GATE 2019 Civil Engineering

The lecture was attended by quite _________ students, so the hall was not very _________.

Which one of the following is correct?

They have come a long way in _________ trust among the users.

Consider a two-dimensional flow through isotropic soil along x direction and z direction. If h is the hydraulic head, the Laplace's equation of continuity is expressed as

On a horizontal ground, the base of a straight ladder is 6 m away from the base of a vertical pole. The ladder makes an angle of 45° to the horizontal. If the ladder is resting at...

A simple mass-spring oscillatory system consists of a mass m, suspended from a spring of stiffness k. Considering z as the displacement of the system at any time t, the equation of...

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

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

The CEO's decision to quit was as shocking to the Board as it was to _________.

A plane truss is shown in the figure (not drawn to scale). Which one of the options contains ONLY zero force members in the truss?

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...

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

Consider the pin-jointed plane truss shown in the figure (not drawn to scale). Let R_P, R_Q, and R_R denote the vertical reactions (upward positive) applied by the supports at P, Q...

In a sports academy of 300 people, 105 play only cricket, 70 play only hockey, 50 play only football, 25 play both cricket and hockey, 15 play both hockey and football and 30 play...

"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...

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 stee...

A square has sides 5 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 ____...

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

P, Q, R, S and T are related and belong to the same family. P is the brother of S. Q is the wife of P. R and T are the children of the siblings P and S respectively. Which one of t...

The interior angles of four triangles are given below: Triangle | Interior Angles ---|--- P | 85°, 50°, 45° Q | 100°, 55°, 25° R | 100°, 45°, 35° S | 130°, 30°, 20° Which of the tr...

The coefficient of average rolling friction of a road is $f_r$, and its grade is +G%. If the grade of this road is doubled, what will be the percentage change in the braking distan...

An isolated concrete pavement slab of length L is resting on a frictionless base. The temperature of the top and bottom fibre of the slab are $T_t$, and $T_b$, respectively. Given:...

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

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

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 estima...

A retaining wall of height H with smooth vertical backface supports a backfill inclined at an angle β with the horizontal. The backfill consists of cohesionless soil having angle o...

In a soil specimen, the total stress, effective stress, hydraulic gradient and critical hydraulic gradient are σ, σ', i and ic, respectively. For initiation of quicksand condition,...

Which one of the following is a secondary pollutant?

For a given loading on a rectangular plain concrete beam with an overall depth of 500 mm, the compressive strain and tensile strain developed at the extreme fibers are of the same...

A completely mixed dilute suspension of sand particles having diameters 0.25, 0.35, 0.40, 0.45 and 0.50 mm are filled in a transparent glass column of diameter 10 cm and height 2.5...

The maximum number of vehicles observed in any five minute period during the peak hour is 160. If the total flow in the peak hour is 1000 vehicles, the five minute peak hour factor...

A circular duct carrying water gradually contracts from a diameter of 30 cm to 15 cm. The figure (not drawn to scale) shows the arrangement of differential manometer attached to th...

The probability that the annual maximum flood discharge will exceed 25000 m³/s, at least once in next 5 years is found to be 0.25. The return period of this flood event (in years,...

A soil has specific gravity of its solids equal to 2.65. The mass density of water is 1000 kg/m³. Considering zero air voids and 10% moisture content of the soil sample, the dry de...

A concentrated load of 500 kN is applied on an elastic half space. The ratio of the increase in vertical normal stress at depths of 2 m and 4 m along the point of the loading, as p...

Which one of the following is NOT a correct statement?

A one-dimensional domain is discretized into N sub-domains of width $\Delta x$ with node numbers $i = 0,1,2,3,..., N$. If the time scale is discretized in steps of $\Delta t$, the...

A rectangular open channel has a width of 5 m and a bed slope of 0.001. For a uniform flow of depth 2 m, the velocity is 2 m/s. The Manning's roughness coefficient for the channel...

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...

Consider two functions: x=ψlnφ and y=φlnψ. Which one of the following is the correct expression for ∂ψ/∂x?

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 kN. The beam is symmetrical about the neutral ax...

The rigid-jointed plane frame QRS shown in the figure is subjected to a load P at the joint R. Let the axial deformations in the frame be neglected. If the support S undergoes a se...

If the section shown in the figure turns from fully-elastic to fully-plastic, the depth of neutral axis (N.A.), $\bar{y}$, decreases by

Sedimentation basin in a water treatment plant is designed for a flow rate of 0.2 m³/s. The basin is rectangular with a length of 32 m, width of 8 m, and depth of 4 m. Assume that...

A survey line was measured to be 285.5 m with a tape having a nominal length of 30 m. On checking, the true length of the tape was found to be 0.05 m too short. If the line lay on...

A 16 mm thick gusset plate is connected to the 12 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 pla...

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 ac...

A box measuring 50 cm x 50 cm x 50 cm is filled to the top with dry coarse aggregate of mass 187.5 kg. The water absorption and specific gravity of the aggregate are 0.5% and 2.5,...

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 kN is acting at joint R in the horizontal dir...

A sample of air analysed at 0°C and 1 atm pressure is reported to contain 0.02 ppm (parts per million) of NO2. Assume the gram molecular mass of NO2 as 46 and its volume at 0°C and...

A 0.80 m deep bed of sand filter (length 4 m and width 3 m) is made of uniform particles (diameter = 0.40 mm, specific gravity = 2.65, shape factor = 0.85) with bed porosity of 0.4...

A wastewater is to be disinfected with 35 mg/L of chlorine to obtain 99% kill of micro-organisms. The number of micro-organisms remaining alive (Nt) at time t, is modelled by Nt =...

A staff is placed on a benchmark (BM) of reduced level (RL) 100.000 m and a theodolite is placed at a horizontal distance of 50 m from the BM to measure the vertical angles. The me...

Consider the ordinary differential equation $x^2 \frac{d^2y}{dx^2} - 2x \frac{dy}{dx} + 2y = 0$. Given the values of y(1) = 0 and y(2) = 2, the value of y(3) (round off to 1 decima...

Average free flow speed and the jam density observed on a road stretch are 60 km/h and 120 vehicles/km, respectively. For a linear speed-density relationship, the maximum flow on t...

Traffic on a highway is moving at a rate of 360 vehicles per hour at a location. If the number of vehicles arriving on this highway follows Poisson distribution, the probability (r...

A parabolic vertical curve is being designed to join a road of grade +5% with a road of grade -3%. The length of the vertical curve is 400 m measured along the horizontal. The vert...

Tie bars of 12 mm diameter are to be provided in a concrete pavement slab. The working tensile stress of the tie bars is 230 MPa, the average bond strength between a tie bar and co...

The hyetograph of a storm event of duration 140 minutes is shown in the figure. The infiltration capacity at the start of this event (t = 0) is 17 mm/hour, which linearly decreases...

Two water reservoirs are connected by a siphon (running full) of total length 5000 m and diameter of 0.10 m, as shown below (figure not drawn to scale). The inlet leg length of the...

Consider a laminar flow in the x-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/...

A reinforced concrete circular pile of 12 m length and 0.6 m diameter is embedded in stiff clay which has an undrained unit cohesion of 110 kN/m². The adhesion factor is 0.5. The N...

A granular soil has a saturated unit weight of 20 kN/m³ and an effective angle of shearing resistance of 30°. The unit weight of water is 9.81 kN/m³. A slope is to be made on this...

A 3m × 3 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 reac...

A square footing of 4 m side is placed at 1 m depth in a sand deposit. The dry unit weight ($\gamma$) of sand is 15 kN/m$^3$. This footing has an ultimate bearing capacity of 600 k...

Daytime temperatures in Delhi can ________ 40°C.

Euclidean norm (length) of the vector [4 -2 -6]⁺ is

The Laplace transform of sinh(at) is

The growth rate of ABC Motors in 2017 was the same ________ XYZ Motors in 2016.

The following inequality is true for all x close to 0. 2 - x²/3 < (x sin x) / (1 - cos x) < 2 What is the value of lim (x sin x) / (1 - cos x) ?

Suresh wanted to lay a new carpet in his new mansion with an area of 70 x 55 sq. mts. However an area of 550 sq. mts. had to be left out for flower pots. If the cost of carpet is R...

A retaining wall with measurements 30m x 12m x 6m was constructed with bricks of dimensions 8cm x 6cm x 6cm. If 60% of the wall consists of bricks, the number of bricks used for th...

What is curl of the vector field 2x²yi + 5z²j – 4yzk ?

A closed thin-walled tube has thickness, t, mean enclosed area within the boundary of the centerline of tube's thickness, Am, and shear stress, τ. Torsional moment of resistance, T...

Hima Das was ________ only Indian athlete to win ________ gold for India.

A steel column is restrained against both translation and rotation at one end and is restrained only against rotation but free to translate at the other end. Theoretical and design...

Mohan, the manager, wants his four workers to work in pairs. No pair should work for more than 5 hours. Ram and John have worked together for 5 hours. Krishna and Amir have worked...

Population of state X increased by x% and the population of state Y increased by y% from 2001 to 2011. Assume that x is greater than y. Let P be the ratio of the population of stat...

If the fineness modulus of a sample of fine aggregates is 4.3, the mean size of the particles in the sample is between

The Newspaper reports that over 500 hectares of tribal land spread across 28 tribal settlements in Mohinitampuram forest division have already been "alienated". A top forest offici...

For a channel section subjected to a downward vertical shear force at its centroid, which one of the following represents the correct distribution of shear stress in flange and web...

Which one of the following options contains ONLY primary air pollutants?

An oil tank can be filled by pipe X in 5 hours and pipe Y in 4 hours, each pump working on its own. When the oil tank is full and the drainage hole is open, the oil is drained in 2...

"Popular Hindi fiction, despite – or perhaps because of – its wide reach, often does not appear in our cinema. As ideals that viewers are meant to look up to rather than identify w...

Analysis of a water sample revealed that the sample contains the following species. CO3^2-, Na+, H+, PO4^3-, Al3+, H2CO3, Cl-, Ca2+, Mg2+, HCO3-, Fe2+, OH- Concentrations of which...

Structural failures considered in the mechanistic method of bituminous pavement design are

A solid sphere of radius, r, and made of material with density, $\rho_s$, is moving through the atmosphere (constant pressure, p) with a velocity, v. The net force ONLY due to atmo...

The velocity field in a flow system is given by v = 2i + (x + y)j + (xyz)k. The acceleration of the fluid at (1, 1, 2) is

An inflow hydrograph is routed through a reservoir to produce an outflow hydrograph. The peak flow of the inflow hydrograph is $P_I$ and the time of occurrence of the peak is $t_I$...

An earthen dam of height H is made of cohesive soil whose cohesion and unit weight are c and γ, respectively. If the factor of safety against cohesion is Fc, the Taylor's stability...

The notation "SC" as per Indian Standard Soil Classification System refers to

An anisotropic soil deposit has coefficient of permeability in vertical and horizontal directions as $k_z$ and $k_x$, respectively. For constructing a flow net, the horizontal dime...

The value of the function f(x) is given at n distinct values of x and its value is to be interpolated at the point x*, using all the n points. The estimate is obtained first by the...

The speed-density relationship in a mid-block section of a highway follows the Greenshield's model. If the free flow speed is $v_f$ and the jam density is $k_j$, the maximum flow o...

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

The characteristic compressive strength of concrete required in a project is 25 MPa and the standard deviation in the observed compressive strength expected at site is 4 MPa. The a...

The data from a closed traverse survey PQRS (run in the clockwise direction) are given in the table The closing error for the traverse PQRS (in degrees) is

A vehicle is moving on a road of grade +4% at a speed of 20 m/s. Consider the coefficient of rolling friction as 0.46 and acceleration due to gravity as 10 m/s². On applying brakes...

The command area of a canal grows only one crop, i.e., wheat. The base period of wheat is 120 days and its total water requirement, Δ, is 40 cm. If the canal discharge is 2 m³/s, t...

Construction of a new building founded on a clayey soil was completed in January 2010. In January 2014, the average consolidation settlement of the foundation in clay was recorded...

The probability density function of a continuous random variable distributed uniformly between x and y (for y > x) is

Consider the hemi-spherical tank of radius 13 m as shown in the figure (not drawn to scale). What is the volume of water (in m³) when the depth of water at the centre of the tank i...

An ordinary differential equation is given below. $\left(\frac{dy}{dx}\right) (x \ln x) = y$ The solution for the above equation is (Note: K denotes a constant in the options)

For a plane stress problem, the state of stress at a point P is represented by the stress element as shown in figure. By how much angle (θ) in degrees the stress element should be...

The critical bending compressive stress in the extreme fibre of a structural steel section is 1000 MPa. It is given that the yield strength of the steel is 250 MPa, width of flange...

In the context of provisions relating to durability of concrete, consider the following assertions: Assertion (1): As per IS 456-2000, air entrainment to the extent of 3% to 6% is...

Chlorine is used as the disinfectant in a municipal water treatment plant. It achieves 50 percent of disinfection efficiency measured in terms of killing the indicator microorganis...

A camera with a focal length of 20 cm fitted in an aircraft is used for taking vertical aerial photographs of a terrain. The average elevation of the terrain is 1200 m above mean s...

A flexible pavement has the following class of loads during a particular hour of the day. i. 80 buses with 2-axles (each axle load of 40 kN); ii. 160 trucks with 2-axles (front and...

The inverse of the matrix $\begin{bmatrix} 2 & 3 & 4 \\ 4 & 3 & 1 \\ 1 & 2 & 4 \end{bmatrix}$ is

A long uniformly distributed load of 10 kN/m and a concentrated load of 60 kN are moving together on the beam ABCD shown in the figure (not drawn to scale). The relative positions...

A plane frame shown in the figure (not to scale) has linear elastic springs at node H. The spring constants are kx = ky = 5 × 10^5 kN/m and kθ = 3 × 10^5 kNm/rad. For the externall...

A rolled I-section beam is supported on a 75 mm wide bearing plate as shown in the figure. Thicknesses of flange and web of the I-section are 20 mm and 8 mm, respectively. Root rad...

When a specimen of M25 concrete is loaded to a stress level of 12.5 MPa, a strain of 500×10-6 is recorded. If this load is allowed to stand for a long time, the strain increases to...

A water treatment plant treats 6000 m³ of water per day. As a part of the treatment process, discrete particles are required to be settled in a clarifier. A column test indicates t...

Raw municipal solid waste (MSW) collected from a city contains 70% decomposable material that can be converted to methane. The water content of the decomposable material is 35%. An...

Consider the reactor shown in the figure. The flow rate through the reactor is Q m³/h. The concentrations (in mg/L) of a compound in the influent and effluent are Co and C, respect...

A series of perpendicular offsets taken from a curved boundary wall to a straight survey line at an interval of 6 m are 1.22, 1.67, 2.04, 2.34, 2.14, 1.87, and 1.15 m. The area (in...

The uniform arrival and uniform service rates observed on an approach road to a signalized intersection are 20 and 50 vehicles/minute, respectively. For this signal, the red time i...

A broad gauge railway line passes through a horizontal curved section (radius = 875 m) of length 200 m. The allowable speed on this portion is 100 km/h. For calculating the cant, c...

The speed-density relationship of a highway is given as u = 100 - 0.5 k where, u = speed in km per hour, k = density in vehicles per km. The maximum flow (in vehicles per hour, rou...

A confined aquifer of 15 m constant thickness is sandwiched between two aquicludes as shown in the figure (not drawn to scale). The heads indicated by two piezometers P and Q are 5...

At the foot of a spillway, water flows at a depth of 23 cm with a velocity of 8.1 m/s, as shown in the figure. The flow enters as an M-3 profile in the long wide rectangular channe...

Two identical pipes (i.e., having the same length, same diameter, and same roughness) are used to withdraw water from a reservoir. In the first case, they are attached in series an...

The ordinates, u, of a 2-hour unit hydrograph (i.e., for 1 cm of effective rain), for a catchment are shown in the table. A 6-hour storm occurs over the catchment such that the eff...

The dimensions of a soil sampler are given in the table. Parameter | Cutting edge | Sampling tube ---|---|--- Inside diameter (mm) | 80 | 86 Outside diameter (mm) | 100 | 90 For th...

A 2m x 4 m rectangular footing has to carry a uniformly distributed load of 120 kPa. As per the 2:1 dispersion method of stress distribution, the increment in vertical stress (in k...

Constant head permeability tests were performed on two soil specimens, S1 and S2. The ratio of height of the two specimens (Ls1:Ls2) is 1.5, the ratio of the diameter of specimens...

A timber pile of length 8 m and diameter 0.2 m is driven with a 20 kN drop hammer, falling freely from a height of 1.5 m. The total penetration of the pile in the last 5 blows is 4...

A square footing of 2 m sides rests on the surface of a homogeneous soil bed having the properties: cohesion c = 24 kPa, angle of internal friction $\phi$ = 25°, and unit weight $\...