk_x = k_y = 5 \times 10^5 \text{ kN/m} and kθ=3×105 kNm/radk_\theta = 3 \times 10^5 \text{ kNm/rad}.
    Plane frame with springs at node H
    For the externally applied moment of 30 kNm30 \text{ kNm} at node F, the rotation (in degrees, round off to 3 decimals) observed in the rotational spring at node H is ___________
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    Question

    A rolled *I*-section beam is supported on a 75 mm75\text{ mm} wide bearing plate as shown in the figure. Thicknesses of flange and web of the *I*-section are 20 mm20\text{ mm} and 8 mm8\text{ mm}, respectively. Root radius of the *I*-section is 10 mm10\text{ mm}. Assume: material yield stress, fy=250 MPaf_y = 250\text{ MPa} and partial safety factor for material, γm0=1.10\gamma_{m0} = 1.10.
    Diagram showing a rolled I-section beam supported on a 75 mm wide bearing plate with arrows indicating the bearing area.
    As per IS: 800-2007, the web bearing strength (in kNkN, round off to 2 decimal places) of the beam is _______
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    Question

    When a specimen of M25 concrete is loaded to a stress level of 12.5 MPa12.5 \text{ MPa}, a strain of 500×10−6500 \times 10^{-6} is recorded. If this load is allowed to stand for a long time, the strain increases to 1000×10−61000 \times 10^{-6}. In accordance with the provisions of IS:456-2000, considering the long-term effects, the effective modulus of elasticity of the concrete (in MPaMPa) is ___________
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    Question

    A water treatment plant treats 6000 m36000\text{ m}^3 of water per day. As a part of the treatment process, discrete particles are required to be settled in a clarifier. A column test indicates that an overflow rate of 1.5 m1.5\text{ m} per hour would produce the desired removal of particles through settling in the clarifier having a depth of 3.0 m3.0\text{ m}. The volume of the required clarifier, (in m3\text{m}^3, round off to 1 decimal place) would be _______
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    Question

    Raw municipal solid waste (MSW) collected from a city contains 70%70\% decomposable material that can be converted to methane. The water content of the decomposable material is 35%35\%. An elemental analysis of the decomposable material yields the following mass percent.
    C : H : O : N : other = 44 : 6 : 43 : 0.8 : 6.2
    The methane production of the decomposable material is governed by the following stoichiometric relationCaHbOcNd+nH2O→mCH4+sCO2+dNH3\text{C}_a\text{H}_b\text{O}_c\text{N}_d + n\text{H}_2\text{O} \rightarrow m\text{CH}_4 + s\text{CO}_2 + d\text{NH}_3Given atomic weights: C = 12, H = 1, O = 16, N = 14. The mass of methane produced (in grams, round off to 1 decimal place) per kg of raw MSW will be _______
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    Question

    Consider the reactor shown in the figure. The flow rate through the reactor is Q m3/hQ\text{ m}^3/\text{h}. The concentrations (in mg/L\text{mg/L}) of a compound in the influent and effluent are C0C_0 and CC, respectively. The compound is degraded in the reactor following the first order reaction. The mixing condition of the reactor can be varied such that the reactor becomes either a completely mixed flow reactor (CMFR) or a plug-flow reactor (PFR). The length of the reactor can be adjusted in these two mixing conditions to LCMFRL_{\text{CMFR}} and LPFRL_{\text{PFR}} while keeping the cross-section of the reactor constant. Assuming steady state and for C/C0=0.8C/C_0 = 0.8, the value of LCMFR/LPFRL_{\text{CMFR}}/L_{\text{PFR}} (round off to 2 decimal places) is _______
    Diagram of a reactor with influent flow Q, C0 and effluent flow Q, C with length L
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    Question

    A series of perpendicular offsets taken from a curved boundary wall to a straight survey line at an interval of 6 m6\text{ m} are 1.22,1.67,2.04,2.34,2.14,1.871.22, 1.67, 2.04, 2.34, 2.14, 1.87, and 1.15 m1.15\text{ m}. The area (in m2\text{m}^2, round off to 2 decimal places) bounded by the survey line, curved boundary wall, the first and the last offsets, determined using Simpson’s rule, is ________
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    Question

    The uniform arrival and uniform service rates observed on an approach road to a signalized intersection are 2020 and 50 vehicles/minute50\text{ vehicles/minute}, respectively. For this signal, the red time is 30 s30\text{ s}, the effective green time is 30 s30\text{ s}, and the cycle length is 60 s60\text{ s}. Assuming that initially there are no vehicles in the queue, the average delay per vehicle using the approach road during a cycle length (in s\text{s}, round off to 2 decimal places) is ________
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    A broad gauge railway line passes through a horizontal curved section (radius =875 m= 875\text{ m}) of length 200 m200\text{ m}. The allowable speed on this portion is 100 km/h100\text{ km/h}. For calculating the cant, consider the gauge as centre-to-centre distance between the rail heads, equal to 1750 mm1750\text{ mm}. The maximum permissible cant (in mm\text{mm}, round off to 1 decimal place) with respect to the centre-to-centre distance between the rail heads is ________
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    The speed-density relationship of a highway is given asu=100−0.5ku = 100 - 0.5 kwhere, u=speed in km per houru = \text{speed in } km \text{ per hour}, k=density in vehicles per kmk = \text{density in vehicles per } km. The maximum flow (in vehicles per hour, round off to the nearest integer) is ________
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    A confined aquifer of 15 m15\text{ m} constant thickness is sandwiched between two aquicludes as shown in the figure (not drawn to scale).
    A cross-section diagram of a confined aquifer between two aquicludes. Two piezometers, P and Q, are installed. Piezometer P shows a head of $55.2\text{ m}$ and piezometer Q shows a head of $34.1\text{ m}$. The horizontal distance between them is $L = 2500\text{ m}$. The aquifer has a constant thickness of $15\text{ m}$. Flow is indicated from P to Q.
    The heads indicated by two piezometers P and Q are 55.2 m55.2\text{ m} and 34.1 m34.1\text{ m}, respectively. The aquifer has a hydraulic conductivity of 80 m/day80\text{ m/day} and its effective porosity is 0.250.25. If the distance between the piezometers is 2500 m2500\text{ m}, the time taken by the water to travel through the aquifer from piezometer location P to Q (in days, round off to 1 decimal place) is ________.
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    At the foot of a spillway, water flows at a depth of 23 cm23\text{ cm} with a velocity of 8.1 m/s8.1\text{ m/s}, as shown in the figure.
    Diagram of a spillway discharging into a channel where a hydraulic jump occurs. Depths 23 cm and y1 are marked.
    The flow enters as an M-3 profile in the long wide rectangular channel with bed slope =11800= \frac{1}{1800} and Manning's n=0.015n = 0.015. A hydraulic jump is formed at a certain distance from the foot of the spillway. Assume the acceleration due to gravity, g=9.81 m/s2g = 9.81\text{ m/s}^2. Just before the hydraulic jump, the depth of flow y1y_1 (in m, round off to 2 decimal places) is ________
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    Two identical pipes (i.e., having the same length, same diameter, and same roughness) are used to withdraw water from a reservoir. In the first case, they are attached in series and discharge freely into the atmosphere. In the second case, they are attached in parallel and also discharge freely into the atmosphere. Neglecting all minor losses, and assuming that the friction factor is same in both the cases, the ratio of the discharge in the parallel arrangement to that in the series arrangement (round off to 2 decimal places) is ________.
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    The ordinates, uu, of a 2-hour unit hydrograph (i.e., for 1 cm1\text{ cm} of effective rain), for a catchment are shown in the table.
    tt (hour)0123456789101112
    uu (m3/sm^3/s)0281832453019127310
    A 6-hour storm occurs over the catchment such that the effective rainfall intensity is 1 cm/hour1\text{ cm/hour} for the first two hours, zero for the next two hours, and 0.5 cm/hour0.5\text{ cm/hour} for the last two hours. If the base flow is constant at 5 m3/s5\text{ m}^3/s, the peak flow due to this storm (in m3/sm^3/s, round off to 1 decimal place) will be ________.
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    The dimensions of a soil sampler are given in the table.
    ParameterCutting edgeSampling tube
    Inside diameter (mmmm)8086
    Outside diameter (mmmm)10090
    For this sampler, the outside clearance ratio (in percent, round off to 2 decimal places) is ___________
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    A 2 m×4 m2\text{ m} \times 4\text{ m} rectangular footing has to carry a uniformly distributed load of 120 kPa120\text{ kPa}. As per the 2:12:1 dispersion method of stress distribution, the increment in vertical stress (in kPa\text{kPa}) at a depth of 2 m2\text{ m} below the footing is ____________
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    Constant head permeability tests were performed on two soil specimens, S1S1 and S2S2. The ratio of height of the two specimens (LS1:LS2L_{S1}:L_{S2}) is 1.51.5, the ratio of the diameter of specimens (DS1:DS2D_{S1}:D_{S2}) is 0.50.5, and the ratio of the constant head (hS1:hS2h_{S1}:h_{S2}) applied on the specimens is 2.02.0. If the discharge from both the specimens is equal, the ratio of the permeability of the soil specimens (kS1:kS2k_{S1}:k_{S2}) is _______
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    A timber pile of length 8 m8\text{ m} and diameter 0.2 m0.2\text{ m} is driven with a 20 kN20\text{ kN} drop hammer, falling freely from a height of 1.5 m1.5\text{ m}. The total penetration of the pile in the last 55 blows is 40 mm40\text{ mm}. Use the Engineering News Record expression. Assume a factor of safety of 66 and empirical factor (allowing reduction in the theoretical set, due to energy losses) of 2.5 cm2.5\text{ cm}. The safe load carrying capacity of the pile (in kN\text{kN}, round off to 2 decimal places) is _______
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    A square footing of 2 m2\text{ m} sides rests on the surface of a homogeneous soil bed having the properties: cohesion c=24 kPac = 24\text{ kPa}, angle of internal friction ϕ=25∘\phi = 25^\circ, and unit weight γ=18 kN/m3\gamma = 18\text{ kN/m}^3. Terzaghi's bearing capacity factors for ϕ=25∘\phi = 25^\circ are Nc=25.1N_c = 25.1, Nq=12.7N_q = 12.7, Nγ=9.7N_\gamma = 9.7, Nc′=14.8N_c' = 14.8, Nq′=5.6N_q' = 5.6, and Nγ′=3.2N_\gamma' = 3.2. The ultimate bearing capacity of the foundation (in kPa\text{kPa}, round off to 2 decimal places) is ___________
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