GATE 2018 Civil Engineering

"The driver applied the _______ as soon as she approached the hotel where she wanted to take a ________." The words that best fill the blanks in the above sentence are

Consider a sequence of numbers $${a_1},{a_2},{a_3},....,{a_n}$$ where $${a_n} = {1 \over n} - {1 \over {n + 2}}$$, for each integer n > 0. What is the sum of the first 50 terms?

A fruit seller sold a basket of fruits at 12.5% loss. Had he sold it for Rs. 108 more, he would have made a 10% gain. What is the loss in Rupees incurred by the fruit seller?

"It is no surprise that every society has had codes of behaviour; however, the nature of these codes is often _________." The word that best fills the blank in the above sentence i...

The price of a wire made of a superalloy material is proportional to the square of its length. The price of 10 m length of the wire is Rs. 1600. What would be the total price (in R...

Tower A is 90 m tall and tower B is 140 m tall. They are 100 m apart. A horizontal skywalk connects the floors at 70 m in both the towers. If a taut rope connects the top of tower...

Hema's age is 5 years more than twice Hari's age. Suresh's age is 13 years less than 10 times Hari's age. If Suresh is 3 times as old as Hema, how old is Hema?

Each of the letters arranged as below represents a unique integer from 1 to 9. The letters are positioned in the figure such that (A $$ \times $$ B $$ \times $$ C), (B $$ \times $$...

$$\underbrace {{\rm{a}}\,{\rm{ + }}\,{\rm{a}}\,{\rm{ + }}\,{\rm{a}}\,{\rm{ + }}\,.......\,{\rm{ + }}\,{\rm{a}}}_{{\rm{n}}\,{\rm{times}}} = {a^2}b$$ and $$\underbrace {b\,{\rm{ + }}...

"His face ___________ with joy when the solution of the puzzle was _______ to him." The words that best fill the blanks in the above sentence are

"Although it does contain some pioneering ideas, one would hardly characterize the work as _________." The word that best fills the blank in the above sentence is

Given that $${{\log \,P} \over {y - z}} = {{\log \,Q} \over {z - x}} = {{\log \,R} \over {x - y}} = 10$$ for $$x \ne y \ne z$$, what is the value of the product PQR?

A three-member committee has to be formed from a group of 9 people. How many such distinct committees can be formed?

In manufacturing industries, loss is usually taken to be proportional to the square of the deviation from a target. If the loss is Rs. 4900 for a deviation of 7 units, what would b...

For non-negative integers, a, b, c, what would be the value of a + b + c if $$$\log \,a\, + \,\log \,b\, + \,\log \,c\, = \,0?$$$

A faulty wall clock is known to gain 15 minutes every 24 hours. It is synchronized to the correct time at 9 AM on 11th July. What will be the correct time to the nearest minute whe...

The solution of the equation $x \frac{dy}{dx} + y = 0$ passing through the point (1,1) is

"His face ________ with joy when the solution of the puzzle was ________ to him." The words that best fill the blanks in the above sentence are

The matrix P is the inverse of a matrix Q. If I denotes the identity matrix, which one of the following options is correct?

"The driver applied the ________ as soon as she approached the hotel where she wanted to take a ________." The words that best fill the blanks in the above sentence are

Consider the following simultaneous equations (with c₁ and c₂ being constants): 3 x₁ + 2 x₂ = c₁ 4 x₁ + x₂ = c₂ The characteristic equation for these simultaneous equations is

Which one of the following matrices is singular?

Let w = f (x, y), where x and y are functions of t. Then, according to the chain rule, dw/dt is equal to

For the given orthogonal matrix Q, Q = [3/7 2/7 6/7; -6/7 3/7 2/7; 2/7 6/7 -3/7]. The inverse is

"It is no surprise that every society has had codes of behaviour; however, the nature of these codes is often ________." The word that best fills the blank in the above sentence is

"Although it does contain some pioneering ideas, one would hardly characterize the work as ________." The word that best fills the blank in the above sentence is

The number of parameters in the univariate exponential and Gaussian distributions, respectively, are

The graph of a function f(x) is shown in the figure. For f(x) to be a valid probability density function, the value of h is

$a + a + a + \dots + a = a^2b$ (n times) and $b + b + b + \dots + b = ab^2$ (m times), where a, b, n and m are natural numbers. What is the value of $(m + m + m + \dots + m)$ (n ti...

Hema's age is 5 years more than twice Hari's age. Suresh's age is 13 years less than 10 times Hari's age. If Suresh is 3 times as old as Hema, how old is Hema?

Given that the scope of the construction work is well-defined with all its drawings, specifications, quantities and estimates, which one of the following types of contract would be...

Let x be a continuous variable defined over the interval (-∞, ∞), and f (x) = e^-x - e^-x. The integral g(x) = ∫ f(x) dx is equal to

At the point x = 0, the function f(x) = x³ has

A probability distribution with right skew is shown in the figure. The correct statement for the probability distribution is

A three-member committee has to be formed from a group of 9 people. How many such distinct committees can be formed?

Let G be the specific gravity of soil solids, w the water content in the soil sample, $\gamma_w$ the unit weight of water, and $\gamma_d$ the dry unit weight of the soil. The equat...

All the members of the planar truss (see figure), have the same properties in terms of area of cross-section (A) and modulus of elasticity (E). For the loads shown on the truss, th...

Tower A is 90 m tall and tower B is 140 m tall. They are 100 m apart. A horizontal skywalk connects the floors at 70 m in both the towers. If a taut rope connects the top of tower...

A column of height h with a rectangular cross-section of size a×2a has a buckling load of P. If the cross-section is changed to 0.5a × 3a and its height changed to 1.5h, the buckli...

An elastic bar of length L, uniform cross sectional area A, coefficient of thermal expansion α, and Young's modulus E is fixed at the two ends. The temperature of the bar is increa...

A steel column of ISHB 350 @72.4 kg/m is subjected to a factored axial compressive load of 2000 kN. The load is transferred to a concrete pedestal of grade M20 through a square bas...

For non-negative integers, a, b, c, what would be the value of a + b + c if log a + log b + log c = 0?

The setting time of cement is determined using

Consider the following statements related to the pore pressure parameters, A and B: P. A always lies between 0 and 1.0 Q. A can be less than 0 or greater than 1.0 R. B always lies...

The temperature T in a room varies as a function of the outside temperature T₀ and the number of persons in the room p, according to the relation T = K (Θp + T₀), where Θ and K are...

A simply supported beam is subjected to a uniformly distributed load. Which one of the following statements is true?

The Le Chatelier apparatus is used to determine

A structural member subjected to compression, has both translation and rotation restrained at one end, while only translation is restrained at the other end. As per IS 456 : 2000,...

Consider a rigid retaining wall with partially submerged cohesionless backfill with a surcharge. Which one of the following diagrams closely represents the Rankine's active earth p...

In manufacturing industries, loss is usually taken to be proportional to the square of the deviation from a target. If the loss is Rs. 4900 for a deviation of 7 units, what would b...

A fruit seller sold a basket of fruits at 12.5% loss. Had he sold it for Rs. 108 more, he would have made a 10% gain. What is the loss in Rupees incurred by the fruit seller?

According to IS 456-2000, which one of the following statements about the depth of neutral axis X_u,bal for a balanced reinforced concrete section is correct?

The figure shows a two-hinged parabolic arch of span L subjected to a uniformly distributed load of intensity q per unit length. The maximum bending moment in the arch is equal to

The deformation in concrete due to sustained loading is

A vertical load of 10 kN acts on a hinge located at a distance of L/4 from the roller support Q of a beam of length L (see figure). The vertical reaction at support Q is

A faulty wall clock is known to gain 15 minutes every 24 hours. It is synchronized to the correct time at 9 AM on 11th July. What will be the correct time to the nearest minute whe...

The price of a wire made of a superalloy material is proportional to the square of its length. The price of 10 m length of the wire is Rs. 1600. What would be the total price (in R...

If a centrifugal pump has an impeller speed of N (in rpm), discharge Q (in m³/s) and the total head H (in m), the expression for the specific speed Ns of the pump is given by

As per Noise Pollution (Regulation and Control) Rules 2000 of India, the day time noise limit for a residential zone, expressed in dB(A) Leq. is

Which of the following function(s) is an accurate description of the graph for the range(s) indicated? (i) y = 2x + 4 for -3 ≤ x ≤ -1 (ii) y = |x-1| for -1 ≤ x ≤ 2 (iii) y = ||x|-1...

Group I lists the type of gain or loss of strength in soils. Group II lists the property or process responsible for the loss or gain of strength in soils. Group I P. Regain of stre...

The annual average rainfall in a tropical city is 1000 mm. On a particular rainy day (24-hour period), the cumulative rainfall experienced by the city is shown in the graph. Over t...

A solid circular beam with radius of 0.25 m and length of 2 m is subjected to a twisting moment of 20 kNm about the z-axis at the free end, which is the only load acting as shown i...

A flownet below a dam consists of 24 equipotential drops and 7 flow channels. The difference between the upstream and downstream water levels is 6 m. The length of the flow line ad...

Consider a sequence of numbers $a_1, a_2, a_3, \dots, a_n$ where $a_n = \frac{1}{n} - \frac{1}{n+2}$, for each integer $n > 0$. What is the sum of the first 50 terms?

Following observations have been made for the elevation and temperature to ascertain the stability of the atmosphere: Elevation (in m) | Temperature (in °C) ---|--- 10 | 15.5 60 |...

The contact pressure and settlement distribution for a footing are shown in the figure. The figure corresponds to a

Given that $\frac{\log P}{y-z} = \frac{\log Q}{z-x} = \frac{\log R}{x-y} = 10$ for $x \neq y \neq z$, what is the value of the product PQR?

A soil sample is subjected to a hydrostatic pressure, σ. The Mohr circle for any point in the soil sample would be

Two rectangular under-reinforced concrete beam sections X and Y are similar in all aspects except that the longitudinal compression reinforcement in section Y is 10% more. Which on...

The percent reduction in the bearing capacity of a strip footing resting on sand under flooding condition (water level at the base of the footing) when compared to the situation wh...

Each of the letters arranged as below represents a unique integer from 1 to 9. The letters are positioned in the figure such that (A x B x C), (B x G x E) and (D x E x F) are equal...

The most important type of species involved in the degradation of organic matter in the case of activated sludge process is

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...

A strip footing is resting on the ground surface of a pure clay bed having an undrained cohesion Cu. The ultimate bearing capacity of the footing is equal to

Which one of the following statements is NOT correct? (A) When the water content of soil lies between its liquid limit and plastic limit, the soil is said to be in plastic state. (...

A uniformly distributed line load of 500 kN/m is acting on the ground surface. Based on Boussinesq's theory, the ratio of vertical stress at a depth 2 m to that at 4 m, right below...

The clay mineral, whose structural units are held together by potassium bond is

For a broad gauge railway track on a horizontal curve of radius R (in m), the equilibrium cant e required for a train moving at a speed of V (in km per hour) is

The width of a square footing and the diameter of a circular footing are equal. If both the footings are placed on the surface of sandy soil, the ratio of the ultimate bearing capa...

Dupuit's assumptions are valid for

For a steady incompressible laminar flow between two infinite parallel stationary plates, the shear stress variation is

Bernoulli's equation is applicable for

The safety within a roundabout and the efficiency of a roundabout can be increased, respectively. by

The reaction rate involving reactants A and B is given by $-k[A]^\alpha [B]^\beta$. Which one of the following statements is valid for the reaction to be a first-order reaction?

There are 20,000 vehicles operating in a city with an average annual travel of 12,000 km per vehicle. The NOx emission rate is 2.0 g/km per vehicle. The total annual release of NOx...

For a given discharge in an open channel, there are two depths which have the same specific energy. These two depths are known as

The method of orientation used, when the plane table occupies a position not yet located on the map, is called as

Consider the frame shown in the figure: If the axial and shear deformations in different members of the frame are assumed to be negligible, the reduction in the degree of kinematic...

A bitumen sample has been graded as VG30 as per IS: 73-2013. The '30' in the grade means that

As per IS 10500:2012, for drinking water in the absence of alternate source of water, the permissible limits for chloride and sulphate, in mg/L, respectively are

The wastewater from a city, containing a high concentration of biodegradable organics, is being steadily discharged into a flowing river at a location S. If the rate of aeration of...

In the figures, Group I represents the atmospheric temperature profiles (P, Q, R and S) and Group II represents dispersion of pollutants from a smoke stack (1, 2, 3 and 4). In the...

Let the characteristic strength be defined as that value, below which not more than 50% of the results are expected to fall. Assuming a standard deviation of 4 MPa, the target mean...

The speed-density relationship for a road section is shown in the figure. The shape of the flow-density relationship is

Which one of the following is NOT present in the acid rain?

In a material under a state of plane strain, a 10×10 mm square centered at a point gets deformed as shown in the figure. If the shear strain $\gamma_{xy}$, at this point is express...

A super-elevation e is provided on a circular horizontal curve such that a vehicle can be stopped on the curve without sliding. Assuming a design speed v and maximum coefficient of...

Peak Hour Factor (PHF) is used to represent the proportion of peak sub-hourly traffic flow within the peak hour. If 15-minute sub-hours are considered, the theoretically possible r...

A well-designed signalized intersection is one in which the

As per IRC:37-2012, in order to control subgrade rutting in flexible pavements, the parameter to be considered is

The plate load test was conducted on a clayey strata by using a plate of 0.3 m × 0.3 m dimensions, and the ultimate load per unit area for the plate was found to be 180 kPa. The ul...

A runway is being constructed in a new airport as per the International Civil Aviation Organization (ICAO) recommendations. The elevation and the airport reference temperature of t...

A flow field is given by u = y², v = -xy, w = 0. Value of the z-component of the angular velocity (in radians per unit time, up to two decimal places) at the point (0, -1, 1) is __...

The accuracy of an Electronic Distance Measuring Instrument (EDMI) is specified as $\pm (a \text{ mm} + b \text{ ppm})$. Which one of the following statements is correct?

The initial concavity in the load-penetration curve of a CBR test is NOT due to

For a construction project, the mean and standard deviation of the completion time are 200 days and 6.1 days, respectively. Assume normal distribution and use the value of standard...

The frequency distribution of the compressive strength of 20 concrete cube specimens is given in the table. If μ is the mean strength of the specimens and σ is the standard deviati...

The number of spectral bands in the Enhanced Thematic Mapper sensor on the remote sensing satellite Landsat-7 is

The divergence of the vector field V = x² i + 2y³ j + z⁴ k at x = 1, y = 2, z = 3 is

Probability (up to one decimal place) of consecutively picking 3 red balls without replacement from a box containing 5 red balls and 1 white ball is _________

In a fillet weld, the direct shear stress and bending tensile stress are 50 MPa and 150 MPa, respectively. As per IS 800: 2007, the equivalent stress (in MPa, up to two decimal pla...

In a shrinkage limit test, the volume and mass of a dry soil pat are found to be 50 cm³ and 88 g, respectively. The specific gravity of the soil solids is 2.71 and the density of w...

A two-faced fair coin has its faces designated as head (H) and tail (T). This coin is tossed three times in succession to record the following outcomes: H, H, H. If the coin is tos...

Consider the following partial differential equation: $3\frac{\partial^2\phi}{\partial x^2} + B\frac{\partial^2\phi}{\partial x\partial y} + 3\frac{\partial^2\phi}{\partial y^2} +...

The quadratic equation $2x^2-3x+3=0$ is to be solved numerically starting with an initial guess as $x_0 = 2$. The new estimate of $x$ after the first iteration using Newton-Raphson...

lim (tanx / (x^2 - x)) is equal to

As per IS 456: 2000, the minimum percentage of tension reinforcement (up to two decimal places) required in reinforced-concrete beams of rectangular cross-section (considering effe...

A sheet pile has an embedment depth of 12 m in a homogeneous soil stratum. The coefficient of permeability of soil is 10⁻⁶ m/s. Difference in the water levels between the two sides...

A core cutter of 130 mm height has inner and outer diameters of 100 mm and 106 mm, respectively. The area ratio of the core cutter (in %, up to two decimal places) is _________

A reinforced-concrete slab with effective depth of 80 mm is simply supported at two opposite ends on 230 mm thick masonry walls. The centre-to-centre distance between the walls is...

A 3 m thick clay layer is subjected to an initial uniform pore pressure of 145 kPa as shown in the figure. For the given ground conditions, the time (in days, rounded to the neares...

A 1:50 model of a spillway is to be tested in the laboratory. The discharge in the prototype spillway is 1000 m³/s. The corresponding discharge (in m³/s, up to two decimal places)...

The VPI (vertical point of intersection) is 100 m away (when measured along the horizontal) from the VPC (vertical point of curvature). If the vertical curve is parabolic, the leng...

A fillet weld is simultaneously subjected to factored normal and shear stresses of 120 MPa and 50 MPa, respectively. As per IS 800: 2007, the equivalent stress (in MPa, up to two d...

A 10 m wide rectangular channel carries a discharge of 20 m³/s under critical condition. Using g = 9.81 m/s², the specific energy (in m, up to two decimal places) is _________

A triangular pipe network is shown in the figure. The head loss in each pipe is given by hf = rQ^1.8, with the variables expressed in a consistent set of units. The value of r for...

During a storm event in a certain period, the rainfall intensity is 3.5 cm/hour and the Φ-index is 1.5 cm/hour. The intensity of effective rainfall (in cm/hour, up to one decimal p...

The infiltration capacity of a soil follows the Horton's exponential model. $f = c_1 + c_2e^{-kt}$. During an experiment, the initial infiltration capacity was observed to be 200 m...

The ordinates of a 2-hour unit hydrograph for a catchment are given as Time (h) 0 1 2 3 4 Ordinate (m³/s) 0 5 12 25 41 The ordinate (in m³/s) of a 4-hour unit hydrograph for this c...

The intensity of irrigation for the Kharif season is 50% for an irrigation project with culturable command area of 50,000 hectares. The duty for the Kharif season is 1000 hectare/c...

For routing of flood in a given channel using the Muskingum method, two of the routing coefficients are estimated as C₀ = -0.25 and C₁ = 0.55. The value of the third coefficient C₂...

A culvert is designed for a flood frequency of 100 years and a useful life of 20 years. The risk involved in the design of the culvert (in percentage, up to two decimal places) is...

While aligning a hill road with a ruling gradient of 6%, a horizontal curve of radius 50 m is encountered. The grade compensation (in percentage, up to two decimal places) to be pr...

A city generates 40×10⁶ kg of municipal solid waste (MSW) per year, out of which only 10% is recovered/recycled and the rest goes to landfill. The landfill has a single lift of 3 m...

Vehicles arriving at an intersection from one of the approach roads follow the Poisson distribution. The mean rate of arrival is 900 vehicles per hour. If a gap is defined as the t...

The tangent to the curve represented by $y = x \ln x$ is required to have 45° inclination with the x-axis. The coordinates of the tangent point would be

The value of the integral $\int_0^\pi x \cos^2x \,dx$ is

The matrix $\begin{pmatrix} 2 & -4 \ 4 & -2 \ \end{pmatrix}$ has

For the function f(x)=a+bx, 0 ≤ x ≤ 1, to be a valid probability density function, which one of the following statements is correct?

The solution of the equation $\frac{dQ}{dt} + Q = 1$ with $Q = 0$ at $t = 0$ is

A cantilever beam of length 2 m with a square section of side length 0.1 m is loaded vertically at the free end. The vertical displacement at the free end is 5 mm. The beam is made...

Consider the following definite integral: $I = \int_0^1 \frac{(\sin^{-1} x)^2}{\sqrt{1-x^2}} dx$ The value of the integral is

The Laplace transform $F(s)$ of the exponential function, $f(t)=e^{at}$ when $t\ge0$, where $a$ is a constant and $(s-a)>0$, is

Consider the matrix $\begin{bmatrix} 5 & -1 \ 4 & 1 \end{bmatrix}$. Which one of the following statements is TRUE for the eigenvalues and eigenvectors of this matrix?

The rank of the following matrix is $\begin{pmatrix} 1 & 1 & 0 & -2 \ 2 & 0 & 2 & 2 \ 4 & 1 & 3 & 1 \end{pmatrix}$

If $A = \begin{bmatrix} 1 & 5 \\ 6 & 2 \end{bmatrix}$ and $B = \begin{bmatrix} 3 & 7 \\ 8 & 4 \end{bmatrix}$, $AB^T$ is equal to

A cylinder of radius 250 mm and weight, W = 10 kN is rolled up an obstacle of height 50 mm by applying a horizontal force P at its centre as shown in the figure. All interfaces are...

Consider the following second-order differential equation: $y'' - 4y' + 3y = 2t - 3t^2$ The particular solution of the differential equation is

Two rigid bodies of mass 5 kg and 4 kg are at rest on a frictionless surface until acted upon by a force of 36 N as shown in the figure. The contact force generated between the two...

A plate in equilibrium is subjected to uniform stresses along its edges with magnitude $\sigma_{xx} = 30$ MPa and $\sigma_{yy} = 50$ MPa as shown in the figure. The Young's modulus...

A planar truss tower structure is shown in the figure. Consider the following statements about the external and internal determinacies of the truss. (P) Externally Determinate (Q)...

Group I contains three broad classes of irrigation supply canal outlets. Group II presents hydraulic performance attributes. Group I P. Non-modular outlet Q. Semi-modular outlet R....

The figure shows a simply supported beam PQ of uniform flexural rigidity EI carrying two moments M and 2M. The slope at P will be

Group I gives a list of test methods and test apparatus for evaluating some of the properties of Ordinary Portland Cement (OPC) and concrete. Group II gives the list of these prope...

Four bolts P, Q, R and S of equal diameter are used for a bracket subjected to a load of 130 kN as shown in the figure. The force in bolt P is

Two prismatic beams having the same flexural rigidity of 1000 kN-m² are shown in the figures. If the mid-span deflections of these beams are denoted by $\delta_1$ and $\delta_2$ (a...

A 1 m wide rectangular channel has a bed slope of 0.0016 and the Manning's roughness coefficient is 0.04. Uniform flow takes place in the channel at a flow depth of 0.5 m. At a par...

A 0.5 m × 0.5 m square concrete pile is to be driven in a homogeneous clayey soil having undrained shear strength, cu = 50 kPa and unit weight, γ = 18.0 kN/m³. The design capacity...

A singly-reinforced rectangular concrete beam of width 300 mm and effective depth 400 mm is to be designed using M25 grade concrete and Fe500 grade reinforcing steel. For the beam...

The following observations are made while testing aggregate for its suitability in pavement construction: i. Mass of oven-dry aggregate in air = 1000 g ii. Mass of saturated surfac...

A closed tank contains 0.5 m thick layer of mercury (specific gravity = 13.6) at the bottom. A 2.0 m thick layer of water lies above the mercury layer. A 3.0 m thick layer of oil (...

A 3 m high vertical earth retaining wall retains a dry granular backfill with angle of internal friction of 30° and unit weight of 20 kN/m³. If the wall is prevented from yielding...

Consider the three prismatic beams with the clamped supports P, Q, and R as shown in the figures. Given that the modulus of elasticity, E is 2.5×10^4 MPa; and the moment of inertia...

The queue length (in number of vehicles) versus time (in seconds) plot for an approach to a signalized intersection with the cycle length of 96 seconds is shown in the figure (not...

Three soil specimens (Soil 1, Soil 2 and Soil 3), each 150 mm long and 100 mm diameter, are placed in series in a constant head flow set-up as shown in the figure. Suitable screens...

A rapid sand filter comprising a number of filter beds is required to produce 99 MLD of potable water. Consider water loss during backwashing as 5%, rate of filtration as 6.0 m/h a...

Consider the following statements: P. Walls of one brick thick are measured in square meters. Q. Walls of one brick thick are measured in cubic meters. R. No deduction in the brick...

A priority intersection has a single-lane one-way traffic road crossing an undivided two-lane two-way traffic road. The traffic stream speed on the single-lane road is 20 kmph and...

Two identical concrete piles having the plan dimensions 50 cm x 50 cm are driven into a homogeneous sandy layer as shown in the figures. Consider the bearing capacity factor Nq for...

In a 5 m wide rectangular channel, the velocity u distribution in the vertical direction y is given by $u=1.25y^{\frac{1}{6}}$. The distance y is measured from the channel bed. If...

The radius of a horizontal circular curve on a highway is 120 m. The design speed is 60 km/hour, and the design coefficient of lateral friction between the tyre and the road surfac...

Following are the statements related to the stress paths in a triaxial testing of soils: P. If σ1 = σ3, the stress point lies at the origin of the p-q plot. Q. If σ1 = σ3, the stre...

A car follows a slow moving truck (travelling at a speed of 10 m/s) on a two-lane two-way highway. The car reduces its speed to 10 m/s and follows the truck maintaining a distance...

The following details refer to a closed traverse: Line | Consecutive coordinate ---|--- | Northing (m) | Southing (m) | Easting (m) | Westing (m) PQ | ---- | 437 | 173 | ---- QR |...

The observed bearings of a traverse are given below: Line Bearing PQ 46°15' QR 108°15' RS 201°30' ST 321°45' Line Bearing QP 226°15' RQ 286°15' SR 20°30' TS 141°45' The station(s)...

A level instrument at a height of 1.320 m has been placed at a station having a Reduced Level (RL) of 112.565 m. The instrument reads –2.835 m on a levelling staff held at the bott...

A square area (on the surface of the earth) with side 100 m and uniform height, appears as 1 cm² on a vertical aerial photograph. The topographic map shows that a contour of 650 m...

The laboratory tests on a soil sample yields the following results: natural moisture content = 18%, liquid limit = 60%, plastic limit = 25%, percentage of clay sized fraction = 25%...

The solution at x = 1, t = 1 of the partial differential equation $\frac{\partial^2 u}{\partial x^2} = 25 \frac{\partial^2 u}{\partial t^2}$ subject to initial conditions of $u(0)...

Consider the equation $\frac{du}{dt} = 3t^2 + 1$ with $u = 0$ at $t = 0$. This is numerically solved by using the forward Euler method with a step size, $\Delta t = 2$. The absolut...

The value (up to two decimal places) of a line integral $\int_{C} \mathbf{F}(\mathbf{r}) \cdot d\mathbf{r}$, for $\mathbf{F}(\mathbf{r})=x^{2}\hat{i}+y^{2}\hat{j}$ along C which is...

A pre-tensioned rectangular concrete beam 150 mm wide and 300 mm depth is prestressed with three straight tendons, each having a cross-sectional area of 50 mm$^2$, to an initial st...

The solution (up to three decimal places) at x = 1 of the differential equation $\frac{d^2 y}{dx^2} + 2\frac{dy}{dx} + y = 0$ subject to boundary conditions $y(0) = 1$ and $\frac{d...

An 8 m long simply-supported elastic beam of rectangular cross-section (100 mm × 200 mm) is subjected to a uniformly distributed load of 10 kN/m over its entire span. The maximum p...

A prismatic beam P-Q-R of flexural rigidity EI=1×10⁴ kNm² is subjected to a moment of 180 kNm at Q as shown in the figure. The rotation at Q (in rad, up to two decimal places) is _...

Variation of water depth (y) in a gradually varied open channel flow is given by the first order differential equation $\frac{dy}{dx} = \frac{1 - e^{-\frac{10}{3}\ln(y)}}{250 - 45e...

Consider the stepped bar made with a linear elastic material and subjected to an axial load of 1 kN, as shown in the figure. Segments 1 and 2 have cross-sectional area of 100 mm² a...

The value of M in the beam ABC shown in the figure is such that the joint B does not rotate. The value of support reaction (in kN) at B should be equal to _________.

A prismatic propped cantilever beam of span L and plastic moment capacity Mₚ is subjected to a concentrated load at its mid-span. If the collapse load of the beam is α Mₚ/L, the va...

An RCC short column (with lateral ties) of rectangular cross section of 250 mm x 300 mm is reinforced with four numbers of 16 mm diameter longitudinal bars. The grades of steel and...

An RCC beam of rectangular cross section has factored shear of 200 kN at its critical section. Its width b is 250 mm and effective depth d is 350 mm. Assume design shear strength $...

Consider the beam ABCD shown in the figure. For a moving concentrated load of 50 kN on the beam, the magnitude of the maximum bending moment (in kN-m) obtained at the support C wil...

A 6 m long simply-supported beam is prestressed as shown in the figure. The beam carries a uniformly distributed load of 6 kN/m over its entire span. If the effective flexural rigi...

Consider two axially loaded columns, namely, 1 and 2, made of a linear elastic material with Young's modulus 2×10^5 MPa, square cross-section with side 10 mm, and length 1 m. For C...

A cable PQ of length 25 m is supported at two ends at the same level as shown in the figure. The horizontal distance between the supports is 20 m. A point load of 150 kN is applied...

The dimensions 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 pl...

Consider the deformable pin-jointed truss with loading, geometry and section properties as shown in the figure. Given that E = 2×10¹¹ N/m², A = 10 mm², L = 1 m and P = 1 kN. The ho...

The compression curve (void ratio, e vs. effective stress, σν') for a certain clayey soil is a straight line in a semi-logarithmic plot and it passes through the points (e = 1.2; σ...

A column is subjected to a load through a bracket as shown in the figure. The resultant force (in kN, up to one decimal place) in the bolt 1 is _________

The total horizontal and vertical stresses at a point X in a saturated sandy medium are 170 kPa and 300 kPa, respectively. The static pore-water pressure is 30 kPa. At failure, the...

At a construction site, a contractor plans to make an excavation as shown in the figure. The water level in the adjacent river is at an elevation of +20.0 m. Unit weight of water i...

A particle of mass 2 kg is travelling at a velocity of 1.5 m/s. A force f (t) = 3t^2 (in N) is applied to it in the direction of motion for a duration of 2 seconds, where t denotes...

The activity details of a project are given below: Activity | Depends on | Duration (in days) ---|---|--- P | -- | 6 Q | P | 15 R | Q, T | 12 S | R | 16 T | P | 10 U | Q, T | 14 V...

A conventional drained triaxial compression test was conducted on a normally consolidated clay sample under an effective confining pressure of 200 kPa. The deviator stress at failu...

A group of nine piles in a 3 x 3 square pattern is embedded in a soil strata comprising dense sand underlying recently filled clay layer, as shown in the figure. The perimeter of a...

It is proposed to drive H-piles up to a depth of 7 m at a construction site. The average surface area of the H-pile is 3 m² per meter length. The soil at the site is homogeneous sa...

The void ratio of a soil is 0.55 at an effective normal stress of 140 kPa. The compression index of the soil is 0.25. In order to reduce the void ratio to 0.4, an increase in the m...

A three-fluid system (immiscible) is connected to a vacuum pump. The specific gravity values of the fluids (S1, S2) are given in the figure. Unit weight of water, $\gamma_w$ = 9.81...

A rigid smooth retaining wall of height 7 m with vertical backface retains saturated clay as backfill. The saturated unit weight and undrained cohesion of the backfill are 17.2 kN/...

The infinite sand slope shown in the figure is on the verge of sliding failure. The ground water table coincides with the ground surface. Unit weight of water $\gamma_w$ = 9.81 kN/...

The total rainfall in a catchment of area 1000 km², during a 6 h storm, is 19 cm. The surface runoff due to this storm computed from triangular direct runoff hydrograph is 1×10⁸ m³...

A sluice gate used to control the flow in a horizontal channel of unit width is shown in the figure. It is observed that the depth of flow is 1.0 m upstream of the gate, while the...

A rough pipe of 0.5 m diameter, 300 m length and roughness height of 0.25 mm, carries water (kinematic viscosity = 0.9×10⁻⁶ m²/s) with velocity of 3 m/s. Friction factor (f) for la...

Rainfall depth over a watershed is monitored through six number of well distributed rain gauges. Gauged data are given below Rain Gauge Number 1 2 3 4 5 6 Rainfall Depth (mm) 470 4...

Water flows through a 90° bend in a horizontal plane as depicted in the figure. A pressure of 140 kPa is measured at Section 1-1. The inlet diameter marked at Section 1-1 is $\frac...

The infiltration rate f in a basin under ponding condition is given by f = 30+10e⁻²ᵗ, where, f is in mm/h and t is time in hour. Total depth of infiltration (in mm, up to one decim...

A flocculation tank contains 1800 m³ of water, which is mixed using paddles at an average velocity gradient G of 100/s. The water temperature and the corresponding dynamic viscosit...

In a laboratory, a flow experiment is performed over a hydraulic structure. The measured values of discharge and velocity are 0.05 m³/s and 0.25 m/s, respectively. If the full scal...

A coal containing 2% sulfur is burned completely to ash in a brick kiln at a rate of 30 kg/min. The sulfur content in the ash was found to be 6% of the initial amount of sulfur pre...

A consolidated undrained (CU) triaxial compression test is conducted on a normally consolidated clay at a confining pressure of 100 kPa. The deviator stress at failure is 80 kPa, a...

A water sample analysis data is given below. Ion Concentration, mg/L Atomic Weight Ca²⁺ 60 40 Mg²⁺ 30 24.31 HCO₃⁻ 400 61 The carbonate hardness (expressed as mg/L of CaCO₃, up to o...

An effective rainfall of 2-hour duration produced a flood hydrograph peak of 200 m³/s. The flood hydrograph has a base flow of 20 m³/s. If the spatial average rainfall in the water...

At a small water treatment plant which has 4 filters, the rates of filtration and backwashing are 200 m³/d/m² and 1000 m³/d/m², respectively. Backwashing is done for 15 min per day...

A schematic flow diagram of a completely mixed biological reactor with provision for recycling of solids is shown in the figure. So, S = readily biodegradable soluble BOD, mg/L Q,...

The equivalent sound power level (in dB) of the four sources with the noise levels of 60 dB, 69 dB, 70 dB and 79 dB is _________

The ultimate BOD (L₀) of a wastewater sample is estimated as 87% of COD. The COD of this wastewater is 300 mg/L. Considering first order BOD reaction rate constant k (use natural l...

The space mean speed (kmph) and density (vehicles/km) of a traffic stream are linearly related. The free flow speed and jam density are 80 kmph and 100 vehicles/km respectively. Th...

A waste activated sludge (WAS) is to be blended with green waste (GW). The carbon (C) and nitrogen (N) contents, per kg of WAS and GW, on dry basis are given in the table. The rati...

The spherical grit particles, having a radius of 0.01 mm and specific gravity of 3.0, need to be separated in a settling chamber. It is given that • g = 9.81 m/s² • the density of...

Given the following data: design life n = 15 years, lane distribution factor D = 0.75, annual rate of growth of commercial vehicles r = 6%, vehicle damage factor F = 4 and initial...

A 7.5 m wide two-lane road on a plain terrain is to be laid along a horizontal curve of radius 510 m. For a design speed of 100 kmph, super-elevation is provided as per IRC: 73-198...

Two wastewater streams A and B, having an identical ultimate BOD are getting mixed to form the stream C. The temperature of the stream A is 20°C and the temperature of the stream C...

The wastewater having an organic concentration of 54 mg/l is flowing at a steady rate of 0.8 m³/day through a detention tank of dimensions 2 m × 4 m × 2 m. If the contents of the t...

An aerial photograph of a terrain having an average elevation of 1400 m is taken at a scale of 1:7500. The focal length of the camera is 15 cm. The altitude of the flight above mea...

An aircraft approaches the threshold of a runway strip at a speed of 200 km/h. The pilot decelerates the aircraft at a rate of 1.697 m/s² and takes 18 s to exit the runway strip. I...

The bacteria in milk are destroyed when it ________ heated to 80 degree Celsius.

________ with someone else's email account is now a very serious offence.

Consider the following sentences: All benches are beds. No bed is a bulb. Some bulbs are lamps. Which of the following can be inferred? i. Some beds are lamps. ii. Some lamps are b...

If the radius of a right circular cone is increased by 50%, its volume increases by

The following sequence of numbers is arranged in increasing order: 1, x, x, x, y, y, 9,16,18. Given that the mean and median are equal, and are also equal to twice the mode, the va...

The old concert hall was demolished because of fears that the foundation would be affected by the construction of the new metro line in the area. Modern technology for underground...

Students applying for hostel rooms are allotted rooms in order of seniority. Students already staying in a room will move if they get a room in their preferred list. Preferences of...

The last digit of (2171)^7 + (2172)^9 + (2173)^11 + (2174)^13 is

Two machines M1 and M2 are able to execute any of four jobs P. Q. R and S. The machines can perform one job on one object at a time. Jobs P. Q, R and S take 30 minutes. 20 minutes,...

The bar graph below shows the output of five carpenters over one month, each of whom made different items of furniture: chairs, tables, and beds. Consider the following statements....