Success TrackerSuccess Tracker
Log inSign up

The PYQ practice room

GATE CE 2019 Set 1

All 65 solved GATE CE 2019 Set 1 questions in exam order. Open a question, commit to an answer, and learn from the step-by-step solution. One question at a time.

Attempt before revealInstant answer feedbackExplore questions
Go beyond PYQs with Success TrackerAI-powered personalised practice and doubt support. Unlimited practice on eligible plans; AI usage limits apply.

Questions

65

Paper marks

100

Question formats

2

MCQ · NAT

Revision mode

Self-paced

No timer. Focus on understanding.

Difficulty mixEasy 23Medium 35Hard 7

Explore the questions

65 of 65 questions

General Aptitude (GA)

10
  1. Think it through. Then check your answer.

    Question

    The lecture was attended by quite ______ students, so the hall was not very ______.
    Your answer

    Choose one option, then check your answer.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page
  2. Think it through. Then check your answer.

    Question

    They have come a long way in ________ trust among the users.
    Your answer

    Choose one option, then check your answer.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page
  3. Think it through. Then check your answer.

    Question

    On a horizontal ground, the base of a straight ladder is 6 m6\text{ m} away from the base of a vertical pole. The ladder makes an angle of 45∘45^\circ to the horizontal. If the ladder is resting at a point located at one-fifth of the height of the pole from the bottom, the height of the pole is ________ meters.
    Your answer

    Choose one option, then check your answer.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page
  4. Think it through. Then check your answer.

    Question

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

    Choose one option, then check your answer.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page
  5. Think it through. Then check your answer.

    Question

    The CEO’s decision to quit was as shocking to the Board as it was to ______.
    Your answer

    Choose one option, then check your answer.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page
  6. Think it through. Then check your answer.

    Question

    The new cotton technology, Bollgard-II, with herbicide tolerant traits has developed into a thriving business in India. However, the commercial use of this technology is not legal in India. Notwithstanding that, reports indicate that the herbicide tolerant Bt cotton had been purchased by farmers at an average of Rs 200 more than the control price of ordinary cotton, and planted in 15% of the cotton growing area in the 2017 Kharif season.
    Which one of the following statements can be inferred from the given passage?
    Your answer

    Choose one option, then check your answer.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page
  7. Think it through. Then check your answer.

    Question

    In a sports academy of 300300 people, 105105 play only cricket, 7070 play only hockey, 5050 play only football, 2525 play both cricket and hockey, 1515 play both hockey and football and 3030 play both cricket and football. The rest of them play all three sports. What is the percentage of people who play at least two sports?
    Your answer

    Choose one option, then check your answer.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page
  8. Think it through. Then check your answer.

    Question

    “The increasing interest in tribal characters might be a mere coincidence, but the timing is of interest. None of this, though, is to say that the tribal hero has arrived in Hindi cinema, or that the new crop of characters represents the acceptance of the tribal character in the industry. The films and characters are too few to be described as a pattern.”
    What does the word ‘arrived’ mean in the paragraph above?
    Your answer

    Choose one option, then check your answer.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page
  9. Think it through. Then check your answer.

    Question

    A square has sides 5 cm5\text{ cm} smaller than the sides of a second square. The area of the larger square is four times the area of the smaller square. The side of the larger square is ______ cm\text{cm}.
    Your answer

    Choose one option, then check your answer.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page
  10. Think it through. Then check your answer.

    Question

    PP, QQ, RR, SS and TT are related and belong to the same family. PP is the brother of SS. QQ is the wife of PP. RR and TT are the children of the siblings PP and SS respectively. Which one of the following statements is necessarily FALSE?
    Your answer

    Choose one option, then check your answer.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page

CE

55
  1. Think it through. Then check your answer.

    Question

    Which one of the following is correct?
    Your answer

    Choose one option, then check your answer.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page
  2. Think it through. Then check your answer.

    Question

    Consider a two-dimensional flow through isotropic soil along xx direction and zz direction. If hh is the hydraulic head, the Laplace's equation of continuity is expressed as
    Your answer

    Choose one option, then check your answer.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page
  3. Think it through. Then check your answer.

    Question

    A simple mass-spring oscillatory system consists of a mass mm, suspended from a spring of stiffness kk. Considering zz as the displacement of the system at any time tt, the equation of motion for the free vibration of the system is mz¨+kz=0m\ddot{z} + kz = 0. The natural frequency of the system is
    Your answer

    Choose one option, then check your answer.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page
  4. Think it through. Then check your answer.

    Question

    For a small value of hh, the Taylor series expansion for f(x+h)f(x+h) is
    Your answer

    Choose one option, then check your answer.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page
  5. Think it through. Then check your answer.

    Question

    A plane truss is shown in the figure (not drawn to scale).
    A plane truss with vertical loads of 20 kN at joints I, K, L, N, and P. The truss has horizontal members of 2 m each and vertical members of 1 m each.
    Which one of the options contains ONLY zero force members in the truss?
    Your answer

    Choose one option, then check your answer.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page
  6. Think it through. Then check your answer.

    Question

    An element is subjected to biaxial normal tensile strains of 0.0030 and 0.0020. The normal strain in the plane of maximum shear strain is
    Your answer

    Choose one option, then check your answer.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page
  7. Think it through. Then check your answer.

    Question

    Consider the pin-jointed plane truss shown in the figure (not drawn to scale). Let RPR_P, RQR_Q, and RRR_R denote the vertical reactions (upward positive) applied by the supports at P, Q, and R, respectively, on the truss. The correct combination of (RPR_P, RQR_Q, RRR_R) is represented by
    A pin-jointed plane truss with a 30 kN downward load at a joint 3m from support P. Supports are located at P, Q, and R. Horizontal dimensions are 3m, 3m, and 3m. Vertical dimensions are 3m at the apex and 2m at the vertical member above Q.
    Your answer

    Choose one option, then check your answer.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page
  8. Think it through. Then check your answer.

    Question

    Assuming that there is no possibility of shear buckling in the web, the maximum reduction permitted by IS 800-2007 in the (low-shear) design bending strength of a semi-compact steel section due to high shear is
    Your answer

    Choose one option, then check your answer.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page
  9. Think it through. Then check your answer.

    Question

    In the reinforced beam section shown in the figure (not drawn to scale), the nominal cover provided at the bottom of the beam as per IS 456-2000, is
    Cross-section of a reinforced concrete beam. Width is 350 mm. Top reinforcement is 2 - 28$\phi$. Bottom reinforcement is 3 - 16$\phi$. Stirrups are 2-legged, 12$\phi$ @ 90 c/c. The distance from the bottom edge to the center of the bottom bars is 50 mm. The distance from the side edge to the center of the side bars is 50 mm.
    All dimensions are in mm
    Your answer

    Choose one option, then check your answer.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page
  10. Think it through. Then check your answer.

    Question

    The interior angles of four triangles are given below:
    TriangleInterior Angles
    P85∘,50∘,45∘85^\circ, 50^\circ, 45^\circ
    Q100∘,55∘,25∘100^\circ, 55^\circ, 25^\circ
    R100∘,45∘,35∘100^\circ, 45^\circ, 35^\circ
    S130∘,30∘,20∘130^\circ, 30^\circ, 20^\circ
    Which of the triangles are ill-conditioned and should be avoided in Triangulation surveys?
    Your answer

    Choose one option, then check your answer.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page
  11. Think it through. Then check your answer.

    Question

    The coefficient of average rolling friction of a road is frf_r and its grade is +G%+G\%. If the grade of this road is doubled, what will be the percentage change in the braking distance (for the design vehicle to come to a stop) measured along the horizontal (assume all other parameters are kept unchanged)?
    Your answer

    Choose one option, then check your answer.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page
  12. Think it through. Then check your answer.

    Question

    An isolated concrete pavement slab of length LL is resting on a frictionless base. The temperature of the top and bottom fibre of the slab are TtT_t and TbT_b, respectively. Given: the coefficient of thermal expansion =α= \alpha and the elastic modulus =E= E. Assuming Tt>TbT_t > T_b and the unit weight of concrete as zero, the maximum thermal stress is calculated as
    Your answer

    Choose one option, then check your answer.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page
  13. Think it through. Then check your answer.

    Question

    In a rectangular channel, the ratio of the velocity head to the flow depth for critical flow condition, is
    Your answer

    Choose one option, then check your answer.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page
  14. Think it through. Then check your answer.

    Question

    If the path of an irrigation canal is below the bed level of a natural stream, the type of cross-drainage structure provided is
    Your answer

    Choose one option, then check your answer.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page
  15. Think it through. Then check your answer.

    Question

    A catchment may be idealised as a rectangle. There are three rain gauges located inside the catchment at arbitrary locations. The average precipitation over the catchment is estimated by two methods: (i) Arithmetic mean (PAP_A), and (ii) Thiessen polygon (PTP_T). Which one of the following statements is correct?
    Your answer

    Choose one option, then check your answer.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page
  16. Think it through. Then check your answer.

    Question

    A retaining wall of height HH with smooth vertical backface supports a backfill inclined at an angle β\beta with the horizontal. The backfill consists of cohesionless soil having angle of internal friction ϕ\phi. If the active lateral thrust acting on the wall is PaP_a, which one of the following statements is TRUE?
    Your answer

    Choose one option, then check your answer.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page
  17. Think it through. Then check your answer.

    Question

    In a soil specimen, the total stress, effective stress, hydraulic gradient and critical hydraulic gradient are σ\sigma, σ′\sigma', ii and ici_c, respectively. For initiation of quicksand condition, which one of the following statements is TRUE?
    Your answer

    Choose one option, then check your answer.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page
  18. Think it through. Then check your answer.

    Question

    Which one of the following is a secondary pollutant?
    Your answer

    Choose one option, then check your answer.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page
  19. Think it through. Then check your answer.

    Question

    For a given loading on a rectangular plain concrete beam with an overall depth of 500 mm500\text{ mm}, the compressive strain and tensile strain developed at the extreme fibers are of the same magnitude of 2.5×10−42.5 \times 10^{-4}. The curvature in the beam cross-section (in m−1m^{-1}, round off to 3 decimal places), is ___________
    Your answer

    Enter a number. Decimals, negative values and scientific notation are accepted.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page
  20. Think it through. Then check your answer.

    Question

    A completely mixed dilute suspension of sand particles having diameters 0.25,0.35,0.40,0.450.25, 0.35, 0.40, 0.45 and 0.50 mm0.50\text{ mm} are filled in a transparent glass column of diameter 10 cm10\text{ cm} and height 2.50 m2.50\text{ m}. The suspension is allowed to settle without any disturbance. It is observed that all particles of diameter 0.35 mm0.35\text{ mm} settle to the bottom of the column in 30 s30\text{ s}. For the same period of 30 s30\text{ s}, the percentage removal (round off to integer value) of particles of diameters 0.450.45 and 0.50 mm0.50\text{ mm} from the suspension is ___________
    Your answer

    Enter a number. Decimals, negative values and scientific notation are accepted.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page
  21. Think it through. Then check your answer.

    Question

    The maximum number of vehicles observed in any five minute period during the peak hour is 160160. If the total flow in the peak hour is 10001000 vehicles, the five minute peak hour factor (round off to 2 decimal places) is ___________
    Your answer

    Enter a number. Decimals, negative values and scientific notation are accepted.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page
  22. Think it through. Then check your answer.

    Question

    A circular duct carrying water gradually contracts from a diameter of 30 cm30\text{ cm} to 15 cm15\text{ cm}. The figure (not drawn to scale) shows the arrangement of differential manometer attached to the duct.
    A circular duct carrying water gradually contracts from a diameter of 30 cm to 15 cm with a differential manometer attached.
    When the water flows, the differential manometer shows a deflection of 8 cm8\text{ cm} of mercury (Hg). The values of specific gravity of mercury and water are 13.613.6 and 1.01.0, respectively. Consider the acceleration due to gravity, g=9.81 m/s2g = 9.81\text{ m/s}^2. Assuming frictionless flow, the flow rate (in m3/s\text{m}^3/\text{s}, round off to 3 decimal places) through the duct is ___________
    Your answer

    Enter a number. Decimals, negative values and scientific notation are accepted.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page
  23. Think it through. Then check your answer.

    Question

    The probability that the annual maximum flood discharge will exceed 25000 m3/s25000\text{ m}^3/\text{s}, at least once in next 55 years is found to be 0.250.25. The return period of this flood event (in years, round off to 1 decimal place) is ___________
    Your answer

    Enter a number. Decimals, negative values and scientific notation are accepted.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page
  24. Think it through. Then check your answer.

    Question

    A soil has specific gravity of its solids equal to 2.652.65. The mass density of water is 1000 kg/m31000\text{ kg/m}^3. Considering zero air voids and 10%10\% moisture content of the soil sample, the dry density (in kg/m3\text{kg/m}^3, round off to 1 decimal place) would be ___________
    Your answer

    Enter a number. Decimals, negative values and scientific notation are accepted.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page
  25. Think it through. Then check your answer.

    Question

    A concentrated load of 500 kN500\text{ kN} is applied on an elastic half space. The ratio of the increase in vertical normal stress at depths of 2 m2\text{ m} and 4 m4\text{ m} along the point of the loading, as per Boussinesq's theory, would be __________
    Your answer

    Enter a number. Decimals, negative values and scientific notation are accepted.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page
  26. Think it through. Then check your answer.

    Question

    Which one of the following is NOT a correct statement?
    Your answer

    Choose one option, then check your answer.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page
  27. Think it through. Then check your answer.

    Question

    A one-dimensional domain is discretized into NN sub-domains of width Δx\Delta x with node numbers i=0,1,2,3,…,Ni = 0, 1, 2, 3, \dots, N. If the time scale is discretized in steps of Δt\Delta t, the forward-time and centered-space finite difference approximation at ithi^{th} node and nthn^{th} time step, for the partial differential equation ∂v∂t=β∂2v∂x2\frac{\partial v}{\partial t} = \beta \frac{\partial^2 v}{\partial x^2} is
    Your answer

    Choose one option, then check your answer.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page
  28. Think it through. Then check your answer.

    Question

    A rectangular open channel has a width of 5 m5\text{ m} and a bed slope of 0.0010.001. For a uniform flow of depth 2 m2\text{ m}, the velocity is 2 m/s2\text{ m/s}. The Manning's roughness coefficient for the channel is
    Your answer

    Choose one option, then check your answer.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page
  29. Think it through. Then check your answer.

    Question

    For the following statements:
    P — The lateral stress in the soil while being tested in an oedometer is always at-rest.
    Q — For a perfectly rigid strip footing at deeper depths in a sand deposit, the vertical normal contact stress at the footing edge is greater than that at its centre.
    R — The corrections for overburden pressure and dilatancy are not applied to measured SPT-NN values in case of clay deposits.
    The correct combination of the statements is
    Your answer

    Choose one option, then check your answer.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page
  30. Think it through. Then check your answer.

    Question

    Consider two functions: x=ψln⁡ϕx = \psi \ln \phi and y=ϕln⁡ψy = \phi \ln \psi. Which one of the following is the correct expression for ∂ψ∂x\frac{\partial \psi}{\partial x}?
    Your answer

    Choose one option, then check your answer.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page
  31. Think it through. Then check your answer.

    Question

    The cross-section of a built-up wooden beam as shown in the figure (not drawn to scale) is subjected to a vertical shear force of 8 kN8\text{ kN}. The beam is symmetrical about the neutral axis (N.A.) shown, and the moment of inertia about N.A. is 1.5×109 mm41.5 \times 10^9\text{ mm}^4. Considering that the nails at the location P are spaced longitudinally (along the length of the beam) at 60 mm60\text{ mm}, each of the nails at P will be subjected to the shear force of
    Cross-section of a built-up wooden beam with dimensions and nail locations
    Your answer

    Choose one option, then check your answer.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page
  32. Think it through. Then check your answer.

    Question

    The rigid-jointed plane frame QRS shown in the figure is subjected to a load PP at the joint R. Let the axial deformations in the frame be neglected. If the support S undergoes a settlement of Δ=PL3βEI\Delta = \frac{PL^3}{\beta EI}, the vertical reaction at the support S will become zero when β\beta is equal to
    Rigid-jointed plane frame QRS with load P and support S
    Your answer

    Choose one option, then check your answer.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page
  33. Think it through. Then check your answer.

    Question

    If the section shown in the figure turns from fully-elastic to fully-plastic, the depth of neutral axis (N.A.), yˉ\bar{y}, decreases by
    T-section with dimensions 60x5 flange and 5x60 web
    Your answer

    Choose one option, then check your answer.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page
  34. Think it through. Then check your answer.

    Question

    Sedimentation basin in a water treatment plant is designed for a flow rate of 0.2 m3/s0.2\text{ m}^3/\text{s}. The basin is rectangular with a length of 32 m32\text{ m}, width of 8 m8\text{ m}, and depth of 4 m4\text{ m}. Assume that the settling velocity of these particles is governed by the Stokes' law. Given: density of the particles =2.5 g/cm3= 2.5\text{ g}/\text{cm}^3; density of water =1 g/cm3= 1\text{ g}/\text{cm}^3; dynamic viscosity of water =0.01 g/(cm⋅s)= 0.01\text{ g}/(\text{cm}\cdot\text{s}); gravitational acceleration =980 cm/s2= 980\text{ cm}/\text{s}^2. If the incoming water contains particles of diameter 25 μm25\text{ }\mu\text{m} (spherical and uniform), the removal efficiency of these particles is
    Your answer

    Choose one option, then check your answer.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page
  35. Think it through. Then check your answer.

    Question

    A survey line was measured to be 285.5 m285.5\text{ m} with a tape having a nominal length of 30 m30\text{ m}. On checking, the true length of the tape was found to be 0.05 m0.05\text{ m} too short. If the line lay on a slope of 1 in 10, the reduced length (horizontal length) of the line for plotting of survey work would be
    Your answer

    Choose one option, then check your answer.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page
  36. Think it through. Then check your answer.

    Question

    A 16 mm16\text{ mm} thick gusset plate is connected to the 12 mm12\text{ mm} thick flange plate of an I-section using fillet welds on both sides as shown in the figure (not drawn to scale). The gusset plate is subjected to a point load of 350 kN350\text{ kN} acting at a distance of 100 mm100\text{ mm} from the flange plate. Size of fillet weld is 10 mm10\text{ mm}.
    Front and side views of a gusset plate welded to an I-section flange showing a 500 mm vertical weld and a 350 kN load at 100 mm eccentricity
    The maximum resultant stress (in MPa, round off to 1 decimal place) on the fillet weld along the vertical plane would be ________
    Your answer

    Enter a number. Decimals, negative values and scientific notation are accepted.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page
  37. Think it through. Then check your answer.

    Question

    The network of a small construction project awarded to a contractor is shown in the following figure. The normal duration, crash duration, normal cost, and crash cost of all the activities are shown in the table. The indirect cost incurred by the contractor is INR 5000INR\ 5000 per day.
    Network diagram showing activities P, Q, R, S, T, U, V and their precedence relationships
    ActivityNormal Duration (days)Crash Duration (days)Normal Cost (INR)Crash Cost (INR)
    P641500025000
    Q52600012000
    R5380009500
    S63700010000
    T3260009000
    U2140006000
    V422000028000
    If the project is targeted for completion in 16 days, the total cost (in INRINR) to be incurred by the contractor would be ______
    Your answer

    Enter a number. Decimals, negative values and scientific notation are accepted.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page
  38. Think it through. Then check your answer.

    Question

    A box measuring 50 cm×50 cm×50 cm50\text{ cm} \times 50\text{ cm} \times 50\text{ cm} is filled to the top with dry coarse aggregate of mass 187.5 kg187.5\text{ kg}. The water absorption and specific gravity of the aggregate are 0.5%0.5\% and 2.52.5, respectively. The maximum quantity of water (in kg, round off to 2 decimal places) required to fill the box completely is ________
    Your answer

    Enter a number. Decimals, negative values and scientific notation are accepted.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page
  39. Think it through. Then check your answer.

    Question

    A portal frame shown in figure (not drawn to scale) has a hinge support at joint P and a roller support at joint R. A point load of 50 kN50\text{ kN} is acting at joint R in the horizontal direction. The flexural rigidity, EIEI, of each member is 106 kNm210^6\text{ kNm}^2. Under the applied load, the horizontal displacement (in mmmm, round off to 1 decimal place) of joint R would be __________
    A portal frame PQR with a hinge at P and a roller at R. A horizontal load of 50 kN is applied at joint R. Member PQ has length 5 m and member QR has length 10 m.
    Your answer

    Enter a number. Decimals, negative values and scientific notation are accepted.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page
  40. Think it through. Then check your answer.

    Question

    A sample of air analysed at 0∘C0^\circ\text{C} and 1 atm1\text{ atm} pressure is reported to contain 0.02 ppm0.02\text{ ppm} (parts per million) of NO2\text{NO}_2. Assume the gram molecular mass of NO2\text{NO}_2 as 4646 and its volume at 0∘C0^\circ\text{C} and 1 atm1\text{ atm} pressure as 22.4 litres per mole22.4\text{ litres per mole}. The equivalent NO2\text{NO}_2 concentration (in microgram per cubic meter, round off to 2 decimal places) would be ________
    Your answer

    Enter a number. Decimals, negative values and scientific notation are accepted.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page
  41. Think it through. Then check your answer.

    Question

    A 0.80 m0.80\text{ m} deep bed of sand filter (length 4 m4\text{ m} and width 3 m3\text{ m}) is made of uniform particles (diameter =0.40 mm= 0.40\text{ mm}, specific gravity =2.65= 2.65, shape factor =0.85= 0.85) with bed porosity of 0.40.4. The bed has to be backwashed at a flow rate of 3.60 m3/min3.60\text{ m}^3/\text{min}. During backwashing, if the terminal settling velocity of sand particles is 0.05 m/s0.05\text{ m/s}, the expanded bed depth (in mm, round off to 2 decimal places) is ________
    Your answer

    Enter a number. Decimals, negative values and scientific notation are accepted.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page
  42. Think it through. Then check your answer.

    Question

    A wastewater is to be disinfected with 35 mg/L35\text{ mg/L} of chlorine to obtain 99%99\% kill of micro-organisms. The number of micro-organisms remaining alive (NtN_t) at time tt, is modelled by Nt=N0e−ktN_t = N_0 e^{-kt}, where N0N_0 is number of micro-organisms at t=0t = 0, and kk is the rate of kill. The wastewater flow rate is 36 m3/h36\text{ m}^3/\text{h}, and k=0.23 min−1k = 0.23\text{ min}^{-1}. If the depth and width of the chlorination tank are 1.5 m1.5\text{ m} and 1.0 m1.0\text{ m}, respectively, the length of the tank (in mm, round off to 2 decimal places) is ________
    Your answer

    Enter a number. Decimals, negative values and scientific notation are accepted.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page
  43. Think it through. Then check your answer.

    Question

    A staff is placed on a benchmark (BM) of reduced level (RL) 100.000 m100.000\text{ m} and a theodolite is placed at a horizontal distance of 50 m50\text{ m} from the BM to measure the vertical angles. The measured vertical angles from the horizontal at the staff readings of 0.400 m0.400\text{ m} and 2.400 m2.400\text{ m} are found to be the same. Taking the height of the instrument as 1.400 m1.400\text{ m}, the RL (in m) of the theodolite station is ________
    Your answer

    Enter a number. Decimals, negative values and scientific notation are accepted.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page
  44. Think it through. Then check your answer.

    Question

    Consider the ordinary differential equation x2d2ydx2−2xdydx+2y=0x^2 \frac{d^2y}{dx^2} - 2x \frac{dy}{dx} + 2y = 0. Given the values of y(1)=0y(1) = 0 and y(2)=2y(2) = 2, the value of y(3)y(3) (round off to 1 decimal place), is ________
    Your answer

    Enter a number. Decimals, negative values and scientific notation are accepted.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page
  45. Think it through. Then check your answer.

    Question

    Average free flow speed and the jam density observed on a road stretch are 60 km/h60\text{ km/h} and 120 vehicles/km120\text{ vehicles/km}, respectively. For a linear speed-density relationship, the maximum flow on the road stretch (in vehicles/h) is ________
    Your answer

    Enter a number. Decimals, negative values and scientific notation are accepted.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page
  46. Think it through. Then check your answer.

    Question

    Traffic on a highway is moving at a rate of 360360 vehicles per hour at a location. If the number of vehicles arriving on this highway follows Poisson distribution, the probability (round off to 2 decimal places) that the headway between successive vehicles lies between 66 and 1010 seconds is ________
    Your answer

    Enter a number. Decimals, negative values and scientific notation are accepted.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page
  47. Think it through. Then check your answer.

    Question

    A parabolic vertical curve is being designed to join a road of grade +5%+5\% with a road of grade −3%-3\%. The length of the vertical curve is 400 m400\text{ m} measured along the horizontal. The vertical point of curvature (VPC) is located on the road of grade +5%+5\%. The difference in height between VPC and vertical point of intersection (VPI) (in m, round off to the nearest integer) is ________
    Your answer

    Enter a number. Decimals, negative values and scientific notation are accepted.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page
  48. Think it through. Then check your answer.

    Question

    Tie bars of 12 mm12\text{ mm} diameter are to be provided in a concrete pavement slab. The working tensile stress of the tie bars is 230 MPa230\text{ MPa}, the average bond strength between a tie bar and concrete is 2 MPa2\text{ MPa}, and the joint gap between the slabs is 10 mm10\text{ mm}. Ignoring the loss of bond and the tolerance factor, the design length of the tie bars (in mm, round off to the nearest integer) is ________
    Your answer

    Enter a number. Decimals, negative values and scientific notation are accepted.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page
  49. Think it through. Then check your answer.

    Question

    The hyetograph of a storm event of duration 140 minutes is shown in the figure.
    Hyetograph showing Infiltration Capacity and Rainfall Intensity over time
    The infiltration capacity at the start of this event (t=0t = 0) is 17 mm/hourmm/hour, which linearly decreases to 10 mm/hourmm/hour after 40 minutes duration. As the event progresses, the infiltration rate further drops down linearly to attain a value of 4 mm/hourmm/hour at t=100t = 100 minutes and remains constant thereafter till the end of the storm event. The value of the infiltration index, ϕ\phi (in mm/hourmm/hour, round off to 2 decimal places), is ________
    Your answer

    Enter a number. Decimals, negative values and scientific notation are accepted.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page
  50. Think it through. Then check your answer.

    Question

    Two water reservoirs are connected by a siphon (running full) of total length 5000 mm and diameter of 0.10 mm, as shown below (figure not drawn to scale).
    Siphon connecting two reservoirs with dimensions
    The inlet leg length of the siphon to its summit is 2000 mm. The difference in the water surface levels of the two reservoirs is 5 mm. Assume the permissible minimum absolute pressure at the summit of siphon to be 2.5 mm of water when running full. Given: friction factor f=0.02f = 0.02 throughout, atmospheric pressure = 10.3 mm of water, and acceleration due to gravity g=9.81g = 9.81 m/s2m/s^2. Considering only major loss using Darcy-Weisbach equation, the maximum height of the summit of siphon from the water level of upper reservoir, hh (in mm, round off to 1 decimal place) is ________
    Your answer

    Enter a number. Decimals, negative values and scientific notation are accepted.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page
  51. Think it through. Then check your answer.

    Question

    Consider a laminar flow in the xx-direction between two infinite parallel plates (Couette flow). The lower plate is stationary and the upper plate is moving with a velocity of 1 cm/scm/s in the xx-direction. The distance between the plates is 5 mmmm and the dynamic viscosity of the fluid is 0.01 N-s/m2N\text{-}s/m^2. If the shear stress on the lower plate is zero, the pressure gradient, ∂p∂x\frac{\partial p}{\partial x} (in N/m2N/m^2 per mm, round off to 1 decimal place) is ________
    Your answer

    Enter a number. Decimals, negative values and scientific notation are accepted.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page
  52. Think it through. Then check your answer.

    Question

    A reinforced concrete circular pile of 12 m12\text{ m} length and 0.6 m0.6\text{ m} diameter is embedded in stiff clay which has an undrained unit cohesion of 110 kN/m2110\text{ kN/m}^2. The adhesion factor is 0.50.5. The Net Ultimate Pullout (uplift) Load for the pile (in kN\text{kN}, round off to 1 decimal place) is ________
    Your answer

    Enter a number. Decimals, negative values and scientific notation are accepted.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page
  53. Think it through. Then check your answer.

    Question

    A granular soil has a saturated unit weight of 20 kN/m320\text{ kN/m}^3 and an effective angle of shearing resistance of 30∘30^\circ. The unit weight of water is 9.81 kN/m39.81\text{ kN/m}^3. A slope is to be made on this soil deposit in which the seepage occurs parallel to the slope up to the free surface. Under this seepage condition for a factor of safety of 1.51.5, the safe slope angle (in degree, round off to 1 decimal place) would be ________
    Your answer

    Enter a number. Decimals, negative values and scientific notation are accepted.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page
  54. Think it through. Then check your answer.

    Question

    A 3 m×3 m3\text{ m} \times 3\text{ m} square precast reinforced concrete segments to be installed by pushing them through an existing railway embankment for making an underpass as shown in the figure. A reaction arrangement using precast PCC blocks placed on the ground is to be made for the jacks.
    Diagram showing the setup for pushing precast RCC segments through an embankment using jacks and PCC blocks for reaction
    At each stage, the jacks are required to apply a force of 1875 kN1875\text{ kN} to push the segment. The jacks will react against the rigid steel plate placed against the reaction arrangement. The footprint area of reaction arrangement on natural ground is 37.5 m237.5\text{ m}^2. The unit weight of PCC block is 24 kN/m324\text{ kN/m}^3. The properties of the natural ground are: c=17 kPac = 17\text{ kPa}; ϕ=25∘\phi = 25^\circ and γ=18 kN/m3\gamma = 18\text{ kN/m}^3. Assuming that the reaction arrangement has rough interface and has the same properties that of soil, the factor of safety (round off to 1 decimal place) against shear failure is ________
    Your answer

    Enter a number. Decimals, negative values and scientific notation are accepted.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page
  55. Think it through. Then check your answer.

    Question

    A square footing of 4 m4\text{ m} side is placed at 1 m1\text{ m} depth in a sand deposit. The dry unit weight (γ\gamma) of sand is 15 kN/m315\text{ kN/m}^3. This footing has an ultimate bearing capacity of 600 kPa600\text{ kPa}. Consider the depth factors: dq=dγ=1.0d_q = d_\gamma = 1.0 and the bearing capacity factor: Nγ=18.75N_\gamma = 18.75. This footing is placed at a depth of 2 m2\text{ m} in the same soil deposit. For a factor of safety of 3.03.0 as per Terzaghi's theory, the safe bearing capacity (in kPa\text{kPa}) of this footing would be ______.
    Your answer

    Enter a number. Decimals, negative values and scientific notation are accepted.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page