GATE 2022 Civil Engineering
232 questions across 4 sessions
Set 1
A 2% sewage sample (in distilled water) was incubated for 3 days at 27$$^\circ$$C temperature. After incubation, a dissolved oxygen depletion of 10 mg/L was recorded. The biochemic...
A set of observations of independent variable (x) and the corresponding dependent variable (y) is given below. x 5 2 4 3 y 16 10 13 12 Based on the data, the coefficient a of the l...
In a water sample, the concentrations of Ca 2+ , Mg 2+ and HCO$$_3^ - $$ are 100 mg/L, 36 mg/L and 122 mg/L, respectively. The atomic masses of various elements are : Ca = 40, Mg =...
Henry's law constant for transferring O 2 from air into water, at room temperature, is 1.3 $${{mmol} \over {liter - atm}}$$. Given that the partial pressure of O 2 in the atmospher...
The Cartesian coordinates of a point P in a right-handed coordinate system are (1, 1, 1). The transformed coordinates of P due to a 45$$^\circ$$ clockwise rotation of the coordinat...
Consider the following recursive iteration scheme for different values of variable P with the initial guess x 1 = 1: $${x_{n + 1}} = {1 \over 2}\left( {{x_n} + {P \over {{x_n}}}} \...
For wastewater coming from a wood pulping industry, Chemical Oxygen Demand (COD) and 5-day Biochemical Oxygen Demand (BOD 5 ) were determined. For this wastewater, which of the fol...
Consider the following expression: z = sin(y + it) + cos(y $$-$$ it) where z, y, and t are variables, and $$i = \sqrt { - 1} $$ is a complex number. The partial differential equati...
A two-phase signalized intersection is designed with a cycle time of 100 s. The amber and red times for each phase are 4 s and 50 s, respectively. If the total lost time per phase...
At a traffic intersection, cars and buses arrive randomly according to independent Poisson processes at an average rate of 4 vehicles per hour and 2 vehicles per hour, respectively...
In the context of elastic theory of reinforced concrete, the modular ratio is defined as the ratio of
A concentrated vertical load of 3000 kN is applied on a horizontal ground surface. Points P and Q are at depths 1 m and 2 m below the ground, respectively, along the line of applic...
At a site, Static Cone Penetration Test was carried out. The measured point (tip) resistance q c was 1000 kPa at a certain depth. The friction ratio (f r ) was estimated as 1% at t...
Let $$\psi $$ represent soil suction head and K represent hydraulic conductivity of the soil. If the soil moisture content $$\theta$$ increases, which one of the following statemen...
Let $$\sigma$$' v and $$\sigma$$' h denote the effective vertical stress and effective horizontal stress, respectively. Which one of the following conditions must be satisfied for...
A raft foundation of 30 m $$\times$$ 25 m is proposed to be constructed at a depth of 8 m in a sand layer. A 25 m thick saturated clay layer exists 2 m below the base of the raft f...
The correct match between the physical states of the soils given in Group-I and the governing conditions given in Group-II is Group-I Group-II 1. normally consolidated soil. P. sen...
An uncompacted heap of soil has a volume of 10000 m 3 and void ratio of 1. If the soil is compacted to a volume of 7500 m 3 , then the corresponding void ratio of the compacted soi...
A square concrete pile of 10 m length is driven into a deep layer of uniform homogenous clay. Average unconfined compressive strength of the clay, determined through laboratory tes...
You should __________ when to say __________.
Two straight lines pass through the origin (x 0 , y 0 ) = (0, 0). One of them passes through the point (x 1 , y 1 ) = (1, 3) and the other passes through the point (x 2 , y 2 ) = (...
The vehicle count obtained in every 10 minute interval of a traffic volume survey done in peak one hour is given below. Time Interval (in minutes) Vehicle Count 0 - 10 10 10 - 20 1...
A horizontal curve is to be designed in a region with limited space. Which of the following measure(s) can be used to decrease the radius of curvature?
If p : q = 1 : 2 q : r = 4 : 3 r : s = 4 : 5 and u is 50% more than s, what is the ratio p : u?
A reinforced concrete beam with rectangular cross section (width = 300 mm, effective depth = 580 mm) is made of M30 grade concrete. It has 1% longitudinal tension reinforcement of...
As per Rankine's theory of earth pressure, the inclination of failure planes is $$\left( {45 + {\phi \over 2}} \right)^\circ $$ with respect to the direction of the minor principal...
Four different soils are classified as CH, ML, SP, and SW, as per the Unified Soil Classification System. Which one of the following options correctly represents their arrangement...
Consider the differential equation $${{dy} \over {dx}} = 4(x + 2) - y$$ For the initial condition y = 3 at x = 1, the value of y at x = 1.4 obtained using Euler's method with a ste...
For the equation $${{{d^3}y} \over {d{x^3}}} + x{\left( {{{dy} \over {dx}}} \right)^{3/2}} + {x^2}y = 0$$ the correct description is
P invested Rs.5000 per month for 6 months of a year and Q invested Rs. x per month for 8 months of the year in a partnership business. The profit is shared in proportion to the tot...
During a particular stage of the growth of a crop, the consumptive use of water is 2.8 mm/day. The amount of water available in the soil is 50% of the maximum depth of available wa...
Healthy eating is a critical component of healthy aging. When should one start eating healthy? It turns out that it is never too early. For example, babies who start eating healthy...
Given the statements : $$\bullet$$ P is the sister of Q. $$\bullet$$ Q is the husband of R. $$\bullet$$ R is the mother of S. $$\bullet$$ T is the husband of P. Based on the above...
A wastewater sample contains two nitrogen species, namely ammonia and nitrate. Consider the atomic weight of N, H, and O as 14 g/mol, 1 g/mol, and 16 g/mol, respectively. In this w...
The total hardness in raw water is 500 milligram per liter as CaCO 3 . The total hardness of this raw water, expressed in milligram equivalent per liter, is (Consider the atomic we...
The matrix M is defined as $$M = \left[ {\matrix{ 1 & 3 \cr 4 & 2 \cr } } \right]$$ and has eigenvalues 5 and $$-$$2. The matrix Q is formed as Q = M 3 $$-$$ 4M 2 $$-$$ 2M Which of...
Which of the following processes can be used for conversion of salt water into fresh water?
The Fourier cosine series of a function is given by : $$f(x) = \sum\limits_{n = 0}^\infty {{f_n}\cos nx} $$ For f(x) = cos 4 x, the numerical value of (f 4 + f 5 ) is _________. (r...
Let max {a, b} denote the maximum of two real numbers a and b. Which of the following statements is/are TRUE about the function f(x) = max{3 $$-$$ x, x $$-$$ 1}?
A water treatment plant has a sedimentation basin of depth 3 m, width 5 m, and length 40 m. The water inflow rate is 500 m 3 /h. The removal fraction of particles having a settling...
The project activities are given in the following table along with the duration and dependency. Activities Duration (days) Depends on P 10 - Q 12 - R 5 P S 10 Q T 10 P, Q Which one...
With respect to fluid flow, match the following in Column X with Column Y: Column X Column Y P. Viscosity I. Mach number Q. Gravity II. Reynolds number R. Compressibility III. Eule...
A rectangular channel with Gradually Varied Flow (GVF) has a changing bed slope. If the change is from a steeper slope to a steep slope, the resulting GVF profile is
Which of the following equations is correct for the Pozzolanic reaction?
Depth of water flowing in a 3 m wide rectangular channel is 2 m. The channel carries a discharge of 12 m 3 /s. Take g = 9.8 m/s 2 . The bed width (in m) at contraction, which just...
A line between stations P and Q laid on a slope of 1 in 5 was measured as 350 m using a 50 m tape. The tape is known to be short by 0.1 m. The corrected horizontal length (in m) of...
An aerial photograph is taken from a flight at a height of 3.5 km above mean sea level, using a camera of focal length 152 mm. If the average ground elevation is 460 m above mean s...
The bearing of a survey line is N31$$^\circ$$17'. Its azimuth observed from north is __________ deg. (round off to two decimal places)
The hoop stress at a point on the surface of a thin cylindrical pressure vessel is computed to be 30.0 MPa. The value of maximum shear stress at this point is
A two-hour duration storm event with uniform excess rainfall of 3 cm occurred on a watershed. The ordinates of streamflow hydrograph resulting from this event are given in the tabl...
In the context of cross-damage structures, the correct statement(s) regarding the relative positions of a natural drain (stream/river) and an irrigation canal, is/are
Set 2
To design an optimum municipal solid waste collection route, which of the following is/are NOT desired :
Consider the polynomial f(x) = x 3 $$-$$ 6x 2 + 11x $$-$$ 6 on the domain S, given by 1 $$\le$$ x $$\le$$ 3. The first and second derivatives are f'(x) and f''(x). Consider the fol...
A pair of six-faced dice is rolled twice. The probability that the sum of the outcomes in each roll equals 4 in exactly two of the three attempts is _________ (round off to three d...
The function f(x, y) satisfies the Laplace equation $$\Delta$$ 2 f(x, y) = 0 on a circular domain of radius r = 1 with its center at point P with coordinates x = 0, y = 0. The valu...
The base length of the runway at the mean sea level (MSL) is 1500 m. If the runway is located at an altitude of 300 m above the MSL, the actual length (in m) of the runway to be pr...
It is given that an aggregate mix has 260 grams of coarse aggregates and 240 grams of fine aggregates. The specific gravities of the coarse and fine aggregates are 2.6 and 2.4 resp...
A parabolic vertical crest curve connects two road segments with grades +1.0% and $$-$$2.0%. If a 200 m stopping sight distance is needed for a driver at a height of 1.2 m to avoid...
Which of the following statements is/are correct?
A post-tensioned concrete member of span 15 m and cross-section of 450 mm $$\times$$ 450 mm is prestressed with three steel tendons, each of cross-sectional area 200 mm 2 . The ten...
Read the following statements relating to flexure of reinforced concrete beams : I. In over-reinforced sections, the failure strain in concrete reaches earlier than the yield strai...
Match the following in Column X with Column Y : Column X Column Y P. In a triaxial compression test, with increase of axial strain in loose sand under drained shear condition. The...
A flood control structure having an expected life of n years is designed by considering a flood of return period T years. When T = n, and n $$\to$$ $$\infty$$, the structures hydro...
The movie was funny and I ____________.
In a partnership business the monthly investment by three friends for the first six months is in the ratio 3 : 4 : 5. After six months, they had to increase their monthly investmen...
For a traffic stream, V is the space mean speed, k is the density, q is the flow. V f is the free flow speed, and k f is the jam density. Assume that the speed decreases linearly w...
A single-lane highway has a traffic density of 40 vehicles km. If the time-mean speed and space-mean speed are 40 kmph and 30 kmph, respectively, the average headway (in seconds) b...
$$x:y:z = {1 \over 2}:{1 \over 3}:{1 \over 4}$$ What is the value of $${{x + z - y} \over y}$$ = ?
Given below are two statements and four conclusions drawn based on the statements. Statement 1 : Some soaps are clean. Statement 2 : All clean objects are wet. Conclusion I : Some...
Consider the following equations of straight lines : Line L1 : 2x $$-$$ 3y = 5 Line L2 : 3x + 2y = 8 Line L3 : 4x $$-$$ 6y = 5 Line L4 : 6x $$-$$ 9y = 6 Which one of the following...
A concentrically loaded isolated square footing of size 2 m $$\times$$ 2 m carries a concentrated vertical load of 1000 kN. Considering Boussinesq's theory of stress distribution,...
The inside diameter of a sampler tube is 50 mm. The inside diameter of the cutting edge is kept such that the Inside Clearance Ratio (ICR) is 1.0% to minimize the friction on the s...
Read the following statements : (P) While designing a shallow footing in sandy soil, monsoon season is considered for critical design in terms of bearing capacity. (Q) For slope st...
A group of total 16 piles are arranged in a square grid format. The center-to-center spacing (s) between adjacent piles is 3 m. The diameter (d) and length of embedment of each pil...
In a triaxial unconsolidated undrained (UU) test on a saturated clay sample, the cell pressure was 100 kPa. If the deviatoric stress at failure was 150 kPa, then the undrained shea...
Let y be a non-zero vector of size 2022 $$\times$$ 1. Which of the following statements is/are TRUE?
Both the numerator and the denominator of $${3 \over 4}$$ are increased by a positive $${15 \over 17}$$ integer, x, and those of _____ are decreased by the same integer. This opera...
$$\int {\left( {x - {{{x^2}} \over 2} + {{{x^3}} \over 3} - {{{x^4}} \over 4} + ....} \right)dx} $$ is equal to :
In the last few years, several new shopping malls were opened in the city. The total number of visitors in the malls is impressive. However, the total revenue generated through sal...
A survey of 450 students about their subjects of interest resulted in the following outcome. $$\bullet$$ 150 students are interested in Mathematics. $$\bullet$$ 200 students are in...
In a certain month, the reference crop evapotranspiration at a location is 6 mm day. If the crop coefficient and soil coefficient are 1.2 and 0.8, respectively, the actual evapotra...
A pump with an efficiency of 80% is used to draw groundwater from a well for irrigating a flat field of area 108 hectares. The base period and delta for paddy crop on this field ar...
Match Column X with Column Y : Column X Column Y (P) Horton equation (I) Design of alluvial channel (Q) Penman method (II) Maximum flood discharge (R) Chezy's formula (III) Evapotr...
In a solid waste handling facility, the moisture contents (MC) of food waste, paper waste, and glass waste were found to be MCf, MCp, and MCg, respectively. Similarly, the energy c...
A 100 mg of HNO 3 (strong acid) is added to water, bringing the final volume to 1.0 liter. Consider the atomic weights of H, N, and O, as 1 g/mol. 14 g mol. and 16 g/mol, respectiv...
In a city, the chemical formula of biodegradable fraction of municipal solid waste (MSW) is C 100 H 250 O 80 N. The waste has to be treated by forced-aeration composting process fo...
A sewage treatment plant receives sewage at a flow rate of 5000 m 3 /day. The total suspended solids (TSS) concentration in the sewage at the inlet of primary clarifier is 200 mg/L...
Match the following attributes of a city with the appropriate scale of measurements. Attribute Scale of measurement (P) Average temperature ($$^\circ $$C) of a city (I) Interval (Q...
The components of pure shear strain in a sheared are given in the matrix form: $$\varepsilon = \left[ {\matrix{ 1 & 1 \cr 1 & { - 1} \cr } } \right]$$ Here, Trace ($$\varepsilon $$...
A process equipment emits, 5 kg/h of volatile organic compounds (VOCs). If a hood placed over the process equipment captures 95% of the VOCs, then the fugitive emission in kg/h is
The activities of a project are given in the following table along with their durations and dependency. Activities Duration (day) Depends on A 10 - B 12 - C 15 A D 14 B E 10 B, C T...
A hydraulic jump takes place in a 6 in wide rectangular channel at a point where the upstream depth is 0.5 m (just before the jump). If the discharge in the channel is 30 m 3 /s an...
The dimension of dynamic viscosity is :
Match all the possible combinations between Column X (Cement compounds) and Column Y (Cement properties) : Column X Column Y (i) $${C_3}S$$ (P) Early age strength (ii) $${C_2}S$$ (...
Two discrete spherical particles (P and Q) of equal mass density are independently released in water. Particle P and particle Q have diameters of 0.5 mm and 1.0 mm, respectively. A...
Water is flowing in a horizontal, frictionless, rectangular channel. A smooth hump is built on the channel floor at a section and its height is gradually increased to reach choked...
The error in measuring the radius of a 5 cm circular rod was 0.2%. If the cross-sectional area of the rod was calculated using this measurement, then the resulting absolute percent...
If the magnetic bearing of the Sun at a place at noon is S 2$$^\circ$$E. The magnetic declination (in degrees) at that place is
For a linear elastic and isotropic material, the correct relationship among Young's modulus of elasticity (E), Poisson's ratio (v), and shear modulus (G) is
P and Q are two square matrices of the same order. Which of the following statements is/are correct?
At a municipal waste handling facility, 30 metric ton mixture of food waste, yard waste, and paper waste was available. The moisture content of this mixture was found to be 10%. Th...
A sample of air analyzed at 25$$^\circ$$C and 1 atm pressure is reported to contain 0.04 ppm of SO 2 . Atomic mass of S = 32. O = 16. The equivalent SO 2 concentration (in $$\mu$$g...
Set 1
You should ________ when to say ________.
Two straight lines pass through the origin $(x_0, y_0) = (0,0)$. One of them passes through the point $(x_1, y_1) = (1,3)$ and the other passes through the point $(x_2, y_2) = (1,2...
If p : q = 1 : 2 q : r = 4 : 3 r : s = 4 : 5 and u is 50% more than s, what is the ratio p : u?
Given the statements: • P is the sister of Q. • Q is the husband of R. • R is the mother of S. • T is the husband of P. Based on the above information, T is ________ of S.
In the following diagram, the point R is the center of the circle. The lines PQ and ZV are tangential to the circle. The relation among the areas of the squares, PXWR, RUVZ and SPQ...
Healthy eating is a critical component of healthy aging. When should one start eating healthy? It turns out that it is never too early. For example, babies who start eating healthy...
P invested ₹ 5000 per month for 6 months of a year and Q invested ₹ x per month for 8 months of the year in a partnership business. The profit is shared in proportion to the total...
The above frequency chart shows the frequency distribution of marks obtained by a set of students in an exam. From the data presented above, which one of the following is CORRECT?
In the square grid shown on the left, a person standing at P2 position is required to move to P5 position. The only movement allowed for a step involves, "two moves along one direc...
Consider a cube made by folding a single sheet of paper of appropriate shape. The interior faces of the cube are all blank. However, the exterior faces that are not visible in the...
Consider the following expression: $z = \sin(y+it)+\cos(y-it)$ where z, y, and t are variables, and $i=\sqrt{-1}$ is a complex number. The partial differential equation derived fro...
For the equation $\frac{d^3y}{dx^3} + x (\frac{dy}{dx})^{3/2} + x^2y = 0$ the correct description is
The hoop stress at a point on the surface of a thin cylindrical pressure vessel is computed to be 30.0 MPa. The value of maximum shear stress at this point is
In the context of elastic theory of reinforced concrete, the modular ratio is defined as the ratio of
Which of the following equations is correct for the Pozzolanic reaction?
Consider the cross-section of a beam made up of thin uniform elements having thickness t (t << a) shown in the figure. The (x, y) coordinates of the points along the center-line of...
Four different soils are classified as CH, ML, SP, and SW, as per the Unified Soil Classification System. Which one of the following options correctly represents their arrangement...
Let $\sigma'_v$ and $\sigma'_h$ denote the effective vertical stress and effective horizontal stress, respectively. Which one of the following conditions must be satisfied for a so...
With respect to fluid flow, match the following in Column X with Column Y: Column X (P) Viscosity (Q) Gravity (R) Compressibility (S) Pressure Column Y (I) Mach number (II) Reynold...
Let $\psi$ represent soil suction head and $K$ represent hydraulic conductivity of the soil. If the soil moisture content $\theta$ increases, which one of the following statements...
A rectangular channel with Gradually Varied Flow (GVF) has a changing bed slope. If the change is from a steeper slope to a steep slope, the resulting GVF profile is
The total hardness in raw water is 500 milligram per liter as CaCO3. The total hardness of this raw water, expressed in milligram equivalent per liter, is (Consider the atomic weig...
An aerial photograph is taken from a flight at a height of 3.5 km above mean sea level, using a camera of focal length 152 mm. If the average ground elevation is 460 m above mean s...
A line between stations P and Q laid on a slope of 1 in 5 was measured as 350 m using a 50 m tape. The tape is known to be short by 0.1 m. The corrected horizontal length (in m) of...
The matrix M is defined as $M = \begin{bmatrix} 1 & 3 \\ 4 & 2 \end{bmatrix}$ and has eigenvalues 5 and -2. The matrix Q is formed as $Q = M^3 - 4M^2 - 2M$ Which of the following i...
For wastewater coming from a wood pulping industry, Chemical Oxygen Demand (COD) and 5-day Biochemical Oxygen Demand (BOD5) were determined. For this wastewater, which of the follo...
Which of the following process(es) can be used for conversion of salt water into fresh water?
A horizontal curve is to be designed in a region with limited space. Which of the following measure(s) can be used to decrease the radius of curvature?
Consider the following recursive iteration scheme for different values of variable P with the initial guess $x_1 = 1$: $x_{n+1} = \frac{1}{2} (x_n + \frac{P}{x_n})$, $n = 1, 2, 3,...
The Fourier cosine series of a function is given by: $f(x) = \sum_{n=0}^{\infty} f_n \cos nx$ For $f(x) = \cos^4 x$, the numerical value of $(f_4 + f_5)$ is __________. (round off...
An uncompacted heap of soil has a volume of 10000 m³ and void ratio of 1. If the soil is compacted to a volume of 7500 m³, then the corresponding void ratio of the compacted soil i...
A concentrated vertical load of 3000 kN is applied on a horizontal ground surface. Points P and Q are at depths 1 m and 2 m below the ground, respectively, along the line of applic...
At a site, Static Cone Penetration Test was carried out. The measured point (tip) resistance q_c was 1000 kPa at a certain depth. The friction ratio (f_r) was estimated as 1 % at t...
During a particular stage of the growth of a crop, the consumptive use of water is 2.8 mm/day. The amount of water available in the soil is 50 % of the maximum depth of available w...
The bearing of a survey line is N31°17′W. Its azimuth observed from north is __________ deg. (round off to two decimal places)
The Cartesian coordinates of a point P in a right-handed coordinate system are (1, 1, 1). The transformed coordinates of P due to a 45° clockwise rotation of the coordinate system...
A semi-circular bar of radius R m, in a vertical plane, is fixed at the end G, as shown in the figure. A horizontal load of magnitude P kN is applied at the end H. The magnitude of...
A weld is used for joining an angle section ISA 100 mm × 100 mm × 10 mm to a gusset plate of thickness 15 mm to transmit a tensile load. The permissible stress in the angle is 150...
The project activities are given in the following table along with the duration and dependency. Activities | Duration (days) | Depends on ---|---|--- P | 10 | - Q | 12 | - R | 5 |...
The correct match between the physical states of the soils given in Group I and the governing conditions given in Group II is Group I 1. normally consolidated soil 2. quick clay 3....
As per Rankine's theory of earth pressure, the inclination of failure planes is $(45 + \frac{\phi}{2})°$ with respect to the direction of the minor principal stress. The above stat...
Henry's law constant for transferring O2 from air into water, at room temperature, is $1.3 \frac{mmol}{liter-atm}$. Given that the partial pressure of O2 in the atmosphere is 0.21...
In a water sample, the concentrations of Ca2+, Mg2+ and HCO3- are 100 mg/L, 36 mg/L and 122 mg/L, respectively. The atomic masses of various elements are: Ca = 40, Mg = 24, H = 1,...
Consider the four points P, Q, R, and S shown in the Greenshields fundamental speed-flow diagram. Denote their corresponding traffic densities by $k_P$, $k_Q$, $k_R$, and $k_S$, re...
Let max {a, b} denote the maximum of two real numbers a and b. Which of the following statement(s) is/are TRUE about the function f(x) = max{3 - x, x - 1} ?
A horizontal force of P kN is applied to a homogeneous body of weight 25 kN, as shown in the figure. The coefficient of friction between the body and the floor is 0.3. Which of the...
In the context of cross-drainage structures, the correct statement(s) regarding the relative positions of a natural drain (stream/river) and an irrigation canal, is/are
Consider the differential equation $\frac{dy}{dx} = 4(x+2)-y$ For the initial condition $y = 3$ at $x = 1$, the value of $y$ at $x = 1.4$ obtained using Euler's method with a step-...
A set of observations of independent variable ($x$) and the corresponding dependent variable ($y$) is given below. | $x$ | 5 | 2 | 4 | 3 | |---|---|---|---|---| | $y$ | 16 | 10 | 1...
The plane truss shown in the figure is subjected to an external force P. It is given that P = 70 kN, a = 2 m, and b = 3 m. The magnitude (absolute value) of force (in kN) in member...
Consider the linearly elastic plane frame shown in the figure. Members HF, FK and FG are welded together at joint F. Joints K, G and H are fixed supports. A counter-clockwise momen...
Consider a simply supported beam PQ as shown in the figure. A truck having 100 kN on the front axle and 200 kN on the rear axle, moves from left to right. The spacing between the a...
A reinforced concrete beam with rectangular cross section (width = 300 mm, effective depth = 580 mm) is made of M30 grade concrete. It has 1% longitudinal tension reinforcement of...
A square concrete pile of 10 m length is driven into a deep layer of uniform homogeneous clay. Average unconfined compressive strength of the clay, determined through laboratory te...
A raft foundation of 30 m × 25 m is proposed to be constructed at a depth of 8 m in a sand layer. A 25 m thick saturated clay layer exists 2 m below the base of the raft foundation...
A two-hour duration storm event with uniform excess rainfall of 3 cm occurred on a watershed. The ordinates of streamflow hydrograph resulting from this event are given in the tabl...
Two reservoirs are connected by two parallel pipes of equal length and of diameters 20 cm and 10 cm, as shown in the figure (not drawn to scale). When the difference in the water l...
Depth of water flowing in a 3 m wide rectangular channel is 2 m. The channel carries a discharge of 12 m³/s. Take g = 9.8 m/s². The bed width (in m) at contraction, which just caus...
A wastewater sample contains two nitrogen species, namely ammonia and nitrate. Consider the atomic weight of N, H, and O as 14 g/mol, 1 g/mol, and 16 g/mol, respectively. In this w...
A 2% sewage sample (in distilled water) was incubated for 3 days at 27 °C temperature. After incubation, a dissolved oxygen depletion of 10 mg/L was recorded. The biochemical oxyge...
A water treatment plant has a sedimentation basin of depth 3 m, width 5 m, and length 40 m. The water inflow rate is 500 m³/h. The removal fraction of particles having a settling v...
A two-phase signalized intersection is designed with a cycle time of 100 s. The amber and red times for each phase are 4 s and 50 s, respectively. If the total lost time per phase...
At a traffic intersection, cars and buses arrive randomly according to independent Poisson processes at an average rate of 4 vehicles per hour and 2 vehicles per hour, respectively...
The vehicle count obtained in every 10 minute interval of a traffic volume survey done in peak one hour is given below. Time Interval (in minutes) | Vehicle Count ---|--- 0 – 10 |...
For the dual-wheel carrying assembly shown in the figure, P is the load on each wheel, a is the radius of the contact area of the wheel, s is the spacing between the wheels, and d...
Set 2
The movie was funny and I __________.
x : y : z = $\frac{1}{2} : \frac{1}{3} : \frac{1}{4}$ What is the value of $\frac{x+z-y}{y}$?
Both the numerator and the denominator of $\frac{3}{4}$ are increased by a positive integer, x, and those of $\frac{15}{17}$ are decreased by the same integer. This operation resul...
A survey of 450 students about their subjects of interest resulted in the following outcome. * 150 students are interested in Mathematics. * 200 students are interested in Physics....
For the picture shown above, which one of the following is the correct picture representing reflection with respect to the mirror shown as the dotted line?
In the last few years, several new shopping malls were opened in the city. The total number of visitors in the malls is impressive. However, the total revenue generated through sal...
In a partnership business the monthly investment by three friends for the first six months is in the ratio 3: 4: 5. After six months, they had to increase their monthly investments...
Consider the following equations of straight lines: Line L1: 2x - 3y = 5 Line L2: 3x + 2y = 8 Line L3: 4x - 6y = 5 Line L4: 6x - 9y = 6 Which one among the following is the correct...
Given below are two statements and four conclusions drawn based on the statements. Statement 1: Some soaps are clean. Statement 2: All clean objects are wet. Conclusion I: Some cle...
An ant walks in a straight line on a plane leaving behind a trace of its movement. The initial position of the ant is at point P facing east. The ant first turns 72º anticlockwise...
The function $f(x, y)$ satisfies the Laplace equation $\nabla^2 f(x, y) = 0$ on a circular domain of radius $r = 1$ with its center at point $P$ with coordinates $x = 0, y = 0$. Th...
$\int \left(x - \frac{x^2}{2} + \frac{x^3}{3} - \frac{x^4}{4} + \dots\right) dx$ is equal to
For a linear elastic and isotropic material, the correct relationship among Young's modulus of elasticity (E), Poisson's ratio ($\nu$), and shear modulus (G) is
Read the following statements relating to flexure of reinforced concrete beams: I. In over-reinforced sections, the failure strain in concrete reaches earlier than the yield strain...
Match all the possible combinations between Column X (Cement compounds) and Column Y (Cement properties): Column X (i) C3S (ii) C2S (iii) C3A Column Y (P) Early age strength (Q) La...
Consider a beam PQ fixed at P, hinged at Q, and subjected to a load F as shown in figure (not drawn to scale). The static and kinematic degrees of indeterminacy, respectively, are
Read the following statements: (P) While designing a shallow footing in sandy soil, monsoon season is considered for critical design in terms of bearing capacity. (Q) For slope sta...
Stresses acting on an infinitesimal soil element are shown in the figure (with $\sigma_z > \sigma_x$). The major and minor principal stresses are $\sigma_1$ and $\sigma_3$, respect...
Match Column X with Column Y: Column X (P) Horton equation (Q) Penman method (R) Chezy's formula (S) Lacey's theory (T) Dicken's formula Column Y (I) Design of alluvial channel (II...
In a certain month, the reference crop evapotranspiration at a location is 6 mm/day. If the crop coefficient and soil coefficient are 1.2 and 0.8, respectively, the actual evapotra...
The dimension of dynamic viscosity is:
A process equipment emits 5 kg/h of volatile organic compounds (VOCs). If a hood placed over the process equipment captures 95% of the VOCs, then the fugitive emission in kg/h is
Match the following attributes of a city with the appropriate scale of measurements. Attribute (P) Average temperature (°C) of a city (Q) Name of a city (R) Population density of a...
If the magnetic bearing of the Sun at a place at noon is S 2º E, the magnetic declination (in degrees) at that place is
P and Q are two square matrices of the same order. Which of the following statement(s) is/are correct?
In a solid waste handling facility, the moisture contents (MC) of food waste, paper waste, and glass waste were found to be MCf, MCp, and MCg, respectively. Similarly, the energy c...
To design an optimum municipal solid waste collection route, which of the following is/are NOT desired:
For a traffic stream, v is the space mean speed, k is the density, q is the flow, vf is the free flow speed, and kj is the jam density. Assume that the speed decreases linearly wit...
The error in measuring the radius of a 5 cm circular rod was 0.2%. If the cross-sectional area of the rod was calculated using this measurement, then the resulting absolute percent...
The components of pure shear strain in a sheared material are given in the matrix form: $\varepsilon = \begin{bmatrix} 1 & 1 \\ 1 & -1 \end{bmatrix}$ Here, Trace($\varepsilon$) = 0...
The inside diameter of a sampler tube is 50 mm. The inside diameter of the cutting edge is kept such that the Inside Clearance Ratio (ICR) is 1.0 % to minimize the friction on the...
A concentrically loaded isolated square footing of size 2 m × 2 m carries a concentrated vertical load of 1000 kN. Considering Boussinesq's theory of stress distribution, the maxim...
In a triaxial unconsolidated undrained (UU) test on a saturated clay sample, the cell pressure was 100 kPa. If the deviatoric stress at failure was 150 kPa, then the undrained shea...
A flood control structure having an expected life of n years is designed by considering a flood of return period T years. When T = n, and n → ∞, the structure's hydrologic risk of...
The base length of the runway at the mean sea level (MSL) is 1500 m. If the runway is located at an altitude of 300 m above the MSL, the actual length (in m) of the runway to be pr...
Consider the polynomial $f(x) = x^3 - 6x^2 + 11x - 6$ on the domain $S$ given by $1 \le x \le 3$. The first and second derivatives are $f'(x)$ and $f''(x)$. Consider the following...
An undamped spring-mass system with mass m and spring stiffness k is shown in the figure. The natural frequency and natural period of this system are $\omega$ rad/s and T s, respec...
For the square steel beam cross-section shown in the figure, the shape factor about Z – Z axis is S and the plastic moment capacity is M_p. Consider yield stress f_y = 250 MPa and...
A post-tensioned concrete member of span 15 m and cross-section of 450 mm x 450 mm is prestressed with three steel tendons, each of cross-sectional area 200 mm². The tendons are te...
Match the following in Column X with Column Y: Column X (P) In a triaxial compression test, with increase of axial strain in loose sand under drained shear condition, the volumetri...
A soil sample is underlying a water column of height h₁, as shown in the figure. The vertical effective stresses at points A, B, and C are $\sigma_A'$, $\sigma_B'$, and $\sigma_C'$...
A 100 mg of HNO3 (strong acid) is added to water, bringing the final volume to 1.0 liter. Consider the atomic weights of H, N, and O, as 1 g/mol, 14 g/mol, and 16 g/mol, respective...
In a city, the chemical formula of biodegradable fraction of municipal solid waste (MSW) is C100H250O80N. The waste has to be treated by forced-aeration composting process for whic...
A single-lane highway has a traffic density of 40 vehicles/km. If the time-mean speed and space-mean speed are 40 kmph and 30 kmph, respectively, the average headway (in seconds) b...
Let y be a non-zero vector of size 2022 × 1. Which of the following statement(s) is/are TRUE?
Which of the following statement(s) is/are correct?
Water is flowing in a horizontal, frictionless, rectangular channel. A smooth hump is built on the channel floor at a section and its height is gradually increased to reach choked...
The concentration $s(x, t)$ of pollutants in a one-dimensional reservoir at position $x$ and time $t$ satisfies the diffusion equation $\frac{\partial s(x, t)}{\partial t} = D \fra...
A pair of six-faced dice is rolled thrice. The probability that the sum of the outcomes in each roll equals 4 in exactly two of the three attempts is ____________. (round off to th...
Consider two linearly elastic rods HI and IJ, each of length b, as shown in the figure. The rods are co-linear, and confined between two fixed supports at H and J. Both the rods ar...
The linearly elastic planar structure shown in the figure is acted upon by two vertical concentrated forces. The horizontal beams UV and WX are connected with the help of the verti...
A uniform rod KJ of weight w shown in the figure rests against a frictionless vertical wall at the point K and a rough horizontal surface at point J. It is given that w = 10 kN, a...
The activities of a project are given in the following table along with their durations and dependency. The total float of the activity E (in days) is __________. (in integer)
A group of total 16 piles are arranged in a square grid format. The center-to-center spacing (s) between adjacent piles is 3 m. The diameter (d) and length of embedment of each pil...
A saturated compressible clay layer of thickness h is sandwiched between two sand layers, as shown in the figure. Initially, the total vertical stress and pore water pressure at po...
A hydraulic jump takes place in a 6 m wide rectangular channel at a point where the upstream depth is 0.5 m (just before the jump). If the discharge in the channel is 30 m³/s and t...
A pump with an efficiency of 80% is used to draw groundwater from a well for irrigating a flat field of area 108 hectares. The base period and delta for paddy crop on this field ar...
Two discrete spherical particles (P and Q) of equal mass density are independently released in water. Particle P and particle Q have diameters of 0.5 mm and 1.0 mm, respectively. A...
At a municipal waste handling facility, 30 metric ton mixture of food waste, yard waste, and paper waste was available. The moisture content of this mixture was found to be 10%. Th...
A sewage treatment plant receives sewage at a flow rate of 5000 m³/day. The total suspended solids (TSS) concentration in the sewage at the inlet of primary clarifier is 200 mg/L....
A sample of air analyzed at 25 °C and 1 atm pressure is reported to contain 0.04 ppm of SO2. Atomic mass of S = 32, O = 16. The equivalent SO2 concentration (in µg/m³) will be ____...
A parabolic vertical crest curve connects two road segments with grades +1.0% and -2.0%. If a 200 m stopping sight distance is needed for a driver at a height of 1.2 m to avoid an...
Assuming that traffic on a highway obeys the Greenshields model, the speed of a shockwave between two traffic streams (P) and (Q) as shown in the schematic is _________ kmph. (in i...
It is given that an aggregate mix has 260 grams of coarse aggregates and 240 grams of fine aggregates. The specific gravities of the coarse and fine aggregates are 2.6 and 2.4, res...
The lane configuration with lane volumes in vehicles per hour of a four-arm signalized intersection is shown in the figure. There are only two phases: the first phase is for the Ea...