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GATE CE 2015 Set 1

All 65 solved GATE CE 2015 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

Revision mode

Self-paced

No timer. Focus on understanding.

Difficulty mixEasy 22Medium 34Hard 9

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65 of 65 questions

General Aptitude (GA)

10
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    Question

    Extreme focus on syllabus and studying for tests has become such a dominant concern of Indian students that they close their minds to anything ________ to the requirements of the exam.
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    Question

    Select the pair that best expresses a relationship similar to that expressed in the pair:
    Children : Pediatrician
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    Question

    The Tamil version of ______ John Abraham-starrer Madras Cafe ____ cleared by the Censor Board with no cuts last week, but the film's distributors ____ no takers among the exhibitors for a release in Tamil Nadu ______ this Friday.
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    Question

    If ROAD is written as URDG, then SWAN should be written as:
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    Question

    A function f(x)f(x) is linear and has a value of 29 at x=−2x = -2 and 39 at x=3x = 3. Find its value at x=5x = 5.
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    Question

    Alexander turned his attention towards India, since he had conquered Persia.
    Which one of the statements below is logically valid and can be inferred from the above sentence?
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    Question

    Most experts feel that in spite of possessing all the technical skills required to be a batsman of the highest order, he is unlikely to be so due to lack of requisite temperament. He was guilty of throwing away his wicket several times after working hard to lay a strong foundation. His critics pointed out that until he addressed this problem, success at the highest level will continue to elude him.
    Which of the statement(s) below is/are logically valid and can be inferred from the above passage?
    (i) He was already a successful batsman at the highest level.
    (ii) He has to improve his temperament in order to become a great batsman.
    (iii) He failed to make many of his good starts count.
    (iv) Improving his technical skills will guarantee success.
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    Question

    The exports and imports (in crores of Rs.) of a country from the year 2000 to 2007 are given in the following bar chart. In which year is the combined percentage increase in imports and exports the highest?
    Bar chart showing exports and imports from 2000 to 2007
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    Question

    Choose the most appropriate equation for the function drawn as a thick line, in the plot below.
    Graph of a function with a thick line along the positive y-axis and a line passing through (2, -1) for y < 0
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    Question

    The head of a newly formed government desires to appoint five of the six selected members P, Q, R, S, T, and U to portfolios of Home, Power, Defense, Telecom, and Finance. U does not want any portfolio if S gets one of the five. R wants either Home or Finance or no portfolio. Q says that if S gets either Power or Telecom, then she must get the other one. T insists on a portfolio if P gets one.
    Which is the valid distribution of portfolios?
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Civil Engineering

55
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    Question

    For what value of pp the following set of equations will have no solution?2x+3y=52x + 3y = 53x+py=103x + py = 10
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    Question

    The integral ∫x1x2x2dx\int_{x_1}^{x_2} x^2 dx with x2>x1>0x_2 > x_1 > 0 is evaluated analytically as well as numerically using a single application of the trapezoidal rule. If II is the exact value of the integral obtained analytically and JJ is the approximate value obtained using the trapezoidal rule, which of the following statements is correct about their relationship?
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    Question

    Consider the following probability mass function (p.m.f.) of a random variable XX:p(x,q)={qif X=01−qif X=10otherwisep(x, q) = \begin{cases} q & \text{if } X = 0 \\ 1 - q & \text{if } X = 1 \\ 0 & \text{otherwise} \end{cases}If q=0.4q = 0.4, the variance of XX is ________________.
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    Question

    Workability of concrete can be measured using slump, compaction factor and Vebe time. Consider the following statements for workability of concrete:
    (i) As the slump increases, the Vebe time increases
    (ii) As the slump increases, the compaction factor increases
    Which of the following is TRUE?
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    Question

    Consider the following statements for air-entrained concrete:
    (i) Air-entrainment reduces the water demand for a given level of workability
    (ii) Use of air-entrained concrete is required in environments where cyclic freezing and thawing is expected
    Which of the following is TRUE?
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    Question

    Consider the singly reinforced beam shown in the figure below:
    Singly reinforced beam with two point loads $P$ and cross-section $XX$
    At cross-section XXXX, which of the following statements is TRUE at the limit state?
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    Question

    For the beam shown below, the stiffness coefficient K22K_{22} can be written as
    Cantilever beam with degrees of freedom 1, 2, 3 at the free end. Note: 1, 2 and 3 are the d.o.f.
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    Question

    The development length of a deformed reinforcement bar can be expressed as (1/k)(ϕσs/τbd)(1/k) (\phi \sigma_s / \tau_{bd}). From the IS:456-2000, the value of kk can be calculated as ________________.
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    Question

    For the beam shown below, the value of the support moment M is __________ kN-m.
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    Question

    Two triangular wedges are glued together as shown in the following figure. The stress acting normal to the interface, σn\sigma_n is __________ MPa.
    A square element with normal stresses of 100 MPa. The horizontal stresses are tensile (arrows pointing away from the vertical faces) and the vertical stresses are compressive (arrows pointing towards the horizontal faces). An interface is shown at an angle of $45^\circ$ with the horizontal, and $\sigma_n$ is the normal stress acting on this interface.
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    Question

    A fine-grained soil has 60% (by weight) silt content. The soil behaves as semi-solid when water content is between 15% and 28%. The soil behaves fluid-like when the water content is more than 40%. The 'Activity' of the soil is
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    Question

    Which of the following statements is TRUE for the relation between discharge velocity and seepage velocity?
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    Question

    Which of the following statements is TRUE for degree of disturbance of collected soil sample?
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    Question

    In an unconsolidated undrained triaxial test, it is observed that an increase in cell pressure from 150 kPa150\text{ kPa} to 250 kPa250\text{ kPa} leads to a pore pressure increase of 80 kPa80\text{ kPa}. It is further observed that, an increase of 50 kPa50\text{ kPa} in deviatoric stress results in an increase of 25 kPa25\text{ kPa} in the pore pressure. The value of Skempton’s pore pressure parameter BB is:
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    Question

    Which of the following statements is NOT correct?
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    Question

    In a two-dimensional steady flow field, in a certain region of the xx-yy plane, the velocity component in the xx-direction is given by vx=x2v_x = x^2 and the density varies as ρ=1x\rho = \frac{1}{x}. Which of the following is a valid expression for the velocity component in the yy-direction, vyv_y?
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    Question

    For steady incompressible flow through a closed-conduit of uniform cross-section, the direction of flow will always be:
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    Question

    A circular pipe has a diameter of 1 m, bed slope of 1 in 1000, and Manning’s roughness coefficient equal to 0.01. It may be treated as an open channel flow when it is flowing just full, i.e., the water level just touches the crest. The discharge in this condition is denoted by QfullQ_{full}. Similarly, the discharge when the pipe is flowing half-full, i.e., with a flow depth of 0.5 m, is denoted by QhalfQ_{half}. The ratio Qfull/QhalfQ_{full} / Q_{half} is:
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    Question

    The two columns below show some parameters and their possible values.
    ParameterValue
    P – Gross Command AreaI – 100 hectares/cumec
    Q – Permanent Wilting PointII – 6∘C6^\circ\text{C}
    R – Duty of canal waterIII – 1000 hectares
    S – Delta of wheatIV – 1000 cm
    V – 40 cm
    VI – 0.12
    Which of the following options matches the parameters and the values correctly?
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    Question

    Total Kjeldahl Nitrogen (TKN) concentration (mg/L as N) in domestic sewage is the sum of the concentrations of:
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    Question

    Solid waste generated from an industry contains only two components, X and Y as shown in the table below
    ComponentComposition (% weight)Density (kg/m3kg/m^3)
    Xc1c_1ρ1\rho_1
    Yc2c_2ρ2\rho_2
    Assuming (c1+c2)=100(c_1 + c_2) = 100, the composite density of the solid waste (ρ\rho) is given by:
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    Question

    The penetration value of a bitumen sample tested at 25∘C25^\circ C is 80. When this sample is heated to 60∘C60^\circ C and tested again, the needle of the penetration test apparatus penetrates the bitumen sample by dd mm. The value of dd CANNOT be less than __________ mm.
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    Question

    Which of the following statements CANNOT be used to describe free flow speed (ufu_f) of a traffic stream?
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    Question

    Which of the following statements is FALSE?
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    Question

    In a closed loop traverse of 1 km1\text{ km} total length, the closing errors in departure and latitude are 0.3 m0.3\text{ m} and 0.4 m0.4\text{ m}, respectively. The relative precision of this traverse will be:
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    Question

    The smallest and largest Eigen values of the following matrix are:[3−224−462−35]\begin{bmatrix} 3 & -2 & 2 \\ 4 & -4 & 6 \\ 2 & -3 & 5 \end{bmatrix}
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    Question

    The quadratic equation x2−4x+4=0x^2 - 4x + 4 = 0 is to be solved numerically, starting with the initial guess x0=3x_0 = 3. The Newton-Raphson method is applied once to get a new estimate and then the Secant method is applied once using the initial guess and this new estimate. The estimated value of the root after the application of the Secant method is ________________.
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    Question

    Consider the following differential equation:x(ydx+xdy)cos⁡yx=y(xdy−ydx)sin⁡yxx(ydx + xdy) \cos \frac{y}{x} = y(xdy - ydx) \sin \frac{y}{x}Which of the following is the solution of the above equation (cc is an arbitrary constant)?
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    Question

    Consider the following complex function:f(z)=9(z−1)(z+2)2f(z) = \frac{9}{(z - 1)(z + 2)^2}Which of the following is one of the residues of the above function?
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    Question

    The directional derivative of the field u(x,y,z)=x2−3yzu(x, y, z) = x^2 - 3yz in the direction of the vector (i^+j^−2k^)(\hat{i} + \hat{j} - 2\hat{k}) at point (2,−1,4)(2, -1, 4) is ________________.
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    Question

    The composition of an air-entrained concrete is given below:
    ComponentAmount
    Water184 kg/m3184\text{ kg/m}^3
    Ordinary Portland Cement (OPC)368 kg/m3368\text{ kg/m}^3
    Sand606 kg/m3606\text{ kg/m}^3
    Coarse aggregate1155 kg/m31155\text{ kg/m}^3
    Assume the specific gravity of OPC, sand and coarse aggregate to be 3.14, 2.67 and 2.74, respectively. The air content is ________________ liters/ m3\text{m}^3.
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    Question

    A bracket plate connected to a column flange transmits a load of 100 kN100\text{ kN} as shown in the following figure. The maximum force for which the bolts should be designed is ________________ kN\text{kN}.
    Bracket plate with 5 bolts and eccentric load
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    Question

    Consider the singly reinforced beam section given below (left figure). The stress block parameters for the cross-section from IS:456-2000 are also given below (right figure). The moment of resistance for the given section by the limit state method is ___________ kN-m.
    Singly reinforced beam section and stress block parameters
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    Question

    For formation of collapse mechanism in the following figure, the minimum value of PuP_u is cMp/Lc M_p/L. MpM_p and 3Mp3M_p denote the plastic moment capacities of beam sections as shown in this figure. The value of cc is ___________.
    Beam with different plastic moment capacities and a point load
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    Question

    A tapered circular rod of diameter varying from 20 mm20 \text{ mm} to 10 mm10 \text{ mm} is connected to another uniform circular rod of diameter 10 mm10 \text{ mm} as shown in the following figure. Both bars are made of same material with the modulus of elasticity, E=2×105 MPaE = 2 \times 10^5 \text{ MPa}. When subjected to a load P=30π kNP = 30\pi \text{ kN}, the deflection at point AA is ___________ mm.
    Tapered and uniform circular rods under axial load
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    The smallest and largest Eigen values of the following matrix are:[3−224−462−35]\begin{bmatrix} 3 & -2 & 2 \\ 4 & -4 & 6 \\ 2 & -3 & 5 \end{bmatrix}
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    Question

    For the 2D truss with the applied loads shown below, the strain energy in the member XYXY is _______________ kN-m. For member XYXY, assume AE=30AE = 30 kN, where AA is cross-section area and EE is the modulus of elasticity.
    A 2D truss structure with three panels, each 3m high and 3m wide. A horizontal load of 10 kN and a vertical load of 5 kN are applied at the top-right joint. Member XY is a horizontal member at the first level below the top.
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    Question

    Consider the following differential equation:x(ydx+xdy)cos⁡yx=y(xdy−ydx)sin⁡yxx(ydx + xdy) \cos \frac{y}{x} = y(xdy - ydx) \sin \frac{y}{x}Which of the following is the solution of the above equation (cc is an arbitrary constant)?
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    Question

    An earth embankment is to be constructed with compacted cohesionless soil. The volume of the embankment is 5000 m35000 \text{ m}^3 and the target dry unit weight is 16.2 kN/m316.2 \text{ kN/m}^3. Three nearby sites (see figure below) have been identified from where the required soil can be transported to the construction site. The void ratios (ee) of different sites are shown in the figure. Assume the specific gravity of soil to be 2.72.7 for all three sites. If the cost of transportation per km is twice the cost of excavation per m3\text{m}^3 of borrow pits, which site would you choose as the most economic solution? (Use unit weight of water = 10 kN/m310 \text{ kN/m}^3)
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    Question

    A water tank is to be constructed on the soil deposit shown in the figure below. A circular footing of diameter 3 m3 \text{ m} and depth of embedment 1 m1 \text{ m} has been designed to support the tank. The total vertical load to be taken by the footing is 1500 kN1500 \text{ kN}. Assume the unit weight of water as 10 kN/m310 \text{ kN/m}^3 and the load dispersion pattern as 2V:1H2\text{V}:1\text{H}. The expected settlement of the tank due to primary consolidation of the clay layer is ‾\underline{\hspace{2cm}} mm\text{mm}.
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    Question

    A non-homogeneous soil deposit consists of a silt layer sandwiched between a fine-sand layer at top and a clay layer below. Permeability of the silt layer is 1010 times the permeability of the clay layer and one-tenth of the permeability of the sand layer. Thickness of the silt layer is 22 times the thickness of the sand layer and two-third of the thickness of the clay layer. The ratio of equivalent horizontal and equivalent vertical permeability of the deposit is ‾\underline{\hspace{2cm}}.
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    Question

    A square footing (2 m×2 m2\text{ m} \times 2\text{ m}) is subjected to an inclined point load, PP as shown in the figure below. The water table is located well below the base of the footing. Considering one-way eccentricity, the net safe load carrying capacity of the footing for a factor of safety of 3.03.0 is ________________ kN.
    The following factors may be used:
    Bearing capacity factors: Nq=33.3,Nγ=37.16N_q = 33.3, N_\gamma = 37.16; Shape factors: Fqs=Fγs=1.314F_{qs} = F_{\gamma s} = 1.314; Depth factors: Fqd=Fγd=1.113F_{qd} = F_{\gamma d} = 1.113; Inclination factors: Fqi=0.444,Fγi=0.02F_{qi} = 0.444, F_{\gamma i} = 0.02
    A square footing of width 2 m and depth 1 m subjected to an inclined load P at 30 degrees to the vertical, acting at 0.85 m from the left edge. Soil properties: unit weight = 18 kN/m³, cohesion = 0, friction angle = 35 degrees.
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    Question

    Two reservoirs are connected through a 930 m930\text{ m} long, 0.3 m0.3\text{ m} diameter pipe, which has a gate valve. The pipe entrance is sharp (loss coefficient =0.5= 0.5) and the valve is half-open (loss coefficient =5.5= 5.5). The head difference between the two reservoirs is 20 m20\text{ m}. Assume the friction factor for the pipe as 0.030.03 and g=10 m/s2g = 10\text{ m/s}^2. The discharge in the pipe accounting for all minor and major losses is ________________ m3/s\text{m}^3/\text{s}.
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    Question

    A hydraulic jump is formed in a 2 m2\text{ m} wide rectangular channel which is horizontal and frictionless. The post-jump depth and velocity are 0.8 m0.8\text{ m} and 1 m/s1\text{ m/s}, respectively. The pre-jump velocity is ________________ m/s\text{m/s}. (use g=10 m/s2g = 10\text{ m/s}^2)
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    Question

    A short reach of a 2 m2\text{ m} wide rectangular open channel has its bed level rising in the direction of flow at a slope of 11 in 1000010000. It carries a discharge of 4 m3/s4\text{ m}^3/\text{s} and its Manning's roughness coefficient is 0.010.01. The flow in this reach is gradually varying. At a certain section in this reach, the depth of flow was measured as 0.5 m0.5\text{ m}. The rate of change of the water depth with distance, dy/dxdy/dx, at this section is ——————————————— (use g=10 m/s2g = 10\text{ m}/\text{s}^2).
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    The drag force, FDF_D, on a sphere kept in a uniform flow field depends on the diameter of the sphere, DD; flow velocity, VV; fluid density, ρ\rho; and dynamic viscosity, μ\mu. Which of the following options represents the non-dimensional parameters which could be used to analyze this problem?
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    In a catchment, there are four rain-gauge stations, PP, QQ, RR, and SS. Normal annual precipitation values at these stations are 780 mm780\text{ mm}, 850 mm850\text{ mm}, 920 mm920\text{ mm}, and 980 mm980\text{ mm}, respectively. In the year 2013, stations QQ, RR, and SS, were operative but PP was not. Using the normal ratio method, the precipitation at station PP for the year 2013 has been estimated as 860 mm860\text{ mm}. If the observed precipitation at stations QQ and RR for the year 2013 were 930 mm930\text{ mm} and 1010 mm1010\text{ mm}, respectively, what was the observed precipitation (in mm) at station SS for that year?
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    The 4-hr unit hydrograph for a catchment is given in the table below. What would be the maximum ordinate of the S-curve (in m3/sm^3/s) derived from this hydrograph?
    Time (hr)024681012141618202224
    Unit hydrograph ordinate (m3/sm^3/s)00.63.110139520.70.30.20.10
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    The concentration of Sulfur Dioxide (SO2SO_2) in ambient atmosphere was measured as 30 μg/m330\ \mu g/m^3. Under the same conditions, the above SO2SO_2 concentration expressed in ppm is __________.
    Given: P/(RT)=41.6 mol/m3P/(RT) = 41.6\ mol/m^3; where, P=PressureP = \text{Pressure}; T=TemperatureT = \text{Temperature}; R=universal gas constantR = \text{universal gas constant}; Molecular weight of SO2=64SO_2 = 64.
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    Consider a primary sedimentation tank (PST) in a water treatment plant with Surface Overflow Rate (SOR) of 40 m3/m2/d40\ m^3/m^2/d. The diameter of the spherical particle which will have 90 percent theoretical removal efficiency in this tank is __________ μm\mu m. Assume that settling velocity of the particles in water is described by Stokes's Law.
    Given: Density of water =1000 kg/m3= 1000\ kg/m^3; Density of particle =2650 kg/m3= 2650\ kg/m^3; g=9.81 m/s2g = 9.81\ m/s^2; Kinematic viscosity of water (ν)=1.10×10−6 m2/s(\nu) = 1.10 \times 10^{-6}\ m^2/s
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    The acceleration-time relationship for a vehicle subjected to non-uniform acceleration is,dvdt=(α−βv0)e−βt\frac{dv}{dt} = (\alpha - \beta v_0)e^{-\beta t}where, vv is the speed in m/s, tt is the time in s, α\alpha and β\beta are parameters, and v0v_0 is the initial speed in m/s. If the accelerating behavior of a vehicle, whose driver intends to overtake a slow moving vehicle ahead, is described as,dvdt=(α−βv)\frac{dv}{dt} = (\alpha - \beta v)Considering α=2 m/s2\alpha = 2 \text{ m/s}^2, β=0.05 s−1\beta = 0.05 \text{ s}^{-1} and dvdt=1.3 m/s2\frac{dv}{dt} = 1.3 \text{ m/s}^2 at t=3 st = 3 \text{ s}, the distance (in m) travelled by the vehicle in 35 s is _______________.
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    On a circular curve, the rate of superelevation is ee. While negotiating the curve a vehicle comes to a stop. It is seen that the stopped vehicle does not slide inwards (in the radial direction). The coefficient of side friction is ff. Which of the following is true:
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    A sign is required to be put up asking drivers to slow down to 30 km/h30 \text{ km/h} before entering Zone YY (see figure). On this road, vehicles require 174 m174 \text{ m} to slow down to 30 km/h30 \text{ km/h} (the distance of 174 m174 \text{ m} includes the distance travelled during the perception-reaction time of drivers). The sign can be read by 6/66/6 vision drivers from a distance of 48 m48 \text{ m}. The sign is placed at a distance of x mx \text{ m} from the start of Zone YY so that even a 6/96/9 vision driver can slow down to 30 km/h30 \text{ km/h} before entering the zone. The minimum value of xx is _______________ m.
    Diagram showing Road, Sign, and Zone Y. Sign is at distance x from start of Zone Y. Direction of vehicle movement is indicated.
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    In a survey work, three independent angles XX, YY and ZZ were observed with weights WXW_X, WYW_Y, WZW_Z, respectively. The weight of the sum of angles XX, YY and ZZ is given by:
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    In a region with magnetic declination of 2∘E2^\circ\text{E}, the magnetic Fore bearing (FB) of a line ABAB was measured as N79∘50′E\text{N}79^\circ50'\text{E}. There was local attraction at AA. To determine the correct magnetic bearing of the line, a point OO was selected at which there was no local attraction. The magnetic FB of line AOAO and OAOA were observed to be S52∘40′E\text{S}52^\circ40'\text{E} and N50∘20′W\text{N}50^\circ20'\text{W}, respectively. What is the true FB of line ABAB?
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