GATE 2023 Question Paper CE Civil Engineering

The Graduate Aptitude Test in Engineering

GATE 2023
Question Paper
GATE is an entrance examination conducted in India that
primarily tests the comprehensive understanding of
undergraduate subjects in engineering and sciences for
admission into technical postgraduate programs.

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General Aptitude (GA)
Q.1 – Q.5 Carry ONE mark Each

Q.1 “I have not yet decided what I will do this evening; I ______ visit a friend.”

(A) mite

(B) would

(C) might

(D) didn’t

Q.2 Eject : Insert : : Advance : _______

(By word meaning)

(A) Advent

(B) Progress

(C) Retreat

(D) Loan

Page 1 of 39

Q.3 In the given figure, PQRSTV is a regular hexagon with each side of length 5 cm. A
circle is drawn with its centre at V such that it passes through P. What is the area
(in cm2 ) of the shaded region? (The diagram is representative)

(A) 25π
3

(B) 20π
3

(C) 6π

(D) 7π

Page 2 of 39

Q.4 A duck named Donald Duck says “All ducks always lie.”

Based only on the information above, which one of the following statements can be
logically inferred with certainty?

(A) Donald Duck always lies.

(B) Donald Duck always tells the truth.

(C) Donald Duck’s statement is true.

(D) Donald Duck’s statement is false.

Page 3 of 39

Q.5 A line of symmetry is defined as a line that divides a figure into two parts in a way
such that each part is a mirror image of the other part about that line.

The figure below consists of 20 unit squares arranged as shown. In addition to the
given black squares, upto 5 more may be coloured black. Which one among the
following options depicts the minimum number of boxes that must be coloured
black to achieve two lines of symmetry? (The figure is representative)

a b

c d

e f g h

i

j k

(A) d

(B) c, d, i

(C) c, i

(D) c, d, i, f, g

Page 4 of 39

Q.6 – Q.10 Carry TWO marks Each

Q.6 Based only on the truth of the statement ‘Some humans are intelligent’, which one
of the following options can be logically inferred with certainty?

(A) No human is intelligent.

(B) All humans are intelligent.

(C) Some non-humans are intelligent.

(D) Some intelligent beings are humans.

Page 5 of 39

Q.7 Which one of the options can be inferred about the mean, median, and mode for the
given probability distribution (i.e. probability mass function), 𝑃(𝑥), of a variable x?

(A) mean = median ≠ mode

(B) mean = median = mode

(C) mean ≠ median = mode

(D) mean ≠ mode = median

Page 6 of 39

Q.8 The James Webb telescope, recently launched in space, is giving humankind
unprecedented access to the depths of time by imaging very old stars formed almost
13 billion years ago. Astrophysicists and cosmologists believe that this odyssey in
space may even shed light on the existence of dark matter. Dark matter is supposed
to interact only via the gravitational interaction and not through the
electromagnetic-, the weak- or the strong-interaction. This may justify the epithet
“dark” in dark matter.

Based on the above paragraph, which one of the following statements is FALSE?

(A) No other telescope has captured images of stars older than those captured by the
James Webb telescope.

(B) People other than astrophysicists and cosmologists may also believe in the existence
of dark matter.

(C) The James Webb telescope could be of use in the research on dark matter.

(D) If dark matter was known to interact via the strong-interaction, then the epithet
“dark” would be justified.

Page 7 of 39

Q.9 Let 𝑎 = 30! , 𝑏 = 50! , and 𝑐 = 100! . Consider the following numbers:

log 𝑎 𝑐, log 𝑐 𝑎, log 𝑏 𝑎, log 𝑎 𝑏

Which one of the following inequalities is CORRECT?

(A) log 𝑐 𝑎 < log 𝑏 𝑎 < log 𝑎 𝑏 < log 𝑎 𝑐

(B) log 𝑐 𝑎 < log 𝑎 𝑏 < log 𝑏 𝑎 < log 𝑏 𝑐

(C) log 𝑐 𝑎 < log 𝑏 𝑎 < log 𝑎 𝑐 < log 𝑎 𝑏

(D) log 𝑏 𝑎 < log 𝑐 𝑎 < log 𝑎 𝑏 < log 𝑎 𝑐

Page 8 of 39

Q.10 A square of side length 4 cm is given. The boundary of the shaded region is defined
by one semi-circle on the top and two circular arcs at the bottom, each of radius
2 cm, as shown.

The area of the shaded region is _______ cm2 .

(A) 8

(B) 4

(C) 12

(D) 10

Page 9 of 39

Q.11 – Q.35 Carry ONE mark Each

For the integral
1
1
Q.11 𝐼=∫ 2
𝑑𝑥
−1 𝑥

which of the following statements is TRUE?

(A) 𝐼=0

(B) 𝐼=2

(C) 𝐼 = −2

(D) The integral does not converge

Page 10 of 39

Q.12 A hanger is made of two bars of different sizes. Each bar has a square cross-section.
The hanger is loaded by three-point loads in the mid vertical plane as shown in the
figure. Ignore the self-weight of the hanger. What is the maximum tensile stress in
N/mm2 anywhere in the hanger without considering stress concentration effects?

100 mm

100 kN 100 kN

50 mm

50 kN

(A) 15.0

(B) 25.0

(C) 35.0

(D) 45.0

Page 11 of 39

Q.13 Creep of concrete under compression is defined as the .

(A) increase in the magnitude of strain under constant stress

(B) increase in the magnitude of stress under constant strain

(C) decrease in the magnitude of strain under constant stress

(D) decrease in the magnitude of stress under constant strain

Q.14 A singly reinforced concrete beam of balanced section is made of M20 grade
concrete and Fe415 grade steel bars. The magnitudes of the maximum compressive
strain in concrete and the tensile strain in the bars at ultimate state under flexure, as
per IS 456: 2000 are , respectively. (round off to four decimal places)

(A) 0.0035 and 0.0038

(B) 0.0020 and 0.0018

(C) 0.0035 and 0.0041

(D) 0.0020 and 0.0031

Page 12 of 39

In cement concrete mix design, with the increase in water-cement ratio, which one
Q.15
of the following statements is TRUE?

(A) Compressive strength decreases but workability increases

(B) Compressive strength increases but workability decreases

(C) Both compressive strength and workability decrease

(D) Both compressive strength and workability increase

Q.16 The specific gravity of a soil is 2.60. The soil is at 50% degree of saturation with a
water content of 15%. The void ratio of the soil is .

(A) 0.35

(B) 0.78

(C) 0.87

(D) 1.28

Page 13 of 39

A group of 9 friction piles are arranged in a square grid maintaining equal spacing
in all directions. Each pile is of diameter 300 mm and length 7 m. Assume that the
Q.17
soil is cohesionless with effective friction angle 𝜙′ = 32°. What is the center-to-
center spacing of the piles (in m) for the pile group efficiency of 60%?

(A) 0.582

(B) 0.486

(C) 0.391

(D) 0.677

Page 14 of 39

A possible slope failure is shown in the figure. Three soil samples are taken from
different locations (I, II and III) of the potential failure plane. Which is the most
appropriate shear strength test for each of the sample to identify the failure
mechanism? Identify the correct combination from the following options:
Q.18
P: Triaxial compression test
Q: Triaxial extension test
R: Direct shear or shear box test
S: Vane shear test

slope face
III

I
II Potential failure plane

(A) I-Q, II-R, III-P

(B) I-R, II-P, III-Q

(C) I-S, II-Q, III-R

(D) I-P, II-R, III-Q

Q.19 When a supercritical stream enters a mild-sloped (M) channel section, the type of
flow profile would become .

(A) M1

(B) M2

(C) M3

(D) M1 and M2

Page 15 of 39

Which one of the following statements is TRUE for Greenhouse Gas (GHG) in the
Q.20
atmosphere?

GHG absorbs the incoming short wavelength solar radiation to the earth surface,
(A) and allows the long wavelength radiation coming from the earth surface to pass
through

GHG allows the incoming long wavelength solar radiation to pass through to the
(B) earth surface, and absorbs the short wavelength radiation coming from the earth
surface

GHG allows the incoming long wavelength solar radiation to pass through to the
(C) earth surface, and allows the short wavelength radiation coming from the earth
surface to pass through

GHG allows the incoming short wavelength solar radiation to pass through to the
(D) earth surface, and absorbs the long wavelength radiation coming from the earth
surface

Q.21 𝐺1 and 𝐺2 are the slopes of the approach and departure grades of a vertical curve,
respectively.

Given |𝐺1 | < |𝐺2 | and |𝐺1 |≠ |𝐺2 | ≠ 0
Statement 1: +𝐺1 followed by +𝐺2 results in a sag vertical curve.
Statement 2: −𝐺1 followed by −𝐺2 results in a sag vertical curve.
Statement 3: +𝐺1 followed by −𝐺2 results in a crest vertical curve.

Which option amongst the following is true?

(A) Statement 1 and Statement 3 are correct; Statement 2 is wrong

(B) Statement 1 and Statement 2 are correct; Statement 3 is wrong

(C) Statement 1 is correct; Statement 2 and Statement 3 are wrong

(D) Statement 2 is correct; Statement 1 and Statement 3 are wrong

Page 16 of 39

The direct and reversed zenith angles observed by a theodolite are 56 o 00' 00" and
Q.22
303o 00' 00", respectively. What is the vertical collimation correction?

(A) +1o 00' 00"

(B) −1o 00' 00"

(C) −0o 30' 00"

(D) +0o 30' 00"

A student is scanning his 10 inch × 10 inch certificate at 600 dots per inch (dpi) to
Q.23 convert it to raster. What is the percentage reduction in number of pixels if the same
certificate is scanned at 300 dpi?

(A) 62

(B) 88

(C) 75

(D) 50

Page 17 of 39

Q.24 If 𝑴 is an arbitrary real 𝑛 × 𝑛 matrix, then which of the following matrices will
have non-negative eigenvalues?

(A) 𝑴2

(B) 𝑴𝑴𝑇

(C) 𝑴𝑇 𝑴

(D) (𝑴𝑇 )2

Q.25 The following function is defined over the interval [−𝐿, 𝐿]:

𝑓(𝑥) = 𝑝𝑥 4 + 𝑞𝑥 5 .

If it is expressed as a Fourier series,
∞
𝜋𝑥 𝜋𝑥
𝑓(𝑥) = 𝑎0 + ∑ {𝑎𝑛 sin ( ) + 𝑏𝑛 cos ( )},
𝐿 𝐿
𝑛=1

which options amongst the following are true?

(A) 𝑎𝑛 , 𝑛 = 1, 2, ⋯ , ∞ depend on 𝑝

(B) 𝑎𝑛 , 𝑛 = 1, 2, ⋯ , ∞ depend on 𝑞

(C) 𝑏𝑛 , 𝑛 = 1, 2, ⋯ , ∞ depend on 𝑝

(D) 𝑏𝑛 , 𝑛 = 1, 2, ⋯ , ∞ depend on 𝑞

Page 18 of 39

Consider the following three structures:

Internal hinge Structure I: Beam with
hinge support at A,
roller at C, guided
A B C D E roller at E, and internal
hinges at B and D

A D Structure II: Pin-jointed
truss, with hinge
support at A, and
rollers at B and D

Q.26 B C

D E F Structure III: Pin-
jointed truss, with
hinge support at A and
roller at C

A C
B

Which of the following statements is/are TRUE?

(A) Structure I is unstable

(B) Structure II is unstable

(C) Structure III is unstable

(D) All three structures are stable

Page 19 of 39

Q.27 Identify the waterborne diseases caused by viral pathogens:

(A) Acute anterior poliomyelitis

(B) Cholera

(C) Infectious hepatitis

(D) Typhoid fever

Which of the following statements is/are TRUE for the Refuse-Derived Fuel (RDF)
Q.28
in the context of Municipal Solid Waste (MSW) management?

Higher Heating Value (HHV) of the unprocessed MSW is higher than the HHV of
(A)
RDF processed from the same MSW

(B) RDF can be made in the powdered form

(C) Inorganic fraction of MSW is mostly converted to RDF

(D) RDF cannot be used in conjunction with oil

The probabilities of occurrences of two independent events A and B are 0.5 and 0.8,
Q.29 respectively. What is the probability of occurrence of at least A or B (rounded off
to one decimal place)? ______________________

Page 20 of 39

𝑑𝑦
In the differential equation 𝑑𝑥 + 𝛼 𝑥 𝑦 = 0, α is a positive constant. If 𝑦 = 1.0 at
Q.30 𝑥 = 0.0, and 𝑦 = 0.8 at 𝑥 = 1.0, the value of α is _______________(rounded
off to three decimal places).

Consider the fillet-welded lap joint shown in the figure (not to scale). The length of
the weld shown is the effective length. The welded surfaces meet at right angle. The
Q.31 weld size is 8 mm, and the permissible stress in the weld is 120 MPa. What is the
safe load P (in kN, rounded off to one decimal place) that can be transmitted by this
welded joint? ____________________

75 mm

50 mm
P P

Q.32 A drained direct shear test was carried out on a sandy soil. Under a normal stress of
50 kPa, the test specimen failed at a shear stress of 35 kPa. The angle of internal
friction of the sample is degree (round off to the nearest integer).

Page 21 of 39

A canal supplies water to an area growing wheat over 100 hectares. The duration
between the first and last watering is 120 days, and the total depth of water required
by the crop is 35 cm. The most intense watering is required over a period of 30 days
Q.33 and requires a total depth of water equal to 12 cm. Assuming precipitation to be
negligible and neglecting all losses, the minimum discharge (in m3/s, rounded off
to three decimal places) in the canal to satisfy the crop requirement
is __________________.

The ordinates of a one-hour unit hydrograph for a catchment are given below:

t (hour) 0 1 2 3 4 5 6 7
Q (m3/s) 0 9 21 18 12 5 2 0
Q.34
Using the principle of superposition, a D-hour unit hydrograph for the catchment
was derived from this one-hour unit hydrograph. The ordinates of the D-hour unit
hydrograph were obtained as 3 m3/s at t = 1 hour and 10 m3/s at t = 2 hour. The
value of D (in integer) is ________________________.

For a horizontal curve, the radius of a circular curve is obtained as 300 m with the
Q.35 design speed as 15 m/s. If the allowable jerk is 0.75 m/s3, what is the minimum
length (in m, in integer) of the transition curve?___________________

Page 22 of 39

Q.36 – Q.65 Carry TWO marks Each

Q.36 A function 𝑓(𝑥), that is smooth and convex-shaped between interval (𝑥𝑙 , 𝑥𝑢 ) is
shown in the figure. This function is observed at odd number of regularly spaced
points. If the area under the function is computed numerically, then .

Actual function
Approximated function

(0,0)

(A) the numerical value of the area obtained using the trapezoidal rule will be less
than the actual

(B) the numerical value of the area obtained using the trapezoidal rule will be more
than the actual

(C) the numerical value of the area obtained using the trapezoidal rule will be exactly
equal to the actual

(D) with the given details, the numerical value of area cannot be obtained using
trapezoidal rule

Page 23 of 39

Consider a doubly reinforced RCC beam with the option of using either Fe250 plain
bars or Fe500 deformed bars in the compression zone. The modulus of elasticity of
Q.37 steel is 2 × 105 N/mm2. As per IS456:2000, in which type(s) of the bars, the stress
in the compression steel ( 𝑓𝑠𝑐 ) can reach the design strength (0.87𝑓𝑦 ) at the limit
state of collapse?

(A) Fe250 plain bars only

(B) Fe500 deformed bars only

(C) Both Fe250 plain bars and Fe500 deformed bars

(D) Neither Fe250 plain bars nor Fe500 deformed bars

Consider the horizontal axis passing through the centroid of the steel beam cross-
Q.38 section shown in the figure. What is the shape factor (rounded off to one decimal
place) for the cross-section?

(A) 1.5

(B) 1.7

(C) 1.3

(D) 2.0

Page 24 of 39

Consider the pin-jointed truss shown in the figure (not to scale). All members have
the same axial rigidity, AE. Members QR, RS, and ST have the same length 𝐿.
Q.39 Angles QBT, RCT, SDT are all 90°. Angles BQT, CRT, DST are all 30°. The joint
𝑃𝐿
T carries a vertical load P. The vertical deflection of joint T is 𝑘 𝐴𝐸 . What is the
value of 𝑘?

Q

R

S

T
B C D

(A) 1.5

(B) 4.5

(C) 3.0

(D) 9.0

Page 25 of 39

Q.40 With reference to the compaction test conducted on soils, which of the following is
INCORRECT?

(A) Peak point of the compaction curve gives the maximum dry unit weight and
optimum moisture content

(B) With increase in the compaction effort, the maximum dry unit weight increases

(C) With increase in the compaction effort, the optimum moisture content decreases

(D) Compaction curve crosses the zero-air-voids curve

Consider that a force P is acting on the surface of a half-space (Boussinesq’s
problem). The expression for the vertical stress (𝜎𝑧 ) at any point (r, 𝑧), within the
half-space is given as,

3𝑃 𝑧3
Q.41 𝜎𝑧 = 5
2𝜋
(𝑟 2 + 𝑧 2 )2
where, r is the radial distance, and 𝑧 is the depth with downward direction taken as
positive. At any given r, there is a variation of 𝜎𝑧 along 𝑧, and at a specific 𝑧, the
value of 𝜎𝑧 will be maximum. What is the locus of the maximum 𝜎𝑧 ?

3 2
(A) 𝑧2 = 𝑟
2

3 2
(B) 𝑧3 = 𝑟
2

5 2
(C) 𝑧2 = 𝑟
2

5 2
(D) 𝑧3 = 𝑟
2

Page 26 of 39

A square footing of size 2.5 m × 2.5 m is placed 1.0 m below the ground surface on
a cohesionless homogeneous soil stratum. Considering that the groundwater table
is located at the base of the footing, the unit weights of soil above and below the
groundwater table are 18 kN/m3 and 20 kN/m3, respectively, and the bearing
capacity factor 𝑁𝑞 is 58, the net ultimate bearing capacity of the soil is estimated as
Q.42 1706 kPa (unit weight of water = 10 kN/m3).

Earlier, a plate load test was carried out with a circular plate of 30 cm diameter in
the same foundation pit during a dry season, when the water table was located
beyond the plate influence zone. Using Terzaghi’s bearing capacity formulation,
what is the ultimate bearing capacity (in kPa) of the plate?

(A) 110.16

(B) 61.20

(C) 204.00

(D) 163.20

Page 27 of 39

A very wide rectangular channel carries a discharge (Q) of 70 m3/s per meter width.
Its bed slope changes from 0.0001 to 0.0009 at a point P, as shown in the figure (not
Q.43
to scale). The Manning’s roughness coefficient of the channel is 0.01. What water
surface profile(s) exist(s) near the point P?

Q = 70 m3/s per meter width

So = 0.0001 P

So = 0.0009

(A) M2 and S2

(B) M2 only

(C) S2 only

(D) S2 and hydraulic jump

Q.44 A jet of water having a velocity of 20 m/s strikes a series of plates fixed radially on
a wheel revolving in the same direction as the jet at 15 m/s. What is the percentage
efficiency of the plates? (round off to one decimal place)

(A) 37.5

(B) 66.7

(C) 50.0

(D) 88.9

Page 28 of 39

In the following table, identify the correct set of associations between the entries
in Column-1 and Column-2.

Column-1 Column-2
Q.45 P: Reverse Osmosis I: Ponding
Q: Trickling Filter II: Freundlich Isotherm
R: Coagulation III: Concentration Polarization
S: Adsorption IV: Charge Neutralization

(A) P-II, Q-I, S-III

(B) Q-III, R-II, S-IV

(C) P-IV, R-I, S-II

(D) P-III, Q-I, R-IV

Page 29 of 39

A plot of speed-density relationship (linear) of two roads (Road A and Road B) is shown
Q.46
in the figure.

uA
Road A
uB
Speed, u

Road B

Density, k kA kB

𝐶𝐴
If the capacity of Road A is CA and the capacity of Road B is CB, what is ?
𝐶𝐵

𝑘𝐴
(A)
𝑘𝐵

𝑢𝐴
(B) 𝑢𝐵

𝑘𝐴 𝑢𝐴
(C)
𝑘𝐵 𝑢𝐵

𝑘𝐴 𝑢𝐵
(D)
𝑘𝐵 𝑢𝐴

Page 30 of 39

For the matrix

1 2 3
Q.47 [𝐴] = [3 2 1]
3 1 2
which of the following statements is/are TRUE?

(A) The eigenvalues of [𝐴]𝑇 are same as the eigenvalues of [𝐴]

(B) The eigenvalues of [𝐴]−1 are the reciprocals of the eigenvalues of [𝐴]

(C) The eigenvectors of [𝐴]𝑇 are same as the eigenvectors of [𝐴]

(D) The eigenvectors of [𝐴]−1 are same as the eigenvectors of [𝐴]

For the function 𝑓(𝑥) = 𝑒 𝑥 |sin 𝑥|; 𝑥 ∈ ℝ, which of the following statements is/are
Q.48
TRUE?

(A) The function is continuous at all 𝑥

(B) The function is differentiable at all 𝑥

(C) The function is periodic

(D) The function is bounded

Page 31 of 39

Q.49 Consider the beam shown in the figure (not to scale), on a hinge support at end A
and a roller support at end B. The beam has a constant flexural rigidity, and is
subjected to the external moments of magnitude 𝑀 at one-third spans, as shown in
the figure. Which of the following statements is/are TRUE?

A B

(A) Support reactions are zero

(B) Shear force is zero everywhere

(C) Bending moment is zero everywhere

(D) Deflection is zero everywhere

Which of the following statements is/are TRUE in relation to the Maximum
Q.50
Mixing Depth (or Height) ‘Dmax’ in the atmosphere?

(A) Dmax is always equal to the height of the layer of unstable air

(B) Ventilation coefficient depends on Dmax

A smaller Dmax will have a smaller air pollution potential if other meteorological
(C)
conditions remain same

(D) Vertical dispersion of pollutants occurs up to Dmax

Page 32 of 39

Q.51 Which of the following options match the test reporting conventions with the given
material tests in the table?

Test reporting convention Material test

(P) Reported as ratio (I) Solubility of bitumen

(Q) Reported as percentage (II) Softening point of bitumen

(R) Reported in temperature (III) Los Angeles abrasion test

(S) Reported in length (IV) Flash point of bitumen

(V) Ductility of bitumen

(VI) Specific gravity of bitumen

(VII) Thin film oven test

(A) (P) - (VI); (Q) - (I); (R) - (II); (S) - (VII)

(B) (P) - (VI); (Q) - (III); (R) - (IV); (S) - (V)

(C) (P) - (VI); (Q) - (I); (R) - (II); (S) - (V)

(D) (P) - (VI); (Q) - (III); (R) - (IV); (S) - (VII)

Page 33 of 39

Q.52 The differential equation,

d𝑢
+ 2𝑡𝑢2 = 1,
d𝑡
is solved by employing a backward difference scheme within the finite difference
framework. The value of 𝑢 at the (𝑛 − 1)th time-step, for some 𝑛, is 1.75.
The corresponding time (t) is 3.14 s. Each time step is 0.01 s long. Then, the value
of (𝑢𝑛 − 𝑢𝑛−1 ) is (round off to three decimal places).

The infinitesimal element shown in the figure (not to scale) represents the state of
Q.53 stress at a point in a body. What is the magnitude of the maximum principal stress
(in N/mm2 , in integer) at the point? ____________________________

6 N/mm2

3 N/mm2
4 N/mm2 5 N/mm2
45°

5 N/mm2 4 N/mm2
3 N/mm2

6 N/mm2

Page 34 of 39

Q.54 An idealised bridge truss is shown in the figure. The force in Member U2L3 is
__________________________ kN (round off to one decimal place).

Q.55 The cross-section of a girder is shown in the figure (not to scale). The section is
symmetric about a vertical axis (Y-Y). The moment of inertia of the section about
the horizontal axis (X-X) passing through the centroid is cm4
(round off to nearest integer).

40 cm
Y
10 cm

X X

50 cm

Y
20 cm

Page 35 of 39

Q.56 A soil having the average properties, bulk unit weight = 19 kN/m3; angle of internal
friction = 25 and cohesion = 15 kPa, is being formed on a rock slope existing at an
inclination of 35 with the horizontal. The critical height (in m) of the soil formation
up to which it would be stable without any failure is (round
off to one decimal place).

[Assume the soil is being formed parallel to the rock bedding plane and there is no
ground water effect.]

Q.57 A smooth vertical retaining wall supporting layered soils is shown in figure.
According to Rankine’s earth pressure theory, the lateral active earth pressure acting
at the base of the wall is kPa (round off to one decimal place).

A vertical trench is excavated in a clayey soil deposit having a surcharge load of
30 kPa. A fluid of unit weight 12 kN/m3 is poured in the trench to prevent collapse
as the excavation proceeds. Assume that the fluid is not seeping through the soil
Q.58
deposit. If the undrained cohesion of the clay deposit is 20 kPa and saturated unit
weight is 18 kN/m3, what is the maximum depth of unsupported excavation (in m,

rounded off to two decimal places)? ______________________________

Page 36 of 39

A 12-hour storm occurs over a catchment and results in a direct runoff depth of
100 mm. The time-distribution of the rainfall intensity is shown in the figure (not
Q.59
to scale). The 𝜙-index of the storm is (in mm, rounded off to two decimal
places) ____________________________.

Rainfall Intensity (mm/hour)

20

0
0 4 6 12
Time (hour)

A hydraulic jump occurs in a 1.0 m wide horizontal, frictionless, rectangular
channel, with a pre-jump depth of 0.2 m and a post-jump depth of 1.0 m. The value
Q.60 of g may be taken as 10 m/s2. The values of the specific force at the pre-jump and
post-jump sections are same and are equal to (in m3, rounded off to two decimal
places) _____________ .

Q.61 In Horton’s equation fitted to the infiltration data for a soil, the initial infiltration
capacity is 10 mm/h; final infiltration capacity is 5 mm/h; and the exponential decay
constant is 0.5 /h. Assuming that the infiltration takes place at capacity rates, the
total infiltration depth (in mm) from a uniform storm of duration 12 h
is _______________________. (round off to one decimal place)

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Q.62 The composition and energy content of a representative solid waste sample are
given in the table. If the moisture content of the waste is 26%, the energy content
of the solid waste on dry-weight basis is MJ/kg (round
off to one decimal place).

Component Percent by Energy content as-discarded basis
mass (MJ/kg)

Food waste 20 4.5

Paper 45 16.0

Cardboard 5 14.0

Plastics 10 32.0

Others 20 8.0

Q.63 A flocculator tank has a volume of 2800 m3. The temperature of water in the tank is
15C, and the average velocity gradient maintained in the tank is 100/s. The
temperature of water is reduced to 5C, but all other operating conditions including
the power input are maintained as the same. The decrease in the average velocity
gradient (in %) due to the reduction in water temperature is (round
off to nearest integer).

[Consider dynamic viscosity of water at 15C and 5C as 1.139×10-3 N-s/m2 and
1.518×10-3 N-s/m2, respectively]

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Q.64 The wastewater inflow to an activated sludge plant is 0.5 m3/s, and the plant is to
be operated with a food to microorganism ratio of 0.2 mg/mg-d. The concentration
of influent biodegradable organic matter of the wastewater to the plant (after
primary settling) is 150 mg/L, and the mixed liquor volatile suspended solids
concentration to be maintained in the plant is 2000 mg/L. Assuming that complete
removal of biodegradable organic matter in the tank, the volume of aeration tank
(in m3, in integer) required for the plant is .

Q.65 Trigonometric levelling was carried out from two stations P and Q to find the
reduced level (R. L.) of the top of hillock, as shown in the table. The distance
between Stations P and Q is 55 m. Assume Stations P and Q, and the hillock
are in the same vertical plane. The R. L. of the top of the hillock (in m)
is _______________________ (round off to three decimal places).

Vertical angle of Staff reading on
Station R. L. of benchmark
the top of hillock benchmark

P 18 ̊ 45ˊ 2.340 m 100.000 m

Q 12 ̊ 45ˊ 1.660 m

END OF QUESTION PAPER

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