Cea GATE Series Quiz: Exam!

1. The closing error in a closed loop traverse of 500 m total length is 0.289 m, then the relative precision of this traverse will be

1 : 1560

1 : 1730

1 : 2170

1 : 1910

2. Let y(x) be the solution of the initial value problem = x and y(0) = 0. Find the value of (Correct up to 2 decimal places).

0.3

0.32

0.6

1.24

3. value of b = ?

0

E

1

None

4. Choose the most approximate word from the options given below to complete the following sentence. If I had known that you were coming, I _______ you at the airport.

Would meet

Would have met

Will have met

Had met

5. Pervious sand having an air content of 15% is used in the foundation of a masonry dam. If the maximum permissible upward gradient for a factor of safety of 3 against boiling is 0.315. The percentage of air voids in the pervious sand will be ______ %.

6

6.4

6.8

7

6. The integrating factor of equation y log y dx + (x – log y) dy = 0 is

Log x

Log y

Log (log x)

Log (log y)

7. Consider the following function: f(x) at x=2 is

Continuous and differentiable

Continuous but not differentiable

Differentiable but not continuous

Neither continuous nor differentiable

8. If n and y are positive integers and 450 y = n³, which of the following must be an integer?

None of these

9. For the state of stress (MPa) shown in the figure below. The ratio of Major principal stress to minor principal stress will be _____ (up to two decimal places)

2.6

5.2

1.3

0

10. For which value of x, the following matrix A is a singular matrix.

1

-1

2

3

11. In a catchment, there are five rain gauge stations A, B, C, D, and E are located on a circular shape basin of a diameter of 24 km as shown in the figure below. If the rainfall at station A, B, C, D, and E in the month of August is 250 cm, 200 cm, 225 cm, 240 cm, and 210 cm respectively, then the average rainfall (in m, up to two decimal place) over the catchment in the month of August will be __________.

0.2

0.23

0.25

0.27

12. Choose the most approximate word from the options given below to complete the following sentence. I believe in the _____ of positive thinking thus always recommend these books to my clients.

Power

Powers

Powerful

Empowering

13. Consider a circle of radius r. Fit the largest possible square inside it and the largest possible circle inside the square. What is the radius of the innermost circle?

R/2

14. A water sample analysis produces alkalinity and hardness of 200 mg/L and 250 mg/L as Caco₃ respectively. The carbonate and non-carbonate hardness respectively will be

200 mg/L and 50 mg/L

200 mg/L and 0 mg/L

250 mg/L and 50 mg/L

250 mg/L and 0 mg/L

15. 2000 cashew nuts are mixed thoroughly in flour. The entire mixture is divided into 1000 equal parts. And each part is used to make 1 biscuit. Assume that no cashews are broken in the process. A biscuit is picked at random. The probability it contents no cashew is _____.

Between 0 and 0.1

Between 0.1 and 0.2

Between 0.2 and 0.3

Between 0.3 and 0.4

16. As per IS 10500:2012, the total concentration of manganese (as Mn) and iron (as Fe) for drinking water purpose shall not exceed

0.1 mg/L

0.2 mg/L

0.3 mg/L

0.5 mg/L

17. In order to prepare 50m³ Ready Mix concrete for a rigid pavement for a mix 1 : 3: 6 by weight, with water/cement ratio of 0.5 and unit weight of concrete as 2250 kg/m³, the amount of coarse aggregate (in tonnes) will be ______ .

20

22

28

32

18. As per IRC 37:2012, the design traffic in terms of the cumulative number of standard axis (in million standard axes, up to two decimal places) based on the below data will be_____. Initial traffic in the year of completion of construction = 4000 commercial vehicle per day (CPVD) Vehicular damage factor = 5 Lane distribution factor = 0.75 The annual rate of growth of commercial vehicle = 9% Design life = 12 years.

100

105

110

115

19. An I-section bean is fabricated with plates having an elastic section modulus of 200 m 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 (X_LT= 1.0)

400

450

500

550

20. The average surface area of a reservoir for a period of two months is 50 hectare-m. The difference of saturated vapour pressure and actual vapour pressure is 15 mm of Hg. If the wind velocity at a height of 9.0 m above the ground is 10m/s, then the daily average evaporation in (mm/day) from the reservoir will be (use k_m = 0.36)

15.55 mm/day

17.55 mm/day

20.55 mm/day

None

21. If the following formula is used for the numerical integration of a function f(x), then what should be the values of the constants a, b, c so that for f(x) = 1 or f(x) = x or f(x) = x², there is no error in the formula

22. The column vector is a simultaneous Eigen vector of and

B = 0 or a = 0

B = a or b = -2a

B = 2a or b = -a

B = a/2 or b = -a/2

23. Satisfy the assumption of Rolle's theorem in the interval [-1, 1], then ordered pair (p, q) is

(2, -1)

(-2, -1)

(-2, 1)

(2, 1)

24. A block of weight 50kN is supported by a rope that is wrapped one-and-one-half times around the circular shaft. If the coefficient of static friction between the rope and the shaft material is 0.15, then the largest possible value of P according to the figure (given below) will be ____x 10⁴ N.

21

22

23

24

25. The liquid limit and plastic limit of the soil is 55% and 25% respectively. If the natural water content of the soil is 30%. The correct statement is

Soil is in plastic stage of consistency with consistency index equal to 0.167

Soil is in plastic stage of consistency with liquidity index equal to 0.833.

Soil is in plastic stage of consistency with consistency index equal to 0.833

Soil is in liquid stage of consistency with ratio of consistency index to liquidity index equals to 1.

26. A completely saturated clay sample was tested in a UU test under a cell pressure of 250 kN/m² and the principal stresses at failure were noted as 350 kN/m² and 200 kN/m² respectively. If the effective shear strength parameters of this clay layer are c^I= 25 kN/m² and ɸ^I= 23°, the pore water pressure at failure will be _____ kN/m²

140

142

144

146

27. A hydraulically efficient trapezoidal section conveying a discharge of 210 m³/s. If the Froude number at a section is 0.489, the bed slope required will be? Assume the flow to be uniform and manning's roughness coefficient to be 0.017.

1 in 1483

1 in 73

1 in 2000

1 in 2500

28. For the Real Beam shown in the figure below, identify the correct conjugate beam

29. Find the laplace transform of t²sin (2t).

30. The graph shows cumulative frequency % of research scholars and the number of papers published by them. Which of the following statements is true?

Majority of the scholars published more than 4 paper

60% of the scholars published at least 2 papers

80% of the scholars published at least 6 papers

30% of scholars have not published only paper

31. Read the following passage and find out the inference stated through passage. Juvenile delinquency is also termed as Teenage Crime. Basically, juvenile delinquency refers to the crimes committed by minors. These crimes are committed by teenagers without any prior knowledge of how it affects the society. These kind of crimes are committed when children do not know much about outside world. Which of the following Inferences is correct with respect to above passage?

These crimes are fuelled with bad knowledge imparted in schools.

These crimes are committed by teenagers with proper knowledge of its consequences.

Teenagers who commit crimes should be detained for crime just as any grown human would be

32. Select the pair that best expresses a relationship similar to that expressed in the pair: Horse: Foal

Deer: Doe

Goose: Gosling

Hen: Rooster

Fox: Vixen

33. Consider the following statement about the municipal solid waste: P. If it is assumed that air contains 23.15 percent oxygen by mass, then the amount of air required for the complete oxidation of 1 kg of carbon would be equal to 11.25kg. Q. The anaerobic digestion will require an optimum C/N ratio of about 30 – 50. R. Pulverization refers to the action of cutting and tearing, whereas shredding refers to the action of crushing and grinding. S. Electrostatic precipitator is also installed in the incineration plant to reduce air pollution, particularly due to the emission of dioxin. T. Pyrolysis is highly exothermic in nature and hence also known as destructive distillation. Which one of the following options is correct?

P – False: Q – False: R – True: S – True: T - True

P – True: Q – True: R – False: S – True: T – False

P – False: Q – True: R – False: S – False: T – True

P – False: Q – True: R – True: S – True: T – False

34. A vertical cut is made in pure saturated clay having undrained shear strength of 150 kN/m² (consider smooth vertical back). How much actual height (m) of this vertical cut be made such that there is a 400% factor of safety against shear failure. Take γ_sat of clay = 19 kN/m³.

6.895

7.895

8.895

9.895

35. A 25 cm long rod of uniform rectangular section of size 10 mm (wide) and 1.4 mm thickness is bend to form an arc of a circle. If the longitudinal strain at the surface of the rod is 0.00084, the central displacement of the rod will be _____ mm. Neglect second order quantities

9

9.3

9.5

9.8

36. A layer of normally consolidated clay of thickness 1.5 m is undergoing one-dimensional consolidation under a pressure increment of 30 kPa. If the final primary consolidation settlement (mm) by using Terzaghi's theory is 20 mm, the initial effective stress within the soil layer will be ______ kN/m². Assume the following soil properties: initial void ratio (e₀) = 1.345. Compression index (C_c) = 0.40.

150

153

160

163

37. Choose the most appropriate words from the options given below to fill in the blanks. She was __ to travel abroad and _ in the field of commerce as per her wishes.

Eager, cease

Restive, oppose

Elated, venture

Jinxed, rest

38. A bird files along the three sides of a field in the shape of an equilateral triangle at speeds of 3, 6, 8 km/hr respectively. The average speed of the bird is

39. While recording sound level two reading has been taken at a site within an hour. 80 dB noise lasting for 40 minutes is followed by 100 dB noise lasting for 20 minutes. The L_equivalentof the above noise levels (in dB) will be ______.

89

91

93

95

40. A flocculation chamber 50m long, 15 m wide, and 5m deep is to treat 250 MLD of water. It is equipped with 18m long and 0.45m wide paddles. The tank contains 2500m³ of water which is mixed using paddles at an average velocity gradient of 106/second. If the kinematic viscosity of water at 28° C temperature is 8.9 m 10^-7m²/s, then the power required (in kW, up to two decimal place) to achieve adequate mixing will be ________.

0.24

0.48

0.96

1

41. In a 1600 m race around a circular track of length 400 m, the faster runner and the slowest runner meet at the end of the sixth minute, for the first time after the start of the race. All the runners maintain uniform speed throughout the race. If the faster runner runs at twice the speed of the slowest runner. Find the time taken by the faster runner to finish the race.

3 minutes

6 minutes

12 minutes

24 minutes

42. Consider the following statements and Identify the correct option with regard to provisions of IS 456: 2000: P. The minimum stripping time for props to slab spanning over 4.5 m is 7 days Q. The minimum stripping time for props to arches spanning over 6 m is 14 days. R. To ensure strength of Designed concrete mix, Random sampling procedure is adopted S. When bar of two different diameter are to be spliced, the lap length shall be calculated on the basis of bar of the larger diameter.

P – True Q – True R – True S – False

P – False Q – False R – True S – True

P – False Q – True R – True S – True

P – False Q – False R – True S – False

43. A rapid sand filter with an area of filter 200m² is used to process the water for a town with a population of 10 million. The rate of filtration of the filter is 25 m³/m²/hour. The porosity of the bed and specific gravity of the material used in the bed are 0.42 and 2.72 respectively. If the bed is expanded to 0.75 m from its original undisturbed depth of 0.675 m, then the head loss in (mm) due to expanded bed will be________.

660

670

680

690

44. For a truss shown in figure below. Find the force in the member GC ______ kN.

0 kN

10 kN(compressive)

20 √2 kN (tensile)

20 kN (compressive)

45. A plate load test is carried out on a 40 cm m 40 cm square plate which is placed at a depth of 3m below the ground surface. Consider the soil strata below the ground surface which are extended up to great depth. Further, the data obtained from the above test is The settlement of a foundation of size 2.5m m 2.5m carrying a load of 1600 kN located at a depth of 4m below ground surface is _____mm. Assume water table is a great depth below the Ground surface and a depth correction factor to be 0.88.

27

29

31

33

46. The velocity components in a two-dimensional flow are given as V = 4x⁴ – y² Identify the correct statement:

Flow is possible, irrotational and stream function does not exist

Flow is possible, irrotational and both stream function and potential function does not exist

Flow is possible, irrotational, stream function exist which is given by potential function exist

Flow is possible, irrotational, potential function exist which is given by stream function also exist

47. A tension member 1SLB 250 @ 273.7 N/m is connected with two 200 wide and 12 mm thick plate with two lines of 16 mm diameter bolt in each flange. If the net section area is 2800 mm² , then the tensile strength (in kN) on the basis of net area cracking of ISLB section using Fe 410 grade of steel will be _________. (Take Partial Safety Factor as 1.25)

725

825

925

None

48. A circular footing of diameter 4m is loaded with 200 kN/m² of load intensity. The vertical stress increment (kN/m²) at 6m depth below the footing will be?

15

30

60

120

49. A square footing of size 3m m 3m is placed at 2m depth below the Ground surface. If the permissible settlement of the foundation rests on sand strata is 40 mm and the final corrected S.P.T Number is 28. The net allowable bearing pressure from settlement consideration according to Peck, Hanson equation will be _____kN/m² Assume water table is at 1m below the base of the footing

265

300

350

365

50. For a construction project, PERT calculation yield a project duration of 50 weeks with a variance of 25 weeks. The probability of completion of the project in 63 weeks will be________%, using the below table.

97

98

99

100

51. A capillary rise in a glass tube when immersed in oil having surface tension 0.0825 N/m at 20° C and specific gravity of 0.96 is 6.25 mm. For 30% increase in height of capillarity, the diameter of glass tube should be decreased by ______ (percentage) Take angle of contact between glass tube and oil will be zero

20

23

26

29

52. A continuous beam ABC of two equal span AB and BC carries load of P at a distance 5 m from end C as shown in given figure. If the length of the beam and the moment carrying capacity of beam is 20 m and M_P then the collapse load P of the beam will be ______ M_P.

0.3

0.4

0.5

0.6

53. The ratio of average normal flow of traffic to the saturation flow in a two intersecting road P and Q are 0.3 and 0.25 respectively. If the total lost time per cycle is 11 seconds, then the optimum cycle length as per Webster's approach in seconds will be ________.

41 sec

43 sec

45 sec

47 sec

54. The ultimate BOD of waste water is 300 mg/L and the reaction rate constant (to the base 'e') at 20°C is 0.3585/day, then the 5 day BOD will be.

175 mg/L

50 mg/L

250 mg/L

200 mg/L

55. A hollow circular shaft of length 4 m is to transmit 500 kW of power at 350 rpm. If the maximum permissible shear stress developed in the shaft is limited to 70 Mpa, the maximum twist in the shaft will be _____ radian. (up to two decimal places.)The ratio of internal diameter to the external diameter of the shaft will be 0.75 and the shear modulus of the shaft maternal will be 90 Gpa.

0.01

0.02

0.05

0.08

56. As per IRC 37: 1984, the practical capacity values suggested for the purpose of design of two lane roads with 7.0 m wide carriageway and earthen shoulders in both direction is

2500 PCU per day

5000 PCU per day

10000 PCU per day

20000 PCU per day.

57. A simply supported rectangular prestressed concrete beam of span 9 m has to be prestressed with a force of 2000 kN. The profile of the cable is parabolic with zero eccentricity at ends. If the maximum dip (allowable) of the tendon at the mid-span to balance the external load is 0.18 m, the maximum uniformly distributed load (throughout the span) the beam can carry will be _____kN/m. (Neglect the self-weight of the beam).

30

35

20

25

58. In order to allow smooth movement of Locomotive with a maximum permissible speed of 120 kmph on a Broad Gauge track in transition curve, the radius of curvature by Martin's formula will be

786 m

687 m

575 m

638 m

59. The measured co-ordinates on the vertical photographs are X_a = +15.50 mm Y_a = -71.20 mm X_b = +109.20 mm Y_b = -25.20 mm The elevations of a and b are 502 m and 525 m respectively. If the flying height above the datum is 1670 m, the ground distance of a line AB will be ______ m. Assume focal length to be 158 mm.

700

760

800

860

60. A traffic survey is conducted on an intersection to compute practical capacity yields the following results: The width of the weaving section = 12m Length of the weaving section = 54 m The proportion of weaving traffic = 60% The average width of entry and exit = 8m The practical capacity (in-vehicle/hr) of the rotary on the basis of the above data will be

3000

3665

4125

5235

61. In an open traverse PQR. If the Bearing of the line PQ and RQ is 60° and N50° W respectively. The included angle ∠PQR will be

130°

180°

250°

110°

62. For specification of split spoon sampler one should follow:

IS 6403 – 1981

IS 4640 – 1980

IS 1892 – 1979

IS 2132 – 1972

63. A 10 m wide rectangular channel carries a distance of 22 m³/s at a depth of 1.2 m. The minimum height of the hump (in cm) required to be placed at a section to cause critical flow over the hump, neglecting energy loss will be

9

18

27

36

64. The specific gravity of the material of the dam is 2.65 and it is designed as an elementary profile with an uplift pressure coefficient of 0.5. If the height of the dam to be built is 45m, then the minimum width of the dam for no tension condition will be approximately

28 m

31 m

25 m

334 m

65. A rectangular block 6m long, 4m wide and 2m high is immersed in a oil of specific gravity 0.90. if the metacentric height for the stable equilibrium is 1.4m, then the depth of immersion of the rectangular block in a oil will be _____m. (up to two decimal places)

0.5

0.6

0.8

0.9

CEA GATE Series Quiz: Exam!

1. The closing error in a closed loop traverse of 500 m total length is 0.289 m, then the relative precision of this traverse will be

2.

What first name or nickname would you like us to use?

2. Let y(x) be the solution of the initial value problem = x and y(0) = 0. Find the value of (Correct up to 2 decimal places).

3. value of b = ?

4. Choose the most approximate word from the options given below to complete the following sentence. If I had known that you were coming, I _______ you at the airport.

5. Pervious sand having an air content of 15% is used in the foundation of a masonry dam. If the maximum permissible upward gradient for a factor of safety of 3 against boiling is 0.315. The percentage of air voids in the pervious sand will be ______ %.

6. The integrating factor of equation y log y dx + (x – log y) dy = 0 is

7. Consider the following function: f(x) at x=2 is

8. If n and y are positive integers and 450 y = n³, which of the following must be an integer?

9. For the state of stress (MPa) shown in the figure below. The ratio of Major principal stress to minor principal stress will be _____ (up to two decimal places)

10. For which value of x, the following matrix A is a singular matrix.

12. Choose the most approximate word from the options given below to complete the following sentence. I believe in the _____ of positive thinking thus always recommend these books to my clients.

13. Consider a circle of radius r. Fit the largest possible square inside it and the largest possible circle inside the square. What is the radius of the innermost circle?

14. A water sample analysis produces alkalinity and hardness of 200 mg/L and 250 mg/L as Caco3 respectively. The carbonate and non-carbonate hardness respectively will be

15. 2000 cashew nuts are mixed thoroughly in flour. The entire mixture is divided into 1000 equal parts. And each part is used to make 1 biscuit. Assume that no cashews are broken in the process. A biscuit is picked at random. The probability it contents no cashew is _____.

16. As per IS 10500:2012, the total concentration of manganese (as Mn) and iron (as Fe) for drinking water purpose shall not exceed

17. In order to prepare 50m3 Ready Mix concrete for a rigid pavement for a mix 1 : 3: 6 by weight, with water/cement ratio of 0.5 and unit weight of concrete as 2250 kg/m3, the amount of coarse aggregate (in tonnes) will be ______ .

21. If the following formula is used for the numerical integration of a function f(x), then what should be the values of the constants a, b, c so that for f(x) = 1 or f(x) = x or f(x) = x2, there is no error in the formula

22. The column vector is a simultaneous Eigen vector of and

23. Satisfy the assumption of Rolle's theorem in the interval [-1, 1], then ordered pair (p, q) is

24. A block of weight 50kN is supported by a rope that is wrapped one-and-one-half times around the circular shaft. If the coefficient of static friction between the rope and the shaft material is 0.15, then the largest possible value of P according to the figure (given below) will be ____x 104 N.

25. The liquid limit and plastic limit of the soil is 55% and 25% respectively. If the natural water content of the soil is 30%. The correct statement is

27. A hydraulically efficient trapezoidal section conveying a discharge of 210 m3/s. If the Froude number at a section is 0.489, the bed slope required will be? Assume the flow to be uniform and manning's roughness coefficient to be 0.017.

28. For the Real Beam shown in the figure below, identify the correct conjugate beam

29. Find the laplace transform of t2sin (2t).

30. The graph shows cumulative frequency % of research scholars and the number of papers published by them. Which of the following statements is true?

32. Select the pair that best expresses a relationship similar to that expressed in the pair: Horse: Foal

34. A vertical cut is made in pure saturated clay having undrained shear strength of 150 kN/m2 (consider smooth vertical back). How much actual height (m) of this vertical cut be made such that there is a 400% factor of safety against shear failure. Take γsat of clay = 19 kN/m3.

35. A 25 cm long rod of uniform rectangular section of size 10 mm (wide) and 1.4 mm thickness is bend to form an arc of a circle. If the longitudinal strain at the surface of the rod is 0.00084, the central displacement of the rod will be _____ mm. Neglect second order quantities

37. Choose the most appropriate words from the options given below to fill in the blanks. She was ______ to travel abroad and _____ in the field of commerce as per her wishes.

38. A bird files along the three sides of a field in the shape of an equilateral triangle at speeds of 3, 6, 8 km/hr respectively. The average speed of the bird is

39. While recording sound level two reading has been taken at a site within an hour. 80 dB noise lasting for 40 minutes is followed by 100 dB noise lasting for 20 minutes. The Lequivalent of the above noise levels (in dB) will be ______.

44. For a truss shown in figure below. Find the force in the member GC ______ kN.

46. The velocity components in a two-dimensional flow are given as V = 4x4 – y2 Identify the correct statement:

48. A circular footing of diameter 4m is loaded with 200 kN/m2 of load intensity. The vertical stress increment (kN/m2) at 6m depth below the footing will be?

50. For a construction project, PERT calculation yield a project duration of 50 weeks with a variance of 25 weeks. The probability of completion of the project in 63 weeks will be________%, using the below table.

52. A continuous beam ABC of two equal span AB and BC carries load of P at a distance 5 m from end C as shown in given figure. If the length of the beam and the moment carrying capacity of beam is 20 m and MP then the collapse load P of the beam will be ______ MP.

53. The ratio of average normal flow of traffic to the saturation flow in a two intersecting road P and Q are 0.3 and 0.25 respectively. If the total lost time per cycle is 11 seconds, then the optimum cycle length as per Webster's approach in seconds will be ________.

54. The ultimate BOD of waste water is 300 mg/L and the reaction rate constant (to the base 'e') at 20°C is 0.3585/day, then the 5 day BOD will be.

56. As per IRC 37: 1984, the practical capacity values suggested for the purpose of design of two lane roads with 7.0 m wide carriageway and earthen shoulders in both direction is

58. In order to allow smooth movement of Locomotive with a maximum permissible speed of 120 kmph on a Broad Gauge track in transition curve, the radius of curvature by Martin's formula will be

61. In an open traverse PQR. If the Bearing of the line PQ and RQ is 60° and N50° W respectively. The included angle ∠PQR will be

62. For specification of split spoon sampler one should follow:

63. A 10 m wide rectangular channel carries a distance of 22 m3/s at a depth of 1.2 m. The minimum height of the hump (in cm) required to be placed at a section to cause critical flow over the hump, neglecting energy loss will be

64. The specific gravity of the material of the dam is 2.65 and it is designed as an elementary profile with an uplift pressure coefficient of 0.5. If the height of the dam to be built is 45m, then the minimum width of the dam for no tension condition will be approximately

65. A rectangular block 6m long, 4m wide and 2m high is immersed in a oil of specific gravity 0.90. if the metacentric height for the stable equilibrium is 1.4m, then the depth of immersion of the rectangular block in a oil will be _____m. (up to two decimal places)

14. A water sample analysis produces alkalinity and hardness of 200 mg/L and 250 mg/L as Caco₃ respectively. The carbonate and non-carbonate hardness respectively will be

17. In order to prepare 50m³ Ready Mix concrete for a rigid pavement for a mix 1 : 3: 6 by weight, with water/cement ratio of 0.5 and unit weight of concrete as 2250 kg/m³, the amount of coarse aggregate (in tonnes) will be ______ .

21. If the following formula is used for the numerical integration of a function f(x), then what should be the values of the constants a, b, c so that for f(x) = 1 or f(x) = x or f(x) = x², there is no error in the formula

27. A hydraulically efficient trapezoidal section conveying a discharge of 210 m³/s. If the Froude number at a section is 0.489, the bed slope required will be? Assume the flow to be uniform and manning's roughness coefficient to be 0.017.

29. Find the laplace transform of t²sin (2t).

34. A vertical cut is made in pure saturated clay having undrained shear strength of 150 kN/m² (consider smooth vertical back). How much actual height (m) of this vertical cut be made such that there is a 400% factor of safety against shear failure. Take γ_sat of clay = 19 kN/m³.

37. Choose the most appropriate words from the options given below to fill in the blanks. She was __ to travel abroad and _ in the field of commerce as per her wishes.

39. While recording sound level two reading has been taken at a site within an hour. 80 dB noise lasting for 40 minutes is followed by 100 dB noise lasting for 20 minutes. The L_equivalentof the above noise levels (in dB) will be ______.

46. The velocity components in a two-dimensional flow are given as V = 4x⁴ – y² Identify the correct statement:

48. A circular footing of diameter 4m is loaded with 200 kN/m² of load intensity. The vertical stress increment (kN/m²) at 6m depth below the footing will be?

52. A continuous beam ABC of two equal span AB and BC carries load of P at a distance 5 m from end C as shown in given figure. If the length of the beam and the moment carrying capacity of beam is 20 m and M_P then the collapse load P of the beam will be ______ M_P.

63. A 10 m wide rectangular channel carries a distance of 22 m³/s at a depth of 1.2 m. The minimum height of the hump (in cm) required to be placed at a section to cause critical flow over the hump, neglecting energy loss will be