All questions of Practice Test: Full Length for Civil Engineering (CE) Exam

6 boys and 6 girls sit in a row at random. Find the probability that 1) The six girls sit together 2) The boys and girls sit alternately.
  • a)
    1/462
  • b)
  • c)
  • d)
Correct answer is option 'A'. Can you explain this answer?

Vertex Academy answered
\Total ways of making sit 12 persons  12!
Considering set of 6 girls as a single group. Within the group girls can be arranged in 6! Ways. Now only among 7 persons—> 6 boys + 1 girl group arrangement needs to be done. Thus, number of ways for the same = 7!. 
Therefore, probability = Favourable outcomes/ total number of outcomes = (7!) (6!) / (12!) = 1/1322
We can only make sit boys and girls in alternate manner in two possible ways, boys at even and girls at even. But, among boys group and girls group itself, rearrangement can be done in 6! Ways each. 
Therefore, probability =(2)(6!)(6!)/ 12! = 1/462

A clayey soil sample in a consolidometer test showed decrease in void ratio from 1.15 to 1.05 when the pressure was increased from 0.30 kgf/cm2 to 0.60 kgf/cm2. If the same soil shows 10% more decrease in void ratio when the pressure was increased from 0.30 kgf/cm2 to 0.80 kgf/cm2, then change in coefficient of consolidation observed during the test will be?
Take initial coefficient of consolidation observed from test when the pressure was increased from 0.30 kgf/cm2 to 0.60 kgf/cm2 to be 12 m2/year.
  • a)
    4.5 m2/year (decrease)
  • b)
    3.22 m2/year (increase)
  • c)
    12 m2/year (increase)
  • d)
    3.22 m2/year (decrease)
Correct answer is option 'B'. Can you explain this answer?

Sanvi Kapoor answered
Coefficient of compressibility (av)=
Δe = change in void ratio
increase in effective stress
 
Coefficient of volume compressibity 
e0 = initial void ratio
Also,
k = cvmvγw
k = permeability of soil Sample
cv = coefficient of consolidation
m= coefficient of volume compressibility
Calculation:
Δe1 = 1.15 – 1.05
Δe1 = 0.10
Δσ1 = 0.60 – 0.30
Δσ1 = 0.30 kgf/cm2



= 3.80×10−3cm2/sec 
k = 3.80 × 10–3 × 0.155 × γw
Now,
Δe2 = 1.10 × 0.10 = 0.11
Δσ2 = 0.80 – 0.30
Δσ2 = 0.50
As permeability of both the sample is Sames,
So,
3.80×10−3×0.155=cv2×0.122 
cv2=4.83×10−3cm2/sec 
cv2=15.22m2/ year
Change in coefficient of consolidation:
Δcv=cv2−cv1 
Δcv = 15.22 – 12
Δcv = 3.22 m2/year

Following data refers to the activities of a project, where, node 1 refers to the start and node 5 refers to the end of the project.
The critical path (CP) in the network is
  • a)
    1-2-3-5
  • b)
    1-4-3-5
  • c)
    1-2-3-4-5
  • d)
    1-4-5
Correct answer is option 'B'. Can you explain this answer?

Ravi Singh answered
The critical path is the sequence of activities with the longest duration. A delay in any of these activities will result in a delay for the whole project.
Critical path = 1‒4‒3‒5 = 3+3+2 = 8
Note: Critical path is the longest path through a network of activities, which in-turn, determines the shortest time possible to complete all tasks in the network (i.e. the shortest time to complete the project).

The length of a new runway to be constructed under the standard condition is 1710 m. The elevation of airport site is 750 m above the mean sea level. The airport reference temperature and the effective gradient of the runway are 25.7oC and 1.6% respectively. If the runway is to be constructed as per the International Civil Aviation Organization (ICAO) recommendations, then the corrected length of the runway after elevation and temperature correction (in km, up to two correct decimal place) will be ______.
    Correct answer is '2307-2310'. Can you explain this answer?

    Tanvi Shah answered
    Correction for elevation: 7% increase per 300 m
    So, correction =
    = 299.25 m
    Corrected length = 1710 + 299.25 = 2009.25 m
    Correction for temperature: 1% increase per degree rise in temperature
    Standard atmospheric temperature = 15 – 0.0065 × 750 = 10.125°C
    Rise of temp = 25.7°C – 10.125°C = 15.575°C
    15.575 = 311.43375m
    Correct length = 2009.25 + 311.43375 = 2320.684 m
    Check for total correction for elevation plus temperature
     
    According to ICAO, the total correction for elevation plus temperature should not exceed by 35%.
    Hence, the total correction for elevation plus temperature correction = 1710 = 598.5m
    Therefore, the corrected length of the runway = 1710 + 598.5 = 2308.5 m

    Two points are chosen randomly on a line 9 cm long. Determine the probability that the distance between them is less than 3 cm
      Correct answer is '0.5-0.6'. Can you explain this answer?

      Lavanya Menon answered
      x: The distance of first point from the start of the line
      y: distance of second point from the start of the line segment
      x,y ϵ[0,9]
      So sample space is Area of region bounded by
       x ≥ 0, y ≥ 0, x ≤ 9, y ≤ 9
      This is square of side 9
      Area = 81 cm2
      The region of our interest is
      |x-y| < 3
      0 ≤ x ≤ 9
      0 ≤ y ≤ 9
      Area of shaded region = 2 (area of triangle) + area of rectangle
       = 45
      Probability = 45/81 =0.55

      Standard 5-day BOD of a waste water sample is nearly x% of the ultimate BOD, where x is
      • a)
        48
      • b)
         
        58
      • c)
        68
      • d)
        78
      Correct answer is option 'C'. Can you explain this answer?

      Ravi Singh answered
      BOD5 = BODu [ 1-10-k x 5] and the usual value of deoxygenation constant is 0.1
      Substituting, the value of k BOD5 = BODu [0.6837] 
      Therefore, value of x will be 68.37%

      A transmission tower carries a vertical load of 10000 kg, the vertical stress increment at a depth 6 m directly below the tower as per Boussinesq’s theory is____Pa.
        Correct answer is between '1300,1350'. Can you explain this answer?

        Tanvi Shah answered
        Concept:
        Vertical stress increment at a any depth (z) at a radial distance (r) as per Boussines’q theory is:
        Where,
        KB = Boussinesq’s influence factor
        Calculation:
        At r = 0 m,
        Q = 10000 × 9.81 = 98100 N
        z = 6 m

        The maximum permissible deflection for a gantry girder, spanning over 6 m, on which an EOT (electric overhead travelling) crane of capacity 200 kN is operating, is
        • a)
          8 mm
        • b)
          10 mm
        • c)
          12 mm
        • d)
          18 mm
        Correct answer is option 'A'. Can you explain this answer?

        Maximum vertical deflection of Gantry girder for EOT of capacity less than 500KN is ( L/750), where L in mm
        For EOT having capacity more then 500KN deflection is (L/1000) and for manually operated crane Deflection is (L/500)

        Portion BC is semi-circulate. If after several oscillation ball of mass 10 Kg comes to rest. The bending moment at A when ball is at rest will be ? Take g = 9.81 m/s2.
        • a)
          1226 N-m
        • b)
          1345 N-m
        • c)
          1468 N-m
        • d)
          1534 N-m
        Correct answer is option 'A'. Can you explain this answer?

        Lavanya Menon answered
        At rest, ball is at lower most potion of  semi-circle.
        BM at A                    =    10g ´ (10 2.5)
                                           =    10 ´ 9.81 ´ 12.5    
                                           =    1226.25 N - m

        An I-section bean is fabricated with plates having an elastic section modulus of 200 × 10-5m3. If the laterally unsupported steel beam is classified as a semi-compact section, then the design plastic moment capacity of the beam considering Fe 410 grade of steel and the partial safety factor of material as 1.1 will be ____ kNm. (Use Bending stress reduction factor (XLT= 1.0) 
        • a)
          453-456
        Correct answer is '453-456'. Can you explain this answer?

        Tanvi Shah answered
        Concept:
        The bending strength or the plastic moment capacity of a laterally unsupported beam is given by:
        Md = βb Zp fbd
        Where
        βb = 1 → for plastic and concept section
         for semi - compact section. 
        Ze = Elastic section modulus
        Zp = Plastic section modulus
        fbd = design bending compressive strength
        ymo = Partial safety factor for material = 1.1
        XLT = bending stress reduction factor to account for lateral torsional buckling
        XLT ≤ 1.0
        Calculation:
        For a semi-compact section of a laterally unsupported steel bean plastic moment capacity
        XLT = 1.0
        γmo = 1.1
        fy = 250 Mpa for grade fe 410
        Md = 200 =  454.54 kNm

        As per IS 10500: 2012, the permissible limits in absence of alternate source of water for calcium and magnesium in the drinking water respectively will be (in ppm)
        • a)
          75 and 30
        • b)
          45 and 30
        • c)
          200 and 100
        • d)
          250 and 125
        Correct answer is option 'C'. Can you explain this answer?

        Shail Rane answered
        As per IS 10500: 2012,
        As per IS 1055: 2012, the permissible limits in absence of alternate source of water for calcium and magnesium in the drinking water respectively will be 200 ppm and 100 ppm.

        The dimensions for the flexural rigidity of a beam element in mass (M), length (L) and time (T) is given by:
        • a)
          MT-2
        • b)
          M-1T2
        • c)
          ML-1T-2
        • d)
          ML3T-2
        Correct answer is option 'D'. Can you explain this answer?

        Sanvi Kapoor answered
        In a beam, the flexural rigidity (EI) varies along the length as a function of x as shown in equation:

        Where E is the young's modulus (in Pasual, Pa), I is the second moment of area (in m4). Y is the traverse displacement of the beam x and M(x) is the bending moment at x. The SI unit of flexural rigidity is thus Pa. m4 or Nm4
        ∴ Dimension is ML3T–2

        The speed and the theoretical maximum capacity of a single lane highway are 5m/s and 900 vehicle per hour respectively. The space headway and time headway respectively are:
        • a)
          5.55 m and 4 sec
        • b)
          15 m and 3 sec
        • c)
          10 m and 2 sec
        • d)
          20 m and 4 sec
        Correct answer is option 'D'. Can you explain this answer?

        Lavanya Menon answered
        Theoretical maximum capacity of single lane can be expressed as
        where, S = Capacity of single lane in vehicle per hour.
        V = Speed in kmph
        S = Space headway
        Theoretical capacity can also be written as
        Where, Ht = time headway
        Calculation:
        Space Headway (S) =
        Time Headway (Ht) = 3600/900 sec
        = 4 sec 

        MPN index is a measure of one of the following :
        • a)
          Coliform bacteria
        • b)
          BOD5
        • c)
          Dissolved Oxygen Content
        • d)
          Hardness
        Correct answer is option 'A'. Can you explain this answer?

        Ravi Singh answered
        MPN- Most Probable Number used to measure Coliform Bacterial
        Wrinkler’s Method is used to measure dissolved oxygen and further, which is used to determine BOD5
        Hardness is measured in mg/L as CaCO3 via various methods like lime treatment, boiling.

        Consider the following statements P and Q:
        (P):If  M =    then M is singular.
        (Q): Let S be a diagonalizable matrix. If T is a matrix such that S + 5 T = I, then T is diagonalizable.
        Which of the above statements hold TRUE?
        • a)
          Both P and Q
        • b)
          Only P
        • c)
          Only Q
        • d)
          Neither P nor Q
        Correct answer is option 'C'. Can you explain this answer?

        Gate Gurus answered
        A matrix is said to be singular, if determinant of that matrix is zero.
        = 1 (18 – 12) - 1 (9 – 4) + 1 (3 – 2)
        = 6 – 5 + 1 = 2 ≠ 0
        M is non singular
        (Q) A matrix can be diagonalizable when it has distinct eigen values
        S is a diagonalizable matrix. Hence, has distinct eigen values.
        Let S be a 3 × 3 matrix and the eigen values of s are λ1, λ2, λ3
        Given that, S + 5T = I
        From the properties of Eigen values,
        (a) If λ1 is an eigen value of matrix A, then -λ1 ­will be on eigen value of matrix -A.
        (b) If λ1 is an eigen value of matrix A, then (λ1 + 1) will be an eigen value of matrix (A + I)
        (c) If λ is an eigen value of matrix A, then  will be an eigen value of matrix  where K is a scalar.
        From the above properties, eigen values of T are,
        As λ1, λ2, λ3 are distinct values, λ′1,λ′2,λ′3 will be distinct.
        Hence, matrix T is diagonalizable
        So, only Q is true.

        The total volume of water applied in 100 hectares of land was 25 × 107 liters. If the water stored in the root zone is 0.20 cm, then the field application efficiency will be_______%
          Correct answer is '80'. Can you explain this answer?

          Total volume of water applied
          = (25 × 107) × 10-3 m3
          = 25 × 104 m3
          Depth of the applied water
          = 0.25 m
          = 25 m
          Also, Depth of water stored in the root zone = 20 cm
          Therefore, field application efficiency

          = 80%

          Which kind of plume has minimum downward mixing as its downward motion is prevented by inversion and upward mixing will be quite turbulent and rapid?
          • a)
            Coming plume
          • b)
            Fanning plume
          • c)
            Lofting plume
          • d)
            Fumigating plume
          Correct answer is option 'B'. Can you explain this answer?

          Janhavi Datta answered
          Explanation:

          Introduction:
          - In atmospheric dispersion models, different types of plumes are used to represent the spread of pollutants released into the atmosphere.
          - The behavior of plumes is influenced by various factors such as atmospheric stability, wind speed, temperature, etc.

          Fanning Plume:
          - A fanning plume is a type of plume that has minimum downward mixing and its downward motion is prevented by an inversion layer in the atmosphere.
          - An inversion layer is a layer of the atmosphere where the temperature increases with height, creating a stable condition.
          - In a fanning plume, the upward mixing of pollutants will be quite turbulent and rapid due to the lack of downward mixing.
          - This turbulent and rapid upward mixing occurs because the downward motion of the plume is prevented by the inversion layer.
          - As a result, the pollutants released in a fanning plume will tend to spread horizontally rather than vertically.
          - This can lead to the pollutants being transported over long distances in the horizontal direction, potentially affecting a larger area.

          Other Types of Plumes:
          - Coming plume: A coming plume is a type of plume where the downward motion is not prevented by any inversion layer. It tends to spread both horizontally and vertically.
          - Lofting plume: A lofting plume is a type of plume that rises rapidly due to buoyancy and convective processes. It tends to spread vertically.
          - Fumigating plume: A fumigating plume is a type of plume that is released close to the ground and tends to spread horizontally near the ground surface.

          Conclusion:
          - Among the given options, the fanning plume has the minimum downward mixing as its downward motion is prevented by an inversion layer.
          - The upward mixing in a fanning plume is quite turbulent and rapid, leading to horizontal spread of pollutants.
          - Understanding the behavior of different types of plumes is important in assessing the dispersion and impact of pollutants in the atmosphere.

          A man sells three articles A, B, C and gains 10% on A, 20% on B and loses 10% on C. He breaks even when combined selling prices of A and C are considered, whereas he gains 5% when combined selling prices of B and C are considered. What is his net loss or gain on the sale of all the articles?
          • a)
            10% gain
          • b)
            20% gain
          • c)
            10.66% gain
          • d)
            6.66% gain
          Correct answer is option 'D'. Can you explain this answer?

          Parth Patel answered
          Let a, b and c be the cost prices of the three articles A, B and C.
          SP = CP + Profit (or) SP = CP – Loss
          ⇒ SP of A = 1.1a; SP of B = 1.2b; SP of C = 0.9c
          By question,
          1.1a + 0.9c = a + c ⇒ 0.1a = 0.1c ⇒ a = c
          1.2b + 0.9c = 1.05(b + c) ⇒ 0.15b = 0.15c ⇒ b = c = a
          Gain% = {(SP – CP)/CP} × 100
          ⇒ Net gain on the sale of all the articles =   =
          ∴ Net gain on the sale of all the articles = 6.66%

          The probability distribution taken to represent the completion time in PERT analysis is:
          • a)
            Gamma distribution
          • b)
            Normal distribution
          • c)
            Beta distribution
          • d)
            none of these
          Correct answer is option 'B'. Can you explain this answer?

          Shivam Sharma answered
          The distribution curve for the time taken in to complete each activity of a project resembles a beta-distribution curve and the distribution curve for the time taken to complete entire project ( consisting of several activities) in general resembles a normal distribution curve.

          Can you explain the answer of this question below:
          Man does not live by __________ alone.
          • A:Food
          • B:Bread
          • C: Meals
          • D:Diet

          The answer is B.

          Shivam Sharma answered
          The answer is B.Physical nourishment is not sufficient for a healthy life; man also has spiritual needs.

          A reinforced Concrete column of size 450mm × 550mm (overall depth) is provided with area of steel in compression as 4 bars of 25mm diameter. If the effective length of the column is 3.5m, the ultimate load carrying capacity of the column will be _______kN.
          Use M-20 concrete and Fe-415 steel.
            Correct answer is '2500-2520'. Can you explain this answer?

            Saikat Gupta answered
            Follow step by step method:
            (i) check for short or long column
            λ = 7.77 < 12
            it is a short column
            (ii) check for Minimum eccentricity
            Minimum eccentricity (ex-x) is greater of
            (ii) 20 mm
            So, ex-x = 25.33 mm
            ex-x < 0.05 × 550
            25.33 < 27.5 mm
            (O.K)
            For ey−y = 22mm
            ey-y < 0.05 × 450
            22 mm < 22.5 mm
            (O.K)
            So, Load carrying capacity of the column will be
            Pu = 0.4 fck Ac + 0.67fy Asc
            fck = 20 N/mm2
             = 1963.50mm2
            fy = 415 N/mm2
            Pu = 0.4 × 20 × [450 × 550 – 1963.50] + 0.67 × 415 × 1963.50
            Pu = 2510.24 kN

            A new flag is to be designed with six vertical stripes using some or all of the colours- yellow, green, blue and red. Then the number of ways this can be done such that no two adjacent stripes have the same colour out is:
            • a)
              12×81
            • b)
              16×25
            • c)
              20×125
            • d)
              24×216
            Correct answer is option 'A'. Can you explain this answer?

            Neha Choudhury answered
            Since no adjacent stripes contain the same color. The second, and the remaining vertical
            stripe will have only three options, while the first will have any of the four options.
            4*3*3*3*3*3 = 12* 3^4 = 12 * 81.
            So the answer is A.

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