GATE 2024 Civil Engineering
235 questions across 4 sessions
Set 1
The primary air pollutant(s) is/are
Consider the data of $f(x)$ given in the table. $i$ $0$ $1$ $2$ $x_i$ $1$ $2$ $3$ $f(x_i)$ $0$ $0.3010$ $0.4771$ The value of $f(1.5)$ estimated using second-order Newton’s interpo...
A 2 m × 2 m tank of 3 m height has inflow, outflow and stirring mechanisms. Initially, the tank was half-filled with fresh water. At $ t = 0 $, an inflow of a salt solution of conc...
A water treatment plant treats 25 MLD water with a natural alkalinity of 4.0 mg/L (as CaCO 3 ). It is estimated that, during the coagulation of this water, 450 kg/day of calcium bi...
Concrete of characteristic strength 30 MPa is required. If 40 specimens of concrete cubes are to be tested, the minimum number of specimens having at least 30 MPa strength should b...
Which one of the following statements related to bitumen is FALSE?
A 30 cm diameter well fully penetrates an unconfined aquifer of saturated thickness 20 m with hydraulic conductivity of 10 m/day. Under the steady pumping rate for a long time, the...
The number of degrees of freedom for a natural open channel flow with a mobile bed is
A flow velocity field $\vec{V} : \vec{V}(x, y)$ for a fluid is represented by $\vec{V} = 3 \hat{i} + (5x) \hat{j}$ In the context of the fluid and the flow, which one of the follow...
Consider the statements P and Q. P: Client’s Preliminary Estimate is used for budgeting costs toward the end of planning and design phase. Q: Client’s Detailed Estimate is used for...
A map is prepared with a scale of 1:1000 and a contour interval of 1 m. If the distance between two adjacent contours on the map is 10 mm, the slope of the ground between the adjac...
During a half-moon phase, the Earth-Moon-Sun form a right triangle. If the Moon-Earth-Sun angle at this half-moon phase is measured to be 89.85°, the ratio of the Earth-Sun and...
Among the following statements relating the fundamental lines of a transit theodolite, which one is CORRECT?
A surveyor observes a zenith angle of 93° 00′ 00″ during a theodolite survey. The corresponding vertical angle is
If the number of sides resulting in a closed traverse is increased from three to four, the sum of the interior angles increases by
The three-dimensional state of stress at a point is given by $$\sigma = \begin{pmatrix} 10 & 0 & 0 \\ 0 & 40 & 0 \\ 0 & 0 & 0 \end{pmatrix} \text{ MPa.}$$ The maximum shear stress...
A car is travelling at a speed of 60 km/hr on a section of a National Highway having a downward gradient of 2%. The driver of the car suddenly observes a stopped vehicle on the car...
A slab panel with an effective depth of 250 mm is reinforced with 0.2% main reinforcement using 8 mm diameter steel bars. The uniform center-to-center spacing (in mm) at which the...
The number of trains and their corresponding speeds for a curved Broad Gauge section with 437 m radius, are 20 trains travel at a speed of 40 km/hr 15 trains travel at a speed of 5...
The free mean speed is 60 km/hr on a given road. The average space headway at jam density on this road is 8 m. For a linear speed-density relationship, the maximum flow (in veh/hr/...
What are the eigenvalues of the matrix $\begin{bmatrix} 2 & 1 & 1 \\ 1 & 4 & 1 \\ 1 & 1 & 2 \end{bmatrix}$ ?
The smallest positive root of the equation $$x^5 - 5 x^4 - 10 x^3 + 50 x^2 + 9 x - 45 = 0$$ lies in the range
The probability that a student passes only in Mathematics is $\frac{1}{3}$. The probability that the student passes only in English is $\frac{4}{9}$. The probability that the stude...
For the following partial differential equation, $x \frac{\partial^2 f}{\partial x^2} + y \frac{\partial^2 f}{\partial y^2} = \frac{x^2 + y^2}{2}$ which of the following option(s)...
A vector field $\vec{p}$ and a scalar field $r$ are given by: $\vec{p} = (2x^2 - 3xy + z^2) \hat{i} + (2y^2 - 3yz + x^2) \hat{j} + (2z^2 - 3xz + x^2) \hat{k}$ $r = 6x^2 + 4y^2 - z^...
The return period of a large earthquake for a given region is 200 years. Assuming that earthquake occurrence follows Poisson’s distribution, the probability that it will be exceede...
Activated carbon is used to remove a pollutant from wastewater in a mixed batch reactor, which follows first-order reaction kinetics. At a reaction rate of 0.38 /day, the time (in...
Consider a balanced doubly-reinforced concrete section. If the material and other sectional properties remain unchanged, for which of the following cases will the section becomes u...
The total primary consolidation settlement ($S_c$) of a building constructed on a 10 m thick saturated clay layer is estimated to be 50 mm. After 300 days of the construction of th...
Which of the following statement(s) is/are CORRECT?
For positive integers $p$ and $q$, with $\frac{p}{q} \neq 1$, $\left(\frac{p}{q}\right)^\frac{p}{q}= p^{\left(\frac{p}{q}-1\right)}$. Then,
Three distinct sets of indistinguishable twins are to be seated at a circular table that has 8 identical chairs. Unique seating arrangements are defined by the relative positions o...
As per the International Civil Aviation Organization (ICAO), the basic runway length is increased by $x$ (%) for every $y$ (m) rise in elevation from the Mean Sea Level (MSL). The...
A bird is resting on a point P at a height of 8 m above the Mean Sea Level (MSL). Upon hearing a loud noise, the bird flies parallel to the ground surface and reaches a point Q whi...
The following data is obtained from an axle load survey at a site: Average rear axle load = 12000 kg Number of commercial vehicles = 800 per day The pavement at this site would be...
The elements that DO NOT increase the strength of structural steel are
The initial cost of an equipment is Rs. 1,00,000. Its salvage value at the end of accounting life of 5 years is Rs. 10,000. The difference in depreciation (in Rs.) computed using ‘...
Consider the statements P and Q. P: Soil particles formed by mechanical weathering, and close to their origin are generally subrounded. Q: Activity of the clay physically signifies...
An embankment is constructed with soil by maintaining the degree of saturation as 75% during compaction. The specific gravity of soil is 2.68 and the moisture content is 17% during...
A 2 m wide strip footing is founded at a depth of 1.5 m below the ground level in a homogeneous pure clay bed. The clay bed has unit cohesion of 40 kPa. Due to seasonal fluctuation...
A soil sample was consolidated at a cell pressure of 20 kPa and a back pressure of 10 kPa for 24 hours during a consolidated undrained (CU) triaxial test. The cell pressure was inc...
An infinite slope is made up of cohesionless soil with seepage parallel to and up to the sloping surface. The angle of slope is 30° with respect to the horizontal ground surface. T...
A vertical smooth rigid retaining wall is supporting horizontal ground with dry cohesionless backfill having a friction angle of 30°. The inclinations of failure planes with respec...
If ‘→’ denotes increasing order of intensity, then the meaning of the words [simmer → seethe → smolder] is analogous to [break → raze → _______ ]. Which one of the given options is...
In the given text, the blanks are numbered (i)-(iv). Select the best match for all the blanks. From the ancient Athenian arena to the modern Olympic stadiums, athletics ___(i)___ t...
On a given day, how many times will the second-hand and the minute-hand of a clock cross each other during the clock time 12:05:00 hours to 12:55:00 hours?
Which one of the given options is a possible value of x in the following sequence? 3, 7, 15, x, 63, 127, 255
In a locality, the houses are numbered in the following way: The house-numbers on one side of a road are consecutive odd integers starting from 301, while the house-numbers on the...
The ordinates of a 1-hour unit hydrograph (UH) are given below. Time (hours) 0 1 2 3 4 5 Ordinates of 1-hour UH (m 3 /s) 0 13 50 80 95 85 Time (hours) 6 7 8 9 10 11 Ordinates of 1-...
A spillway has unit discharge of 7.5 m 3 /s/m. The flow depth at the downstream horizontal apron is 0.5 m. The tail water depth (in meters) required to form a hydraulic jump is ___...
The second-order differential equation in an unknown function $$u : u(x, y)$$ is defined as $$\frac{\partial^2 u}{\partial x^2}= 2$$ Assuming $$g : g(x)$$, $$f : f(y)$$, and $$h :...
The following table gives various components of Municipal Solid Waste (MSW) and a list of treatment/separation techniques. Component of MSW Treatment/separation technique P - Ferro...
For assessing the compliance with the emissions standards of incineration plants, a correction needs to be applied to the measured concentrations of air pollutants. The emission st...
Set 2
What is the CORRECT match between the air pollutants and treatment techniques given in the table? Air pollutants Treatment techniques P - NO 2 i - Flaring Q - SO 2 ii - Cyclonic se...
Consider two matrices $A = \begin{bmatrix}2 & 1 & 4 \\ 1 & 0 & 3\end{bmatrix}$ and $B = \begin{bmatrix}-1 & 0 \\ 2 & 3 \\ 1 & 4 \end{bmatrix}$. The determinant of the matrix $AB$ i...
The second derivative of a function $f$ is computed using the fourth-order Central Divided Difference method with a step length $h$. The CORRECT expression for the second derivativ...
Three vectors $\overrightarrow{p}$, $\overrightarrow{q}$, and $\overrightarrow{r}$ are given as $ \overrightarrow{p} = \hat{i} + \hat{j} + \hat{k}$ $ \overrightarrow{q} = \hat{i} +...
The expression for computing the effective interest rate $(i_{eff})$ using continuous compounding for a nominal interest rate of 5% is $i_{eff} = \lim\limits_{m \to \infty} \left(1...
A circular settling tank is to be designed for primary treatment of sewage at a flow rate of 10 million liters/day. Assume a detention period of 2.0 hours and surface loading rate...
An organic waste is represented as C 240 O 200 H 180 N 5 S 5 . (Atomic weights: S-32, H-1, C-12, O-16, N-14). Assume complete conversion of S to SO 2 while burning. SO 2 generated...
A critical activity in a project is estimated to take 15 days to complete at a cost of Rs. 30,000. The activity can be expedited to complete in 12 days by spending a total amount o...
Consider the following data for a project of 300 days duration. Budgeted Cost of Work Scheduled (BCWS) = Rs. 200 Budgeted Cost of Work Performed (BCWP) = Rs. 150 Actual Cost of Wor...
A round-bottom triangular lined canal is to be laid at a slope of 1 in 1500, to carry a discharge of 25 m 3 /s. The side slopes of the canal cross-section are to be kept at 1.25H :...
In the context of pavement material characterization, the CORRECT statement(s) is/are
A 2 m × 1.5 m tank of 6 m height is provided with a 100 mm diameter orifice at the center of its base. The orifice is plugged and the tank is filled up to 5 m height. Consider the...
Consider the statements P and Q. P: In a Pure project organization, the project manager maintains complete authority and has maximum control over the project. Q: A Matrix organizat...
The table shows the activities and their durations and dependencies in a project. Activity Duration (Days) Depends on A 8 - B 4 A C 4 B D 4 C, L F 4 A G 4 F H 6 G, L K 10 A L 6 F,...
A 500 m long water distribution pipeline P with diameter 1.0 m, is used to convey 0.1 m 3 /s of flow. A new pipeline Q, with the same length and flow rate, is to replace P. The fri...
A rectangular channel is 4.0 m wide and carries a discharge of 2.0 m 3 /s with a depth of 0.4 m. The channel transitions to a maximum width contraction at a downstream location, wi...
A hypothetical multimedia filter, consisting of anthracite particles (specific gravity: 1.50), silica sand (specific gravity: 2.60), and ilmenite sand (specific gravity: 4.20), is...
A 2 m wide rectangular channel is carrying a discharge of 30 m 3 /s at a bed slope of 1 in 300. Assuming the energy correction factor as 1.1 and acceleration due to gravity as 10 m...
A child walks on a level surface from point P to point Q at a bearing of 30°, from point Q to point R at a bearing of 90° and then directly returns to the starting point P at a bea...
What is the CORRECT match between the survey instruments/parts of instruments shown in the table and the operations carried out with them? Instruments/Parts of instruments Operatio...
To finalize the direction of a survey, four surveyors set up a theodolite at a station P and performed all the temporary adjustments. From the station P, each of the surveyors obse...
For a reconnaissance survey, it is necessary to obtain vertical aerial photographs of a terrain at an average scale of 1: 13000 using a camera. If the permissible flying height is...
A homogeneous, prismatic, linearly elastic steel bar fixed at both the ends has a slenderness ratio (l/r) of 105, where l is the bar length and r is the radius of gyration. The coe...
A storm with a recorded precipitation of 11.0 cm, as shown in the table, produced a direct run-off of 6.0 cm. Time from start (hours) 1 2 3 4 5 6 7 8 Recorded cumulative precipitat...
The consolidated data of a spot speed study for a certain stretch of a highway is given in the table. Speed range (kmph) Number of observations 0 - 10 7 10 - 20 31 20 - 30 76 30 -...
The longitudinal sections of a runway have gradients as shown in the table. End to end for sections of runway (m) Gradient (%) 0 to 200 +1.0 200 to 600 −1.0 600 to 1200 +0.8 1200 t...
A vertical summit curve on a freight corridor is formed at the intersection of two gradients, +3.0% and −5.0%. Assume the following: - Only large-sized trucks are allowed on this c...
The statements P and Q are related to matrices A and B , which are conformable for both addition and multiplication. P: $(A + B)^T = A^T + B^T$ Q: $(AB)^T = B^T A^T$ Which one of t...
Consider two Ordinary Differential Equations (ODEs): P: $ \dfrac{dy}{dx} = \dfrac{x^4 + 3x^2 y^2 + 2y^4}{x^3 y} $ Q: $ \dfrac{dy}{dx} = -\dfrac{y^2}{x^2} $ Which one of the followi...
The function $f(x) = x^3 - 27x + 4$, $1 \leq x \leq 6$ has
Which one of the following products is NOT obtained in anaerobic decomposition of glucose?
In a sample of 100 heart patients, each patient has 80% chance of having a heart attack without medicine X. It is clinically known that medicine X reduces the probability of having...
In general, the outer edge is raised above the inner edge in horizontal curves for
The in-situ percentage of voids of a sand deposit is 50%. The maximum and minimum densities of sand determined from the laboratory tests are 1.8 g/cm 3 and 1.3 g/cm 3 , respectivel...
A drained triaxial test was conducted on a saturated sand specimen using a stress-path triaxial testing system. The specimen failed when the axial stress reached a value of 100 kN/...
Consider the statements P and Q related to the analysis/design of retaining walls. P : When a rough retaining wall moves toward the backfill, the wall friction force/resistance mob...
Which one of the following saturated fine-grained soils can attain a negative Skempton’s pore pressure coefficient (A)?
A homogeneous earth dam has a maximum water head difference of 15 m between the upstream and downstream sides. A flownet was drawn with the number of potential drops as 10 and the...
In the given text, the blanks are numbered (i)–(iv). Select the best match for all the blanks. Yoko Roi stands _____ (i) _____ as an author for standing _____ (ii) _____ as an hono...
Visualize a cube that is held with one of the four body diagonals aligned to the vertical axis. Rotate the cube about this axis such that its view remains unchanged. The magnitude...
A student was supposed to multiply a positive real number $p$ with another positive real number $q$. Instead, the student divided $p$ by $q$. If the percentage error in the student...
If the sum of the first 20 consecutive positive odd numbers is divided by $20^2$, the result is
A horizontal curve of radius 1080 m (with transition curves on either side) in a Broad Gauge railway track is designed and constructed for an equilibrium speed of 70 kmph. However,...
Various stresses in jointed plain concrete pavement with slab size of 3.5 m × 4.5 m are denoted as follows: Wheel load stress at interior = $S_{wl}^i$ Wheel load stress at edge = $...
The structural design method that DOES NOT take into account the safety factors on the design loads is
A simply supported, uniformly loaded, two-way slab panel is torsionally unrestrained. The effective span lengths along the short span (x) and long span (y) directions of the panel...
Statements: 1. All heroes are winners. 2. All winners are lucky people. Inferences: I. All lucky people are heroes. II. Some lucky people are heroes. III. Some winners are heroes....
If '→' denotes increasing order of intensity, then the meaning of the words [drizzle → rain → downpour] is analogous to [ ______ → quarrel → feud]. Which one of the given options i...
Consider the statements P, Q, and R. P: Compacted fine-grained soils with flocculated structure have isotropic permeability. Q: Phreatic surface/line is the line along which the po...
A reinforced concrete pile of 10 m length and 0.7 m diameter is embedded in a saturated pure clay with unit cohesion of 50 kPa. If the adhesion factor is 0.5, the net ultimate upli...
A partial differential equation $$\frac{\partial^2 T}{\partial x^2} + \frac{\partial^2 T}{\partial y^2} = 0$$ is defined for the two-dimensional field $T: T(x, y)$, inside a planar...
The ratio of the number of girls to boys in class VIII is the same as the ratio of the number of boys to girls in class IX. The total number of students (boys and girls) in classes...
Set 1
If '→' denotes increasing order of intensity, then the meaning of the words [simmer → seethe → smolder] is analogous to [break → raze → _________]. Which one of the given options i...
In a locality, the houses are numbered in the following way: The house-numbers on one side of a road are consecutive odd integers starting from 301, while the house-numbers on the...
For positive integers p and q, with $\frac{p}{q} \neq 1$, $(\frac{p}{q})^{\frac{p}{q}} = p^{(\frac{p}{q}-1)}$. Then,
Which one of the given options is a possible value of x in the following sequence? 3, 7, 15, x, 63, 127, 255
On a given day, how many times will the second-hand and the minute-hand of a clock cross each other during the clock time 12:05:00 hours to 12:55:00 hours?
In the given text, the blanks are numbered (i)-(iv). Select the best match for all the blanks. From the ancient Athenian arena to the modern Olympic stadiums, athletics _______ (i)...
Three distinct sets of indistinguishable twins are to be seated at a circular table that has 8 identical chairs. Unique seating arrangements are defined by the relative positions o...
The chart given below compares the Installed Capacity (MW) of four power generation technologies, T1, T2, T3, and T4, and their Electricity Generation (MWh) in a time of 1000 hours...
In the 4 x 4 array shown below, each cell of the first three columns has either a cross (X) or a number, as per the given rule. Rule: The number in a cell represents the count of c...
During a half-moon phase, the Earth-Moon-Sun form a right triangle. If the Moon-Earth-Sun angle at this half-moon phase is measured to be 89.85°, the ratio of the Earth-Sun and Ear...
The smallest positive root of the equation x^5 - 5x^4 - 10x^3 + 50x^2 + 9x - 45 = 0 lies in the range
The second-order differential equation in an unknown function u: u(x, y) is defined as $\frac{\partial^2 u}{\partial x^2} = 2$. Assuming g:g(x), f: f(y), and h: h(y), the general s...
The probability that a student passes only in Mathematics is $\frac{1}{3}$. The probability that the student passes only in English is $\frac{4}{9}$. The probability that the stude...
The three-dimensional state of stress at a point is given by $\sigma = \begin{pmatrix} 10 & 0 & 0 \\ 0 & 40 & 0 \\ 0 & 0 & 0 \end{pmatrix}$ MPa. The maximum shear stress at the poi...
Concrete of characteristic strength 30 MPa is required. If 40 specimens of concrete cubes are to be tested, the minimum number of specimens having at least 30 MPa strength should b...
Consider the statements P and Q. P: Client's Preliminary Estimate is used for budgeting costs toward the end of planning and design phase. Q: Client's Detailed Estimate is used for...
The following figure shows the arrangement of formwork for casting a cantilever RC beam. The correct sequence of removing the Shores/Props is
A 2 m wide strip footing is founded at a depth of 1.5 m below the ground level in a homogeneous pure clay bed. The clay bed has unit cohesion of 40 kPa. Due to seasonal fluctuation...
Consider the statements P and Q. P: Soil particles formed by mechanical weathering, and close to their origin are generally subrounded. Q: Activity of the clay physically signifies...
The number of degrees of freedom for a natural open channel flow with a mobile bed is
The following table gives various components of Municipal Solid Waste (MSW) and a list of treatment/separation techniques. Component of MSW P - Ferrous metals Q - Aluminum and copp...
A car is travelling at a speed of 60 km/hr on a section of a National Highway having a downward gradient of 2%. The driver of the car suddenly observes a stopped vehicle on the car...
As per the International Civil Aviation Organization (ICAO), the basic runway length is increased by x (%) for every y (m) raise in elevation from the Mean Sea Level (MSL). The val...
Which one of the following statements related to bitumen is FALSE?
If the number of sides resulting in a closed traverse is increased from three to four, the sum of the interior angles increases by
A surveyor observes a zenith angle of 93° 00'00" during a theodolite survey. The corresponding vertical angle is
Among the following statements relating the fundamental lines of a transit theodolite, which one is CORRECT?
For the following partial differential equation, $x \frac{\partial^2 f}{\partial x^2} + y \frac{\partial^2 f}{\partial y^2} = \frac{x^2 + y^2}{2}$ which of the following option(s)...
The elements that DO NOT increase the strength of structural steel are
Consider a balanced doubly-reinforced concrete section. If the material and other sectional properties remain unchanged, for which of the following cases will the section becomes u...
The primary air pollutant(s) is/are
Consider the data of $f(x)$ given in the table. | $i$ | 0 | 1 | 2 | |---|---|---|---| | $x_i$ | 1 | 2 | 3 | | $f(x_i)$ | 0 | 0.3010 | 0.4771 | The value of $f(1.5)$ estimated using...
The plane frame shown in the figure has fixed support at joint A, hinge support at joint F, and roller support at joint I. In the figure, A to I indicate joints of the frame. If th...
An embankment is constructed with soil by maintaining the degree of saturation as 75% during compaction. The specific gravity of soil is 2.68 and the moisture content is 17% during...
A 30 cm diameter well fully penetrates an unconfined aquifer of saturated thickness 20 m with hydraulic conductivity of 10 m/day. Under the steady pumping rate for a long time, the...
What are the eigenvalues of the matrix $\begin{bmatrix} 2 & 1 & 1 \\ 1 & 4 & 1 \\ 1 & 1 & 2 \end{bmatrix}$?
A vector field $\vec{p}$ and a scalar field $r$ are given by $\vec{p} = (2x^2 – 3xy + z^2 ) \hat{i} + ( 2y^2 – 3yz + x^2 ) \hat{j} + (2z^2 – 3xz + x^2 ) \hat{k}$ $r = 6x^2 + 4y^2 –...
Find the correct match between the plane stress states and the Mohr's circles. (P) 10 10 (Q) 10 10 10 10 (R) 10 110 (S) 10 10 (I) τ -10 σ (II) τ -10 σ (III) τ 10 σ (IV) τ -10 10 σ
The beam shown in the figure is subjected to a uniformly distributed downward load of intensity q between supports A and B. Considering the upward reactions as positive, the suppor...
A homogeneous shaft PQR with fixed supports at both ends is subjected to a torsional moment T at point Q, as shown in the figure. The polar moments of inertia of the portions PQ an...
A vertical smooth rigid retaining wall is supporting horizontal ground with dry cohesionless backfill having a friction angle of 30°. The inclinations of failure planes with respec...
A flow velocity field $\vec{V}: \vec{V}(x, y)$ for a fluid is represented by $\vec{V} = 3 \hat{i} + (5x) \hat{j}$ In the context of the fluid and the flow, which one of the followi...
For assessing the compliance with the emissions standards of incineration plants, a correction needs to be applied to the measured concentrations of air pollutants. The emission st...
The free mean speed is 60 km/hr on a given road. The average space headway at jam density on this road is 8 m. For a linear speed-density relationship, the maximum flow (in veh/hr/...
A map is prepared with a scale of 1:1000 and a contour interval of 1 m. If the distance between two adjacent contours on the map is 10 mm, the slope of the ground between the adjac...
Which of the following statement(s) is/are CORRECT?
The return period of a large earthquake for a given region is 200 years. Assuming that earthquake occurrence follows Poisson's distribution, the probability that it will be exceede...
A 2m x 2m tank of 3 m height has inflow, outflow and stirring mechanisms. Initially, the tank was half-filled with fresh water. At t = 0, an inflow of a salt solution of concentrat...
The plane truss shown in the figure has 13 joints and 22 members. The truss is made of a homogeneous, prismatic, linearly elastic material. All members have identical axial rigidit...
An inverted T-shaped concrete beam (B1) in the figure, with centroidal axis X – X, is subjected to an effective prestressing force of 1000 kN acting at the bottom kern point of the...
The initial cost of an equipment is Rs. 1,00,000. Its salvage value at the end of accounting life of 5 years is Rs. 10,000. The difference in depreciation (in Rs.) computed using '...
A slab panel with an effective depth of 250 mm is reinforced with 0.2% main reinforcement using 8 mm diameter steel bars. The uniform center-to-center spacing (in mm) at which the...
The total primary consolidation settlement (S_c) of a building constructed on a 10 m thick saturated clay layer is estimated to be 50 mm. After 300 days of the construction of the...
An infinite slope is made up of cohesionless soil with seepage parallel to and up to the sloping surface. The angle of slope is 30° with respect to horizontal ground surface. The u...
A soil sample was consolidated at a cell pressure of 20 kPa and a back pressure of 10 kPa for 24 hours during a consolidated undrained (CU) triaxial test. The cell pressure was inc...
The ordinates of a 1-hour unit hydrograph (UH) are given below. Time (hours): 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 Ordinates of 1-hour UH (m³/s): 0, 13, 50, 80, 95, 85, 55, 35, 15,...
A standard round bottom triangular canal section as shown in the figure has a bed slope of 1 in 200. Consider the Chezy's coefficient as 150 m^(1/2)/s. The normal depth of flow, y...
A spillway has unit discharge of 7.5 m³/s/m. The flow depth at the downstream horizontal apron is 0.5 m. The tail water depth (in meters) required to form a hydraulic jump is _____...
A 5 m × 5 m closed tank of 10 m height contains water and oil, and is connected to an overhead water reservoir as shown in the figure. Use $\gamma_w$ = 10 kN/m³ and Specific gravit...
Activated carbon is used to remove a pollutant from wastewater in a mixed batch reactor, which follows first-order reaction kinetics. At a reaction rate of 0.38 /day, the time (in...
A water treatment plant treats 25 MLD water with a natural alkalinity of 4.0 mg/L (as CaCO3). It is estimated that, during coagulation of this water, 450 kg/day of calcium bicarbon...
The number of trains and their corresponding speeds for a curved Broad Gauge section with 437 m radius, are • 20 trains travel at a speed of 40 km/hr • 15 trains travel at a speed...
The figure presents the trajectories of six vehicles within a time-space domain. The number in the parentheses represents unique identification of each vehicle. (Figure NOT to scal...
The following data is obtained from an axle load survey at a site: Average rear axle load = 12000 kg Number of commercial vehicles = 800 per day The pavement at this site would be...
A bird is resting on a point P at a height of 8 m above the Mean Sea Level (MSL). Upon hearing a loud noise, the bird flies parallel to the ground surface and reaches a point Q whi...
Set 2
If '→' denotes increasing order of intensity, then the meaning of the words [drizzle → rain → downpour] is analogous to [______ → quarrel → feud]. Which one of the given options is...
Statements: 1. All heroes are winners. 2. All winners are lucky people. Inferences: I. All lucky people are heroes. II. Some lucky people are heroes. III. Some winners are heroes....
A student was supposed to multiply a positive real number p with another positive real number q. Instead, the student divided p by q. If the percentage error in the student's answe...
If the sum of the first 20 consecutive positive odd numbers is divided by 20^2, the result is
The ratio of the number of girls to boys in class VIII is the same as the ratio of the number of boys to girls in class IX. The total number of students (boys and girls) in classes...
In the given text, the blanks are numbered (i)-(iv). Select the best match for all the blanks. Yoko Roi stands ________ (i) as an author for standing ________ (ii) as an honorary f...
Seven identical cylindrical chalk-sticks are fitted tightly in a cylindrical container. The figure below shows the arrangement of the chalk-sticks inside the cylinder. The length o...
The plot below shows the relationship between the mortality risk of cardiovascular disease and the number of steps a person walks per day. Based on the data, which one of the follo...
Five cubes of identical size and another smaller cube are assembled as shown in Figure A. If viewed from direction X, the planar image of the assembly appears as Figure B. If viewe...
Visualize a cube that is held with one of the four body diagonals aligned to the vertical axis. Rotate the cube about this axis such that its view remains unchanged. The magnitude...
A partial differential equation $\frac{\partial^2 T}{\partial x^2} + \frac{\partial^2 T}{\partial y^2} = 0$ is defined for the two-dimensional field $T: T(x, y)$, inside a planar s...
The statements P and Q are related to matrices A and B, which are conformable for both addition and multiplication. P: (A + B)ᵀ = Aᵀ + Bᵀ Q: (AB)ᵀ = AᵀBᵀ Which one of the following...
The second derivative of a function f is computed using the fourth-order Central Divided Difference method with a step length h. The CORRECT expression for the second derivative is
The function $f(x) = x^3 - 27x + 4$, $1 \le x \le 6$ has
Consider two Ordinary Differential Equations (ODEs): P: $\frac{dy}{dx} = \frac{x^4+3x^2y^2+2y^4}{x^3y}$ Q: $\frac{dy}{dx} = \frac{-y^2}{x^2}$ Which one of the following options is...
A 3 m long, horizontal, rigid, uniform beam PQ has negligible mass. The beam is subjected to a 3 kN concentrated vertically downward force at 1 m from P, as shown in the figure. Th...
Consider the statements P and Q. P: In a Pure project organization, the project manager maintains complete authority and has maximum control over the project. Q: A Matrix organizat...
For a thin-walled section shown in the figure, points P, Q, and R are located on the major bending axis X – X of the section. Point Q is located on the web whereas point S is locat...
Consider the following data for a project of 300 days duration. Budgeted Cost of Work Scheduled (BCWS) = Rs. 200 Budgeted Cost of Work Performed (BCWP) = Rs. 150 Actual Cost of Wor...
A simply supported, uniformly loaded, two-way slab panel is torsionally unrestrained. The effective span lengths along the short span (x) and long span (y) directions of the panel...
The structural design method that DOES NOT take into account the safety factors on the design loads is
The contact pressure distribution shown in the figure belongs to a
Which one of the following saturated fine-grained soils can attain a negative Skempton's pore pressure coefficient (A)?
The following figure shows a plot between shear stress and velocity gradient for materials/fluids P, Q, R, S, and T. Which one of the following options is CORRECT?
What is the CORRECT match between the air pollutants and treatment techniques given in the table? Air pollutants P - NO2 Q - SO2 R - CO S - Particles Treatment techniques i - Flari...
Which one of the following products is NOT obtained in anaerobic decomposition of glucose?
The longitudinal sections of a runway have gradients as shown in the table. End to end for sections of runway (m) 0 to 200 200 to 600 600 to 1200 1200 to 1600 1600 to 2000 Gradient...
In general, the outer edge is raised above the inner edge in horizontal curves for
Various stresses in jointed plain concrete pavement with slab size of 3.5 m x 4.5 m are denoted as follows: Wheel load stress at interior = $S_{wl}^i$ Wheel load stress at edge = $...
For a reconnaissance survey, it is necessary to obtain vertical aerial photographs of a terrain at an average scale of 1: 13000 using a camera. If the permissible flying height is...
What is the CORRECT match between the survey instruments/parts of instruments shown in the table and the operations carried out with them? Instruments/Parts of instruments P - Bubb...
To finalize the direction of a survey, four surveyors set up a theodolite at a station P and performed all the temporary adjustments. From the station P, each of the surveyors obse...
The steel angle section shown in the figure has elastic section modulus of 150.92 cm³ about the horizontal X - X axis, which passes through the centroid of the section. The shape f...
A reinforced concrete pile of 10 m length and 0.7 m diameter is embedded in a saturated pure clay with unit cohesion of 50 kPa. If the adhesion factor is 0.5, the net ultimate upli...
A 2 m wide rectangular channel is carrying a discharge of 30 m³/s at a bed slope of 1 in 300. Assuming the energy correction factor as 1.1 and acceleration due to gravity as 10 m/s...
In a sample of 100 heart patients, each patient has 80% chance of having a heart attack without medicine X. It is clinically known that medicine X reduces the probability of having...
A linearly elastic beam of length 2l with flexural rigidity EI has negligible mass. A massless spring with a spring constant k and a rigid block of mass m are attached to the beam...
A critical activity in a project is estimated to take 15 days to complete at a cost of Rs. 30,000. The activity can be expedited to complete in 12 days by spending a total amount o...
A homogeneous, prismatic, linearly elastic steel bar fixed at both the ends has a slenderness ratio (l/r) of 105, where l is the bar length and r is the radius of gyration. The coe...
Consider the statements P and Q related to the analysis/design of retaining walls. P: When a rough retaining wall moves toward the backfill, the wall friction force/resistance mobi...
A round-bottom triangular lined canal is to be laid at a slope of 1 in 1500, to carry a discharge of 25 m³/s. The side slopes of the canal cross-section are to be kept at 1.25H : 1...
A hypothetical multimedia filter, consisting of anthracite particles (specific gravity: 1.50), silica sand (specific gravity: 2.60), and ilmenite sand (specific gravity: 4.20), is...
The consolidated data of a spot speed study for a certain stretch of a highway is given in the table. Speed range (kmph) | Number of observations 0 - 10 | 7 10 - 20 | 31 20 - 30 |...
Three vectors $\vec{p}$, $\vec{q}$, and $\vec{r}$ are given as $\vec{p} = \hat{i} + \hat{j} + \hat{k}$ $\vec{q} = \hat{i} + 2\hat{j} + 3\hat{k}$ $\vec{r} = 2\hat{i} + 3\hat{j} + 4\...
Consider the statements P, Q, and R. P: Compacted fine-grained soils with flocculated structure have isotropic permeability. Q: Phreatic surface/line is the line along which the po...
In the context of pavement material characterization, the CORRECT statement(s) is/are (A) The load penetration curve of CBR test may need origin correction due to the non-vertical...
The expression for computing the effective interest rate ($i_{eff}$) using continuous compounding for a nominal interest rate of 5% is $i_{eff} = \lim_{m\to\infty} (1 + \frac{0.05}...
Consider two matrices A = $\begin{bmatrix} 2 & 1 & 4 \\ 1 & 0 & 3 \end{bmatrix}$ and B = $\begin{bmatrix} -1 & 0 \\ 2 & 3 \\ 1 & 4 \end{bmatrix}$. The determinant of the matrix AB...
For the 6 m long horizontal cantilever beam PQR shown in the figure, Q is the mid-point. Segment PQ of the beam has flexural rigidity EI = 2 × 10$^5$ kN. m$^2$ whereas the segment...
The horizontal beam PQRS shown in the figure has a fixed support at point P, an internal hinge at point Q, and a pin support at point R. A concentrated vertically downward load (V)...
A concrete column section of size 300 mm × 500 mm as shown in the figure is subjected to both axial compression and bending along the major axis. The depth of the neutral axis (Xu)...
The table shows the activities and their durations and dependencies in a project. Activity | Duration (Days) | Depends on A | 8 | - B | 4 | A C | 4 | B D | 4 | C, L F | 4 | A G | 4...
A homogeneous earth dam has a maximum water head difference of 15 m between the upstream and downstream sides. A flownet was drawn with the number of potential drops as 10 and the...
The in-situ percentage of voids of a sand deposit is 50%. The maximum and minimum densities of sand determined from the laboratory tests are 1.8 g/cm³ and 1.3 g/cm³, respectively....
A drained triaxial test was conducted on a saturated sand specimen using a stress-path triaxial testing system. The specimen failed when the axial stress reached a value of 100 kN/...
A storm with a recorded precipitation of 11.0 cm, as shown in the table, produced a direct run-off of 6.0 cm. Time from start (hours): 1, 2, 3, 4, 5, 6, 7, 8 Recorded cumulative pr...
A 500 m long water distribution pipeline P with diameter 1.0 m, is used to convey 0.1 m³/s of flow. A new pipeline Q, with the same length and flow rate, is to replace P. The frict...
A 2m x 1.5 m tank of 6 m height is provided with a 100 mm diameter orifice at the center of its base. The orifice is plugged and the tank is filled up to 5 m height. Consider the a...
A rectangular channel is 4.0 m wide and carries a discharge of 2.0 m³/s with a depth of 0.4 m. The channel transitions to a maximum width contraction at a downstream location, with...
A circular settling tank is to be designed for primary treatment of sewage at a flow rate of 10 million liters/day. Assume a detention period of 2.0 hours and surface loading rate...
An organic waste is represented as C240O200H180N5S. (Atomic weights: S-32, H-1, C-12, O-16, N-14). Assume complete conversion of S to SO2 while burning. SO2 generated (in grams) pe...
A horizontal curve of radius 1080 m (with transition curves on either side) in a Broad Gauge railway track is designed and constructed for an equilibrium speed of 70 kmph. However,...
A vertical summit curve on a freight corridor is formed at the intersection of two gradients, +3.0% and -5.0%. Assume the following: Only large-sized trucks are allowed on this cor...
A child walks on a level surface from point P to point Q at a bearing of 30°, from point Q to point R at a bearing of 90° and then directly returns to the starting point P at a bea...
Differential levelling is carried out from point P (BM: +200.000 m) to point R. The readings taken are given in the table. Staff readings (m) Points Back Sight Fore Sight Remarks P...