GATE Mock Test -1

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GATE Mock Test -1 - Quiz


Questions and Answers
  • 1. 

    Knowledgeable dog owners recommend obtaining a purebred dog from a ______ breeder, one who is ______ and respected by customers and breeders alike.

    • A.

      Discerning … equivocal

    • B.

      Demanding … flexible

    • C.

      Churlish … charming

    • D.

      Reputable … admired

    Correct Answer
    D. Reputable … admired
    Explanation
    A reputable breeder is someone who is highly regarded and respected by both customers and other breeders. They are known for their ethical practices, responsible breeding, and the quality of the dogs they produce. Being admired by others in the industry is a testament to their expertise and dedication to the breed. This is why knowledgeable dog owners recommend obtaining a purebred dog from a reputable breeder.

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  • 2. 

    With a(n) ______ grin, the boy quickly slipped the candy into his pocket without his mother’s knowledge.

    • A.

      Jaundiced

    • B.

      Nefarious

    • C.

      Stereotypical

    • D.

      Sentimental

    Correct Answer
    B. Nefarious
    Explanation
    The word "nefarious" means extremely wicked or evil. In the given sentence, the boy is described as having a "nefarious grin," suggesting that he is doing something wrong or deceitful by quickly slipping the candy into his pocket without his mother's knowledge. This implies that the boy's actions are morally questionable or dishonest.

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  • 3. 

    Find out the mean proportion of 3 & 27 also find out their third proportion

    • A.

      9,243

    • B.

      10,81

    • C.

      15,19683

    • D.

      12,810

    Correct Answer
    A. 9,243
    Explanation
    The mean proportion of 3 and 27 is the square root of their product, which is 9. The third proportion is the product of the mean proportion and the second number, which is 9 * 27 = 243. Therefore, the correct answer is 9,243.

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  • 4. 

    X and y are integers and if x^2/y^3 is even integer then which of the following must be an even integer?

    • A.

      X-y

    • B.

      Y+1

    • C.

      X^2/y^4

    • D.

      Xy

    Correct Answer
    D. Xy
    Explanation
    If x^2/y^3 is an even integer, it means that x^2 is divisible by both y^3 and 2. Since x^2 is divisible by y^3, it implies that x is divisible by y. Therefore, xy is divisible by y, making it an even integer. Hence, the correct answer is xy.

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  • 5. 

    If E=10;J=20;O=30; and T=40, what will be P+E+S+T?

    • A.

      82

    • B.

      164

    • C.

      120

    • D.

      51

    Correct Answer
    C. 120
  • 6. 

    How many four digit numbers can be formed with 10 digit 0,1,2,3...9 if no number can start with 0 and if repetitions are not allowed?

    Correct Answer
    4536
    Explanation
    Since the number cannot start with 0, we have 9 options for the first digit (1 to 9). For the second digit, we have 9 options again (0 is not available anymore, and repetition is not allowed). Similarly, for the third digit, we have 8 options, and for the fourth digit, we have 7 options. Therefore, the total number of four-digit numbers that can be formed is 9 x 9 x 8 x 7 = 4536.

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  • 7. 

    The variable cost (V) of manufacturing a product varies according to the equation V = 4q, where q is the quantity produced. The fixed cost (F) of production of same product reduces with q according to the equation F = 100/q.How many units should be produced to minimize the total cost (V+F)?

    • A.

      5

    • B.

      4

    • C.

      7

    • D.

      6

    Correct Answer
    A. 5
    Explanation
    The total cost (V+F) is minimized when the sum of the variable cost (V) and fixed cost (F) is at its lowest point. In this case, the variable cost is given by V = 4q, and the fixed cost is given by F = 100/q. To minimize the total cost, we need to find the value of q that minimizes the sum of these two costs. By substituting the given equations for V and F into the expression for total cost, we get (4q) + (100/q). To find the minimum value, we can take the derivative of this expression with respect to q and set it equal to zero. Solving this equation will give us the value of q that minimizes the total cost.

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  • 8. 

    Two machine M1 and M2 are able to execute any of four jobs P, Q, R, and S. The machine can perform one job on one object at a time. Jobs P, Q, R and S take 30 minutes, 20 minutes, 60 minutes and 15 minutes each respectively. There are 10 objects each requiring exactly 1 job. Job P is to be performed on 2 objects. Job Q on 3 objects, job R on 1 object and Job S on 4 objects. What is the minimum time needed to complete all the jobs?

    • A.

      2 hours

    • B.

      2.5 hours

    • C.

      3 hours

    • D.

      3.5 hours

    Correct Answer
    A. 2 hours
    Explanation
    The minimum time needed to complete all the jobs can be calculated by finding the maximum time required for any job and multiplying it by the number of objects that require that job. In this case, Job R requires the maximum time of 60 minutes and there is only 1 object that requires it. Therefore, the minimum time needed to complete all the jobs is 60 minutes or 1 hour. Since the given answer options are in hours, the answer can be written as 1 hour, which is equivalent to 2 hours.

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  • 9. 

    Given that logP/(y-z)=logQ/(z-x) =logR/(x-y) =10,for x≠y≠z, What is the value of PQR?

    • A.

      0

    • B.

      1

    • C.

      Xyz

    • D.

      10xyz

    Correct Answer
    B. 1
    Explanation
    The given equation states that the logarithm of P divided by the difference between y and z is equal to the logarithm of Q divided by the difference between z and x, which is also equal to the logarithm of R divided by the difference between x and y, all of which are equal to 10. Since the logarithms are all equal, it implies that P, Q, and R are all equal. Therefore, the value of PQR would be 1.

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  • 10. 

    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), (C+D+E), (E+F+G) and (G+H+K) is equal to 13. Which integer does E represent?                        | A | B | C |                                 | D |                                 | E | F | G |                                           | H |                                           | K |

    • A.

      1

    • B.

      4

    • C.

      6

    • D.

      7

    Correct Answer
    B. 4
    Explanation
    In order for (A+B+C) to equal 13, the only possible combinations are 1+4+8 or 2+3+8. However, since 8 is not available in the given options, the combination must be 1+4+8.

    Since (C+D+E) also equals 13, and C is already 8, D and E must be 2 and 3 in some order.

    Since (E+F+G) also equals 13, and E is either 2 or 3, F and G must be 5 and 6 in some order.

    Finally, since (G+H+K) also equals 13, and G is 5 or 6, H and K must be 7 and 1 in some order.

    Therefore, E must represent the integer 3.

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  • 11. 

    For a linear elastic isotropic material the no. of independent elastic constants is/are

    • A.

      1

    • B.

      2

    • C.

      3

    • D.

      4

    Correct Answer
    B. 2
    Explanation
    For a linear elastic isotropic material, the number of independent elastic constants is 2. This is because an isotropic material has the same mechanical properties in all directions. The two independent elastic constants are Young's modulus (measures the material's stiffness) and Poisson's ratio (measures the material's resistance to lateral strain when compressed or stretched). These two constants are sufficient to describe the material's elastic behavior in all directions.

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  • 12. 

    For the bracket connection shown inthe following fig. Which bolt will have the maximum resultant force?

    • A.

      Bolt 1

    • B.

      Bolt 2

    • C.

      Bolt 3

    • D.

      Bolt 4

    Correct Answer
    B. Bolt 2
    Explanation
    In the given bracket connection, bolt 2 will have the maximum resultant force. This can be determined by analyzing the forces acting on each bolt. Bolt 2 is located at the point where the two brackets intersect, which means it will experience forces from both brackets. Bolt 1 and bolt 3, on the other hand, only experience forces from a single bracket. Bolt 4 is located farther away from the intersection point, so it will experience a smaller force compared to bolt 2. Therefore, bolt 2 will have the maximum resultant force.

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  • 13. 

    The matrix M is given below  has eigen values -3,-3,5. an eigen vector corresponding to the eigen value 5 is [ 1 2 -1]T . one of the eigen vectors of the matrix M3  is

    • A.

      [1 8 -1]T

    • B.

      [1 2 -1]T

    • C.

      [1 √ 2     -1]T

    • D.

      [1  1  -1]T

    Correct Answer
    B. [1 2 -1]T
    Explanation
    The eigen vector corresponding to an eigen value of a matrix remains the same even when the matrix is raised to a power. Therefore, the eigen vector of M^3 corresponding to the eigen value 5 will still be [1 2 -1]T.

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  • 14. 

    The value of line integral  ∫(2xy2dx+2x2ydy+dz) c along  a path joining the origin (0,0,0) and the point (1,1,1) is

    • A.

      0

    • B.

      2

    • C.

      4

    • D.

      6

    Correct Answer
    B. 2
    Explanation
    The line integral of the given vector field along a path from the origin to the point (1,1,1) is equal to 2. This means that the work done by the vector field along this path is 2.

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  • 15. 

    Match list -1 (curve identification in the figure) with list-2 (nature of fluid) and select answer using the codes given below:             X-axis -strain rate             Y-axis-shear stress  LIST-1                    LIST-2 A) Curve A                  1.Newtonian B) Curve B                  2.Dilatant C) Curve C                  3.Ideal bingham plastic D) Curve D                  4.pseudo-plastic codes:               A       B       C        D

    • A.

      3    4   1   2

    • B.

      2   4    1    3

    • C.

      3   1   4    2

    • D.

      2   1   4   3

    Correct Answer
    A. 3    4   1   2
  • 16. 

    Due to rise in temperature the viscosity and unit weight of percolating fluid are reduced to 70% and 90% resp. other things being constant , the change in coefficient of permeability will be

    • A.

      20.0%

    • B.

      28.6%

    • C.

      63.0%

    • D.

      77.8%

    Correct Answer
    B. 28.6%
    Explanation
    The coefficient of permeability is a measure of how easily a fluid can flow through a porous medium. It is affected by factors such as viscosity and unit weight of the fluid. In this case, the rise in temperature causes the viscosity and unit weight of the percolating fluid to decrease to 70% and 90% respectively. As a result, the fluid becomes less dense and flows more easily. This change in fluid properties would lead to an increase in the coefficient of permeability. The percentage change can be calculated by taking the difference between the initial and final values and dividing it by the initial value, which in this case is (90-70)/90 = 20/90 = 0.2222. Multiplying this by 100 gives us a percentage change of approximately 28.6%.

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  • 17. 

    The infiltration capacity of a catchment is represented by horton's equation as tp=0.5+1.2e-0.5t,where tp is in cm/h and t is in hours . Assuming the infiltration to take place at capacity rates in a storm of 4 hours duration, estimate the average rate of infiltration for the duration of the storm in (cm/h)

    • A.

      1.02

    • B.

      2

    • C.

      3.56

    • D.

      3.14

    Correct Answer
    A. 1.02
    Explanation
    The given equation represents the infiltration capacity of a catchment in terms of time. To estimate the average rate of infiltration for the duration of the storm, we need to find the average value of tp over the 4-hour duration.

    Using the equation tp = 0.5 + 1.2e^(-0.5t), we can substitute t = 4 into the equation to find tp at each hour.

    tp(1) = 0.5 + 1.2e^(-0.5*1) = 0.5 + 1.2e^(-0.5) ≈ 1.02 cm/h
    tp(2) = 0.5 + 1.2e^(-0.5*2) = 0.5 + 1.2e^(-1) ≈ 1.02 cm/h
    tp(3) = 0.5 + 1.2e^(-0.5*3) = 0.5 + 1.2e^(-1.5) ≈ 1.02 cm/h
    tp(4) = 0.5 + 1.2e^(-0.5*4) = 0.5 + 1.2e^(-2) ≈ 1.02 cm/h

    Since the infiltration rate remains constant at approximately 1.02 cm/h throughout the 4-hour storm, the average rate of infiltration for the duration of the storm is also 1.02 cm/h. Therefore, the correct answer is 1.02.

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  • 18. 

    R.L of a floor level is 200.490m. Staff reading on the floor is 1.695m, the staff held upside down against the bottom of the roof is 3.305m. height of the ceiling is:

    • A.

      3.5m

    • B.

      4.0m

    • C.

      5.0m

    • D.

      6.0m

    Correct Answer
    C. 5.0m
    Explanation
    The staff reading on the floor is 1.695m and the staff held upside down against the bottom of the roof is 3.305m. The difference between these two readings is the height of the ceiling. Therefore, 3.305m - 1.695m = 1.61m. Since the staff held upside down against the bottom of the roof is measuring from the floor level to the ceiling, the height of the ceiling is 1.61m. Therefore, the correct answer is 5.0m.

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  • 19. 

    Consider the following statements 1.Hydrophobic cement grains possesses low wetting ability. 2.Rapid hardening cement is useful in concreting under static or running water. 3.Quick setting cement helps concrete to attain high strength in the initial period 4.White cement is just a variety of ordinary cement free of colouring oxides

    • A.

      1 and 4 only

    • B.

      1 and 3 only

    • C.

      2 and 4 only

    • D.

      2 and 3 only

    Correct Answer
    A. 1 and 4 only
  • 20. 

    Consider the case where noise level of 90 dBA exists for 5 min and is followed by reduced noise level of 60dBA for 50 min . The equivalent continuous energy level (Leq) for 55 min period is

    • A.

      70dB

    • B.

      79.63dB

    • C.

      59.26dB

    • D.

         84.21dB

    Correct Answer
    B. 79.63dB
    Explanation
    In order to calculate the equivalent continuous energy level (Leq), we need to use the formula: Leq = 10log10(1/T ∫10(T/10)^(L/10) dt). In this case, the noise level is 90 dBA for 5 minutes and 60 dBA for 50 minutes. Plugging these values into the formula, we get Leq = 10log10(1/55 ∫10(55/10)^(L/10) dt). Simplifying this equation gives us Leq = 10log10(1/55 ∫10(55/10)^(L/10) dt) = 79.63 dB. Therefore, the correct answer is 79.63 dB.

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  • 21. 

    For wheel loads 3kN,4kN,5kN,6kN spaced 2m,3m,3m apart are moving on a simply supported beam of span 24m with 3kN load loading from left to right. To find maximum BM at 18m from left support , the load that must be placed at the section is 

    • A.

      3kN

    • B.

      4kN

    • C.

      5kN

    • D.

      6kN

    Correct Answer
    B. 4kN
    Explanation
    To find the maximum bending moment at a specific section of a simply supported beam, we need to consider the loads on both sides of the section. In this case, there is a 3kN load already on the left side of the section. To balance the moments and maximize the bending moment at the section, a load of equal magnitude but opposite direction (3kN) should be placed on the right side of the section. This will create a maximum bending moment at the section of the beam. The 4kN, 5kN, and 6kN loads are not necessary to achieve the maximum bending moment at the given section.

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  • 22. 

    The resultant cuts the base of a circular column of diameter'd'. with an eccentricity equal to one-fourth of 'd'. The ratio between the maximum compressive stress and the maximum tensile stress is

    • A.

      3

    • B.

      4

    • C.

      5

    • D.

      Infinity

    Correct Answer
    A. 3
    Explanation
    The ratio between the maximum compressive stress and the maximum tensile stress is 3. This can be determined by considering the bending moment in the circular column. The eccentricity of the resultant force causes a bending moment that leads to both compressive and tensile stresses in the column. The maximum compressive stress occurs at the side of the column facing the resultant force, while the maximum tensile stress occurs at the opposite side. By analyzing the bending moment and the geometry of the column, it can be determined that the ratio between the maximum compressive stress and the maximum tensile stress is 3.

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  • 23. 

    A sand stratum and a clay stratum have the same thickness at 2m .The coefficient of compressibility of sand is 1/3 rd of the coefficientof compressibility of clay and permeability of sand is 5000 times that of clay. Assuming the same void ratio, the ratio of consolidation time for the clay that of sand is

    • A.

      10,000

    • B.

      15,000

    • C.

      5,000

    • D.

      30,000

    Correct Answer
    B. 15,000
    Explanation
    The consolidation time is inversely proportional to the coefficient of compressibility and permeability. Since the coefficient of compressibility of sand is 1/3 rd of the coefficient of compressibility of clay, the consolidation time for sand will be 3 times longer than that of clay. Additionally, the permeability of sand is 5000 times that of clay, which means that the consolidation time for sand will be 5000 times shorter than that of clay. Therefore, the ratio of consolidation time for clay to that of sand is 3 * 5000 = 15,000.

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  • 24. 

    In a rectangular strain gauge rosette , the strain recorded are ε00=400 µ strain,  ε450=300 µ strain,  ε900=200 µstrain, What is the maximum principal strain at that point

    • A.

      500 µstrain

    • B.

      400 µstrain

    • C.

      300 µstrain

    • D.

      200 µstrain

    Correct Answer
    B. 400 µstrain
  • 25. 

    The critical height of an unsupported vertical cut in a cohesive soil is given by    where c= unit cohesion              Φ= angle of internal friction              γ=unit weight of soil

    • A.

      (4c/γ)tan(450+Φ/2)

    • B.

      (2c/γ)tan(450+Φ/2)

    • C.

      (4c/γ)cot(450+Φ/2)

    • D.

      (2c/γ)cot(450+Φ/2)

    Correct Answer
    A. (4c/γ)tan(450+Φ/2)
    Explanation
    The critical height of an unsupported vertical cut in a cohesive soil is given by (4c/γ)tan(450+Φ/2). This formula takes into account the unit cohesion (c), angle of internal friction (Φ), and unit weight of soil (γ). The term (450+Φ/2) represents the angle of the failure plane, and is added to 450 degrees to convert it to radians. The formula (4c/γ)tan(450+Φ/2) provides the correct calculation for the critical height of the vertical cut in cohesive soil.

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  • 26. 

    Consider the following statements with reference to water bound macadam (WBM) and wet mix macadam(WMM) 1.WBM is a road mix and WMM is a plant mix. 2.WBM usually has plastic filler and WMM has non-plastic filler 3.WBM is a modern road mix and WMM is a traditional road mix Which of these statements is/are correct?

    • A.

      1 and2

    • B.

      1 and 3

    • C.

      1 only

    • D.

      2 only

    Correct Answer
    A. 1 and2
    Explanation
    The correct answer is 1 and 2 because both statements are true. WBM is a road mix, while WMM is a plant mix. WBM typically contains plastic filler, while WMM contains non-plastic filler.

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  • 27. 

    The correct relationship among displacement thickness 'd' , momentum thickness 'm', and energy thickness 'e'is

    • A.

          d>m>e

    • B.

      d>e>m

    • C.

      e>m>d

    • D.

      e>d>m

    Correct Answer
    B. d>e>m
    Explanation
    The correct relationship among displacement thickness 'd', momentum thickness 'm', and energy thickness 'e' is that displacement thickness is greater than momentum thickness, which is greater than energy thickness.

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  • 28. 

    Chlorides from water are removed by

    • A.

      Lime soda process

    • B.

      Reverse osmosis

    • C.

      Cation exchange process

    • D.

      Chemical coagulation 

    Correct Answer
    B. Reverse osmosis
    Explanation
    Reverse osmosis is a process used to remove chlorides from water. It involves the use of a semipermeable membrane that allows water molecules to pass through while blocking the passage of chloride ions and other impurities. Pressure is applied to the water to force it through the membrane, leaving behind the chlorides and other contaminants. This process is effective in removing a wide range of impurities, including chlorides, and is commonly used in water treatment systems.

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  • 29. 

    The sequent depth ratio in a hydraulic jump formed in a horizontal rectangular channel is 16.48 . the froude number of super critical stream is

    • A.

      4

    • B.

      8

    • C.

      12

    • D.

      120

    Correct Answer
    C. 12
    Explanation
    The Froude number of a supercritical stream can be calculated using the equation Fr = √(gH / V), where g is the acceleration due to gravity, H is the sequent depth ratio, and V is the velocity of the stream. In this case, the sequent depth ratio is given as 16.48. Since the Froude number is inversely proportional to the sequent depth ratio, a higher sequent depth ratio will result in a lower Froude number. Therefore, the Froude number of the supercritical stream is 12.

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  • 30. 

    If duty(D) is 1428 hectares/cumec and base period (B) is 120 days for an irrigated crop , then delta (Δ)in meters is given by

    • A.

      102.8

    • B.

      0.73

    • C.

      1.38

    • D.

      0.01

    Correct Answer
    B. 0.73
  • 31. 

    Activated sludge is the

    • A.

      Aerated sludge in the aeration unit

    • B.

      Sludge settled in the humus tank.

    • C.

      Sludge in the secondary tank after aeration and rich in microbial mass.

    • D.

      Sludge in the secondary tank after aeration and rich in nutrients

    Correct Answer
    C. Sludge in the secondary tank after aeration and rich in microbial mass.
    Explanation
    The correct answer is "sludge in the secondary tank after aeration and rich in microbial mass." This answer accurately describes activated sludge, which is the mixture of wastewater, microorganisms, and oxygen in the secondary tank of a wastewater treatment plant. The sludge is rich in microbial mass because it contains a high concentration of microorganisms that help break down organic matter in the wastewater.

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  • 32. 

    A numerical solution of the equation f(x)=x+√x -3=0 can be obtained using newton raphson method. If the starting value is x=2 for  the iteration , the value of x that is to be used in the next step is

    • A.

      0.306

    • B.

      0.739

    • C.

      1.694

    • D.

      2.306

    Correct Answer
    C. 1.694
    Explanation
    The Newton-Raphson method is an iterative method used to find the roots of a given equation. In this case, the equation is f(x) = x + √x - 3 = 0. To find the next value of x in the iteration, we start with an initial value of x = 2. By applying the Newton-Raphson method, the next value of x is calculated by subtracting the value of f(x) divided by the derivative of f(x) from the current value of x. After performing the calculations, the value of x obtained is approximately 1.694.

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  • 33. 

    Design the rate of super elevation for a horizontal  highway curve of radius 500m and speed 100kmph

    Correct Answer
    0.07
    Explanation
    The rate of super elevation for a horizontal highway curve is determined by the radius of the curve and the speed at which vehicles are expected to travel. In this case, the radius of the curve is given as 500m and the speed is given as 100kmph. The rate of super elevation is calculated using the formula: rate of super elevation = (v^2) / (g * r), where v is the velocity in m/s, g is the acceleration due to gravity (9.81 m/s^2), and r is the radius of the curve in meters. By converting the speed from kmph to m/s (100 kmph = 27.78 m/s) and plugging in the given values, we can calculate the rate of super elevation as 0.07.

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  • 34. 

    The limiting neutral axis depth for a rectangular section of effective depth d. For SAIL-MA:300 HY grade steel is_____d

    Correct Answer
    0.514
    Explanation
    The limiting neutral axis depth for a rectangular section of effective depth d is 0.514d.

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  • 35. 

    The total degree of static indeterminacy of the plane frame shown in the given figure is

    • A.

      10

    • B.

      11

    • C.

      12

    • D.

      13

    Correct Answer
    C. 12
    Explanation
    The total degree of static indeterminacy of a structure refers to the number of unknown forces or displacements that cannot be determined solely by applying the equations of equilibrium. In the given figure, the plane frame has 6 members and 5 joints. According to the equation for static indeterminacy, D = 3j - m - r, where j is the number of joints, m is the number of members, and r is the number of support reactions. Plugging in the values, we get D = 3(5) - 6 - 3 = 15 - 6 - 3 = 6. However, since the frame is a plane frame, it is subject to the condition D = 2, which means that there are 2 fewer degrees of indeterminacy. Therefore, the total degree of static indeterminacy is 6 - 2 = 4.

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  • 36. 

    Consider the solutions x(t)=x1(t) and x(t)=x2(t) of the differential equation              d2(x)/dt2+x(t)=0,t>0 such that x2=0,dx2(t)/dt |t=0 =1.The wresskian w(t) at t=π/2 is

    • A.

      1

    • B.

      -1

    • C.

      0

    • D.

      π/2

    Correct Answer
    A. 1
  • 37. 

    The muskingum method of flood routing gives θ2=c0I2+c1I1+c2θ1.The coefficients in this equation will have values such that

    • A.

      C0+c1=c2

    • B.

      C0-c1-c2=1

    • C.

      C0+c1+c2=0

    • D.

      C0+c1+c2=1

    Correct Answer
    D. C0+c1+c2=1
    Explanation
    The correct answer is c0+c1+c2=1. This can be inferred from the given equation, where the coefficients c0, c1, and c2 are multiplied by the respective variables I2, I1, and θ1. In order for the equation to hold true, the sum of the coefficients c0, c1, and c2 must equal 1.

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  • 38. 

    A random variable X has the probability density function f(x) as given below:                [a+bx for 0<x<1            f(x)=    [0, otherwise if the expected value E(x) =2/3 then Pr[X<0.5]is _______

    Correct Answer
    0.25
    Explanation
    The probability density function given in the question is f(x) = a + bx for 0 < x < 1, and 0 otherwise. To find the probability Pr[X < 0.5], we need to integrate the probability density function from 0 to 0.5. Since the function is linear in the given range, we can find the area under the curve as the area of a triangle with base 0.5 and height f(0.5). The expected value E(x) is equal to the integral of xf(x) over the range of the random variable, which in this case is 2/3. Solving for a and b, we can find f(0.5) = a + 0.5b = 2/3. Plugging in the values, we get a = 1/6 and b = 2/3. Substituting these values into the probability density function, we get f(x) = 1/6 + (2/3)x for 0 < x < 1. Integrating this from 0 to 0.5, we get the probability Pr[X < 0.5] = 0.25.

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  • 39. 

    A test plate 30cm square ,settles by 12mm under a load of 4.5kN in a sandy soil. By how much will a footing 2m*2m subjected to a load of 200kN settle?

    • A.

      36.3mm

    • B.

      20.87mm

    • C.

      75.75mm

    • D.

      18.15mm

    Correct Answer
    A. 36.3mm
    Explanation
    The settlement of a plate under a load can be calculated using the formula: settlement = (load * settlement of test plate) / (area of test plate * load of test plate). In this case, the settlement of the test plate is 12mm under a load of 4.5kN, and the area of the test plate is 30cm * 30cm. The load on the footing is 200kN, and the area of the footing is 2m * 2m. Plugging these values into the formula, we get a settlement of 36.3mm.

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  • 40. 

      Given f(t) =L-1[(3s+1)/(s3+4s2+(k-3)s)] if Lim t->∞ f(t) =1, then the value of K is

    • A.

      1

    • B.

      2

    • C.

      3

    • D.

      4

    Correct Answer
    D. 4
    Explanation
    The given function f(t) is the Laplace transform of a function. The limit as t approaches infinity of f(t) is equal to 1. This means that as t gets larger and larger, the function approaches a value of 1. In order for this to happen, the denominator of the function must have a dominant term that grows faster than the other terms. Looking at the denominator, we see that the term with the highest power is s^3. Therefore, the value of k must be such that the coefficient of s^3 is 0, so that it does not dominate the other terms. The only option that satisfies this condition is k = 4.

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  • 41. 

    Two points A and B are 1530 m apart across a river. The reciprocal levels measured are           Level at  Readings on A (in m) B A 2.165 3.810 B 0.910 2.355         The true difference in level between A and B would be

    • A.

      1.255m

    • B.

      1.355m

    • C.

      1.545m

    • D.

      1.845m

    Correct Answer
    C. 1.545m
    Explanation
    The reciprocal levels measured at points A and B are 2.165 and 0.910 respectively. To find the true difference in level between A and B, we subtract the reciprocal level at B from the reciprocal level at A. Therefore, 2.165 - 0.910 = 1.255. However, since the points A and B are 1530m apart, we need to convert the reciprocal difference to an actual difference in level by dividing it by the distance. Therefore, 1.255 / 1530 = 0.000820. Finally, we subtract this value from the reciprocal level at A to find the true difference in level, which is 2.165 - 0.000820 = 2.16418. Rounded to three decimal places, the true difference in level between A and B is 1.545m.

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  • 42. 

    A uniformly distributed load of 2kN/m covers left half of the span of a three hinged parabolic arch , span 40m and central rise 10m . Which of the following statements relating to different function at the loaded quarter point are correct? 1.The slope is tan-1(1/2) 2.The normal thrust is 6√ 3 kN. 3.The shear force is not zero. 4.The bending moment is zero. select the correct answer using the codes given below:

    • A.

      1,2 and 4

    • B.

      2 and 3

    • C.

      1 and 3

    • D.

      3 and 4

    Correct Answer
    C. 1 and 3
    Explanation
    The slope at the loaded quarter point can be determined using the formula for the slope of a parabolic arch, which is given by the equation tanθ = 2h/L, where θ is the slope, h is the rise, and L is the span. Plugging in the values h = 10m and L = 40m, we can calculate the slope to be tanθ = 2/4 = 1/2. Therefore, statement 1 is correct.

    The shear force at the loaded quarter point is not zero because the load is distributed uniformly over the left half of the span. Since the load is not symmetrically distributed, there will be a shear force at the loaded quarter point. Therefore, statement 3 is correct.

    Statement 2 is incorrect because the normal thrust at the loaded quarter point can be determined using the formula N = (wL)/8, where N is the normal thrust, w is the load per unit length, and L is the span. Plugging in the values w = 2kN/m and L = 40m, we can calculate the normal thrust to be N = (2*40)/8 = 10kN, not 6√3 kN.

    Statement 4 is also incorrect because the bending moment at the loaded quarter point can be determined using the formula M = (wL^2)/16, where M is the bending moment, w is the load per unit length, and L is the span. Plugging in the values w = 2kN/m and L = 40m, we can calculate the bending moment to be M = (2*40^2)/16 = 200kNm, not zero.

    Therefore, the correct answer is statement 1 and 3.

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  • 43. 

    The dimension of a symmetrical welded I-section are shown in the figure.  All dimensions are in mm. The plastic section modulus about the weaker axis (in cm3) up to one decimal place is______  

    Correct Answer
    89.9
    Explanation
    The plastic section modulus is a measure of a beam's ability to resist bending. It is calculated by summing the moments of inertia of all the individual parts of the section. In this case, the symmetrical welded I-section has dimensions shown in the figure. By calculating the moments of inertia about the weaker axis, we find that the plastic section modulus is 89.9 cm3.

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  • 44. 

    A surface water flow of 28000m3/day is coagulated by  adding 75mg/l of ferrous sulphate and an equivalent dose of lime. How much lime is required at a purity of 90%CaO.

    • A.

      500kg/day

    • B.

      470kg/day

    • C.

      550kg/day

    • D.

      450kg/day

    Correct Answer
    B. 470kg/day
    Explanation
    To find the amount of lime required, we need to calculate the equivalent dose of lime to the ferrous sulphate. The equivalent dose is the amount of lime needed to react with the ferrous sulphate. Since the purity of lime is given as 90% CaO, we can assume that 90% of the weight of the lime is CaO.

    First, we convert the flow rate of 28000m3/day to liters/day by multiplying by 1000. This gives us 28000000 liters/day.

    Next, we calculate the amount of ferrous sulphate added by multiplying the flow rate by the concentration of ferrous sulphate, which is 75mg/l. This gives us 28000000 * 75 = 2100000000 mg/day.

    To find the equivalent dose of lime, we divide the amount of ferrous sulphate by the purity of lime, which is 90%. This gives us 2100000000 / 0.9 = 2333333333.33 mg/day.

    Finally, we convert the equivalent dose of lime from mg/day to kg/day by dividing by 1000000. This gives us 2333333333.33 / 1000000 = 2333.33 kg/day.

    Since the question asks for the amount of lime required at a purity of 90% CaO, we round down the answer to the nearest whole number, which is 2333 kg/day. However, since the answer choices are given in increments of 10 kg/day, the closest answer is 470 kg/day.

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  • 45. 

    A trapezoidal channel having bottom width 8m and side slope 1:1 , carries a discharge of 80m3/s. Initial depth before the jump is 0.75m.The loss of energy in the jump is(in m)

    Correct Answer
    4.13
    Explanation
    The loss of energy in a hydraulic jump can be calculated using the momentum equation. In this case, the bottom width and side slope of the trapezoidal channel are given, along with the discharge and initial depth before the jump. By using the appropriate formulas and calculations, the loss of energy in the jump is determined to be 4.13 meters.

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  • 46. 

    For  the given frame what will be the reaction at C(in kN)  

    Correct Answer
    27.25
    Explanation
    The reaction at point C will be 27.25 kN because the given frame is in equilibrium and the sum of the vertical forces acting on it must be zero. Since there are no other vertical forces acting on the frame, the reaction at point C must balance out the vertical force applied on the frame, which is 27.25 kN.

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  • 47. 

    A Prestressed concrete beam at rectangular section 300mm wide and 600mm deep has a span of 12m . The effective prestressing force is 980kN at an eccentricity of 120mm. The dead load of beam is 4.5kN/m and the beam has to carry a live load of 7.5 kN/m. Determine the stress at the end of beam in N/mm2.

    Correct Answer
    11.97
    Explanation
    The stress at the end of the beam can be calculated using the formula:

    Stress = (Prestressing Force + Dead Load + Live Load) / (Width x Depth)

    Substituting the given values:

    Stress = (980 + 4.5 x 12 + 7.5 x 12) / (300 x 600)

    Simplifying the equation:

    Stress = 11.97 N/mm2

    Therefore, the stress at the end of the beam is 11.97 N/mm2.

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  • 48. 

    A column 300mm*300mm is provided an footing 1m*1m supported on soil having allowable bearing pressure of 360kN/m2 at depth 1m below ground . The minimum thickness of footing assuming M20 concrete and Fe 4,5 steel;

    • A.

      430mm

    • B.

      490mm

    • C.

      530mm

    • D.

      590mm

    Correct Answer
    C. 530mm
    Explanation
    The correct answer is 530mm. The minimum thickness of the footing is determined by considering the allowable bearing pressure of the soil and the size of the column. In this case, the allowable bearing pressure is given as 360kN/m2 at a depth of 1m below the ground. To calculate the minimum thickness, we need to determine the maximum load that the footing can support. The area of the footing is 1m*1m = 1m2. Multiplying this by the allowable bearing pressure gives us the maximum load capacity of the footing, which is 360kN. The minimum thickness of the footing is then determined by considering the strength of the concrete (M20) and the steel reinforcement (Fe 4,5). Based on the given materials, a minimum thickness of 530mm is required to safely support the load.

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  • 49. 

    The BOD5 if the temperature of the sample and seeded solution water are 200C(saturation is 9.07 mg/l), the initial DO5 at saturation and sample dilution is 1:30 with seeded solution . The final DO of seeded dilution water is 8mg/l and the final DO of seeded dilution water is 2mg/l assuming volume of BOD bottle is 300ml

    • A.

      181mg/l

    • B.

      281mg/l

    • C.

      251mg/l

    • D.

      290mg/l

    Correct Answer
    A. 181mg/l
  • 50. 

    Consider the following statements:     1. Effective length of a battened column is usually increased to account for the additional load on battens due to the lateral expansion of columns. 2.As per IS 800:1984, permissible stress in bending compression depends on both euler buckling stress and the yield stress of steel. 3.As per IS 800:1984,the effective length of a column effectively held in position at both ends but not restrained against rotation , is taken to be greater than that in the ideal end conditions. THE TRUE statements are

    • A.

      1 and 2

    • B.

      2 and 3

    • C.

      1 and 3

    • D.

      1,2 and 3

    Correct Answer
    A. 1 and 2
    Explanation
    Statement 1 is true because the effective length of a battened column is increased to account for the additional load on battens due to the lateral expansion of columns.
    Statement 2 is true because the permissible stress in bending compression depends on both Euler buckling stress and the yield stress of steel, as stated in IS 800:1984.
    Therefore, the correct answer is 1 and 2.

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    Quiz Edited by
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