GATE 2026 Question Paper Civil Engineering (CE-2)

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GATE 2026
Question Paper · Civil
Engineering (CE 2)
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GATE 2026 Question Paper Civil Engineering (CE 2)

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

Q.1 ‘The team ______ more than 300 runs in 20 overs ___________ rains.
However, some players needed to improve their batting skills.’
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Choose the option with the correct sequence of words to fill the blanks.

.co s e m
s em l a
g la ag
(A) a score; despite

(B) scoring; instead of

(C) scored; despite

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(D) scoring; in spite of

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las
ag

m
m .co
m .co s e m
s e g l a
g la a
a

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.co s e m
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Civil Engineering (CE2)

Q.2 If a positive real 𝑥 satisfies the following equation

log 2 𝑥 + log √2 𝑥 = 48,

then the value of 𝑥 is _________________

(A) 216

(B) 416

(C) 214

(D) 414

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Q.3 The next figure (indicated by ‘?’) in the sequence is

m
m .co
m .co s e m
s e l a
g l a ag
a

(A)

m
m .co
s e
la
(B)

ag

(C)

m
m .co
m .co s e m
s e (D)
g l a
g la a
a

m .
.co s e m
s em l a
la
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Civil Engineering (CE2)

Q.4 ‘All the mangoes in the basket are good.’

If the above statement is false, then which one of the following statements is
necessarily true?

(A) All the mangoes in the basket are not good.

(B) No mango in the basket is good.

(C) In the basket, some of the mangoes are good and some are not good.

(D) There exists at least one mango in the basket that is not good.

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Q.5 Consider the following statements about four numbers:

(S1) The average of the four numbers is 25

(S2) Each number is at most 40

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(S3) Each number is at least 20
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Choose the option that is necessarily correct.
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(A) (S1) and (S2) together imply (S3)

(B) (S2) and (S3) together imply (S1)

(C) (S1) and (S3) together imply (S2)
m
(D) (S1) implies (S3)
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s e
g la
a

m
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m .co s e m
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a

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Civil Engineering (CE2)

Q.6 – Q.10 Carry TWO marks Each

Q.6 ‘People are crowding around ___ pit into which ___ elephant has fallen. I have
never seen an elephant looking more bewildered ___ miserable. Here it is in a
most undignified position, thrust into a pit and made to look up ___ a vast,
curiosity-stricken crowd.’

Choose the option with the correct sequence of words to fill the blanks.

(A) an; a; at; and

(B) a; an; and; at

(C) and; a; an; at

(D) at; a; an; and

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Q.7 The table lists the unit selling price of five products P, Q, R, S, and T. On a
particular day, 250 items were sold with the average selling price of Rs. 60.
The following observations were made:

(i) The quantity of S sold was twice that of T.
(ii) The quantity of R sold was thrice that of T.
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(iii)
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The quantity of Q sold was four times that of T.
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Product P Q R S T

g la
a Unit selling price (Rs.) 100 50 40 60 60

What is the quantity of product P sold on that day?

m
(A) 40
m .co
s e
(B) 50
g la
a
(C) 60

(D) 70

m
m .co
m .co s e m
s e g l a
g la a
a

m .
.co s e m
s em l a
la
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Civil Engineering (CE2)

Q.8 Consider a string P of length 𝑙 that is laid out as a straight-line segment. Another
string K is laid out as a semicircular arc with string P as its diameter, as
represented in Figure (i). When both the strings are shortened by a length 𝑥 they
can be re-arranged such that the shortened string K forms a full circle with the
shortened string P as its diameter, as represented in Figure (ii). The value of 𝑥/𝑙
is __________

(A) 𝜋

(B) 𝜋−1
2𝜋

(C) 𝜋
2(𝜋−1)

(D) 𝜋
𝜋−1

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Q.9 The Roman senator Meritorius, his brother, his son, and his daughter have
varying oratory skill levels. They are seated in rows and columns as shown
in the figure with exactly one person sitting in each box. It is known that

(i) Meritorius’ daughter and his brother are seated in the same column.
(ii) His son is seated diagonally across the sibling of the worst orator.
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(iii) The best and worst orators are seated in the same row.
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Who is the best orator?
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a

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a
(A) Meritorius

(B) Meritorius’ brother

(C) Meritorius’ son
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m
c. o(D) Meritorius’ daughter
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m s e
s e g l a
g la a
a

m .
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Civil Engineering (CE2)

Q.10 Which one of the patterns labelled P, Q, R, and S is used to generate the following
figure?

P Q

R S

(A) P

(B) Q

(C) R

(D) S

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Q.11 – Q.35 Carry ONE mark Each

Q.11 Matrix A has the eigenvalues 1, 2, and 3. The Trace of A2 is

m
m .co
.co m
(A) 6

m s e
14 s
e l a
(B)
g l a ag
a
(C) 20

(D) 8

m
m .co
s e
g la
a

m
m .co
m .co s e m
s e g l a
g la a
a

m .
.co s e m
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Civil Engineering (CE2)

Q.12 A fifth-degree polynomial in 𝑥 is defined for 𝑥 > 0. All coefficients of the
polynomial are positive. The first derivative of the polynomial is obtained
numerically at a point by using the first-order forward as well as the first-order
backward difference methods. Identical step lengths are used for both the methods.

Following statements are made.

(I) Forward difference method underestimates the true derivative.
(II) Backward difference method overestimates the true derivative.

Which one of the following options is CORRECT?

(A) Both statements (I) and (II) are FALSE.

(B) Both statements (I) and (II) are TRUE.

(C) Statement (I) is TRUE and statement (II) is FALSE.

(D) Statement (I) is FALSE and statement (II) is TRUE.

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Q.13 Periodic function 𝑓(𝑥) is given below.

−1, when −𝜋 <𝑥 <0
𝑓(𝑥) = { } ; 𝑓(𝑥 + 2𝜋) = 𝑓(𝑥)
1, when 0<𝑥<𝜋
The CORRECT option representing the Fourier series expansion of 𝑓(𝑥) is:
m
m .co
.co s e m
s em l a
(A)
g la 4 sin3𝑥 sin5𝑥 ag
a 𝑓(𝑥) = [sin 𝑥 +
𝜋 3
+
5
+⋯]

(B) 4 sin3𝑥 sin5𝑥
𝑓(𝑥) = − [sin 𝑥 + + +⋯]
𝜋 3 5

(C) 4 sin3𝑥 sin5𝑥
𝑓(𝑥) = 1 + [sin 𝑥 + + +⋯]
𝜋 3 5
o m
. c
(D) 4
+ e +⋯]
sin3𝑥 sin5𝑥 m
𝑓(𝑥) = 1 − [sin 𝑥 +
𝜋 3
l as5
ag

m
m .co
m .co s e m
s e g l a
g la a
a

m .
.co s e m
s em l a
la
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Civil Engineering (CE2)

Q.14 A rectangular singly reinforced concrete beam has a width of 300 mm and an
effective depth of 550 mm. The grades of steel and concrete are Fe500 and M25,
respectively. The area of steel in tension is 1963 mm2. The depth of neutral axis is
302 mm. The ratio of the limiting depth of the neutral axis (𝑥𝑢,𝑚𝑎𝑥 ) to the effective
depth (d) of the beam is 0.456.

The most probable mode of failure of the beam is

(A) compression failure

(B) bond failure

(C) shear failure

(D) ductile failure

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Q.15 As per IS:800-2007, design of a cantilever steel beam section for its moment
capacity requires fulfilment of an upper bound, expressed as:

𝑓𝑦
𝑀𝑑 ≤ 1.5𝑍𝑒
𝛾𝑚0

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.co
The reason for such upper bound is to
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.co s e m
s em l a
g l a
(A) a control deflection
ag

(B) restrain lateral-torsional buckling

(C) avoid plastic deformation under working load

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(D) avoid yielding at ultimate load

s em
g la
Q.16 A plane strain problem (in a
X-Y plane) must satisfy the condition:

(A) 𝜎𝑧𝑧 = 0

m
m
(B) 𝜖𝑧𝑧 = 𝜖𝑥𝑧 = 𝜖𝑦𝑧 = 0
.co
m .co s e m
s e (C) 𝜎𝑥𝑥 ≠ 𝜎𝑥𝑦 ≠ 𝜎𝑥𝑧 ≠ 0
g l a
g la a
a (D) 𝜖𝑥𝑥 ≠ 𝜀𝑦𝑦 ≠ 𝜖𝑥𝑦 ≠ 0

m .
.co s e m
s em l a
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Civil Engineering (CE2)

Q.17 Which one of the following stress conditions represents the state of pure shear
stress?

(A)

(B)

(C)

(D)

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Q.18 The horizontal beam shown in the figure has fixed supports at F and L. Internal
hinges are provided at locations G and J. The beam supports vertically downward
concentrated loads as well as uniformly distributed loads, as shown in the figure.

m
m .co
m .co s e m
s e l a
g l a ag
a
(Figure not to scale)

The upward vertical reaction (in kN) at the support L is

m
m .co
(A) 23
s e
g la
(B) 33 a
(C) 43

(D) 58

m
m .co
m .co s e m
s e g l a
g la a
a

m .
.co s e m
s em l a
la
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Civil Engineering (CE2)

Q.19 The Culturable Command Area (CCA) for a canal is 10000 hectares. The base
period for a crop in the CCA is 140 days. Watering depth for the crop is 40 cm. The
outlet discharge (in m3/s) lies between

(A) 3 and 4

(B) 13 and 14

(C) 23 and 24

(D) 33 and 34

Q.20 Following statements are made with respect to the mass curve of rainfall:

(I) Slope at a point on the curve can be positive.
(II) Slope at a point on the curve can be zero.

Which one of the following options is CORRECT?

(A) Both statements (I) and (II) are TRUE.

(B) Both statements (I) and (II) are FALSE.

(C) Statement (I) is TRUE and statement (II) is FALSE.

(D) Statement (I) is FALSE and statement (II) is TRUE.

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Q.21 Based on the Casagrande’s plasticity chart, plasticity index (in %) of inorganic clays
having a liquid limit of 40 %, ranges between

m
(A) 18.0 and 28.8
m .co
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s em l a
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(B) 14.6 and 28.8

g la
(C) a 14.6 and 23.4

(D) 18.0 and 43.8

m
m .co
s e
g la
a

m
m .co
m .co s e m
s e g l a
g la a
a

m .
.co s e m
s em l a
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Civil Engineering (CE2)

Q.22 Information related to foundation design is provided in table below.

Column 1 Column 2

(I) Converse-Labarre formula (P) Pile capacity from dynamic formula

(II) Hiley formula (Q) Pile group efficiency

(III) Newmark’s influence chart (R) Bearing capacity factor of saturated
clay

(IV) Skempton’s equation (S) Increase in vertical stress below footing

Option giving the CORRECT match between Column 1 and Column 2 is:

(A) (I) – (Q) ; (II) – (P) ; (III) – (S) ; (IV) – (R)

(B) (I) – (R) ; (II) – (S) ; (III) – (Q) ; (IV) – (P)

(C) (I) – (P) ; (II) – (Q) ; (III) – (S) ; (IV) – (R)

(D) (I) – (R) ; (II) – (S) ; (III) – (P) ; (IV) – (Q)

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Q.23 An incident occurred on one side of a median on a four-lane dual carriageway road
section. This incident disrupted the traffic movement in one direction. Traffic police
diverted the traffic from disrupted side to the other side through an opening in a
median. The desired sight distance on the four-lane dual carriageway was kept as
360 m under normal conditions. The Stopping Sight Distance (SSD, in m), which

m
should be available on the operating road section after the incident, is

m .co
m .co s e m
s e l a
(A)
g l
360a ag
a
(B) 240

(C) 180

(D) 720
m
.co
s em
g la is TRUE?
Q.24
a
Which one of the following statements

(A) Cant deficiency is related to train moving faster, and Cant excess is related to train
moving slower.

m
m
(B) Cant deficiency is related to train moving slower, and Cant excess is related to train
.co
.co em
moving faster.

e m s
laand Cant excess is
las (C)
ag
Cant deficiency is related to train moving on the main line,
ag related to train moving on the branch line.

(D) Cant deficiency is related to train moving on the branch line, and Cant excess is
related to train moving on the main line.

m .
.co s e m
s em l a
la
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Civil Engineering (CE2)

Q.25 The primary purpose of the Windrose diagram is for the design of

(A) length of a runway.

(B) orientation of a runway.

(C) width of a runway.

(D) gradient of a runway.

Q.26 Which one of the following statements is TRUE with respect to levelling survey?

(A) A level surface at all points is normal to the direction of the force of gravity.

(B) Two level surfaces can cross each other.

(C) Ellipsoid is an irregular surface approximating the physical surface of the Earth.

(D) Geoid is a regular surface approximating the physical surface of the Earth.

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Q.27 Column I presents common air pollutants, and column II presents treatment
technologies commonly employed to control air pollutants.

Air pollutant Treatment technology

m
1
m
Dust (size 5-25 µm) P Cyclone separator
.co
.co s e m
s emCarbon monoxide (CO) l a
ag
2 Q Wet lime-water scrubber

g la
a 3 Sulfur dioxide (SO ) 2 R Electrostatic precipitator

4 Fly ash (size ˂ 2.5 µm) S Catalytic converter

The option that CORRECTLY matches the air pollutant with its treatment
technology is:
m
m .co
s e
1  P ; 2  S ; 3  Q ; 4  Rg
la
(A)
a
(B) 1P; 2R; 3S; 4Q

(C) 1R; 2Q; 3P; 4S

1R; 2Q; 3S; 4P
m
.co
(D)
m
m .co s e m
s e g l a
g la a
a

m .
.co s e m
s em l a
la
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Civil Engineering (CE2)

Q.28 One-third of the solid matter in a sludge containing 90 % water is composed of fixed
mineral solids with specific gravity 2.5, and two-third is composed of volatile solids
with specific gravity 1.0.

Specific gravity of all solids lies between

(A) 1.2 and 1.3

(B) 1.5 and 1.6

(C) 1.7 and 1.8

(D) 2.0 and 2.1

Q.29 The grown algae are useful in the operation of

(A) oxidation pond.

(B) slow sand filter.

(C) cyclone separator.

(D) septic tank.

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Q.30 A partial differential equation is given below.

𝜕2𝑢 𝜕2𝑢
− = 0
𝜕𝑥 2 𝜕𝑦 2
Possible solution(s) is/are:
m
m .co
.co s e m
s em l a
gl(𝑥a+ 𝑦)5 ag
(A)
a
(B) (𝑥 − 2𝑦)3

(C) cos(𝑥 + 𝑦)

m
.co
(D) sin(𝑥 − 2𝑦)

e m
las
ag
Q.31 2 −3.5 6
The eigenvalues of [𝐴] = [3.5 5 2 ] are
8 1 8.5
1 = 1.547, 2 = 12.330, and 3 = 4.711.

The absolute value of the determinant of matrix 𝐴 is ______ (rounded off to two
decimal places).
m
m
c. oQ.32 m.co
m
The probability (in %) that a storm having return period of 15 years may occur in
s e
s e the next 10 years is ______ (rounded off to two decimal places).
g l a
g la a
a Q.33 A fully saturated sandy soil deposit has water content 20 % and specific gravity
2.65.

The critical hydraulic gradient for seepage through the soil to create the quicksand
condition is _____________ (rounded off to two decimal places).

m .
.co s e m
s em l a
la
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Civil Engineering (CE2)

Q.34 A downgrade of 1 in 100 meets an upgrade of 1 in 125 on a road. If the rate of
change of grade is 0.10 % per 30 m, the length (in m) of the vertical curve between
the two grades is ______ (rounded off to the nearest integer).

Q.35 A tourist visiting a city holds a map prepared at a scale of 1:25000. The tourist
measures the distance between place A and place B in the city as 12.0 cm on the
map. Assuming both the places are connected by a straight road, the distance
(in km) the tourist needs to walk from A to B is __________ (rounded off to the
nearest integer).

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Q.36 – Q.65 Carry TWO marks Each

Q.36 𝑥3 sin 𝑥 cos 𝑥
Let 𝑓(𝑥) = | 6 −1 0 |
𝑝 𝑝2 𝑝3

m
.co
where p is a constant.

o m m
c
The value .of
𝑑 3
𝑓(𝑥) at x = 0 is
s e
e m 𝑑𝑥 3
l a
l as ag
ag
(A) 6 p3

(B) p + p2

m
.co
(C) p + p3

e m
(D) independent of p
las
ag

m
m .co
m .co s e m
s e g l a
g la a
a

m .
.co s e m
s em l a
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Civil Engineering (CE2)

Q.37 ⃗ is defined as
Vector field 𝑉

⃗ = 3𝑥 2 𝑦𝑧 𝑖̂ − 5𝑥𝑦 𝑗̂ + 6𝑦𝑧 2 𝑘̂
𝑉
⃗ at point (2,1,1) is
The curl of 𝑉

(A) 6𝑖̂ − 12𝑗̂ − 7𝑘̂

(B) −12𝑖̂ − 10𝑗̂ − 12𝑘̂

(C) − 34

(D) −12 12 −12
[ 5 −10 0 ]
0 6 −12

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Q.38 A simply supported, linearly elastic, homogeneous, prismatic beam of length L and
flexural rigidity EI is shown in the figure.

𝑥
m
.co
B
A
m
m .co 𝜃𝐵 (𝑥)
s e m
s e l a
g l a L
ag
a
The expression for the Influence Line Diagram (ILD) of the rotation 𝜃𝐵 (𝑥) at the
support B is

m
.co
(A) 1
(𝑥 2 − 𝐿2 )
6𝐸𝐼
e m
las
(B) 1
(𝑥 3 − 𝐿2 𝑥) ag
6𝐸𝐼𝐿

(C) 1
(𝑥 2 − 𝐿𝑥)
3𝐸𝐼

(D) 1
(𝑥 3 − 𝐿2 𝑥)
3𝐸𝐼𝐿
m
m .co
m .co s e m
s e g l a
g la a
a

m .
.co s e m
s em l a
la
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Civil Engineering (CE2)

Q.39 The plane truss shown in the figure is hinge-supported at E and F. The truss is
subjected to vertical downward force at R and horizontal force at G.

(Figure not to scale)

The force (in kN) along with its nature in member JF is

(A) 10√2 compression

(B) 10√2 tension

(C) 25√2 compression

(D) 25√2 tension

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Q.40 Consider the following statements with respect to rigid pavements:

Statement-1: Bottom-up cracking (BUC) in rigid pavements is caused at the edge
of the slab due to combined effect of single or tandem rear axle load
and positive temperature differential.

m
.co
Statement-2: Top-down fatigue cracking (TDC) in rigid pavements is caused due to

o m
repeated cycles of axle loads and negative temperature differential.
m
c
. option is: s e
e m
The CORRECT
l a
l as ag
ag
(A) Both statements are TRUE.

(B) Statement-1 is TRUE, but Statement-2 is FALSE.

(C) Statement-1 is FALSE, but Statement-2 is TRUE.
m
m .co
(D) Both statements are FALSE.
s e
g la
a

m
m .co
m .co s e m
s e g l a
g la a
a

m .
.co s e m
s em l a
la
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Civil Engineering (CE2)

Q.41 For the traverse given below, the benchmark is at ground point L. The Reduced
Level (RL) of L is 150.000 m. The direction of the traverse is from L to N. The
readings on levelling staff using the same levelling instrument kept at Stations S1
and S2 during the traversing are shown in the figure.

Column 1 Column 2
(P) 3.300 m

(I) Sum of Back Sights (Q) 2.500 m

(II) Sum of Fore Sights (R) 150.300 m

(III) RL of Point N (S) 3.000 m

(T) 150.500 m

Matching the information given under Column 1 and Column 2, which one of the
following options is CORRECT?

(A) (I)  (P) ; (II)  (S) ; (III)  (R)

(B) (I)  (P) ; (II)  (Q) ; (III)  (R)

(C) (I)  (S) ; (II)  (P) ; (III)  (T)

(D) (I)  (S) ; (II)  (Q) ; (III)  (T)

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Q.42 The 2.4 ml of raw sewage is diluted to 240 ml. The Dissolved Oxygen (DO) of the
diluted sample at the beginning of Biochemical Oxygen Demand (BOD) test was
8 mg/l and it was 6 mg/l after 5-day incubation at 20  C.

The BOD5 (in mg/l) of the raw sewage is

m
m .co
m .co s e m
s e l a
a ag
(A) 200

g l
(B) a 100

(C) 250

(D) 150

m
m .co
s e
g la
a

m
m .co
m .co s e m
s e g l a
g la a
a

m .
.co s e m
s em l a
la
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Civil Engineering (CE2)

Q.43 Types of flood routing and methods are given in the table below.

Column 1 Column 2

Type of Flood Routing Method

(P) Hydrologic routing (i) Muskingum method

(Q) Hydraulic routing (ii) Modified Pul’s method

(R) Reservoir routing (iii) Method of Characteristics

(S) Channel routing

Option(s) giving the CORRECT match(es) between Column 1 and Column 2 is/are:

(A) (P) – (i) ; (Q) – (iii) ; (R) – (ii)

(B) (Q) – (i) ; (R) – (iii) ; (S) – (ii)

(C) (P) – (i) ; (R) – (ii) ; (S) – (i)

(D) (P) – (ii) ; (Q) – (iii) ; (R) – (ii)

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Q.44 A shallow footing is subjected to a vertical load. Within the elastic limit of the
underlying soil, the TRUE statement(s) is/are:

m
(A)
m
Vertical displacement below a rigid shallow footing is uniform in clay as well as
.co
sand.
m .co s e m
s e g l a
l a contact pressure below a rigid shallow footing is uniform in clay as wellaas
agsand.
(B) Vertical

(C) Vertical displacement below a flexible shallow footing is uniform in clay as well as
sand.

(D) Vertical contact pressure below a flexible shallow footing is uniform in clay as well
as sand.
m
.co
s em
g la is/are TRUE with respect to the type of stresses
Q.45
a
Which of the following statements
to be considered for the design of rigid pavements?

(A) Warping stress due to temperature differential between the top and bottom of the
pavement slab as a result of daily variation in temperature

o m
m c
. of the
c. o(B) pavement slab as a result of seasonal variation in temperature e m
Frictional stress due to the overall increase or decrease in temperature
s
e m l a
las g
g Critical stress obtained as the maximum of the wheel loadastress, the warping stress,
a (C)
and the frictional stress

(D) Critical stress obtained as the sum of wheel load stresses at edge, interior, and corner
of the pavement slab

m .
.co s e m
s em l a
la
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Civil Engineering (CE2)

𝑑𝑦
Consider differential equation + 𝑥𝑦 = 𝑥 with the condition as y = 0 at x = 0.
Q.46 𝑑𝑥
The value of y at x = 1.0 is ______ (rounded off to two decimal places).

Q.47 The age (in years) of a population is normally distributed with a mean of 36 and
standard deviation of 12. The height (in cm) of the same population is also normally
distributed with a mean of 160 and standard deviation of 10.

If the probability of age greater than 50 years is equal to the probability of height
greater than h, the value of h (in cm) is ______ (rounded off to two decimal places).

Q.48 A 250 mm wide × 600 mm deep rectangular concrete beam is prestressed by means
of 4 high-tensile tendons, each of 14 mm diameter. The centre of the tendons is
200 mm from the soffit of the beam. The effective stress in each tendon is
700 N/mm2.

The maximum bending moment (in kN-m), that can be applied to the section
without causing tension at the soffit of the beam due to prestressing only, is ______
(rounded off to one decimal place).

Use  = 3.14

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Q.49 A rigid-jointed portal frame, shown in the figure, consists of beam and columns of
equal length L. The frame has a fixed support at one end and a roller support at the
other end. The frame is subjected to a uniformly distributed load w and a lateral load
P as shown in the figure. The plastic moment capacity of the beam and column
sections is 𝑀𝑝 . Consider a combined beam-column mechanism for plastic collapse.

m
By applying the virtual work equation corresponding to the combined plastic

.co
collapse mechanism, 𝑀𝑝 is expressed as
m
m .co 𝑀𝑝 = 𝐶1 𝑃𝐿 + 𝐶2 𝑤𝐿2
s e m
s e l a
g la C and C are constants.
where 1 2
ag
a w per w/m
unit length

PP
L

L L

m
m .co
s e
1
g
2
la integer).
The value of (C /C ) is ______ (in
a

m
m .co
m .co s e m
s e g l a
g la a
a

m .
.co s e m
s em l a
la
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Civil Engineering (CE2)

Q.50 Linearly elastic, homogeneous, uniform bars BCD and FG shown in the figure have
fixed supports at B and G, respectively. For both the bars, axial rigidity is
20000 kN. A gap of 2 mm exists between D and F prior to application of any load
(i.e. P = 0). Small deformation and infinitesimal strain assumptions are valid for the
given bars.

(Figure not to scale)

The magnitude of the horizontal reaction (in kN) at B after application of the axial
force P of 20 kN at C is ______ (rounded off to the nearest integer).

Q.51 A simply-supported rectangular reinforced concrete beam has a width 250 mm and
an overall depth 600 mm. The effective span of the beam is 6.23 m. The beam
carries a live load of 5 kN/m and super imposed dead load of 5 kN/m, in addition to
its own weight. The unit weight of reinforced concrete is 25 kN/m3. Consider the
load factor of 1.5 for all stated loads.

The design bending moment (in kN-m) for the limit state of collapse is ______
(rounded off to two decimal places).

Q.52 Width (in m) of a rectangular channel required to carry a discharge of 96 m 3/s at a
critical depth of 9.8 m is _____ (rounded off to two decimal places).

Use acceleration due to gravity = 9.8 m/s2

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Q.53 The cross section of a 0.5 m wide vertical gate holding water and oil is shown in
the figure. The unit weights of water and oil are 10 kN/m3 and 7.5 kN/m3,
respectively.

m
m .co
m .co s e m
s e l a
g l a ag
a

(Figure not to scale)
m
.co
The horizontal hydrostatic force (in kN) acting on the vertical gate

em
is _________ (rounded off to two decimal places).
s
la water from an underground tank to an overhead
Q.54 ag
A centrifugal pump is delivering
reservoir against a static head of 35 m through a 2 km long, 250 mm diameter pipe.
The head-discharge characteristic of the pump is given by

𝐻 = 140 − 9000𝑄 2

where 𝐻 is the head (in m) generated by the pump and 𝑄 is the discharge (in m3/s)
of the pump.

m
.co
Neglecting all minor losses, the head (in m) generated by the pump is ______
m
.co
(rounded off to the nearest integer).
e m
e m Use: Darcy-Weisbach friction factor f = 0.04
l as
las Acceleration due to gravity = 9.81 m/s2
ag
ag  = 3.14

Q.55 The flow depth for a discharge of 10 m3/s in a wide rectangular channel is 2.0 m.
Assume that the flow is uniform.

If the discharge is doubled, the flow depth (in m) in this channel is _________
(rounded off to two decimal places).
m .
.co s e m
s em l a
la
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Civil Engineering (CE2)

Q.56 For a clayey soil stratum, the time required for degree of consolidation from 25 %
to 50 % is 30 days.

The total time (in days) required for 90 % degree of consolidation of the same soil
stratum is ______ (rounded off to the nearest integer).

Q.57 The ultimate bearing capacity of a 1 m wide strip footing is 532.80 kPa, when it is
embedded at 1 m depth in dry cohesionless soil. The soil has a unit weight of
18 kN/m3. The ultimate bearing capacity is 864 kPa when the depth of embedment
becomes 2 m.

Neglecting the effect of the depth factor, the bearing capacity factor Nq is ______
(rounded off to one decimal place).

Q.58 A building is proposed in an area having thick deposit of silty clay. The water table
is at the ground surface. The saturated unit weight of soil is 18 kN/m3 and unit
weight of water is 10 kN/m3. The maximum vertical load (P) on a column of the
proposed building is 2000 kN.

Consider 𝜎𝑧 ≤ 0.1 𝜎𝑣′ for computation of the minimum depth of soil exploration.

𝜎𝑣′ is the effective vertical overburden stress. 𝜎𝑧 is the increase in the vertical stress
at depth z below load P as per the Boussinesq’s stress theory.

Based on above, the minimum depth (in m) of soil exploration required for the
foundation design is ________ (rounded off to two decimal places).

Q.59 A soil sample has following properties:

Natural water content = 30 %

Plasticity index = 40 %

Liquidity index = 50 %

The estimated plastic limit (in %) of the soil is ________ (rounded off to one
decimal place).

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Q.60 For a given traffic stream, the speed-density relationship is given as:
𝑘𝑗
𝑣 = 𝑣𝑜 ln ( )
𝑘

where 𝑣 is the mean speed (in km/h), and 𝑘 is the density (in veh/km).
m
m
Considering 𝑣𝑜 as 45 km/h, and 𝑘𝑗 as 200 veh/km, the maximum flow (in veh/h) for
.co
.co
the given stream is __________ (rounded off to the nearest integer).
m s e m
s e g l a
l a a
aggradient of 1 in 50. Consider the following:
Q.61 A vertical curve is formed by a descending gradient of 1 in 40 meeting an ascending

Stopping Sight Distance (SSD) = 90 m

Height of headlight of a vehicle above the road surface = 0.75 m

Headlight beam angle with respect to the longitudinal axis of the vehicle = 1.2o

Based on the sight distance criteria, the design length (in m) of the vertical curve is
m
.co
__________ (rounded off to the nearest integer).

e m
Q.62
las
Interior angles measured at the locations of a closed traverse ABCDA are given in
table below.
ag
Location Interior angle

A 71o 1′ 40′′

B 104o 54′ 23′′
m
m .co
.co m
107o 54′ 10′′
e
C

e m l as
las D 76o 20′ 42′′
ag
ag
The total error in the measured angles (in degrees) is ______________ (rounded off
to three decimal places).

m .
.co s e m
s em l a
la
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Civil Engineering (CE2)

Q.63 The analysis of major cations and anions in a water sample collected from a city’s
water supply is given below. Ions present in minor concentrations are not given.

Anions 𝐶𝑙 − 𝑆𝑂42− 𝐻𝐶𝑂3− 𝐶𝑂32−

Concentration (mM) 1.5 0.5 1.0 0.01

Cations Na+ Ca2+ Mg2+ K+

Concentration (mM) 2 0.5 0.25 0.02

𝐻𝐶𝑙 ⇌ 𝐻 + + 𝐶𝑙 − 𝑝𝐾 = −3

𝐻2 𝑆𝑂42− ⇌ 2𝐻 + + 𝑆𝑂42− 𝑝𝐾 = −3

𝐻2 𝐶𝑂3 ⇌ 𝐻 + + 𝐻𝐶𝑂3− 𝑝𝐾 = 6.3

𝐻𝐶𝑂3− ⇌ 𝐻 + + 𝐶𝑂32− 𝑝𝐾 = 10.3

𝐻𝑂𝐶𝑙 ⇌ 𝐻 + + 𝑂𝐶𝑙 − 𝑝𝐾 = 7.5

𝐻𝑂𝐶𝑙 (in %) present in the total free chlorine in the water is _____ (rounded off to
the nearest integer).

Q.64 Anaerobic bacteria are being utilized for the destruction of biodegradable organic
content of wastewater measured in terms of Chemical Oxygen Demand (COD). The
yield coefficient (Y) is 0.06 gram Volatile Suspended Solids (VSS) per gram of
COD. Bacterial biomass forms the sludge during the process. The proximate
chemical formula of anaerobic bacteria is C6H7NO2.

The COD (in %) converted into bacterial biomass is ______ (rounded off to the
nearest integer).

Q.65 In an industry, a cyclone collector with 80 % efficiency is installed for air
purification, followed by an electrostatic precipitator with 50 % efficiency. The
concentration of particles entering the cyclone collector is 10 mg/m3.

The concentration (in mg/m3) of particles exiting the precipitator is __________
(rounded off to two decimal places).

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