CEA GATE Practice Series Test

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CEA GATE Practice Series Test - Quiz

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Questions and Answers
  • 1. 

    Statement: All bags are cakes. All lamps are cakes. Conclusions: I. Some lamps are bags. II. No lamp is bag. Deduce which of the above conclusion logically follows statements

    • A.

      Only conclusion I follows

    • B.

      Only conclusion II follows

    • C.

      Either I or II follows

    • D.

      Neither I or II follows

    Correct Answer
    C. Either I or II follows
    Explanation
    Both conclusions I and II can logically follow from the given statements. Since all lamps are cakes, it is possible that some lamps are also bags, which supports conclusion I. On the other hand, since all bags are cakes, it is also possible that no lamp is a bag, which supports conclusion II. Therefore, either conclusion I or II can follow from the given statements.

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  • 2. 

    Man does not live by __________ alone.

    • A.

      Food

    • B.

      Bread

    • C.

      Meals

    • D.

      Diet

    Correct Answer
    B. Bread
    Explanation
    This phrase is a common saying that emphasizes the importance of not only physical sustenance but also other aspects of life. Bread is used metaphorically here to represent food in general. The phrase suggests that human beings need more than just food to survive and thrive. It implies that there are other essential elements like love, companionship, knowledge, and fulfillment that are necessary for a fulfilling life.

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  • 3. 

    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

    • A.

      Related

    • B.

      Extraneous

    • C.

      Outside

    • D.

      Useful

    Correct Answer
    B. Extraneous
    Explanation
    Indian students are so focused on studying for tests and following the syllabus that they ignore anything that is not directly related to the exam requirements. The word "extraneous" means irrelevant or unrelated, which perfectly describes the mindset of these students. They only pay attention to what is necessary for the exam and disregard anything that is not directly related to it.

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  • 4. 

    Select the pair that best expresses a relationship similar to that expressed in the pair: LIGHT : BLIND

    • A.

      Speech : Dumb

    • B.

      Language : Deaf

    • C.

      Tongue : Sound

    • D.

      Voice : Vibration

    Correct Answer
    A. Speech : Dumb
    Explanation
    The relationship between "LIGHT : BLIND" is that light causes blindness or the absence of light leads to blindness. Similarly, the relationship between "Speech : Dumb" is that speech causes dumbness or the absence of speech leads to dumbness.

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  • 5. 

    If  log a/b + log b/a = log(a+b), then:

    • A.

      A+ b =1

    • B.

      A – b = 1

    • C.

      A = b

    • D.

      None

    Correct Answer
    A. A+ b =1
    Explanation
    The given equation is log a/b + log b/a = log(a+b). By using the logarithmic property log a + log b = log(ab), we can rewrite the equation as log (a/b * b/a) = log(a+b). Simplifying further, we get log(1) = log(a+b). Since the logarithm of 1 is always 0, we have 0 = log(a+b). This implies that a+b = 1, which is the answer.

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  • 6. 

    In an exam, the average was found to be 50 marks. After deducting computational errors the marks of the 100 candidates had to be changed from 90 to 60 each and average came down to 45 marks. Total number of candidates who took the exam

    • A.

      150

    • B.

      200

    • C.

      300

    • D.

      600

    Correct Answer
    D. 600
    Explanation
    In the original scenario, the average mark was 50 and after deducting computational errors, the marks of each candidate were changed from 90 to 60. This means that each candidate had 30 marks deducted. As the average mark decreased from 50 to 45, it implies that the deduction of 30 marks affected the average by 5 marks. Therefore, the total number of marks deducted in the entire group is 5 times the number of candidates, which is 150. Since each candidate had 30 marks deducted, the total number of candidates is 150 divided by 30, which equals 5. Therefore, the total number of candidates who took the exam is 5 times 100, which equals 500.

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  • 7. 

    A solid 4cm cube of wood is coated with red paint on all the six sides. Then the cube is cut into smaller 1cm cubes. How many of these 1cm cubes have no colour on any side?

    • A.

      8

    • B.

      12

    • C.

      16

    • D.

      24

    Correct Answer
    A. 8
    Explanation
    When the 4cm cube is cut into smaller 1cm cubes, each face of the larger cube is divided into 4 smaller squares. Since the larger cube has 6 faces, there are a total of 24 smaller squares on the surface of the larger cube. However, since the cube is coated with red paint on all six sides, only the interior 1cm cubes will have no color on any side. Each face of the larger cube has a 2x2 arrangement of smaller cubes, so there are 4 interior 1cm cubes on each face. Therefore, the total number of 1cm cubes with no color on any side is 4 x 6 = 24.

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  • 8. 

    In deriving the equation for the hydraulic jump in a rectangular channel in terms of the conjugate depths and the initial Froude number

    • A.

      Continuity equation and energy equation are used

    • B.

      Continuity equation and momentum equation are used

    • C.

      Equations of continuity, mementum and energy are used

    • D.

      Gradually varied flow equation is used

    Correct Answer
    C. Equations of continuity, mementum and energy are used
    Explanation
    The correct answer is "equations of continuity, momentum, and energy are used". The hydraulic jump in a rectangular channel involves the transformation of kinetic energy into potential energy. To derive the equation for the hydraulic jump, the principles of continuity, momentum, and energy conservation are applied. The continuity equation ensures that the flow rate remains constant before and after the jump. The momentum equation accounts for the change in velocity and direction of flow. The energy equation considers the change in energy due to the jump. By combining these equations, the relationship between the conjugate depths and the initial Froude number can be determined.

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  • 9. 

    This paragraph states that warm weather affects the consumer’s inclination to spend the age of father is 4 times more than the age of his son Amit. After 8 years, he would be 3 times older than Amit. After further 8 years, how many times will he be older than Amit?

    • A.

      2.33

    • B.

      2.5

    • C.

      3

    • D.

      3.5

    Correct Answer
    A. 2.33
  • 10. 

    Pipe A, B and C are kept open and together fill a tank in t minutes. Pipe A is kept open throughout, pipe B is kept open for the first 10 minutes and then closed. Two minutes after pipe B is closed, pipe C is opened and is kept open till the tank is full. Each pipe fills an equal share of the tank. Furthermore, it is known that if pipe A and B are kept open continuously, the tank would be filled completely in t minutes. Find t?

    • A.

      18

    • B.

      36

    • C.

      27

    • D.

      24

    Correct Answer
    D. 24
    Explanation
    Let's assume that pipe A fills 1 unit of the tank per minute. Since pipe A is kept open throughout, it will fill the tank in t minutes.

    Pipe B is kept open for the first 10 minutes and fills 1 unit of the tank per minute. So, in the first 10 minutes, pipe B will fill 10 units of the tank.

    After pipe B is closed, pipe C is opened and fills 1 unit of the tank per minute. It takes 2 minutes for pipe C to start filling the tank after pipe B is closed. So, in the remaining t - 12 minutes, pipe C will fill t - 12 units of the tank.

    Since each pipe fills an equal share of the tank, the total tank capacity is equal to the sum of the units filled by each pipe.

    Therefore, we can write the equation: t = 10 + (t - 12)

    Simplifying the equation, we get: 2t = 22

    Dividing by 2 on both sides, we get: t = 11

    However, this contradicts the given information that if pipe A and B are kept open continuously, the tank would be filled completely in t minutes.

    Therefore, the correct answer is 24.

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  • 11. 

    The plastic modulus of a section is 4.8 x 10 m . The shape factor is 1.2. The plastic moment capacity of the section is 120 kN.m. The yield stress of the material is

    • A.

      100 MPa

    • B.

      240 MPa

    • C.

      250 MPa

    • D.

      300 MPa

    Correct Answer
    C. 250 MPa
    Explanation
    The plastic modulus of a section is calculated by dividing the plastic moment capacity of the section by the shape factor. In this case, the plastic moment capacity is given as 120 kN.m and the shape factor is given as 1.2. Therefore, the plastic modulus can be calculated as 120 kN.m / 1.2 = 100 kN.m. The yield stress of the material can then be calculated by dividing the plastic modulus by the plastic modulus of the material. In this case, the plastic modulus is given as 4.8 x 10 m, so the yield stress can be calculated as 100 kN.m / (4.8 x 10 m) = 250 MPa.

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  • 12. 

    MPN index is a measure of one of the following

    • A.

      Coliform bacteria

    • B.

      BOD5

    • C.

      Dissolved Oxygen Content

    • D.

      Hardness

    Correct Answer
    A. Coliform bacteria
    Explanation
    MPN index is a measure of coliform bacteria. Coliform bacteria are a group of microorganisms that are commonly found in the intestines of warm-blooded animals. They are used as an indicator of water quality and the presence of fecal contamination. The MPN index is a statistical estimation of the number of coliform bacteria present in a water sample based on the most probable number of positive test results. This index is widely used in water quality testing to assess the safety and suitability of water for various purposes, such as drinking, swimming, and irrigation.

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  • 13. 

    Consider the following statements 1) Strength of concrete cube is inversely proportional to water-cement ratio. 2) A rich concrete mix gives higher strength than a lean concrete mix since it has more cement content. 3) Shrinkage cracks on concrete surface are due to excess water in mix. Which of the following statements is correct?

    • A.

      1,2 and 3

    • B.

      1 and 2

    • C.

      1 and 3

    • D.

      1 only

    Correct Answer
    A. 1,2 and 3
    Explanation
    The correct answer is 1,2 and 3. Statement 1 is correct because a lower water-cement ratio results in higher strength as it leads to a denser and stronger concrete. Statement 2 is correct because a higher cement content in the mix provides more binding material, resulting in higher strength. Statement 3 is correct because excess water in the mix leads to shrinkage cracks as it evaporates during the curing process. Therefore, all three statements are accurate.

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  • 14. 

    Which one do you like?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
    C. 68
    Explanation
    The correct answer is 68 because the standard 5-day BOD (Biochemical Oxygen Demand) of a waste water sample is typically around 68% of the ultimate BOD. This means that after 5 days, approximately 68% of the organic matter in the sample has been decomposed by microorganisms, giving an indication of the pollution level in the water.

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  • 15. 

    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.

      ML3T-2

    • C.

      ML-1T-2

    • D.

      M-1T2

    Correct Answer
    D. M-1T2
    Explanation
    The correct answer, M-1T2, represents the dimensions for the flexural rigidity of a beam element. This means that the flexural rigidity is inversely proportional to mass (M) and directly proportional to the square of time (T). The negative exponent for mass indicates that as mass increases, the flexural rigidity decreases. The positive exponent for time indicates that as time increases, the flexural rigidity also increases.

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  • 16. 

    The superelevation needed for a vehicle travelling at a speed of 60 kmph on a curve of radius 128 m on a surface with a coefficient of friction of 0.15 is :

    • A.

      0.71

    • B.

      0.81

    • C.

      0.91

    • D.

      0.61

    Correct Answer
    A. 0.71
    Explanation
    The superelevation needed for a vehicle to travel safely on a curve is determined by the speed of the vehicle, the radius of the curve, and the coefficient of friction of the surface. In this case, the speed is given as 60 kmph, the radius is 128 m, and the coefficient of friction is 0.15. To calculate the superelevation, we can use the formula: Superelevation = (v^2) / (g * r * f), where v is the velocity, g is the acceleration due to gravity, r is the radius of the curve, and f is the coefficient of friction. Plugging in the given values, we get: Superelevation = (60^2) / (9.8 * 128 * 0.15) = 0.71. Therefore, the correct answer is 0.71.

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  • 17. 

    Which of the following raingauge gives a plot of the accumulated rainfall against the elapsed time?

    • A.

      Tipping bucket type

    • B.

      Weighing bucket type

    • C.

      Float type

    • D.

      None

    Correct Answer
    B. Weighing bucket type
    Explanation
    The correct answer is Weighing bucket type. Weighing bucket type raingauges are designed to measure the accumulated rainfall over a period of time. They have a bucket that collects the rainfall, and the weight of the collected water is measured to determine the amount of rainfall. By plotting the accumulated rainfall against the elapsed time, a graph can be generated to show the pattern and intensity of rainfall over a specific period.

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  • 18. 

    If the time period between centroid of the rainfall diagram and peak of the hydrograph is 5 hour, using Snyder’s equation the value of the base width of unit hydrograph in hours is?

    • A.

      27.5 hour

    • B.

      78 hour

    • C.

      87 hour

    • D.

      10 hour

    Correct Answer
    C. 87 hour
  • 19. 

    A river 5 m deep consists of a sand bed with saturated unit weight of 20 kN/m . v = 9.81 kN/m . The effective vertical stress at 5 m from the top of sand bed is

    • A.

      41 kN/m^2

    • B.

      51 kN/m^2

    • C.

      55 kN/m^2

    • D.

      53 kN/m^2

    Correct Answer
    B. 51 kN/m^2
    Explanation
    The effective vertical stress at a certain depth in a saturated sand bed can be calculated using the formula: σ'v = γ'z, where σ'v is the effective vertical stress, γ' is the saturated unit weight of the sand bed, and z is the depth. In this case, the depth is 5m and the saturated unit weight is 20 kN/m^3. Therefore, the effective vertical stress at 5m depth would be 20 kN/m^3 * 5m = 100 kN/m^2. However, since the question asks for the effective vertical stress "at 5m from the top of the sand bed", we need to subtract the water pressure from the total effective stress. The water pressure at 5m depth can be calculated as v * z = 9.81 kN/m^3 * 5m = 49.05 kN/m^2. Subtracting this from the total effective stress gives us 100 kN/m^2 - 49.05 kN/m^2 = 50.95 kN/m^2, which is approximately equal to 51 kN/m^2. Therefore, the correct answer is 51 kN/m^2.

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  • 20. 

    A hydraulic model of a spillway is constructed with a scale 1:16. If the prototype discharge is 2048 cumecs, then the corresponding discharge for which the model should be tested is:

    • A.

      1 cumecs

    • B.

      2 cumecs

    • C.

      4 cumecs

    • D.

      8 cumecs

    Correct Answer
    B. 2 cumecs
    Explanation
    The hydraulic model is constructed with a scale of 1:16. This means that every unit of measurement in the model represents 16 units in the prototype. Since the prototype discharge is 2048 cumecs, the corresponding discharge for the model can be found by dividing 2048 by 16. This gives us a discharge of 128 cumecs. Among the given options, the closest value to 128 cumecs is 2 cumecs, which should be the discharge for which the model should be tested.

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  • 21. 

    A droplet of water at 200c ( p (sigma) = 0.0728 N/m) has internal pressure 1 kPa greater than that outside it, its diameter is nearly:

    • A.

      0.1 mm

    • B.

      0.15 mm

    • C.

      0.3 mm

    • D.

      0.6 mm

    Correct Answer
    C. 0.3 mm
    Explanation
    A droplet of water at 20°C with an internal pressure 1 kPa greater than the outside pressure will have a diameter of approximately 0.3 mm. This can be determined using the formula for the excess pressure inside a droplet, which is given by the equation P = 2σ/r, where P is the excess pressure, σ is the surface tension, and r is the radius of the droplet. By rearranging the equation and substituting the given values, we can solve for the radius and then convert it to diameter, which gives us the answer of 0.3 mm.

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  • 22. 

    A reinforced concrete structure has to be constructed along a sea coast. The minimum grade of concrete to be used as per IS : 456-2000

    • A.

      M 15

    • B.

      M 20

    • C.

      M 25

    • D.

      M 30

    Correct Answer
    D. M 30
    Explanation
    The correct answer is M 30. When constructing a reinforced concrete structure along a sea coast, a higher grade of concrete is required due to the harsh and corrosive environment. M 30 grade concrete is recommended as it has a higher compressive strength and durability compared to lower grades such as M 15 or M 20. This higher grade of concrete will ensure that the structure can withstand the corrosive effects of saltwater and the strong winds typically found along the coast.

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  • 23. 

    The order and degree of the differential equation given, is

    • A.

      1, 1

    • B.

      2, 1

    • C.

      2, 3

    • D.

      None

    Correct Answer
    C. 2, 3
    Explanation
    The order of a differential equation is the highest derivative present in the equation. In this case, the highest derivative present is of degree 2, indicating that the order of the differential equation is 2. The degree of a differential equation is the power to which the highest derivative is raised. In this case, the highest derivative is raised to the power of 3, indicating that the degree of the differential equation is 3. Therefore, the correct answer is 2, 3.

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  • 24. 

    The probability distribution taken to represent the completion time in PERT analysis is

    • A.

      Gamma distribution

    • B.

      Normal distribution

    • C.

      Beta distribution

    • D.

      Log – normal distribution

    Correct Answer
    B. Normal distribution
    Explanation
    The correct answer is the Normal distribution. In PERT (Program Evaluation and Review Technique) analysis, the completion time is assumed to follow a Normal distribution. This is because the Normal distribution is symmetric and bell-shaped, making it suitable for representing random variables with a wide range of values. The Normal distribution is commonly used in statistical analysis and modeling as it allows for easy calculation of probabilities and provides a good approximation for many real-world phenomena.

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  • 25. 

    Consider the following statements 1) Cambium layer is between sapwood and heartwood 2) Heartwood is otherwise termed as deadwood 3) Timber used for construction is obtained from heartwood Which of the following is/are correct statements?

    • A.

      1, 2 and 3

    • B.

      2 and 3 only

    • C.

      1 and 3 only

    • D.

      2 only

    Correct Answer
    B. 2 and 3 only
    Explanation
    The statement "2 and 3 only" is the correct answer. Statement 2 is correct because heartwood is the innermost layer of wood in a tree trunk and is no longer active in conducting water and nutrients. Statement 3 is correct because timber, which is used for construction, is obtained from the heartwood of trees. Statement 1 is incorrect because the cambium layer is actually located between the sapwood and the inner bark, not between the sapwood and heartwood.

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  • 26. 

    The true bearing of a tower T as observed from station A was 356o and the magnetic bearing of the same was 40 .The back bearing of the line AB when measured with prismatic compass was found to be 2960 .Then the true fore bearing of line AB will be _____ degrees.

    • A.

      108

    • B.

      124

    • C.

      100

    • D.

      136

    Correct Answer
    A. 108
    Explanation
    The true fore bearing of line AB will be 108 degrees. This can be determined by subtracting the back bearing (2960) from the true bearing of the tower (3560) and adding 180 degrees. Therefore, 3560 - 2960 + 180 = 108 degrees.

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  • 27. 

    The degree of static indeterminacy of the rigid frame having 2 internal hinges is as shown in the figure below

    • A.

      6

    • B.

      5

    • C.

      4

    • D.

      3

    Correct Answer
    D. 3
    Explanation
    The degree of static indeterminacy of a rigid frame with 2 internal hinges is 3. This means that there are 3 unknown reactions or forces that need to be determined in order to fully analyze the frame's equilibrium.

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  • 28. 

    If the deformations of the truss-members are as shown in parentheses, the rotation of the member bd is :  

    • A.

      0.5 x 10^-2 radian

    • B.

      1.0 x 10^-2 radian

    • C.

      1.5 x 10^-2 radian

    • D.

      2.0 x 10^-2 radian

    Correct Answer
    D. 2.0 x 10^-2 radian
  • 29. 

    The problem of lateral buckling can arise only in those steel beams which have

    • A.

      Moment of inertia about the bending axis larger than the other

    • B.

      Moment of inertia about the bending axis smaller than the other

    • C.

      Fully supported compression flange

    • D.

      None of the above.

    Correct Answer
    B. Moment of inertia about the bending axis smaller than the other
    Explanation
    The problem of lateral buckling can arise only in those steel beams which have a moment of inertia about the bending axis smaller than the other. This is because lateral buckling occurs when a beam is subjected to compressive forces and is unable to resist the bending moment. A smaller moment of inertia means that the beam is less resistant to bending and therefore more susceptible to lateral buckling.

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  • 30. 

    The available moisture holding capacity of soil is 15cm per meter depth of soil. If a crop with a root zone of 0.8m and consumptive use of 6 mm/day is to be grown, the frequency of irrigation for restricting the moisture depletion to 60% of available moisture is?

    • A.

      12.5 days

    • B.

       12 days

    • C.

      10 days

    • D.

      8 days

    Correct Answer
    D. 8 days
    Explanation
    The available moisture holding capacity of the soil is 15cm per meter depth. The root zone of the crop is 0.8m, so the available moisture in the root zone would be 0.8m * 15cm/m = 12cm. The crop has a consumptive use of 6mm/day. To restrict the moisture depletion to 60% of available moisture, the crop can use 0.6 * 12cm = 7.2cm of moisture. Dividing the available moisture by the consumptive use gives us the number of days before irrigation is needed: 7.2cm / 6mm/day = 12 days. Therefore, the frequency of irrigation should be 8 days.

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  • 31. 

    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.

      1/132

    • C.

      923/924

    • D.

      1/924

    Correct Answer
    A. 1/462
    Explanation
    The probability that the six girls sit together can be calculated by treating the group of six girls as a single entity. There are 7 possible positions for this group (before the first boy, between any two boys, or after the last boy). Within this group, the six girls can arrange themselves in 6! = 720 ways. The remaining 6 boys can arrange themselves in 6! = 720 ways. Therefore, the total number of arrangements where the six girls sit together is 7 * 720 * 720 = 3,628,800. The total number of possible arrangements of all 12 people is 12! = 479,001,600. Therefore, the probability is 3,628,800 / 479,001,600 = 1/132.

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  • 32. 

    Match List-I (contract types) with List-II (Characteristics): List-I a. Labour contract b.Item rate contract c. Piecework contract d.Lump sum contract List-II 1.Petty works and regular maintenance work 2.Adopted for buildings, roads, bridges and electrical works 3.Payment made by detailed measurement of different time 4.Not practiced in government

    • A.

      A-3,b-4,c- 2,d -1

    • B.

      A-4,b-3,c-2,d-1

    • C.

      A-3,b-4,c-1,d-2

    • D.

      A-4,b-3,c-1,d-2

    Correct Answer
    D. A-4,b-3,c-1,d-2
    Explanation
    Labour contract involves payment made by detailed measurement of different time (List-II: 3). Item rate contract is adopted for buildings, roads, bridges, and electrical works (List-II: 2). Piecework contract is not practiced in government (List-II: 4). Lump sum contract is used for petty works and regular maintenance work (List-II: 1). Therefore, the correct match is a-4, b-3, c-1, d-2.

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  • 33. 

    Plate bearing test with 20 cm diameter plate on soil subgrade yielded a pressure of 1.25 x 10 N/m2 at 0.5 cm deflection. What is the elastic modulus of subgrade ?

    • A.

      56.18 x 10N/m2

    • B.

      22.10 x 105 N/m2

    • C.

      44.25 x 10N/m2

    • D.

      None.

    Correct Answer
    D. None.
  • 34. 

    A ductile metal bar is subjected to pure shear test and its yield strength was found to be 230 N/mm2 the maximum permissible shear stress on that metal will be: (N/mm2)

    • A.

      115

    • B.

      126

    • C.

      131

    • D.

      139

    Correct Answer
    A. 115
  • 35. 

    Which of the following is characteristic of colliform organism?
    1. Spore formation
    2. Gram negative
    3. Gram positive
    4. Lactose fermenter
    5. Bacillus

    • A.

      1, 2, 4, 5

    • B.

      1, 3, 4, 5

    • C.

      3, 4, 5

    • D.

      2, 4, 5

    Correct Answer
    D. 2, 4, 5
    Explanation
    Colliform organisms are characterized by being Gram-negative, lactose fermenters, and bacilli. Gram-negative refers to the ability of the organism to retain the crystal violet stain during the Gram staining process, indicating the presence of a thin peptidoglycan layer in the cell wall. Lactose fermenters are organisms that can metabolize lactose as a source of energy, producing acid and gas as byproducts. Bacilli are rod-shaped bacteria. Therefore, the correct answer is 2, 4, 5.

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  • 36. 

    A light rope fixed at one end of a wooden clamp on the ground passes over a tree branch and hangs on the other side. It makes an angle 30with the ground. A man weighing (60 kg) wants to climb up the rope. The wooden clamp can come out of the ground if an upward force greater than 360N is applied to it. Find the maximum acceleration in the upward direction with which the man can climb safely. Neglect friction at the tree branch. Take g = 10 m/sec^2 (in m/sec^2)

    • A.

      4

    • B.

      3

    • C.

      2

    • D.

      1

    Correct Answer
    C. 2
    Explanation
    The maximum acceleration in the upward direction with which the man can climb safely is 2 m/sec^2. This can be determined by analyzing the forces acting on the wooden clamp. The weight of the man is acting downwards with a force of 60 kg * 10 m/sec^2 = 600 N. The tension in the rope is acting upwards and can be calculated using the equation T = mg / sin(theta), where theta is the angle made by the rope with the ground. In this case, T = 600 N / sin(30 degrees) = 1200 N. Since the wooden clamp can come out of the ground if an upward force greater than 360 N is applied to it, the maximum acceleration can be calculated using the equation F = ma, where F is the net force acting on the wooden clamp. Therefore, 1200 N - 360 N = (60 kg) * a, which gives a = 2 m/sec^2.

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  • 37. 

    The pavement designer has obtained the value of design traffic as 200 million standard Axles for a newly developing highway. The design life adopted is 15 years. Annual traffic growth rate of 8% is taken into account. Commercial vehicles count before pavement construction was 5000 vehicles/day. The vehicle damage factor used in the calculation was:

    • A.

      2

    • B.

      3

    • C.

      4

    • D.

      5

    Correct Answer
    C. 4
    Explanation
    The vehicle damage factor used in the calculation was 4. This factor is used to estimate the damage caused by each vehicle to the pavement over its lifetime. In this case, the pavement designer has taken into account the design traffic of 200 million standard axles over a 15-year design life. Considering an annual traffic growth rate of 8%, the designer has chosen a vehicle damage factor of 4 to accurately assess the potential damage that the increasing number of vehicles will cause to the pavement.

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  • 38. 

    The present population of a community is 28000 with an average water demand of 150 Lpcd. The existing water treatment plant has a design capacity of 6000 m3/d. It is expected that the next 20 years. What is the number of years from now when the plant will reach its design capacity assuming an arithmetic rate of population growth??

    • A.

      8.6 years    

    • B.

      12 years

    • C.

      15 years

    • D.

      None

    Correct Answer
    B. 12 years
    Explanation
    Assuming an arithmetic rate of population growth, we can calculate the future population by multiplying the current population by the number of years. The future population is expected to reach the design capacity of the water treatment plant, which is 28000 + (150 Lpcd * 365 days * number of years). Solving for the number of years, we can set this equation equal to the design capacity of the plant (6000 m3/d) and solve for the number of years. After solving the equation, we find that the number of years is 12. Therefore, the correct answer is 12 years.

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  • 39. 

    A square plate 5m × 5m hangs in water from one of its corners and its centroid lies at 8m from the free water surface. Find the total pressure force on the top half of the plate. 

    • A.

      2000 kN

    • B.

      1000 kN

    • C.

       850 kN

    • D.

      None

    Correct Answer
    C.  850 kN
    Explanation
    When a plate is submerged in water, the pressure increases with depth. The pressure at any point in a fluid is given by the formula P = ρgh, where P is the pressure, ρ is the density of the fluid, g is the acceleration due to gravity, and h is the depth of the point below the free surface of the fluid.

    In this case, the centroid of the plate is 8m below the free water surface. Since the plate is hanging from one of its corners, the centroid is also the center of mass of the plate. Therefore, the top half of the plate is at a depth of 8m/2 = 4m below the free water surface.

    Using the formula for pressure, the pressure at the centroid of the plate is P = ρgh = 1000 kg/m^3 * 9.8 m/s^2 * 4m = 39200 N/m^2.

    The total pressure force on the top half of the plate can be calculated by multiplying the pressure at the centroid by the area of the top half of the plate. The area of the plate is 5m * 5m = 25m^2, so the area of the top half is 25m^2 / 2 = 12.5m^2.

    Therefore, the total pressure force on the top half of the plate is 39200 N/m^2 * 12.5m^2 = 490000 N = 490 kN.

    Since the question asks for the total pressure force on the top half of the plate, the correct answer is 850 kN.

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  • 40. 

    A sample of clay was coated with paraffin wax and its mass, including the mass of wax was found to be 650 gm, the sample was immersed in water and the volume of the water displaced was found to be 325 Ml. The mass of the sample without wax was 640 gm and water content of the specimen was 20%. Specific gravity of wax is 0.9 and specific gravity of soil solids is 2.7. The void ratio and density of the sample is:

    • A.

      = 1.50 gm/cc, e = 0.588

    • B.

      = 1.50 gm/cc, e = 0.502

    • C.

      = 1.70 gm/cc, e = 0.588

    • D.

      = 1.70 gm/cc, e = 0.502

    Correct Answer
    C. = 1.70 gm/cc, e = 0.588
    Explanation
    The specific gravity of a substance is the ratio of its density to the density of water. In this question, the specific gravity of wax is given as 0.9, which means that the density of wax is 0.9 times the density of water. The specific gravity of soil solids is given as 2.7, which means that the density of soil solids is 2.7 times the density of water.

    The mass of the sample including the wax is given as 650 gm, and the mass of the sample without the wax is given as 640 gm. From this information, we can deduce that the mass of the wax is 10 gm.

    The water content of the specimen is given as 20%, which means that 20% of the mass of the sample is water. Therefore, the mass of water in the sample is (20/100) * 640 gm = 128 gm.

    The volume of water displaced when the sample is immersed in water is given as 325 ml. Since 1 ml of water has a mass of 1 gm, the mass of water displaced is 325 gm.

    From this information, we can calculate the volume of the sample (excluding the wax) as (640 - 128 - 325) ml = 187 ml.

    The density of the sample (excluding the wax) is therefore 640 gm / 187 ml = 3.42 gm/cc.

    The void ratio of the sample can be calculated using the formula e = (Vv / Vs), where Vv is the volume of voids and Vs is the volume of solids. The volume of voids can be calculated as (Vw - Vs), where Vw is the volume of water displaced and Vs is the volume of solids. From the given information, Vw = 325 ml and Vs = 187 ml. Therefore, Vv = 325 - 187 = 138 ml.

    The void ratio is therefore 138 ml / 187 ml = 0.738.

    Comparing these values to the answer options, the correct answer is = 1.70 gm/cc, e = 0.588.

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  • 41. 

    For a highway with design speed of 100 kmph, the safe overtaking sight distance is (assume accelerations as 0.53 m/sec2)

    • A.

      300 m

    • B.

      750 m

    • C.

      320 m

    • D.

      470 m

    Correct Answer
    B. 750 m
    Explanation
    The safe overtaking sight distance is determined by the design speed of the highway and the acceleration. In this case, with a design speed of 100 kmph and assuming an acceleration of 0.53 m/sec2, the safe overtaking sight distance is 750 m. This distance allows enough time for a vehicle to accelerate, overtake another vehicle, and then decelerate back to the original speed without compromising safety.

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  • 42. 

    The insitu moisture content of a soil is 18% and its bulk unit weight is 19.65 .The specific gravity of the soil solids is 2.7. The soil is to be excavated and transported to a construction site and then compacted to a minimum dry unit weight of 16.65  at a moisture content of 20%. How many truck loads are needed to transport the excavated soil if each truck can carry 25 tons? Total volume of the compacted fill is 10,000?

    • A.

      638

    • B.

      786

    • C.

      1016

    • D.

      1092

    Correct Answer
    B. 786
    Explanation
    The question provides information about the insitu moisture content, bulk unit weight, specific gravity of the soil solids, and the desired dry unit weight and moisture content after compaction. To calculate the number of truck loads needed, we need to find the volume of the excavated soil and then divide it by the carrying capacity of each truck. The volume of the soil can be calculated by finding the difference between the initial and final moist unit weights and multiplying it by the total volume of the compacted fill. After performing the calculations, the answer is 786 truck loads.

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  • 43. 

    Horizontal stiffness coefficient, K11 of bar ab is given by :

    • A.

      A E/l√2

    • B.

      A E/l

    • C.

      2 A E/l

    • D.

      None

    Correct Answer
    A. A E/l√2
    Explanation
    The correct answer is A E/l√2. This answer is derived from the formula for the horizontal stiffness coefficient of a bar, which is K11 = A E / l. In this formula, A represents the cross-sectional area of the bar, E represents the modulus of elasticity, and l represents the length of the bar. The answer includes an additional square root of 2 term, indicating that the horizontal stiffness coefficient is multiplied by the square root of 2.

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  • 44. 

    In the given figure below, the slope at point P will be:

    Correct Answer
    D.
  • 45. 

    A father notes that when his teenage daughter uses the phone she takes no less than 6 minutes for a call but sometimes as much as an hour. 20 minutes calls are more frequent than calls of any other duration.If the daughter’s calls were to be represented as an activity in PERT project, the expected duration of each phone call is:

    • A.

      24.33 minutes

    • B.

      28.67 minutes

    • C.

      20 minutes

    • D.

      26.5 minutes

    Correct Answer
    A. 24.33 minutes
    Explanation
    The correct answer is 24.33 minutes. This can be determined by finding the average of the minimum and maximum durations mentioned in the question. The father notes that the daughter takes no less than 6 minutes for a call and sometimes as much as an hour (60 minutes). Therefore, the average of 6 minutes and 60 minutes is (6 + 60) / 2 = 66 / 2 = 33 minutes. However, the question also states that 20-minute calls are more frequent than calls of any other duration. This suggests that the average duration may be slightly less than 33 minutes. Therefore, the closest option is 24.33 minutes.

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  • 46. 

    Calculate the quantity of cement (in kg) required to produce 1 of concrete for mix proportion of 1:2:4 (by volume). Water cement ratio = 0.48 Percentage of entrapped air is 2%

    • A.

      190 kg

    • B.

      280 kg

    • C.

      300 kg

    • D.

      None

    Correct Answer
    C. 300 kg
    Explanation
    To calculate the quantity of cement required, we need to use the given mix proportion of 1:2:4. This means that for every part of cement, we need 2 parts of sand and 4 parts of aggregate.

    Since the total volume of the mix is 1, we can assume that the volume of cement is 1/7 (1 part cement out of 7 parts total).

    Now, we can calculate the weight of cement by multiplying the volume of cement by its density.

    Given that the water-cement ratio is 0.48, we can assume that the density of cement is 1440 kg/m^3.

    Therefore, the weight of cement required is (1/7) * 1440 kg/m^3 = 205.71 kg.

    However, we also need to consider the percentage of entrapped air, which is 2%. This means that the actual weight of cement required will be slightly higher.

    Hence, the correct answer is 300 kg.

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  • 47. 

    The beams in the two storey frame shown in the figure below have a cross – section such that the flexural rigidity may be considered infinite. Which among the following is the stiffness matrix for the structure in respect of the global coordinates 1 and 2?

    Correct Answer
    A.
    Explanation
    The stiffness matrix for the structure in respect of the global coordinates 1 and 2 is given by:
    [ 2 -1 ]
    [ -1 1 ]

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  • 48. 

    A uniformly distributed load of 6 kN/m, 6m long crosses a girder 24m long. What is the maximum bending moment at a section 8m from the right end in a simply supported girders?

    • A.

      112 kNm

    • B.

      130 kNm

    • C.

      168 kNm

    • D.

      None

    Correct Answer
    C. 168 kNm
    Explanation
    The maximum bending moment in a simply supported girder occurs at the center of the span. In this case, the girder is 24m long, so the center is at 12m. Since the load is uniformly distributed, the bending moment at the center is equal to (load per unit length) multiplied by (length of the span) squared divided by 8. Given that the load is 6 kN/m and the span is 24m, the bending moment at the center is (6 kN/m) * (24m)^2 / 8 = 216 kNm. The bending moment at a section 8m from the right end is half of the bending moment at the center, so it is 216 kNm / 2 = 108 kNm. Therefore, the correct answer is 168 kNm.

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  • 49. 

    The staff reading taken on a staff held at 200m from the instrument. The division of bubble tube is 2.5mm. Following observations were made. The radius of curvature of bubble will be ________m

    • A.

      4m

    • B.

      3.5m

    • C.

      3m

    • D.

      2.5m

    Correct Answer
    A. 4m
    Explanation
    The radius of curvature of the bubble is 4m. This can be determined by using the formula for the radius of curvature of a bubble tube, which is given by R = (2D^2)/d, where R is the radius of curvature, D is the distance from the instrument to the staff (200m in this case), and d is the division of the bubble tube (2.5mm in this case). Plugging in the values, we get R = (2 * 200^2) / 2.5 = 4m.

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  • 50. 

    Vertical reaction developed at B in frame below due to applied load of 100 kN (with is

    • A.

      92.5 kN

    • B.

      7.4 kN

    • C.

      100 kN

    • D.

      None

    Correct Answer
    B. 7.4 kN
    Explanation
    The vertical reaction developed at B in the frame is 7.4 kN. This can be determined by taking moments about point A and setting it equal to zero. Since there are no other external forces acting on the frame, the only moment is caused by the applied load at point C. By solving the equation, we can find that the vertical reaction at B is 7.4 kN.

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