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GATE CE 2015 Set 2

All 65 solved GATE CE 2015 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 22Medium 38Hard 5

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65 of 65 questions

General Aptitude (GA)

10
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    Question

    Choose the most appropriate word from the options given below to complete the following sentence.
    The official answered _______________ that the complaints of the citizen would be looked into.
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    Question

    Choose the statement where underlined word is used correctly.
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    Question

    Which word is not a synonym for the word vernacular?
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    Question

    Mr. Vivek walks 6 meters North-east, then turns and walks 6 meters South-east, both at 60 degrees to east. He further moves 2 meters South and 4 meters West. What is the straight distance in metres between the point he started from and the point he finally reached?
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    Question

    Four cards are randomly selected from a pack of 52 cards. If the first two cards are kings, what is the probability that the third card is a king?
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    Question

    The word similar in meaning to 'dreary' is
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    Question

    The given question is followed by two statements; select the most appropriate option that solves the question.
    Capacity of a solution tank A is 70% of the capacity of tank B. How many gallons of solution are in tank A and tank B?
    Statements:
    (I) Tank A is 80% full and tank B is 40% full.
    (II) Tank A if full contains 14,000 gallons of solution.
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    Question

    How many four digit numbers can be formed with the 10 digits 0, 1, 2, ..., 9 if no number can start with 0 and if repetitions are not allowed?
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    Question

    Read the following table giving sales data of five types of batteries for years 2006 to 2012:
    YearType IType IIType IIIType IVType V
    200675144114102108
    20079012610284126
    20089611475105135
    2009105901509075
    201090751357590
    20111056016545120
    201211585160100145
    Out of the following, which type of battery achieved highest growth between the years 2006 and 2012?
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    Question

    There are 16 teachers who can teach Thermodynamics (TD), 11 who can teach Electrical Sciences (ES), and 5 who can teach both TD and Engineering Mechanics (EM). There are a total of 40 teachers. 6 cannot teach any of the three subjects, i.e. EM, ES or TD. 6 can teach only ES. 4 can teach all three subjects, i.e. EM, ES and TD. 4 can teach ES and TD. How many can teach both ES and EM but not TD?
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Civil Engineering

55
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    Question

    While minimizing the function f(x)f(x), necessary and sufficient conditions for a point, x0x_0 to be a minima are:
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    Question

    In Newton-Raphson iterative method, the initial guess value (xinix_{ini}) is considered as zero while finding the roots of the equation: f(x)=−2+6x−4x2+0.5x3f(x) = -2 + 6x - 4x^2 + 0.5x^3. The correction, Δx\Delta x, to be added to xinix_{ini} in the first iteration is ________________.
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    Question

    Given, i=−1i = \sqrt{-1}, the value of the definite integral, I=∫0π/2cos⁡x+isin⁡xcos⁡x−isin⁡xdxI = \int_{0}^{\pi/2} \frac{\cos x + i \sin x}{\cos x - i \sin x} dx is:
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    Question

    lim⁡x→∞(1+1x)2x\lim_{x \to \infty} \left( 1 + \frac{1}{x} \right)^{2x} is equal to
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    Question

    Let A =[aij],1≤i,j≤n= [a_{ij}], 1 \leq i, j \leq n with n≥3n \geq 3 and aij=i⋅ja_{ij} = i \cdot j. The rank of A is:
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    Question

    A horizontal beam ABCABC is loaded as shown in the figure below. The distance of the point of contraflexure from end AA (in m) is ________.
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    Question

    For the plane stress situation shown in the figure, the maximum shear stress and the plane on which it acts are:
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    Question

    A guided support as shown in the figure below is represented by three springs (horizontal, vertical and rotational) with stiffness kxk_x, kyk_y and kθk_\theta respectively. The limiting values of kxk_x, kyk_y and kθk_\theta are:
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    Question

    A column of size 450 mm×600 mm450\text{ mm} \times 600\text{ mm} has unsupported length of 3.0 m3.0\text{ m} and is braced against side sway in both directions. According to IS 456: 2000, the minimum eccentricities (in mm) with respect to major and minor principal axes are:
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    Question

    Prying forces are:
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    Question

    A steel member 'MM' has reversal of stress due to live loads, whereas another member 'NN' has reversal of stress due to wind load. As per IS 800: 2007, the maximum slenderness ratio permitted is:
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    Question

    If the water content of a fully saturated soil mass is 100%100\%, the void ratio of the sample is:
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    Question

    In friction circle method of slope stability analysis, if rr defines the radius of the slip circle, the radius of friction circle is:
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    Question

    Net ultimate bearing capacity of a footing embedded in a clay stratum
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    Question

    Let A=[aij],1≤i,j≤nA = [a_{ij}], 1 \leq i, j \leq n with n≥3n \geq 3 and aij=i⋅ja_{ij} = i \cdot j. The rank of AA is:
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    Question

    A horizontal beam ABCABC is loaded as shown in the figure below. The distance of the point of contraflexure from end AA (in m) is ________.
    Diagram of a horizontal beam ABC fixed at A, with a support at B and a 10 kN load at C. Dimensions: AB = 0.75 m, BC = 0.25 m.
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    Question

    For the plane stress situation shown in the figure, the maximum shear stress and the plane on which it acts are:
    Stress element showing tensile stresses of 50 MPa in both x and y directions.
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    Question

    A hydraulic jump takes place in a frictionless rectangular channel. The pre-jump depth is ypy_p. The alternate and sequent depths corresponding to ypy_p are yay_a and ysy_s respectively. The correct relationship among ypy_p, yay_a and ysy_s is:
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    Question

    The relationship between porosity (nn), specific yield (SyS_y) and specific retention (SrS_r) of an unconfined aquifer is:
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    Question

    A groundwater sample was found to contain 500 mg/L total dissolved solids (TDS). TDS (in %) present in the sample is __________.
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    Question

    SO2SO_2 and COCO adversely affect
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    Question

    A superspeedway in New Delhi has among the highest super-elevation rates of any track on the Indian Grand Prix circuit. The track requires drivers to negotiate turns with a radius of 335 m335\text{ m} and 33∘33^\circ banking. Given this information, the coefficient of side friction required in order to allow a vehicle to travel at 320 km/h320\text{ km/h} along the curve is:
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    Question

    The following statements are made related to the lengths of turning lanes at signalised intersections:
    (i) 1.51.5 times the average number of vehicles (by vehicle type) that would store in turning lane per cycle during the peak hour
    (ii) 22 times the average number of vehicles (by vehicle type) that would store in turning lane per cycle during the peak hour
    (iii) Average number of vehicles (by vehicle type) that would store in the adjacent through lane per cycle during the peak hour
    (iv) Average number of vehicles (by vehicle type) that would store in all lanes per cycle during the peak hour
    As per the IRC recommendations, the correct choice for design length of storage lanes is:
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    Question

    In a leveling work, sum of the Back Sight (B.S.) and Fore Sight (F.S.) have been found to be 3.085 m and 5.645 m respectively. If the Reduced Level (R.L.) of the starting station is 100.000 m, the R.L. (in m) of the last station is __________.
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    Question

    The combined correction due to curvature and refraction (in m) for a distance of 1 km on the surface of Earth is:
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    Question

    The probability density function of a random variable, xx isf(x)=x4(4−x2) for 0≤x≤2f(x) = \frac{x}{4}(4 - x^2) \text{ for } 0 \leq x \leq 2=0 otherwise= 0 \text{ otherwise}The mean, μx\mu_x of the random variable is __________.
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    Question

    Consider the following second order linear differential equationd2ydx2=−12x2+24x−20\frac{d^2y}{dx^2} = -12x^2 + 24x - 20The boundary conditions are: at x=0,y=5x = 0, y = 5 and at x=2,y=21x = 2, y = 21
    The value of yy at x=1x = 1 is __________.
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    Question

    The two Eigen values of the matrix [211p]\begin{bmatrix} 2 & 1 \\ 1 & p \end{bmatrix} have a ratio of 3:1 for p=2p = 2. What is another value of pp for which the Eigen values have the same ratio of 3:1?
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    Question

    For step-size, Δx=0.4\Delta x = 0.4, the value of following integral using Simpson's 1/3 rule is __________∫00.8(0.2+25x−200x2+675x3−900x4+400x5)dx\int_{0}^{0.8} (0.2 + 25x - 200x^2 + 675x^3 - 900x^4 + 400x^5) dx
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    Question

    In a system, two connected rigid bars ACAC and BCBC are of identical length, LL with pin supports at AA and BB. The bars are interconnected at CC by a frictionless hinge. The rotation of the hinge is restrained by a rotational spring of stiffness, kk. The system initially assumes a straight line configuration, ACBACB. Assuming both the bars as weightless, the rotation at supports, AA and BB, due to a transverse load, PP applied at CC is:
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    Question

    A simply supported reinforced concrete beam of length 10 m sags while undergoing shrinkage. Assuming a uniform curvature of 0.004 m−10.004\text{ m}^{-1} along the span, the maximum deflection (in m) of the beam at mid-span is _______________.
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    Question

    A superspeedway in New Delhi has among the highest super-elevation rates of any track on the Indian Grand Prix circuit. The track requires drivers to negotiate turns with a radius of 335 m335\text{ m} and 33∘33^\circ banking. Given this information, the coefficient of side friction required in order to allow a vehicle to travel at 320 km/h320\text{ km/h} along the curve is:
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    Question

    A simply supported beam ABAB of span, L=24 mL = 24\text{ m} is subjected to two wheel loads acting at a distance, d=5 md = 5\text{ m} apart as shown in the figure below. Each wheel transmits a load, P=3 kNP = 3\text{ kN} and may occupy any position along the beam. If the beam is an II-section having section modulus, S=16.2 cm3S = 16.2\text{ cm}^3, the maximum bending stress (in GPa) due to the wheel loads is ___________.
    A simply supported beam AB of length L with two point loads P at distance d apart.
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    Question

    According to the concept of Limit State Design as per IS 456: 2000, the probability of failure of a structure is ___________.
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    Question

    In a pre-stressed concrete beam section shown in the figure, the net loss is 10%10\% and the final prestressing force applied at XX is 750 kN750\text{ kN}. The initial fiber stresses (in N/mm2\text{N/mm}^2) at the top and bottom of the beam were:
    Cross-section of a pre-stressed concrete beam with dimensions b, d1, d2 and prestressing point X.
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    Question

    A fixed end beam is subjected to a load, WW at 1/3rd span from the left support as shown in the figure. The collapse load of the beam is:
    A fixed end beam of length $L$ with a point load $W$ at $L/3$ from the left support $X$. The beam is divided into two segments at its midpoint $Y$. The segment $XY$ has a plastic moment capacity of $2M_p$ and the segment $YZ$ has a plastic moment capacity of $M_p$.
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    Question

    A 588 cm3588 \text{ cm}^3 volume of moist sand weighs 1010 gm1010 \text{ gm}. Its dry weight is 918 gm918 \text{ gm} and specific gravity of solids, GG is 2.67. Assuming density of water as 1 gm/cm31 \text{ gm/cm}^3, the void ratio is _______________.
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    Question

    A 4 m4 \text{ m} thick layer of normally consolidated clay has an average void ratio of 1.30. Its compression index is 0.6 and coefficient of consolidation is 1 m2/yr1 \text{ m}^2/\text{yr}. If the increase in vertical pressure due to foundation load on the clay layer is equal to the existing effective overburden pressure, the change in the thickness of the clay layer is _______________ mm
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    Question

    A pile of diameter 0.4 m0.4\text{ m} is fully embedded in a clay stratum having 5 layers, each 5 m5\text{ m} thick as shown in the figure below. Assume a constant unit weight of soil as 18 kN/m318\text{ kN/m}^3 for all the layers. Using λ\lambda-method (λ=0.15\lambda = 0.15 for 25 m25\text{ m} embedment length) and neglecting the end bearing component, the ultimate pile capacity (in kN) is __________.
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    Question

    Stress path equation for tri-axial test upon application of deviatoric stress is, q=103+0.5 pq = 10\sqrt{3} + 0.5\ p. The respective values of cohesion, cc (in kPa) and angle of internal friction, ϕ\phi are:
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    Question

    A 6 m6\text{ m} high retaining wall having a smooth vertical back face retains a layered horizontal backfill. Top 3 m3\text{ m} thick layer of the backfill is sand having an angle of internal friction, ϕ=30∘\phi = 30^\circ while the bottom layer is 3 m3\text{ m} thick clay with cohesion, c=20 kPac = 20\text{ kPa}. Assume unit weight for both sand and clay as 18 kN/m318\text{ kN/m}^3. The total active earth pressure per unit length of the wall (in kN/m) is:
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    Question

    A field channel has cultivable commanded area of 2000 hectares. The intensities of irrigation for gram and wheat are 30% and 50% respectively. Gram has a kor period of 18 days, kor depth of 12 cm, while wheat has a kor period of 18 days and a kor depth of 15 cm. The discharge (in m3/sm^3/s) required in the field channel to supply water to the commanded area during the kor period is ___________
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    Question

    A triangular gate with a base width of 2 m and a height of 1.5 m lies in a vertical plane. The top vertex of the gate is 1.5 m below the surface of a tank which contains oil of specific gravity 0.8. Considering the density of water and acceleration due to gravity to be 1000 kg/m3kg/m^3 and 9.81 m/s2m/s^2 respectively, the hydrostatic force (in kN) exerted by the oil on the gate is ___________
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    Question

    The velocity components of a two dimensional plane motion of a fluid are: u=y33+2x−x2yu = \frac{y^3}{3} + 2x - x^2y and v=xy2−2y−x33v = xy^2 - 2y - \frac{x^3}{3}.
    The correct statement is:
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    Question

    In a pre-stressed concrete beam section shown in the figure, the net loss is 10% and the final prestressing force applied at XX is 750 kN. The initial fiber stresses (in N/mm2^2) at the top and bottom of the beam were:
    Cross-section of a pre-stressed concrete beam with dimensions b=250mm, d1=200mm, d2=100mm, and prestressing force applied at point X
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    Question

    A fixed end beam is subjected to a load, WW at 1/3rd span from the left support as shown in the figure. The collapse load of the beam is:
    Fixed beam of length L with a point load W at L/3 from left support. Plastic moment capacities are 2Mp for left half and Mp for right half.
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    Question

    A 588 cm3^3 volume of moist sand weighs 1010 gm. Its dry weight is 918 gm and specific gravity of solids, GG is 2.67. Assuming density of water as 1 gm/cm3^3, the void ratio is __________.
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    Question

    A water treatment plant of capacity, 1 m3/s1\text{ m}^3/\text{s} has filter boxes of dimensions 6 m×10 m6\text{ m} \times 10\text{ m}. Loading rate to the filters is 120 m3/day/m2120\text{ m}^3/\text{day}/\text{m}^2. When two of the filters are out of service for back washing, the loading rate (in m3/day/m2\text{m}^3/\text{day}/\text{m}^2) is __________.
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    Question

    Ultimate BOD of a river water sample is 20 mg/L20\text{ mg/L}. BOD rate constant (natural log) is 0.15 day−10.15\text{ day}^{-1}. The respective values of BOD (in %) exerted and remaining after 7 days are:
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    Question

    In a wastewater treatment plant, primary sedimentation tank (PST) designed at an overflow rate of 32.5 m3/day/m232.5\text{ m}^3/\text{day}/\text{m}^2 is 32.5 m32.5\text{ m} long, 8.0 m8.0\text{ m} wide and liquid depth of 2.25 m2.25\text{ m}. If the length of the weir is 75 m75\text{ m}, the weir loading rate (in m3/day/m\text{m}^3/\text{day/m}) is __________.
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    Question

    The relation between speed uu (in km/h) and density kk (number of vehicles / km) for a traffic stream on a road is u=70−0.7ku = 70 - 0.7k. The capacity on this road is ________ vph (vehicles/hour).
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    Question

    Match the information related to tests on aggregates given in Group-I with that in Group-II.
    Group-IGroup-II
    P. Resistance to impact1. Hardness
    Q. Resistance to wear2. Strength
    R. Resistance to weathering action3. Toughness
    S. Resistance to crushing4. Soundness
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    Question

    In Marshall method of mix design, the coarse aggregate, fine aggregate, fines and bitumen having respective values of specific gravity 2.60, 2.70, 2.65 and 1.01, are mixed in the relative proportions (% by weight) of 55.0, 35.8, 3.7 and 5.5 respectively. The theoretical specific gravity of the mix and the effective specific gravity of the aggregates in the mix respectively are:
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    Question

    The bearings of two inaccessible stations, S1S_1 (Easting 500 m500\text{ m}, Northing 500 m500\text{ m}) and S2S_2 (Easting 600 m600\text{ m}, Northing 450 m450\text{ m}) from a station S3S_3 were observed as 225∘225^\circ and 153∘26′153^\circ 26' respectively. The independent Easting (in m) of station S3S_3 is:
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    Question

    Two Pegs A and B were fixed on opposite banks of a 50 m50\text{ m} wide river. The level was set up at A and the staff readings on Pegs A and B were observed as 1.350 m1.350\text{ m} and 1.550 m1.550\text{ m}, respectively. Thereafter the instrument was shifted and set up at B. The staff readings on Pegs B and A were observed as 0.750 m0.750\text{ m} and 0.550 m0.550\text{ m}, respectively. If the R.L. of Peg A is 100.200 m100.200\text{ m}, the R.L. (in m) of Peg B is __________.
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