Two straight lines pass through the origin $(x$, $y$) = (0,0). One of them passes through the point $(x$, $y$) = (1,3) and the other passes through the point $(x$, $y$) = (1,2). What is the area enclosed between the straight lines in the interval [0, 1] on the $x-axis?$
a.
0.5
Correct Answer
b.
1.0
c.
1.5
d.
2.0 CE-1 Page 1 of 42
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Q2mcq
$xβΆyβΆz=$::. What is the value of ?
a.
0.75
Correct Answer
b.
1.25
c.
2.25
d.
3.25 CE-2 Page 1 of 40
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Q3mcq
If $pβΆq=1βΆ2$ $qβΆr=4βΆ3$ $rβΆs=4βΆ5$ and $u$ is 50% more than $s,$ what is the ratio $p$ βΆ $u?$
a.
2 βΆ 15
b.
16 βΆ 15
c.
1: 5
d.
16: 45 CE-1 Page 2 of 42
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Q3mcq
Both the numerator and the denominator of are increased by a positive integer, $x,$ and those of are decreased by the same integer. This operation results in the same value for both the fractions. What is the value of $x?$
a.
1
b.
2
c.
3
d.
4 CE-2 Page 2 of 40
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Q4mcq
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.
a.
the grandfather
b.
an uncle
Correct Answer
c.
the father
d.
a brother CE-1 Page 3 of 42
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Q4mcq
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. $$ 175 students are interested in Chemistry. $$ 50 students are interested in Mathematics and Physics. $$ 60 students are interested in Physics and Chemistry. $$ 40 students are interested in Mathematics and Chemistry. $$ 30 students are interested in Mathematics, Physics and Chemistry. $$ Remaining students are interested in Humanities. Based on the above information, the number of students interested in Humanities is
a.
10
b.
30
Correct Answer
c.
40
d.
45 CE-2 Page 3 of 40
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Q5mcq
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 SPQT is
a.
Area of SPQT = Area of RUVZ = Area of PXWR
b.
Area of SPQT = Area of PXWR $-$ Area of RUVZ
Correct Answer
c.
Area of PXWR = Area of SPQT $-$ Area of RUVZ
d.
Area of PXWR = Area of RUVZ $-$ Area of SPQT CE-1 Page 4 of 42
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Q5mcq
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?
a.
b.
Correct Answer
c.
d.
CE-2 Page 4 of 40
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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 in the first year are more likely to have better overall health as they get older. Which one of the following is the CORRECT logical inference based on the information in the above passage?
a.
Healthy eating is important for those with good health conditions, but not for others
b.
Eating healthy can be started at any age, earlier the better
c.
Eating healthy and better overall health are more correlated at a young age, but not older age
d.
Healthy eating is more important for adults than kids CE-1 Page 5 of 42
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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 sales in the shops in these malls is generally low. Which one of the following is the CORRECT logical inference based on the information in the above passage?
a.
Fewer people are visiting the malls but spending more
b.
More people are visiting the malls but not spending enough
c.
More people are visiting the malls and spending more
d.
Fewer people are visiting the malls and not spending enough CE-2 Page 5 of 40
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P invested βΉ 5000 per month for 6 months of a year and Q invested βΉ $x$ per month for 8 months of the year in a partnership business. The profit is shared in proportion to the total investment made in that year. If at the end of that investment year, Q receives of the total profit, what is the value of $x$ (in βΉ)?
a.
2500
b.
3000
c.
4687
d.
8437 CE-1 Page 6 of 42
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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 by 10%, 15% and 20%, respectively, of their initial monthly investment. The new investment ratio was kept constant for the next six months. What is the ratio of their shares in the total profit (in the same order) at the end of the year such that the share is proportional to their individual total investment over the year?
a.
22: 23: 24
b.
22: 33: 50
c.
33: 46: 60
d.
63: 86: 110 CE-2 Page 6 of 40
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16
14 14
11 12 Frequency 9 10
7 8 6 4 3
4
2 2 0
3 4 5 6 7 8 9
Marks 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?
a.
mean > mode > median
b.
mode > median > mean
c.
mode > mean > median
d.
median > mode > mean CE-1 Page 7 of 42
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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 statement?
a.
L1 is parallel to L2 and L1 is perpendicular to L3
b.
L2 is parallel to L4 and L2 is perpendicular to L1
c.
L3 is perpendicular to L4 and L3 is parallel to L2
d.
L4 is perpendicular to L2 and L4 is parallel to L3 CE-2 Page 7 of 40
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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, βtwo moves along one direction followed by one move in a perpendicular directionβ. The permissible directions for movement are shown as dotted arrows in the right. For example, a person at a given position Y can move only to the positions marked X on the right. Without occupying any of the shaded squares at the end of each step, the minimum number of steps required to go from P2 to P5 is
1 2 3 4 5 P Q R S T
Example: Allowed steps for a person at Y
a.
4
b.
5
c.
6
d.
7 CE-1 Page 8 of 42
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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 clean objects are soaps. Conclusion II: No clean object is a soap. Conclusion III: Some wet objects are soaps. Conclusion IV: All wet objects are soaps. Which one of the following options can be logically inferred?
a.
Only conclusion I is correct
b.
Either conclusion I or conclusion II is correct
c.
Either conclusion III or conclusion IV is correct
d.
Only conclusion I and conclusion III are correct CE-2 Page 8 of 40
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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 above view may not be blank. Which one of the following represents a possible unfolding of the cube?
a.
b.
c.
d.
CE-1 Page 9 of 42
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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 72 o anticlockwise at P, and then does the following two steps in sequence exactly FIVE times before halting. 1. moves forward for 10 cm. 2. turns 144 o clockwise. The pattern made by the trace left behind by the ant is
a.
b.
c.
d.
CE-2 Page 9 of 40
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Consider the following expression: z $=$ sin $($ y $+$ it $) +$ cos $($ y $-$ it $)$ where z, y, and t are variables, and i $= -$ 1 is a complex number. The partial differential equation derived from the above expression is
a.
b.
c.
d.
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The function $f(x, y)$ satisfies the Laplace equation
β $f(x, y)$ = 0 on a circular domain of radius $r$ = $1$ with its center at point $P$ with coordinates $x$ = $0, y$ = $0.$ The value of this function on the circular boundary of this domain is equal to 3. The numerical value of $f(0, 0)$ is:
a.
0
b.
2
c.
3
d.
1 CE-2 Page 10 of 40
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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.
7.5 MPa
b.
15.0 MPa
c.
30.0 MPa
d.
22.5 MPa CE-1 Page 11 of 42
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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 in steel. II. In under-reinforced sections, steel reaches yielding at a load lower than the load at which the concrete reaches failure strain. III. Over-reinforced beams are recommended in practice as compared to the under-reinforced beams. IV. In balanced sections, the concrete reaches failure strain earlier than the yield strain in tensile steel. Each of the above statements is either True or False. Which one of the following combinations is correct?
a.
I (True), II (True), III (False), IV (False)
b.
I (True), II (True), III (False), IV (True)
c.
I (False), II (False), III (True), IV (False)
d.
I (False), II (True), III (True), IV (False) CE-2 Page 12 of 40
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Consider the cross-section of a beam made up of thin uniform elements having thickness $t (t$ βͺ $a)$ shown in the figure. The (x, y) coordinates of the points along the center-line of the cross-section are given in the figure. The coordinates of the shear center of this cross-section are:
a.
$x$ = 0, $y$ = $3a$
b.
$x$ = $2a, y$ = $2a$
c.
$x$ = $-a, y$ = $2a$
d.
$x$ = $-2a, y$ = $a$ CE-1 Page 13 of 42
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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
a.
2 and 1
b.
2 and 0
c.
1 and 2
d.
2 and 2 CE-2 Page 14 of 40
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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 in the decreasing order of hydraulic conductivity?
a.
SW, SP, ML, CH
b.
CH, ML, SP, SW
c.
SP, SW, CH, ML
d.
ML, SP, CH, SW
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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 stability of an earthen dam, sudden drawdown is never a critical condition. (R) In a sandy sea beach, quicksand condition can arise only if the critical hydraulic gradient exceeds the existing hydraulic gradient. (S) The active earth thrust on a rigid retaining wall supporting homogeneous cohesionless backfill will reduce with the lowering of water table in the backfill. Which one of the following combinations is correct?
a.
(P)-True, (Q)-False, (R)-False, (S)-False
b.
(P)-False, (Q)-True, (R)-True, (S)-True
c.
(P)-True, (Q)-False, (R)-True, (S)-True
d.
(P)-False, (Q)-True, (R)-False, (S)-False CE-2 Page 15 of 40
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Let $Ο$ and $Ο$ denote the effective vertical stress and effective horizontal stress, respectively. Which one of the following conditions must be satisfied for a soil element to reach the failure state under Rankineβs passive earth pressure condition?
a.
$Ο <Ο$
b.
$Ο >Ο$
c.
$Ο =Ο$
d.
$Ο +Ο$ = 0 CE-1 Page 14 of 42
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Stresses acting on an infinitesimal soil element are shown in the figure (with $Ο$ > $Ο$). The major and minor principal stresses are $Ο$ and $Ο$, respectively. Considering the compressive stresses as positive, which one of the following expressions correctly represents the angle between the major principal stress plane and the horizontal plane?
a.
b.
c.
d.
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Let $$ represent soil suction head and K represent hydraulic conductivity of the soil. If the soil moisture content $$ increases, which one of the following statements is TRUE?
a.
b.
c.
d.
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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 evapotranspiration in mm/day is
a.
5.76
b.
7.20
c.
6.80
d.
8.00
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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
a.
S 3
b.
S 1
c.
S 2
d.
either S 1 or S 2, depending on the magnitude of the slopes CE-1 Page 16 of 42
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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 weights of Ca, C, and O as 40 g/mol, 12 g/mol, and 16 g/mol, respectively.)
a.
10
b.
100
c.
1
d.
5
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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
a.
0.25
b.
4.75
c.
2.50
d.
0.48 CE-2 Page 19 of 40
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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 sea level, then the scale of the photograph is
a.
1: 20000
b.
1: 20
c.
1: 100000
d.
1: 2800 CE-1 Page 17 of 42
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Match the following attributes of a city with the appropriate scale of measurements.
Attribute Scale of
measurement
(P) Average temperature (Β°C) of a city (I) Interval
(Q) Name of a city (II) Ordinal
(R) Population density of a city (III) Nominal
(S) Ranking of a city based on ease of (IV) Ratio
business Which one of the following combinations is correct?
a.
(P)-(I), (Q)-(III), (R)-(IV), (S)-(II)
b.
(P)-(II), (Q)-(I), (R)-(IV), (S)-(III)
c.
(P)-(II), (Q)-(III), (R)-(IV), (S)-(I)
d.
(P)-(I), (Q)-(II), (R)-(III), (S)-(IV) CE-2 Page 20 of 40
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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 line PQ will be
a.
342.52
b.
349.30
c.
356.20
d.
350.70
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The matrix M is defined as
$M=$
1 3
4 2 and has eigenvalues $5$ and - $2.$ The matrix $Q$ is formed as
$Q$ = $M$ - $4M$ - $2M$ Which of the following is/are the eigenvalue(s) of matrix Q ?
a.
$ 15$
b.
25
c.
$-20$
d.
$-30$ $ $ CE-1 Page 18 of 42
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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 following statement(s) is/are correct?
a.
COD > BOD 5
b.
COD $=ΜΈ$ BOD 5
c.
COD < BOD 5
d.
COD = BOD 5
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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 contents (EC) of plastic waste, food waste, and glass waste were found to be ECpp, ECf, and ECg, respectively. Which of the following statement(s) is/are correct?
a.
MCf > MCp > MCg
b.
ECpp > ECf > ECg
c.
MCf < MCp < MCg
d.
ECpp < ECf < ECg
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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?
a.
Decrease the design speed.
b.
Increase the superelevation.
c.
Increase the design speed.
d.
Restrict vehicles with higher weight from using the facility. CE-1 Page 20 of 42
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For a traffic stream, v is the space mean speed, k is the density, q is the flow, v is the free flow speed, and k is the jam density. Assume that the speed f j decreases linearly with density. Which of the following relation(s) is/are correct?
a.
b.
c.
d.
$q=k v- v$
$k$
$v$
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Consider the following recursive iteration scheme for different values of variable $P$ with the initial guess $x$ = $1$:
$x$ = $x$ +, $n$ = 1, 2, 3, 4, 5
1 $P$
2 $x$ For $P$ = $2, x$ is obtained to be 1.414, rounded-off to three decimal places. For $P$ = $3, x$ is obtained to be 1.732, rounded-off to three decimal places. If $P$ = $10,$ the numerical value of $x$ is _________. (round off to three decimal places)
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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 percentage error in the computed area is______. (round off to two decimal places)
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The Fourier cosine series of a function is given by:
$f(x)$ = $f$ cos $nx$ For $f(x)$ = cos $x$, the numerical value of $(f$ + $f$) is ______. (round off to three decimal places)
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The components of pure shear strain in a sheared material are given in the matrix form:
$Ξ΅=$
1 1
1 -1 Here, $Trace(Ξ΅)$ = 0. Given, $P$ = $Trace(Ξ΅$) and $Q$ = $Trace(Ξ΅$). The numerical value of $(P$ + $Q)$ is ________. (in integer) CE-2 Page 23 of 40
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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 soil is __________. (round off to one decimal place)
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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 sample as the sampler tube enters into the soil. The inside diameter (in mm) of the cutting edge is _________________. (round off to two decimal places)
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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 application of the load. Considering the ground to be a linearly elastic, isotropic, semi-infinite medium, the ratio of the increase in vertical stress at P to the increase in vertical stress at Q is ________. (in integer) CE-1 Page 21 of 42
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A concentrically loaded isolated square footing of size 2 m $\times$ 2 m carries a concentrated vertical load of 1000 kN. Considering Boussinesqβs theory of stress distribution, the maximum depth (in m) of the pressure bulb corresponding to 10 % of the vertical load intensity will be ___________. (round off to two decimal places)
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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 the same depth. The value of sleeve (side) friction (in kPa) at that depth was ___________________. (in integer)
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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 shear strength of the soil is _________ kPa. (in integer)
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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 water in the root zone. Consider the maximum root zone depth of the crop as 80 mm and the irrigation efficiency as 70 %. The interval between irrigation (in days) will be _________. (round off to the nearest integer)
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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 $\to,$ the structureβs hydrologic risk of failure in percentage is. (round off to one decimal place)
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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 provided is ____________. (round off to the nearest integer) CE-2 Page 24 of 40
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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 about the positive x-axis are
a.
1, 0, $\sqrt{2}$
b.
1, 0, $-\sqrt{2}$
c.
$-1,$ 0, $\sqrt{2}$
d.
$-1,$ 0, $-\sqrt{2}$ CE-1 Page 23 of 42
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Consider the polynomial $f(x)$ = $x$ - $6x$ + $11x$ - 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 statements: I. The given polynomial is zero at the boundary points $x$ = $1$ and $x$ = $3.$ II. There exists one local maxima of $f(x)$ within the domain S. III. The second derivative $fβ²β²(x)$ > 0 throughout the domain S. IV. There exists one local minima of $f(x)$ within the domain S. The correct option is:
a.
Only statements I, II and III are correct.
b.
Only statements I, II and IV are correct.
c.
Only statements I and IV are correct.
d.
Only statements II and IV are correct. CE-2 Page 25 of 40
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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 $$ rad/s and T s, respectively. If the stiffness of the spring is doubled and the mass is halved, then the natural frequency and the natural period of the modified system, respectively, are
a.
b.
c.
d.
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A weld is used for joining an angle section ISA 100 mm $\times$ 100 mm $\times$ 10 mm to a gusset plate of thickness 15 mm to transmit a tensile load. The permissible stress in the angle is 150 MPa and the permissible shear stress on the section through the throat of the fillet weld is 108 MPa. The location of the centroid of the angle is represented by C yy in the figure, where C yy = 28.4 mm. The area of cross-section of the angle is 1903 mm 2. Assuming the effective throat thickness of the weld to be 0.7 times the given weld size, the lengths L 1 and L 2 (rounded- off to the nearest integer) of the weld required to transmit a load equal to the full strength of the tension member are, respectively
a.
541 mm and 214 mm
b.
214 mm and 541 mm
c.
380 mm and 151 mm
d.
151 mm and 380 mm CE-1 Page 25 of 42
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For the square steel beam cross-section shown in the figure, the shape factor about $z$ - $z$ axis is S and the plastic moment capacity is $M$. Consider yield stress f y = 250 MPa and a = 100 mm. The values of S and $M$ (rounded-off to one decimal place) are
a.
S = 2.0, $M$ = 58.9 kN-m
b.
S = 2.0, $M$ = 100.2 kN-m
c.
S = 1.5, $M$ = 58.9 kN-m
d.
S = 1.5, $M$ = 100.2 kN-m CE-2 Page 27 of 40
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A post-tensioned concrete member of span 15 m and cross-section of 450 mm $$ 450 mm is prestressed with three steel tendons, each of cross-sectional area 200 mm 2. The tendons are tensioned one after another to a stress of 1500 MPa. All the tendons are straight and located at 125 mm from the bottom of the member. Assume the prestress to be the same in all tendons and the modular ratio to be 6. The average loss of prestress, due to elastic deformation of concrete, considering all three tendons is
a.
14.16 MPa
b.
7.08 MPa
c.
28.32 MPa
d.
42.48 MPa CE-2 Page 28 of 40
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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 P. sensitivity > 16 2. quick clay Q. dilation angle = 0 3. sand in critical state R. liquid limit > 50 4. clay of high plasticity S. over consolidation ratio = 1
a.
1-S, 2-P, 3-Q, 4-R
b.
1-Q, 2-S, 3-P, 4-R
c.
1-Q, 2-P, 3-R, 4-S
d.
1-S, 2-Q, 3-P, 4-R CE-1 Page 27 of 42
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Match the following in Column X with Column Y:
Column X Column Y (P) In a triaxial compression test, with increase of axial (I) decreases. strain in loose sand under drained shear condition, the volumetric strain (Q) In a triaxial compression test, with increase of axial (II) increases. strain in loose sand under undrained shear condition, the excess pore water pressure (R) In a triaxial compression test, the pore pressure (III) remains same.
parameter βBβ for a saturated soil (S) For shallow strip footing in pure saturated clay, (IV) is always 0.0. Terzaghiβs bearing capacity factor (N q) due to surcharge
(V) is always 1.0.
(VI) is always 0.5. Which one of the following combinations is correct?
a.
(P)-(I), (Q)-(II), (R)-(V), (S)-(V)
b.
(P)-(II), (Q)-(I), (R)-(IV), (S)-(V)
c.
(P)-(I), (Q)-(III), (R)-(VI), (S)-(IV)
d.
(P)-(I), (Q)-(II), (R)-(V), (S)-(VI) CE-2 Page 29 of 40
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As per Rankineβs theory of earth pressure, the inclination of failure planes is
$$ $(45$ +)Β° with respect to the direction of the minor principal stress.
$2$ The above statement is correct for which one of the following options?
a.
Only the active state and not the passive state
b.
Only the passive state and not the active state
c.
Both active as well as passive states
d.
Neither active nor passive state
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A soil sample is underlying a water column of height h 1, as shown in the figure. The vertical effective stresses at points A, B, and C are $Ο$, $Ο$, and $Ο$, respectively. Let $Ξ³$ and $Ξ³$ be the saturated and submerged unit weights of the soil sample, respectively, and $Ξ³$ w be the unit weight of water. Which one of the following expressions correctly represents the sum $(Ο$ A + $Ο$ B + $Ο$) ?
a.
(2β + β $)Ξ³$
b.
(β + β + β $)Ξ³$
c.
(β + β) $(Ξ³$ sat - $Ξ³$ w)
d.
(β + β + β $)Ξ³$ sat CE-2 Page 30 of 40
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Henryβs law constant for transferring O 2 from air into water, at room temperature, is 1.3. Given that the partial pressure of O 2 in the
mmol
liter-atm atmosphere is 0.21 atm, the concentration of dissolved oxygen (mg/liter) in water in equilibrium with the atmosphere at room temperature is (Consider the molecular weight of O 2 as 32 g/mol)
a.
8.7
b.
0.8
c.
198.1
d.
0.2 CE-1 Page 28 of 42
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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, respectively. The final pH of this water is (Ignore the dissociation of water.)
a.
2.8
b.
6.5
c.
3.8
d.
8.5
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- 2+ 2+ In a water sample, the concentrations of Ca, Mg 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 = 24, H = 1, C = 12, O = 16. The total hardness and the temporary hardness in the water sample (in mg/L as CaCO 3) will be
a.
400 and 100, respectively.
b.
400 and 300, respectively.
c.
500 and 100, respectively.
d.
800 and 200, respectively. CE-1 Page 29 of 42
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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 for which air requirement has to be estimated. Assume oxygen in air (by weight) = 23 %, and density of air = 1.3 kg/m 3. Atomic mass: C = 12, H = 1, O = 16, N = 14. C and H are oxidized completely whereas N is converted only into NH 3 during oxidation. For oxidative degradation of 1 tonne of the waste, the required theoretical volume of air (in m 3 /tonne) will be (round off to the nearest integer)
a.
4749
b.
8025
c.
1418
d.
1092 CE-2 Page 31 of 40
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Consider the four points P, Q, R, and S shown in the Greenshields fundamental speed-flow diagram. Denote their corresponding traffic densities by $k$, $k$, $k$, and $k$, respectively. The correct order of these densities is
a.
$k$ > $k$ > $k$ > $k$
b.
$k$ > $k$ > $k$ > $k$
c.
$k$ > $k$ > $k$ > $k$
d.
$k$ > $k$ > $k$ > $k$ CE-1 Page 30 of 42
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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) between the vehicles is
a.
3.00
b.
2.25
c.
8.33 $\times$ 10 $-$ 4
d.
6.25 $\times$ 10 $-$ 4
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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.
It is continuous on its domain.
b.
It has a local minimum at $x$ = 2.
c.
It has a local maximum at $x$ = 2.
d.
It is differentiable on its domain. CE-1 Page 31 of 42
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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 following statement(s) is/are correct?
a.
The motion of the body will occur by overturning.
b.
Sliding of the body never occurs.
c.
No motion occurs for P $\le$ 6 kN.
d.
The motion of the body will occur by sliding only. CE-1 Page 32 of 42
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Which of the following statement(s) is/are correct?
a.
If a linearly elastic structure is subjected to a set of loads, the partial derivative of the total strain energy with respect to the deflection at any point is equal to the load applied at that point.
b.
If a linearly elastic structure is subjected to a set of loads, the partial derivative of the total strain energy with respect to the load at any point is equal to the deflection at that point.
c.
If a structure is acted upon by two force system P a and P b, in equilibrium separately, the external virtual work done by a system of forces P b during the deformations caused by another system of forces P a is equal to the external virtual work done by the P a system during the deformation caused by the P b system.
d.
The shear force in a conjugate beam loaded by the M/EI diagram of the real beam is equal to the corresponding deflection of the real beam.
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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
a.
In an aqueduct, natural drain water goes under the irrigation canal, whereas in a super-passage, natural drain water goes over the irrigation canal.
b.
In a level crossing, natural drain water goes through the irrigation canal.
c.
In an aqueduct, natural drain water goes over the irrigation canal, whereas in a super-passage, natural drain water goes under the irrigation canal.
d.
In a canal syphon, natural drain water goes through the irrigation canal. CE-1 Page 33 of 42
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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 condition in the channel. The depth of water at this section is y
2 and that at its upstream section is y. The correct statement(s) for the choked and
1 unchoked conditions in the channel is/are
a.
In choked condition, y decreases if the flow is supercritical and increases if the
1 flow is subcritical.
b.
In choked condition, y is equal to the critical depth if the flow is supercritical
2 or subcritical.
c.
In unchoked condition, y remains unaffected when the flow is supercritical or
1 subcritical.
d.
In choked condition, y increases if the flow is supercritical and decreases if the
1 flow is subcritical. CE-2 Page 33 of 40
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Consider the differential equation
d y $()$
$=$ 4 x $+$ 2 $-$ y
d x For the initial condition y = 3 at x = 1, the value of $y$ at x = 1.4 obtained using Eulerβs method with a step-size of 0.2 is _________. (round off to one decimal place)
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The concentration $s(x, t)$ of pollutants in a one-dimensional reservoir at position $x$ and time $t$ satisfies the diffusion equation
$βs(x, t) β s(x, t)$
= $D$
$βt βx$ on the domain 0 $\le x \le L,$ where $D$ is the diffusion coefficient of the pollutants. The initial condition $s(x,$ 0) is defined by the step-function shown in the figure.
(,) = 0 at the boundary The boundary conditions of the problem are given by points $x$ = $π$ and $x$ = $L$ at all times. Consider $D$ = $0. 1 m 2 /s,$ $s$ = $5 ΞΌmol/m$, and $L$ = $10 m.$ The steady-state concentration $sΜ$ = $s$, $\infty$ at the center $x$ = of the reservoir (in $ΞΌmol/m)$ is ___________. (in integer)
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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 linear regression model
$y$ = $a$ + $bx$ is estimated as 6.1. The coefficient b is ______________. (round off to one decimal place) CE-1 Page 34 of 42
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CE-2 Page 34 of 40
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 three decimal places)
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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 EF is _______. (round off to the nearest integer) CE-1 Page 35 of 42
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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 are initially stress free. The coefficient of linear thermal expansion is $Ξ±$ for both the rods. The temperature of the rod IJ is raised by $βT,$ whereas the temperature of rod HI remains unchanged. An external horizontal force P is now applied at node I. It is given that $Ξ±$ = $10 6$ β $1$, $βT$ = $50$ β, $b$ = $2 m, AE$ = $10 6 N.$ The axial rigidities of the rods HI and IJ are 2AE and AE, respectively. To make the axial force in rod HI equal to zero, the value of the external force P (in N) is _________. (round off to the nearest integer)
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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 moment M is applied at joint F. Consider flexural rigidity EI = 10 5 kN-m 2 for each member and neglect axial deformations. If the magnitude (absolute value) of the support moment at H is 10 kN-m, the magnitude (absolute value) of the applied moment M (in kN-m) to maintain static equilibrium is ___________. (round off to the nearest integer) CE-1 Page 36 of 42
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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 vertical linear spring with spring constant k = 20 kN/m. The fixed supports are provided at U and X. It is given that flexural rigidity EI = $10 5$ kN-m 2, P = 100 kN, and a = 5 m. Force Q is applied at the center of beam WX such that the force in the spring VW becomes zero. The magnitude of force Q (in kN) is ________. (round off to the nearest integer) CE-2 Page 35 of 40
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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 axles is 3 m. The maximum bending moment at point R is _________ kNm. (in integer)
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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 = 4 m and b = 3 m. The minimum coefficient of static friction that is required at the point J to hold the rod in equilibrium is ___________. (round off to three decimal places)
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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 Fe 415 grade steel. The design shear strength for this beam is 0.66 N/mm 2. The beam has to resist a factored shear force of 440 kN. The spacing of two-legged, 10 mm diameter vertical stirrups of Fe 415 grade steel is __________mm. (round off to the nearest integer) CE-1 Page 37 of 42
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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 tests on undisturbed samples extracted from the clay layer, is 100 kPa. If the ultimate compressive load capacity of the driven pile is 632 kN, the required width of the pile is _______ mm. (in integer) (Bearing capacity factor N c = 9; adhesion factor $$ = 0.7)
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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 pile are 1 m and 20 m, respectively. The design capacity of each pile is 1000 kN in the vertical downward direction. The pile group efficiency ($$) is given by $g$
$$ = 1- $ΞΈ$ - $1)m$ + - $1)n$
$(n (m$
90 $mn$ where m and n are number of rows and columns in the plan grid of pile arrangement, and $ΞΈ$ = tan. The design value of the pile group capacity (in kN) in the vertical downward direction is __________________. (round off to the nearest integer)
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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 foundation. Below the clay layer, a dense sand layer exists at the site. A 25 mm thick undisturbed sample was collected from the mid-depth of the clay layer and tested in a laboratory oedometer under double drainage condition. It was found that the soil sample had undergone 50 % consolidation settlement in 10 minutes. The time (in days) required for 25 % consolidation settlement of the raft foundation will be ____________________. (round off to the nearest integer)
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CE-2 Page 37 of 40
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 point P, which is located at the mid-depth of the clay layer,
were 150 kPa and 25 kPa, respectively. Construction of a building caused an
additional total vertical stress of 100 kPa at P. When the vertical effective stress
at P is 175 kPa, the percentage of consolidation in the clay layer at P is
_____________. (in integer)
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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 table. Time (hours) Streamflow (m 3 /s)
0 1 2 3 4 5 6 7
10 16 34 40 31 25 16 10 Considering a constant baseflow of 10 m 3 /s, the peak flow ordinate (in m 3 /s) of one-hour unit hydrograph for the watershed is ________. (in integer) CE-1 Page 38 of 42
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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 m 3 /s and the energy loss in the jump is 1.6 m, then the Froude number computed at the end of the jump is ___________. (round off to two decimal places) (Consider the acceleration due to gravity as 10 m/s 2.)
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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 levels of the reservoirs is 5 m, the ratio of discharge in the larger diameter pipe to the discharge in the smaller diameter pipe is ____________. (round off to two decimal places) (Consider only loss due to friction and neglect all other losses. Assume the friction factor to be the same for both the pipes)
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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 are 120 days and 144 cm, respectively. Water application efficiency in the field is 80%. The lowest level of water in the well is 10 m below the ground. The minimum required horse power (h.p.) of the pump is ________. (round off to two decimal places) (Consider 1 h.p. = 746 W; unit weight of water = 9810 N/m 3)
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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 causes the critical flow, is _________ without changing the upstream water level. (round off to two decimal places)
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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. Assume Stokesβ law is valid. The drag force on particle Q will be________ times the drag force on particle P. (round off to the nearest integer)
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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 wastewater, the concentration of ammonia is 34 mg NH 3 /liter and that of nitrate is 6.2 mg NO $-$ /liter. The total nitrogen
3 concentration in this wastewater is _______ milligram nitrogen per liter. (round off to one decimal place) CE-1 Page 39 of 42
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CE-2 Page 38 of 40
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%. The ideal moisture content for composting this mixture is
50%. The amount of water to be added to this mixture to bring its moisture
content to the ideal condition is _______metric ton. (in integer)
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A 2 % sewage sample (in distilled water) was incubated for 3 days at 27 Β°C temperature. After incubation, a dissolved oxygen depletion of 10 mg/L was recorded. The biochemical oxygen demand (BOD) rate constant at 27 Β°C was found to be 0.23 day -1 (at base e). The ultimate BOD (in mg/L) of the sewage will be_____________. (round off to the nearest integer)
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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. After the primary treatment, the TSS concentration in sewage is reduced by 60 %. The sludge from the primary clarifier contains 2 % solids concentration. Subsequently, the sludge is subjected to gravity thickening process to achieve a solids concentration of 6 %. Assume that the density of sludge, before and after thickening, is 1000 kg/m 3. The daily volume of the thickened sludge (in m 3 /day) will be_________. (round off to the nearest integer)
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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 velocity of 1.0 m/h is_______. (round off to one decimal place) (Consider the particle density as 2650 kg/m 3 and liquid density as 991 kg/m 3)
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A sample of air analyzed at 25 Β°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 Β΅g/m 3) will be__________. (round off to the nearest integer)
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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 due to start-up and clearance is 2 s, the effective green time of each phase is ______s. (in integer)
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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 obstacle of height 0.15 m, then the minimum curve length should be ______ m. (round off to the nearest integer)
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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 probability of observing at least 2 vehicles in 30 minutes is ______. (round off to two decimal places) CE-1 Page 40 of 42
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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 integer) CE-2 Page 39 of 40
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The vehicle count obtained in every 10 minute interval of a traffic volume survey done in peak one hour is given below.
Time Interval Vehicle Count
(in minutes)
0 β
10
10
10 β
20
11
20 β
30
12
30 β
40
15
40 β
50
13
50 β
60
11
The peak hour factor (PHF) for 10 minute sub-interval is __________. (round off to one decimal place) CE-1 Page 41 of 42
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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, respectively. The bulk specific gravity of the mix is 2.3. The percentage air voids in the mix is ____________. (round off to the nearest integer)
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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 is the clear distance between the wheels. Assuming that the ground is an elastic, homogeneous, and isotropic half space, the ratio of Equivalent Single Wheel Load (ESWL) at depth z = d/2 to the ESWL at depth z = 2 s is ___________. (round off to one decimal place) (Consider the influence angle to be 45 Β° for the linear dispersion of stress with depth) END OF THE QUESTION PAPER CE-1 Page 42 of 42
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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 East-West and the West-East through movements, and the second phase is for the North-South and the South-North through movements. There are no turning movements. Assume that the saturation flow is 1800 vehicles per hour per lane for each lane and the total lost time for the first and the second phases together is 9 seconds. The optimum cycle length (in seconds), as per the Websterβs method, is ____________. (round off to the nearest integer) CE-2 Page 40 of 40
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