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GATE CE 2018 Set 2

All 65 solved GATE CE 2018 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

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Difficulty mixEasy 34Medium 26Hard 5

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65 of 65 questions

General Aptitude (GA)

10
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    Question

    “His face _________ with joy when the solution of the puzzle was _____ to him.”
    The words that best fill the blanks in the above sentence are
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    Question

    “Although it does contain some pioneering ideas, one would hardly characterize the work as _________.”
    The word that best fills the blank in the above sentence is
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    Question

    a+a+a+⋯+a⏟n times=a2b\underbrace{a + a + a + \dots + a}_{n \text{ times}} = a^2b and b+b+b+⋯+b⏟m times=ab2\underbrace{b + b + b + \dots + b}_{m \text{ times}} = ab^2, where a,b,na, b, n and mm are natural numbers. What is the value of (m+m+m+⋯+m⏟n times)(n+n+n+⋯+n⏟m times)(\underbrace{m + m + m + \dots + m}_{n \text{ times}}) (\underbrace{n + n + n + \dots + n}_{m \text{ times}})?
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    Question

    A three-member committee has to be formed from a group of 9 people. How many such distinct committees can be formed?
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    Question

    For non-negative integers, a,b,ca, b, c, what would be the value of a+b+ca + b + c if log⁡a+log⁡b+log⁡c=0\log a + \log b + \log c = 0?
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    Question

    In manufacturing industries, loss is usually taken to be proportional to the square of the deviation from a target. If the loss is Rs. 4900 for a deviation of 7 units, what would be the loss in Rupees for a deviation of 4 units from the target?
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    Question

    A faulty wall clock is known to gain 15 minutes every 24 hours. It is synchronized to the correct time at 9 AM on 11th July. What will be the correct time to the nearest minute when the clock shows 2 PM on 15th July of the same year?
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    Question

    The annual average rainfall in a tropical city is 1000 mm. On a particular rainy day (24-hour period), the cumulative rainfall experienced by the city is shown in the graph. Over the 24-hour period, 50% of the rainfall falling on a rooftop, which had an obstruction-free area of 50 m250\text{ m}^2, was harvested into a tank. What is the total volume of water collected in the tank in liters?
    A graph showing cumulative rainfall in mm over 24 hours. The graph starts at (0,0), goes to (6,50), then to (12,200), then to (15,200), then to (18,300), and stays at 300 until 24 hours.
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    Question

    Given that log⁡Py−z=log⁡Qz−x=log⁡Rx−y=10\frac{\log P}{y-z} = \frac{\log Q}{z-x} = \frac{\log R}{x-y} = 10 for x≠y≠zx \neq y \neq z, what is the value of the product PQRPQR?
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    Question

    Each of the letters in the figure below represents a unique integer from 1 to 9. The letters are positioned in the figure such that each of (A+B+C)(A+B+C), (C+D+E)(C+D+E), (E+F+G)(E+F+G) and (G+H+K)(G+H+K) is equal to 13. Which integer does EE represent?
    A grid of letters where A, B, C are in the first row; D and E are in a column below C; E, F, G are in a row starting from E; and H, K are in a column below G.
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Civil Engineering (Set 2)

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    Question

    The solution of the equation xdydx+y=0x \frac{dy}{dx} + y = 0 passing through the point (1,1)(1,1) is
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    Question

    The graph of a function f(x)f(x) is shown in the figure.
    graph of f(x) with three triangular peaks
    For f(x)f(x) to be a valid probability density function, the value of hh is
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    Question

    A probability distribution with right skew is shown in the figure.
    right skewed probability distribution graph
    The correct statement for the probability distribution is
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    Question

    All the members of the planar truss (see figure), have the same properties in terms of area of cross-section (AA) and modulus of elasticity (EE).
    A planar square truss with a diagonal member and horizontal loads
    For the loads shown on the truss, the statement that correctly represents the nature of forces in the members of the truss is:
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    Question

    The setting time of cement is determined using
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    Question

    A structural member subjected to compression, has both translation and rotation restrained at one end, while only translation is restrained at the other end. As per IS 456 : 2000, the effective length factor recommended for design is
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    Question

    A vertical load of 10 kN10\text{ kN} acts on a hinge located at a distance of L/4L/4 from the roller support QQ of a beam of length LL (see figure).
    A beam fixed at support P, with an internal hinge at distance 3L/4 from P. A 10 kN vertical load acts at the hinge. A roller support Q is located at the end, distance L/4 from the hinge.
    The vertical reaction at support QQ is
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    Question

    A flownet below a dam consists of 24 equipotential drops and 7 flow channels. The difference between the upstream and downstream water levels is 6 m6\text{ m}. The length of the flow line adjacent to the toe of the dam at exit is 1 m1\text{ m}. The specific gravity and void ratio of the soil below the dam are 2.70 and 0.70, respectively. The factor of safety against piping is
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    Question

    The contact pressure and settlement distribution for a footing are shown in the figure.
    Contact pressure and settlement distribution for a footing
    The figure corresponds to a
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    Question

    Which one of the following statements is NOT correct?
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    Question

    The clay mineral, whose structural units are held together by potassium bond is
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    Question

    Dupuit’s assumptions are valid for
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    Question

    For a given discharge in an open channel, there are two depths which have the same specific energy. These two depths are known as
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    Question

    As per IS 10500:2012, for drinking water in the absence of alternate source of water, the permissible limits for chloride and sulphate, in mg/L, respectively are
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    Question

    In the figures, Group I represents the atmospheric temperature profiles (P, Q, R and S) and Group II represents dispersion of pollutants from a smoke stack (1, 2, 3 and 4). In the figures of Group I, the dashed line represents the dry adiabatic lapse rate, whereas the horizontal axis represents temperature and the vertical axis represents the altitude.
    Matching diagrams for atmospheric temperature profiles (Group I) and plume dispersion types (Group II)
    The correct match is
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    Question

    Peak Hour Factor (PHF) is used to represent the proportion of peak sub-hourly traffic flow within the peak hour. If 15-minute sub-hours are considered, the theoretically possible range of PHF will be
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    Question

    As per IRC:37-2012, in order to control subgrade rutting in flexible pavements, the parameter to be considered is
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    Question

    The initial concavity in the load-penetration curve of a CBR test is NOT due to
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    Question

    Probability (up to one decimal place) of consecutively picking 3 red balls without replacement from a box containing 5 red balls and 1 white ball is ______
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    Question

    The quadratic equation 2x2−3x+3=02x^2 - 3x + 3 = 0 is to be solved numerically starting with an initial guess as x0=2x_0 = 2. The new estimate of xx after the first iteration using Newton-Raphson method is ______
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    Question

    As per IS 456 : 2000, the minimum percentage of tension reinforcement (up to two decimal places) required in reinforced-concrete beams of rectangular cross-section (considering effective depth in the calculation of area) using Fe500 grade steel is ______
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    Question

    A reinforced-concrete slab with effective depth of 80 mm is simply supported at two opposite ends on 230 mm thick masonry walls. The centre-to-centre distance between the walls is 3.3 m. As per IS 456 : 2000, the effective span of the slab (in m, up to two decimal places) is ______
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    Question

    A fillet weld is simultaneously subjected to factored normal and shear stresses of 120 MPa and 50 MPa, respectively. As per IS 800 : 2007, the equivalent stress (in MPa, up to two decimal places) is ______
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    Question

    The intensity of irrigation for the Kharif season is 50% for an irrigation project with culturable command area of 50,000 hectares. The duty for the Kharif season is 1000 hectare/cumec. Assuming transmission loss of 10%, the required discharge (in cumec, up to two decimal places) at the head of the canal is ______
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    Question

    A culvert is designed for a flood frequency of 100 years and a useful life of 20 years. The risk involved in the design of the culvert (in percentage, up to two decimal places) is ______
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    Question

    The matrix (2−44−2)\begin{pmatrix} 2 & -4 \\ 4 & -2 \end{pmatrix}has
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    Question

    The Laplace transform F(s)F(s) of the exponential function, f(t)=eatf(t) = e^{at} when t≥0t \geq 0, where aa is a constant and (s−a)>0(s-a) > 0, is
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    Question

    The rank of the following matrix is(110−220224131)\begin{pmatrix} 1 & 1 & 0 & -2 \\ 2 & 0 & 2 & 2 \\ 4 & 1 & 3 & 1 \end{pmatrix}
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    Question

    Two rigid bodies of mass 5 kg and 4 kg are at rest on a frictionless surface until acted upon by a force of 36 N as shown in the figure. The contact force generated between the two bodies is
    Two blocks of mass 5 kg and 4 kg on a frictionless surface being pushed by a 36 N force from the left side of the 5 kg block.
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    Question

    Four bolts P, Q, R and S of equal diameter are used for a bracket subjected to a load of 130 kN as shown in the figure.
    A bracket connected to a vertical support by four bolts P, Q, R, S arranged in a rectangle. A 130 kN downward load is applied at an eccentricity of 200 mm from the bolt group center-line. The vertical spacing between bolts is 240 mm and horizontal spacing is 100 mm.
    The force in bolt P is
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    Question

    A singly-reinforced rectangular concrete beam of width 300 mm and effective depth 400 mm is to be designed using M25 grade concrete and Fe500 grade reinforcing steel. For the beam to be under-reinforced, the maximum number of 16 mm diameter reinforcing bars that can be provided is
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    Question

    A 3 m high vertical earth retaining wall retains a dry granular backfill with angle of internal friction of 30∘30^\circ and unit weight of 20 kN/m3^3. If the wall is prevented from yielding (no movement), the total horizontal thrust (in kN per unit length) on the wall is
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    Question

    Three soil specimens (Soil 1, Soil 2 and Soil 3), each 150 mm long and 100 mm diameter, are placed in series in a constant head flow set-up as shown in the figure. Suitable screens are provided at the boundaries of the specimens to keep them intact. The values of coefficient of permeability of Soil 1, Soil 2 and Soil 3 are 0.01, 0.003 and 0.03 cm/s, respectively.
    Constant head flow set-up with three soil specimens in series
    The value of hh in the set-up is
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    Question

    In a 5 m wide rectangular channel, the velocity uu distribution in the vertical direction yy is given by u=1.25y1/6u = 1.25 y^{1/6}. The distance yy is measured from the channel bed. If the flow depth is 2 m, the discharge per unit width of the channel is
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    Question

    A car follows a slow moving truck (travelling at a speed of 10 m/s) on a two-lane two-way highway. The car reduces its speed to 10 m/s and follows the truck maintaining a distance of 16 m from the truck. On finding a clear gap in the opposing traffic stream, the car accelerates at an average rate of 4 m/s2^2, overtakes the truck and returns to its original lane. When it returns to its original lane, the distance between the car and the truck is 16 m. The total distance covered by the car during this period (from the time it leaves its lane and subsequently returns to its lane after overtaking) is
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    Question

    A level instrument at a height of 1.320 m has been placed at a station having a Reduced Level (RL) of 112.565 m. The instrument reads −2.835-2.835 m on a levelling staff held at the bottom of a bridge deck. The RL (in m) of the bottom of the bridge deck is
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    Question

    The value (up to two decimal places) of a line integral ∫CF(r)⋅dr\int_C \mathbf{F}(\mathbf{r}) \cdot d\mathbf{r}, for F(r)=x2i+y2j\mathbf{F}(\mathbf{r}) = x^2 \mathbf{i} + y^2 \mathbf{j} along CC which is a straight line joining (0,0)(0,0) to (1,1)(1,1) is ______
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    Question

    An 8 m long simply-supported elastic beam of rectangular cross-section (100 mm ×\times 200 mm) is subjected to a uniformly distributed load of 10 kN/m over its entire span. The maximum principal stress (in MPa, up to two decimal places) at a point located at the extreme compression edge of a cross-section and at 2 m from the support is ______
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    Question

    A prismatic beam P-Q-R of flexural rigidity EI=1×104EI = 1 \times 10^4 kNm2^2 is subjected to a moment of 180 kNm at Q as shown in the figure.
    A prismatic beam P-Q-R fixed at both ends P and R, with a moment of 180 kNm applied at the intermediate point Q. The span PQ is 5 m and QR is 4 m.
    The rotation at Q (in rad, up to two decimal places) is ______
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    Question

    A prismatic propped cantilever beam of span LL and plastic moment capacity MpM_p is subjected to a concentrated load at its mid-span. If the collapse load of the beam is αMpL\alpha \frac{M_p}{L}, the value of α\alpha is ______
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    Question

    A 6 m long simply-supported beam is prestressed as shown in the figure.
    The beam carries a uniformly distributed load of 6 kN/m over its entire span. If the effective flexural rigidity EI=2×104 kNm2EI = 2 \times 10^4\text{ kNm}^2 and the effective prestressing force is 200 kN, the net increase in length of the prestressing cable (in mm, up to two decimal places) is ______
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    Question

    A cable PQ of length 25 m is supported at two ends at the same level as shown in the figure. The horizontal distance between the supports is 20 m. A point load of 150 kN is applied at point R which divides it into two equal parts.
    A cable PQ supported at both ends with a 150 kN point load at its midpoint R.
    Neglecting the self-weight of the cable, the tension (in kN, in integer value) in the cable due to the applied load will be ______
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    Question

    The compression curve (void ratio, ee vs. effective stress, σv′\sigma_v') for a certain clayey soil is a straight line in a semi-logarithmic plot and it passes through the points (e=1.2e = 1.2; σv′=50\sigma_v' = 50 kPa) and (e=0.6e = 0.6; σv′=800\sigma_v' = 800 kPa). The compression index (up to two decimal places) of the soil is ______
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    Question

    The total horizontal and vertical stresses at a point X in a saturated sandy medium are 170 kPa and 300 kPa, respectively. The static pore-water pressure is 30 kPa. At failure, the excess pore-water pressure is measured to be 94.50 kPa, and the shear stresses on the vertical and horizontal planes passing through the point X are zero. Effective cohesion is 0 kPa and effective angle of internal friction is 36∘36^\circ. The shear strength (in kPa, up to two decimal places) at point X is ______
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    Question

    A group of nine piles in a 3×33 \times 3 square pattern is embedded in a soil strata comprising dense sand underlying recently filled clay layer, as shown in the figure. The perimeter of an individual pile is 126 cm. The size of pile group is 240 cm ×\times 240 cm. The recently filled clay has undrained shear strength of 15 kPa and unit weight of 16 kN/m3^3.
    Diagram showing a 3x3 pile group passing through a 2m layer of recently filled clay into a 5m layer of dense sand. The group size is 240 cm x 240 cm.
    The negative frictional load (in kN, up to two decimal places) acting on the pile group is ______
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    Question

    A three-fluid system (immiscible) is connected to a vacuum pump. The specific gravity values of the fluids (S1S_1, S2S_2) are given in the figure.
    A three-fluid system diagram connected to a vacuum pump. Fluid I has $S_1 = 0.88$, Fluid II has $S_2 = 0.95$, and Fluid III is water. Heights are marked as 1.5 m, 1.0 m, and 0.5 m from the bottom. Side tubes are open to atmospheric pressure $p_{atm}$ at the 1.0 m level.
    Unit weight of water, γw=9.81\gamma_w = 9.81 kN/m3^3
    Atmospheric Pressure, patm=95.43p_{atm} = 95.43 kPa
    The gauge pressure value (in kN/m2^2, up to two decimal places) of p1p_1 is ______
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    Question

    The total rainfall in a catchment of area 1000 km2^2, during a 6 h storm, is 19 cm. The surface runoff due to this storm computed from triangular direct runoff hydrograph is 1×1081 \times 10^8 m3^3. The ϕindex\phi_{index} for this storm (in cm/h, up to one decimal place) is ______
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    Question

    A rough pipe of 0.5 m0.5\text{ m} diameter, 300 m300\text{ m} length and roughness height of 0.25 mm0.25\text{ mm}, carries water (kinematic viscosity =0.9×10−6 m2/s= 0.9 \times 10^{-6}\text{ m}^2\text{/s}) with velocity of 3 m/s3\text{ m/s}. Friction factor (ff) for laminar flow is given by f=64/Ref = 64/R_e, and for turbulent flow it is given by 1f=2log⁡10(rk)+1.74\frac{1}{\sqrt{f}} = 2 \log_{10} \left( \frac{r}{k} \right) + 1.74 where, Re=Reynolds numberR_e = \text{Reynolds number}, r=radius of piper = \text{radius of pipe}, k=roughness heightk = \text{roughness height} and g=9.81 m/s2g = 9.81\text{ m/s}^2. The head loss (in m, up to three decimal places) in the pipe due to friction is ______
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    A flocculation tank contains 1800 m31800\text{ m}^3 of water, which is mixed using paddles at an average velocity gradient GG of 100/s100/\text{s}. The water temperature and the corresponding dynamic viscosity are 30∘C30^\circ\text{C} and 0.798×10−3 Ns/m20.798 \times 10^{-3}\text{ Ns/m}^2, respectively. The theoretical power required to achieve the stated value of GG (in kW, up to two decimal places) is ______
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    A coal containing 2% sulfur is burned completely to ash in a brick kiln at a rate of 30 kg/min. The sulfur content in the ash was found to be 6% of the initial amount of sulfur present in the coal fed to the brick kiln. The molecular weights of S, H and O are 32, 1 and 16 g/mole, respectively. The annual rate of sulfur dioxide (SO2_2) emission from the kiln (in tonnes/year, up to two decimal places) is ______
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    At a small water treatment plant which has 4 filters, the rates of filtration and backwashing are 200 m3/d/m2200\text{ m}^3/\text{d/m}^2 and 1000 m3/d/m21000\text{ m}^3/\text{d/m}^2, respectively. Backwashing is done for 15 min15\text{ min} per day. The maturation, which occurs initially as the filter is put back into service after cleaning, takes 30 min30\text{ min}. It is proposed to recover the water being wasted during backwashing and maturation. The percentage increase in the filtered water produced (up to two decimal places) would be ______
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    A schematic flow diagram of a completely mixed biological reactor with provision for recycling of solids is shown in the figure.
    schematic flow diagram of a biological reactor
    S0,S=readily biodegradable soluble BOD, mg/LS_0, S = \text{readily biodegradable soluble BOD, mg/L}
    Q,Qr,Qw=flow rates, m3/dQ, Q_r, Q_w = \text{flow rates, m}^3/\text{d}
    X0,X,Xe,Xu=microorganism concentrations (mixed-liquor volatile suspended solids or MLVSS), mg/LX_0, X, X_e, X_u = \text{microorganism concentrations (mixed-liquor volatile suspended solids or MLVSS), mg/L}The mean cell residence time (in days, up to one decimal place) is ______.
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    The space mean speed (kmph) and density (vehicles/km) of a traffic stream are linearly related. The free flow speed and jam density are 80 kmph and 100 vehicles/km respectively. The traffic flow (in vehicles/h, up to one decimal place) corresponding to a speed of 40 kmph is ______.
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    A 7.5 m wide two-lane road on a plain terrain is to be laid along a horizontal curve of radius 510 m. For a design speed of 100 kmph, super-elevation is provided as per IRC: 73-1980. Consider acceleration due to gravity as 9.81 m/s29.81 \text{ m/s}^2. The level difference between the inner and outer edges of the road (in m, up to three decimal places) is ______.
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    An aerial photograph of a terrain having an average elevation of 1400 m is taken at a scale of 1:7500. The focal length of the camera is 15 cm. The altitude of the flight above mean sea level (in m, up to one decimal place) is ______
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