GATE 2025 Question Paper Civil Engineering (CE-1) (Forenoon)

GATE
2025
Question Paper | Answer Key
Graduate Aptitude Test in Engineering
(GATE) is a prestigious national-level exam
that assesses candidates for
comprehensive understanding in various
undergraduate-level subjects in
Engineering, Technology, Science,
Architecture, and Humanities.

General Aptitude
Q.1 – Q.5 Carry ONE mark Each

Q.1 Is there any good show _______ television tonight?

Select the most appropriate option to complete the above sentence.

(A) in

(B) at

(C) within

(D) on

Q.2 As the police officer was found guilty of embezzlement, he was _______ dismissed
from the service in accordance with the Service Rules.

Select the most appropriate option to complete the above sentence.

(A) sumptuously

(B) brazenly

(C) unintentionally

(D) summarily

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Q.3 The sum of the following infinite series is:

1 1 1 1 1
+ + + + +⋯
1! 2! 3! 4! 5!

(A) 𝜋

(B) 1+𝑒

(C) 𝑒−1

(D) 𝑒

Q.4 A thin wire is used to construct all the edges of a cube of 1 m side by bending,
cutting and soldering the wire. If the wire is 12 m long, what is the minimum number
of cuts required to construct the wire frame to form the cube?

(A) 3

(B) 4

(C) 6

(D) 12

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Q.5 The figures I, II and III are parts of a sequence. Which one of the following options
comes next in the sequence at IV?

?

I II III IV

(A)

(B)

(C)

(D)

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Q.6 – Q.10 Carry TWO marks Each

Q.6 “Why do they pull down and do away with crooked streets, I wonder, which are my
delight, and hurt no man living? Every day the wealthier nations are pulling down
one or another in their capitals and their great towns: they do not know why they do
it; neither do I. It ought to be enough, surely, to drive the great broad ways which
commerce needs and which are the life-channels of a modern city, without
destroying all history and all the humanity in between: the islands of the past.”

(From Hilaire Belloc’s “The Crooked Streets”)

Based only on the information provided in the above passage, which one of the
following statements is true?

(A) The author of the passage takes delight in wondering.

(B) The wealthier nations are pulling down the crooked streets in their capitals.

(C) In the past, crooked streets were only built on islands.

(D) Great broad ways are needed to protect commerce and history.

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Q.7 Rohit goes to a restaurant for lunch at about 1 PM. When he enters the restaurant,
he notices that the hour and minute hands on the wall clock are exactly coinciding.
After about an hour, when he leaves the restaurant, he notices that the clock hands
are again exactly coinciding. How much time (in minutes) did Rohit spend at the
restaurant?

(A) 6
64 11

(B) 5
66
13

(C) 5
65 11

(D) 6
66 13

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Q.8 A color model is shown in the figure with color codes: Yellow (Y), Magenta (M),
Cyan (Cy), Red (R), Blue (Bl), Green (G), and Black (K).

Which one of the following options displays the color codes that are consistent with
the color model?

(A)

(B)

(C)

(D)

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Q.9 A circle with center at (𝑥, 𝑦) = (0.5, 0) and radius = 0.5 intersects with another
circle with center at (𝑥, 𝑦) = (1, 1) and radius = 1 at two points. One of the points
of intersection (𝑥, 𝑦) is:

(A) (0, 0)

(B) (0.2, 0.4)

(C) (0.5, 0.5)

(D) (1, 2)

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Q.10 An object is said to have an 𝑛-fold rotational symmetry if the object, rotated by an
2𝜋
angle of , is identical to the original.
𝑛

Which one of the following objects exhibits 4-fold rotational symmetry about an
axis perpendicular to the plane of the screen?

Note: The figures shown are representative.

(A)

(B)

(C)

(D)

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Q.11 – Q.35 Carry ONE mark Each

Q.11 Suppose 𝜆 is an eigenvalue of matrix 𝐴 and 𝑥 is the corresponding eigenvector. Let
𝑥 also be an eigenvector of the matrix 𝐵 = 𝐴 − 2𝐼, where 𝐼 is the identity matrix.
Then, the eigenvalue of 𝐵 corresponding to the eigenvector 𝑥 is equal to

(A) 𝜆

(B) 𝜆+2

(C) 2𝜆

(D) 𝜆−2

Q.12 1 1 𝑏1
Let 𝐴 = [ 1 3 ] and 𝑏 = [𝑏2 ]. For 𝐴𝑥 = 𝑏 to be solvable, which one of the
−2 −3 𝑏3
following options is the correct condition on 𝑏1 , 𝑏2 , and 𝑏3 :

(A) 𝑏1 + 𝑏2 + 𝑏3 = 1

(B) 3𝑏1 + 𝑏2 + 2𝑏3 = 0

(C) 𝑏1 + 3𝑏2 + 𝑏3 = 2

(D) 𝑏1 + 𝑏2 + 𝑏3 = 2

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Q.13 Which one of the following options is the correct Fourier series of the periodic
function 𝑓(𝑥) described below:

0 if − 2 < 𝑥 < −1
𝑓(𝑥) = {2𝑘 if − 1 < 𝑥 < 1 ; period = 4
0 if 1 < 𝑥 < 2

(A) 𝑘 2𝑘 𝜋 1 3𝜋 1 5𝜋
𝑓(𝑥) = + (cos 𝑥 − cos 𝑥 + cos 𝑥 − + ⋯)
2 𝜋 2 3 2 5 2

(B) 𝑘 2𝑘 𝜋 1 3𝜋 1 5𝜋
𝑓(𝑥) = + (sin 𝑥 − sin 𝑥 + sin 𝑥 − + ⋯)
2 𝜋 2 3 2 5 2

(C) 4𝑘 𝜋 1 3𝜋 1 5𝜋
𝑓(𝑥) = 𝑘 + (cos 𝑥 − cos 𝑥 + cos 𝑥 − + ⋯)
𝜋 2 3 2 5 2

(D) 4𝑘 𝜋 1 3𝜋 1 5𝜋
𝑓(𝑥) = 𝑘 + (sin 𝑥 − sin 𝑥 + sin 𝑥 − + ⋯)
𝜋 2 3 2 5 2

Organising Institute: IIT Roorkee Page 10 of 43

Q.14 𝑋 is a random variable that can take any one of the values 0, 1, 7, 11, and 12. The
probability mass function for 𝑋 is

𝑃(𝑋 = 0) = 0.4; 𝑃(𝑋 = 1) = 0.3; 𝑃(𝑋 = 7) = 0.1;

𝑃(𝑋 = 11) = 0.1; 𝑃(𝑋 = 12) = 0.1

Then, the variance of 𝑋 is

(A) 20.81

(B) 28.40

(C) 31.70

(D) 10.89

Q.15 As per IS 456:2000 provisions for two-way slabs with continuous edges, the
longitudinal steel reinforcement to be provided in the edge strip is based on

(A) the calculated minimum bending moment

(B) the area of longitudinal steel provided in the middle strip in the shorter span

(C) the area of longitudinal steel provided in the middle strip in the longer span

(D) the prescribed minimum cross-sectional area of longitudinal steel for slabs

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Q.16 Identify the FALSE statement from the following options:

The compressive strength of a concrete test specimen can vary depending on its
(A)
shape and size

Air-dried and saturated test specimens show the same compressive strength for
(B)
concrete

Curing conditions, such as temperature and relative humidity, can influence the
(C)
compressive strength of concrete

Compressive strength depends on the water-to-binder ratio used in the concrete
(D)
mixture

Organising Institute: IIT Roorkee Page 12 of 43

Q.17 The results of a consolidated drained triaxial test on a normally consolidated clay
are shown in the figure. The angle of internal friction is

(A) 1
sin−1 ( )
2

(B) 1
sin−1 ( )
3

(C) 2
sin−1 ( )
3

(D) 3
sin−1 ( )
4

Organising Institute: IIT Roorkee Page 13 of 43

Q.18 The standard plasticity chart for the classification of a fine-grained soil is shown in
the figure. As per the Indian standard soil classification system, X represents

Plasticity Index (%)

A-Line
X

Liquid Limit (%)
20 35 50

(A) inorganic clay with medium plasticity

(B) inorganic silt with medium plasticity

(C) inorganic clay with high plasticity

(D) inorganic silt with high compressibility

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Q.19 For a flowing fluid, a dimensionless combination of velocity (𝑉), length scale (𝑙),
and acceleration due to gravity (𝑔) would be

(A) 𝑉2
𝑔𝑙

(B) 𝑉𝑔
𝑙

(C) 𝑔𝑙 2
𝑉

(D) 𝑙
𝑉 2𝑔

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Q.20 To derive the total flood hydrograph at a catchment outlet from an isolated storm,
the order in which the following methods are applied, from the first method to the
last method, is

P. Obtaining the hyetograph

Q. Addition of baseflow

R. Estimation of initial and infiltration losses

S. Application of unit hydrograph

(A) PRSQ

(B) PQRS

(C) RPSQ

(D) PSQR

Q.21 Fecal Coliform (FC) concentration in river water was measured as 10780 cfu/100
ml. The FC concentration after the conventional water treatment, but before
chlorination, was measured as 23 cfu/100 ml. The ‘Log Kill’ (inactivation) of FC
due to the conventional water treatment is closest to

(A) 4.00

(B) 2.50

(C) 2.67

(D) 3.00

Organising Institute: IIT Roorkee Page 16 of 43

Q.22 A hydrocarbon (CnHm) is burnt in air (O2 + 3.78N2). The stoichiometric fuel to air
mass ratio for this process is

Note: Atomic Weight: C(12), H(1)

Effective Molecular Weight: Air(28.8)

Ignore any conversion of N2 in air to the oxides of nitrogen (NOx)

(A) (4n + m)
0.0291
(12n + m)

(B) (12n + m)
34.42
(4n + m)

(C) (4n + m)
34.42
(12n + m)

(D) (12n + m)
0.0291
(4n + m)

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Q.23 All the vehicles that come during a particular peak hour come during a 10-minute
period within this hour. The 15-minute peak hour factor for this peak hour is

(A) 0.25

(B) 0.167

(C) 0.75

(D) 1.0

Q.24 In the context of testing bitumen, which one of the following statements is FALSE:

(A) The depth of penetration of needle in the standard penetration test is measured in
the units of one-tenth of millimeter

(B) Softening point is measured using a ring and ball apparatus

(C) Softening point is measured in the units of time

(D) Ductility is measured in the units of length

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Q.25 The maximum degree of the curve that can be used for railways in a mountainous
region is

(A) 10

(B) 20

(C) 50

(D) 40

Q.26 If the horizontal distance between a staff point and the point of observation is
𝑑, the error due to the curvature of earth is proportional to

(A) 𝑑

(B) 1
𝑑

(C) 𝑑2

(D) 1
𝑑2

Organising Institute: IIT Roorkee Page 19 of 43

Q.27 If the quadrantal bearing of a line is N30W, then the whole circle bearing of the
line is

(A) 120

(B) 210

(C) 300

(D) 330

Q.28 Which of the following equations belong/belongs to the class of second-order,
linear, homogeneous partial differential equations:

(A) 𝜕 2𝑢 2
𝜕 2𝑢 𝜕 2𝑢
= 𝑐 ( + ) + 𝑥𝑦
𝜕𝑡 2 𝜕𝑥 2 𝜕𝑦 2

(B) 𝜕 2𝑢 𝜕 2𝑢 𝜕 2𝑢
+ + =0
𝜕𝑥 2 𝜕𝑦 2 𝜕𝑧 2

(C) 𝜕𝑢 𝜕𝑢
=𝑐
𝜕𝑡 𝜕𝑥

(D) 2
𝜕 2𝑢 𝜕 2𝑢
( 2 ) = 𝑐2 2
𝜕𝑡 𝜕𝑥

Organising Institute: IIT Roorkee Page 20 of 43

Q.29 Consider the frame shown in the figure under the loading of 100 kN.m couples at
the joints B and G. Considering only the effects of flexural deformations, which of
the following statements is/are true:

100 kN.m 100 kN.m
B 4EI C 4EI G

2EI 2EI 2EI 6m

A D F

8m 8m

(A) Axial force is zero in the member CD

(B) Shear force is zero in the member CD

(C) There is no rotation in the joint C

(D) The magnitude of bending moment developed in the member BC at the end C is
more than 50 kN.m

Q.30 For the Bernoulli’s equation to be applicable in a fluid flow situation, which of the
following conditions is/are to be satisfied:

(A) Fluid should be frictionless

(B) Fluid should be incompressible

(C) Flow should be steady

(D) Flow should be rotational

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Q.31 The Surface Overflow Rate (SOR) in a rectangular sedimentation tank is 45
m3/m2/d. Minimum diameters of spherical inorganic and organic particles expected
to be completely removed in this tank are calculated. Assume that Stoke’s law is
applicable. Which of the following options is/are correct:

Specific gravity of inorganic particles = 2.65

Specific gravity of organic particles = 1.20

Acceleration due to gravity (g) = 9.81 m/s2

Kinematic viscosity (𝜈) = 1×10-6 m2/s

(A) Minimum diameter of inorganic particles is 24 m

(B) Minimum diameter of organic particles is 69 m

(C) Minimum diameter of inorganic particles is 15 m

(D) Minimum diameter of organic particles is 55 m

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Q.32 Aeration is employed as a treatment option for the removal of several pollutants
from contaminated water.

Identify the pollutant(s), where aeration is employed as a part of their removal:

(A) Iron

(B) Cadmium

(C) Manganese

(D) Zinc

Q.33 If the weights retained on the 2.36 mm, 1.18 mm, 600 µm, and 300 µm sieves are
30%, 35%, 15%, and 20%, respectively, of the total weight of an aggregate
sample, then the fineness modulus of the sample is __________________
(rounded off to 2 decimal places).

Q.34 A water resources project with an expected life of 25 years has to be designed for
an acceptable risk of 5% against a design flood. The return period for the design
flood (in years) is _________________ (rounded off to the nearest integer).

Organising Institute: IIT Roorkee Page 23 of 43

Q.35 Road A and Road B are joined by a circular horizontal curve of radius 200 m as
shown in the figure. Road A and Road B are tangential to the curve at the points C
and D, respectively. Had the curve not been there, straight roads A and B would
have met at the point E. The distance from C to E is 92 m. The value of angle 𝜃 (in
degrees) is ______________ (rounded off to 1 decimal place).

Note: The value of angle 𝜃 is to be calculated only from the consideration of
Euclidean geometry and the data given in the problem.

E 𝜃

C
D

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Q.36 – Q.65 Carry TWO marks Each

Q.36 The value of lim (𝑥 − √𝑥 2 + 𝑥) is equal to
𝑥→∞

(A) -1

(B) -0.5

(C) -2

(D) 0

Organising Institute: IIT Roorkee Page 25 of 43

Q.37 In the rigid-jointed frame shown in the figure, the distribution factor of the member
AD is closest to

B

L EI

L/2 L/2
2EI D
C
L A 2EI EI

L
2EI

F

(A) 0.254

(B) 0.267

(C) 0.398

(D) 0.421

Organising Institute: IIT Roorkee Page 26 of 43

Q.38 In an oedometer apparatus a specimen of fully saturated clay has been consolidated
under a vertical pressure of 100 kPa and is at equilibrium state. Immediately on
increasing the vertical pressure to 150 kPa, the effective stress 𝜎 ′ and excess pore
water pressure ∆𝑢 will be

(A) 𝜎 ′ = 50 kPa, ∆𝑢 = 100 kPa

(B) 𝜎 ′ = 100 kPa, ∆𝑢 = 50 kPa

(C) 𝜎 ′ = 150 kPa, ∆𝑢 = 50 kPa

(D) 𝜎 ′ = 100 kPa, ∆𝑢 = 150 kPa

Organising Institute: IIT Roorkee Page 27 of 43

Q.39 The mean rainfall over a catchment has to be estimated. The data for four rain
gauges located in and around the catchment is listed in the table. Which one of the
following statements is correct:

Rain gauge station P Q R S

Whether located inside the Yes Yes Yes No
catchment

Thiessen weightage factor 0.25 0.50 0.10 0.15

Rainfall (mm) 100 110 100 125

(A) The estimate obtained from the Thiessen-mean method is greater than that obtained
using the arithmetic-mean method

(B) The estimate obtained from the Thiessen-mean method is equal to that obtained
using the arithmetic-mean method

(C) The estimate obtained from the Thiessen-mean method is less than that obtained
using the arithmetic-mean method

(D) The Thiessen-mean method cannot be applied in this case

Organising Institute: IIT Roorkee Page 28 of 43

Q.40 The speed-density relation on a one-way, single lane road is shown in the figure,
where speed 𝑢 is in km/hour and density 𝑘 is in vehicles/km. The maximum flow
(in vehicles/hour) on this road is

𝑢
90

0 10 100 𝑘

(A) 2500

(B) 900

(C) 2250

(D) 2000

Organising Institute: IIT Roorkee Page 29 of 43

Q.41 Consider the beam ACDEB given in the figure. Which of the following statements
is/are correct:

3 kN 2 kN

4 kN
1m E
A C 1m D B
internal hinge 4 kN

5m 2m 2m 2m

(A) Bending moment is zero between the points A and C

(B) There is a sudden jump in shear force at the point D

(C) There is a sudden jump in bending moment at the point E

(D) Bending moment is zero somewhere between the points D and E

Organising Institute: IIT Roorkee Page 30 of 43

Q.42 In the context of construction project management, which of the following
statements is/are true:

(A) A dummy activity will consume time and resources

(B) The programme evaluation and review technique (PERT) is best suited for
projects with large uncertainties in the duration of activities

(C) A Gantt chart is commonly used for identifying the ‘critical path’ of activities in a
project

(D) Free float is the amount of time by which the start of an activity can be delayed
without causing a delay in the start of a following activity

Q.43 Lacey’s regime equations, followed in India for making scour calculations while
designing hydraulic structures across alluvial channels, are given below.
Regarding these equations, which of the following statements is/are true:

𝑄 1/3
𝐷 = 0.470 × [ ]
𝑓𝑠
𝑃 = 4.75 × √𝑄
𝑓𝑠 = 1.76 × √𝑑

where, 𝑄 is discharge and 𝑓𝑠 is silt factor.

(A) D is the depth of scour below the existing riverbed

(B) P is the Lacey’s waterway width

(C) d is the average grain size diameter of the bed material in centimetres

(D) D is the depth of scour below the design flood level

Organising Institute: IIT Roorkee Page 31 of 43

Q.44 MgCl2 and CaSO4 salts are added to 1 litre of distilled deionized water and mixed
until completely dissolved. Total Dissolved Solids (TDS) concentration is 500 mg/l,
and Total Hardness (TH) is 400 mg/l (as CaCO3). The amounts of MgCl2 and CaSO4
added are calculated (rounded off to the nearest integer). Which of the following
options is/are true:

Atomic weights: Ca(40), Mg(24), S(32), O(16), Cl(35.5), C(12)

(A) Amount of MgCl2 added is 143 mg

(B) Amount of CaSO4 added is 357 mg

(C) Amount of MgCl2 added is 103 mg

(D) Amount of CaSO4 added is 397 mg

Q.45 A facultative pond system is employed for wastewater treatment. Which of the
following statements is/are true:

(A) The dissolved oxygen concentration will be high during daytime compared to
night-time

(B) The pH will be high during daytime compared to night-time

(C) The dissolved oxygen concentration will be low during daytime compared to
night-time

(D) The pH will be low during daytime compared to night-time

Organising Institute: IIT Roorkee Page 32 of 43

Q.46 Organic fraction of municipal solid waste (OFMSW) with bulk density of 315 kg/m3
and water content of 30% is mixed with municipal sludge of bulk density 700 kg/m3
and water content of 70%, such that the water content of the mixture is 40%. The
amount (in kg) of sludge to be mixed per kg of OFMSW (rounded off to 2 decimal
places) and the density of the mixture (in kg/m3) (rounded off to the nearest integer)
are calculated. Which of the following options is/are true:

(A) 0.33 kg of sludge added per kg of OFMSW

(B) Density of the mixture is 365 kg/m3

(C) 0.66 kg of sludge added per kg of OFMSW

(D) Density of the mixture is 450 kg/m3

Q.47 Let 𝑦 be the solution of the initial value problem 𝑦 ′′ + 0.8𝑦 ′ + 0.16𝑦 = 0, where
𝑦(0) = 3 and 𝑦 ′ (0) = 4.5. Then, 𝑦(1) is equal to ______________________
(rounded off to 1 decimal place).

Q.48 The maximum value of the function ℎ(𝑥) = −𝑥 3 + 2𝑥 2 in the interval [-1,1.5] is
equal to _________________________ (rounded off to 1 decimal place).

Organising Institute: IIT Roorkee Page 33 of 43

Q.49 Consider the differential equation given below. Using the Euler method with the
step size (ℎ) of 0.5, the value of 𝑦 at 𝑥 = 1.0 is equal to ____________ (rounded off
to 1 decimal place).

𝑑𝑦
= 𝑦 + 2𝑥 − 𝑥 2 ; 𝑦(0) = 1 (0 ≤ 𝑥 < ∞)
𝑑𝑥

Q.50 For the beam and loading shown in the figure, the second derivative of the
deflection curve of the beam at the mid-point of AC is given by  M 0 8 EI . The
value of  is ___________________ (rounded off to the nearest integer).

A C B
Mo
2EI EI
L L

Organising Institute: IIT Roorkee Page 34 of 43

Q.51 Consider the rigid bar ABC supported by the pin-jointed links BD and CE and
subjected to a load P at the end A, as shown in the figure. The axial rigidities of BD
and CE are 22500 kN and 15000 kN, respectively. If CE elongates by 5 mm due to
the load P, the magnitude of the downward deflection (in mm) of the end A would
be ________________________ (rounded off to the nearest integer).

D
200 mm
A C
B
P 300 mm
E
200 mm 200 mm

Q.52 Consider a reinforced concrete beam section of 300 mm width and 700 mm depth.
The beam is reinforced with the tension steel of 2000 mm2 area at an effective cover
of 50 mm. Concrete in the tension zone is assumed to be cracked. Assume the
modular ratio of 12 and Young’s modulus of 200 GPa for steel. When the extreme
fibre in the compression zone undergoes the strain of 0.0004 due to the applied
bending moment, the stress in the steel (in MPa) is ______________ (rounded off
to the nearest integer).

Organising Institute: IIT Roorkee Page 35 of 43

Q.53 Consider the beam section shown in the figure, with y indicating the depth of
neutral axis (NA). The section is only subjected to an increasing bending moment.
It is given that y = 18.75 mm, when the section has not yielded at the top and
bottom fibres. Further, y decreases to 5 mm, when the entire section has yielded.
The shape factor of the section is _____________ (rounded off to 2 decimal places).

60

5
𝑦ത

N A 60
m All dimensions are in mm

5

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Q.54 Consider the built-up column made of two I-sections as shown in the figure, with
each batten plate bolted to a component I-section of the column through 6 black
bolts. Each connection of the batten plate with the component section is to be
designed for a longitudinal shear of 70 kN and moment of 10 kN.m. The minimum
bolt value required (in kN) is _____________ (rounded off to the nearest integer).

30
140
140
30
210

All dimensions are in mm

70 100 70

Organising Institute: IIT Roorkee Page 37 of 43

Q.55 A cut slope is made in a silty clay soil for a new road project, as shown in the figure.
The locations of ground water table (GWT) and potential failure surface are shown
in the figure. After the cut is made, the excess pore water pressure is fully dissipated,
and the shear stress at the point A is 60 kN/m2. The factor of safety at the point A
for long-term stability is ___________________ (rounded off to 2 decimal places).

Note:

Shear strength properties of silty clay: c′ = 15 kN/m2, ′ = 15, and cu = 75 kN/m2

Unit weight of soil above the GWT () = 19 kN/m3

Unit weight of soil below the GWT (sat) = 20 kN/m3

Unit weight of water (w) = 9.81 kN/m3

Organising Institute: IIT Roorkee Page 38 of 43

Q.56 A 6 m × 6 m square footing constructed in clay is subjected to a vertical load of
2500 kN at its centre. The base of the footing is 2 m below the ground surface, as
shown in the figure. The footing is made of 2 m thick concrete. The ground water
table is at a great depth. Considering Terzaghi’s bearing capacity theory, the factor
of safety of footing against the bearing capacity failure is ____________ (rounded
off to 2 decimal places).

Note:

Unit weight of concrete = 24 kN/m3

Properties of clay: c = 50 kN/m2,  = 0, and  = 19 kN/m3

For  = 0: Nc = 5.7, Nq = 1, N = 0

2500 kN

Ground surface
Footing 2m

6m

Q.57 A clayey soil has a moisture content of 18%, a specific gravity of soil solids of 2.74,
and a degree of saturation of 65%. The soil soaks up water during a rain event, and
the degree of saturation increases to 85.2%. The change of the volume during the
soaking is negligible. The new moisture content (in %) of the soil will be
____________________ (rounded off to 2 decimal places).

Organising Institute: IIT Roorkee Page 39 of 43

Q.58 A single pile with 450 mm diameter has been driven into a homogeneous clay
layer, which has an undrained cohesion (cu) of 20 kPa and unit weight of 18
kN/m3. The ground water table is found to be at the surface of the clay layer. The
adhesion factor (α) of the soil is 0.95 and bearing capacity factor (Nc) is 9. The
pile is supporting a column load of 144 kN with a factor of safety of 3.0 against
ultimate axial pile capacity in compression.

The required embedment depth of the pile (in m) is ________________ (rounded
off to the nearest integer).

Q.59 Two soils of permeabilities k1 and k2 are placed in a horizontal flow apparatus, as
shown in the figure. For Soil 1, L1 = 50 cm, and k1 = 0.055 cm/s; for Soil 2, L2 = 30
cm, and k2 = 0.035 cm/s. The cross sectional area of the horizontal pipe is 100 cm2,
and the head difference (h) is 150 cm. The discharge (in cm3/s) through the soils
is ___________ (rounded off to 2 decimal places).

h

Soil 1 (k1) Soil 2 (k2)

Direction of flow
L1 L2

Organising Institute: IIT Roorkee Page 40 of 43

Q.60 A hydraulic jump is formed in a 5 m wide rectangular channel, which has a
horizontal bed and is carrying a discharge of 15 m3/s. The depth of water upstream
of the jump is 0.5 m. The power dissipated by the jump (in kW) is ___________
(rounded off to the nearest integer).

Note:

Acceleration due to gravity = 9.81 m/s2

Density of water = 1000 kg/m3

Kinetic energy correction factor = 1.0

Q.61 A symmetrical trapezoidal canal is 100 km long. The bottom width is 10 m and
the side slope is 1 Horizontal : 1 Vertical. The average flow depth in the canal is
2.5 m throughout the month of April. The measurement from a Class-A
evaporimeter in the vicinity of the canal indicated an average evaporation rate of
0.5 cm/day in April.

The volume of water evaporated from the canal (in m3) in the month of April is
close to __________________ ×103 (rounded off to 1 decimal place).

Q.62 A 5.0 m wide rectangular channel carries a discharge of 10 m3/s at a depth of 1.5 m
under uniform flow. To produce critical flow conditions without affecting the
upstream conditions, the channel bottom elevation should be raised (in m) by
__________________ (rounded off to 2 decimal places).

Assume that there is no loss of head at the raise, kinetic energy correction factor is
1.0, and acceleration due to gravity is 9.81 m/s2.

Organising Institute: IIT Roorkee Page 41 of 43

Q.63 A one-way, single lane road has traffic that consists of 30% trucks and 70% cars.
The speed of trucks (in km/h) is a uniform random variable on the interval (30, 60),
and the speed of cars (in km/h) is a uniform random variable on the interval (40, 80).
The speed limit on the road is 50 km/h. The percentage of vehicles that exceed the
speed limit is __________________ (rounded off to 1 decimal place).

Note: 𝑋 is a uniform random variable on the interval (𝛼, 𝛽), if its probability density
function is given by

1
𝛼<𝑥<𝛽
𝑓(𝑥) = {𝛽 − 𝛼
0 otherwise

Q.64 In levelling between two points A and B on the opposite banks of a river, the
readings are taken by setting the instrument both at A and B, as shown in the table.
If the RL of A is 150.000 m, the RL of B (in m) is _______________ (rounded off
to 3 decimal places).

Staff readings
Level position
A B

A 1.800 1.350

B 1.450 0.950

Organising Institute: IIT Roorkee Page 42 of 43

Q.65 During determination of the bulk specific gravity of compacted bituminous
specimen, the mass in air of the specimen is 1260 g and volume is 525 cm3. The
density of water is 1.0 g/cm3. The theoretical maximum specific gravity of mix is
2.510.

The percentage air voids in the compacted specimen is ____________________
(rounded off to 2 decimal places).

Organising Institute: IIT Roorkee Page 43 of 43

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