GATE 2021 Question Paper CE Civil Engineering 1

General Aptitude (GA)

Q.1 – Q.5 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong
answer: – 1/3).

Q.1 Getting to the top is ________________ than staying on top.

(A) more easy

(B) much easy

(C) easiest

(D) easier

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Q.2

The mirror image of the above text about the x-axis is

(A)

(B)

(C)

(D)

Q.3 In a company, 35% of the employees drink coffee, 40% of the employees
drink tea and 10% of the employees drink both tea and coffee. What % of
employees drink neither tea nor coffee?

(A) 15

(B) 25

(C) 35

(D) 40

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Q.4  and ⊙ are two operators on numbers p and q such that
p2 + q2 𝒑𝟐
pq = and 𝒑 ⊙ 𝒒 = 𝒒 ;
pq
If 𝒙 ⊕ 𝒚 = 𝟐 ⊙ 𝟐, then x =

(A) y
2

(B) y

(C) 3y
2

(D) 2y

Q.5 Four persons P, Q, R and S are to be seated in a row, all facing the same
direction, but not necessarily in the same order. P and R cannot sit adjacent
to each other. S should be seated to the right of Q. The number of distinct
seating arrangements possible is:

(A) 2

(B) 4

(C) 6

(D) 8

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Q. 6 – Q. 10 Multiple Choice Question (MCQ), carry TWO marks each (for each wrong
answer: – 2/3).

Q.6 Statement: Either P marries Q or X marries Y
Among the options below, the logical NEGATION of the above statement is:

(A) P does not marry Q and X marries Y.

(B) Neither P marries Q nor X marries Y.

(C) X does not marry Y and P marries Q.

(D) P marries Q and X marries Y.

Q.7 Consider two rectangular sheets, Sheet M and Sheet N of dimensions
6 cm x 4 cm each.
Folding operation 1: The sheet is folded into half by joining the short edges of
the current shape.
Folding operation 2: The sheet is folded into half by joining the long edges of
the current shape.
Folding operation 1 is carried out on Sheet M three times.
Folding operation 2 is carried out on Sheet N three times.
The ratio of perimeters of the final folded shape of Sheet N to the final folded
shape of Sheet M is ______.

(A) 13 : 7

(B) 3:2

(C) 7:5

(D) 5 : 13

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Q.8 P

θ
T Q

S R

Five line segments of equal lengths, PR, PS, QS, QT and RT are used to
form a star as shown in the figure above.
The value of , in degrees, is ______

(A) 36

(B) 45

(C) 72

(D) 108

Q.9 A function, , is defined by
 ( p − q )2 , if p  q,
 ( p,q ) = 
 p + q, if p  q.

 ( − ( −3 + 2 ) ,( −2 + 3) )
The value of the expression is:
( − ( −2 + 1) )
(A) −1

(B) 0

(C) 16
3
(D) 16

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Q.10 Humans have the ability to construct worlds entirely in their minds, which
don’t exist in the physical world. So far as we know, no other species
possesses this ability. This skill is so important that we have different words
to refer to its different flavors, such as imagination, invention and
innovation.
Based on the above passage, which one of the following is TRUE?

(A) No species possess the ability to construct worlds in their minds.

(B) The terms imagination, invention and innovation refer to unrelated skills.

(C) We do not know of any species other than humans who possess the ability to
construct mental worlds.

(D) Imagination, invention and innovation are unrelated to the ability to construct
mental worlds.

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Q.1 – Q.16 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong
answer: – 1/3).

Q.1 𝟏 𝟐 𝟐 𝟑
𝟑 𝟒 𝟐 𝟓
The rank of matrix [ ] is
𝟓 𝟔 𝟐 𝟕
𝟕 𝟖 𝟐 𝟗

(A) 1

(B) 2

(C) 3

(D) 4

Q.2 𝟏 𝟐 𝟎 𝟏
If 𝑷 = [ ] and 𝑸 = [ ] then 𝑸𝑻 𝑷𝑻 is
𝟑 𝟒 𝟏 𝟎
(A) 1 2
[ ]
3 4
(B) 1 3
[ ]
2 4
(C) 2 1
[ ]
4 3
(D) 2 4
[ ]
1 3

Q.3 The shape of the cumulative distribution function of Gaussian distribution is

(A) Horizontal line

(B) Straight line at 45 degree angle

(C) Bell-shaped

(D) S-shaped

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Q.4 A propped cantilever beam EF is subjected to a unit moving load as shown in
the figure (not to scale). The sign convention for positive shear force at the left
and right sides of any section is also shown.

Unit moving load

E G F

Sign convention for
positive shear force

The CORRECT qualitative nature of the influence line diagram for shear
force at G is

(A)
+
E _ G F

(B)
+
_ F
E G

(C)
+
E _ G F

(D)
+
E G _ F

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Q.5 Gypsum is typically added in cement to

(A) prevent quick setting

(B) enhance hardening

(C) increase workability

(D) decrease heat of hydration

Q.6 The direct and indirect costs estimated by a contractor for bidding a project is
₹160000 and ₹20000 respectively. If the mark up applied is 10% of the bid price,
the quoted price (in ₹) of the contractor is

(A) 200000

(B) 198000

(C) 196000

(D) 182000

Q.7 In an Oedometer apparatus, a specimen of fully saturated clay has been
consolidated under a vertical pressure of 50 kN/m2 and is presently at
equilibrium. The effective stress and pore water pressure immediately on
increasing the vertical stress to 150 kN/m2, respectively are

(A) 150 kN/m2 and 0

(B) 100 kN/m2 and 50 kN/m2

(C) 50 kN/m2 and 100 kN/m2

(D) 0 and 150 kN/m2

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Q.8 A partially-saturated soil sample has natural moisture content of 25% and bulk
unit weight of 18.5 kN/m3. The specific gravity of soil solids is 2.65 and unit
weight of water is 9.81 kN/m3. The unit weight of the soil sample on full
saturation is

(A) 21.12 kN/m3

(B) 19.03 kN/m3

(C) 20.12 kN/m3

(D) 18.50 kN/m3

Q.9 If water is flowing at the same depth in most hydraulically efficient triangular
and rectangular channel sections then the ratio of hydraulic radius of triangular
section to that of rectangular section is

(A) 1
√2

(B) √2

(C) 1

(D) 2

Q.10 ‘Kinematic viscosity’ is dimensionally represented as

(A) M
LT

(B) M
L2T

(C) T2
L

(D) L2
T

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Q.11 Which one of the following statements is correct?

(A) Pyrolysis is an endothermic process, which takes place in the absence of oxygen.

(B) Pyrolysis is an exothermic process, which takes place in the absence of oxygen.

(C) Combustion is an endothermic process, which takes place in the abundance of
oxygen.

(D) Combustion is an exothermic process, which takes place in the absence of oxygen.

Q.12 Which one of the following is correct?

(A) The partially treated effluent from a food processing industry, containing high
concentration of biodegradable organics, is being discharged into a flowing river at
a point P. If the rate of degradation of the organics is higher than the rate of aeration,
then dissolved oxygen of the river water will be lowest at point P.

(B) The most important type of species involved in the degradation of organic matter in
the case of activated sludge process based wastewater treatment is
chemoheterotrophs.

(C) For an effluent sample of a sewage treatment plant, the ratio BOD5-day,20oC upon
ultimate BOD is more than 1.

(D) A young lake characterized by low nutrient content and low plant productivity is
called eutrophic lake.

Q.13 The liquid forms of particulate air pollutants are

(A) dust and mist

(B) mist and spray

(C) smoke and spray

(D) fly ash and fumes

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Q.14 The shape of the most commonly designed highway vertical curve is

(A) circular (single radius)

(B) circular (multiple radii)

(C) parabolic

(D) spiral

Q.15 A highway designed for 80 km/h speed has a horizontal curve section with
radius 250 m. If the design lateral friction is assumed to develop fully, the
required super elevation is

(A) 0.02

(B) 0.05

(C) 0.07

(D) 0.09

Q.16 Which of the following is NOT a correct statement?

(A) The first reading from a level station is a ‘Fore Sight’.

(B) Basic principle of surveying is to work from whole to parts.

(C) Contours of different elevations may intersect each other in case of an overhanging
cliff.

(D) Planimeter is used for measuring ‘area’.

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Q.17 Multiple Select Question (MSQ), carry ONE mark (no negative marks).

Q.17 Which of the following is/are correct statement(s)?

(A) Back Bearing of a line is equal to Fore Bearing  180o.

(B) If the whole circle bearing of a line is 270o, its reduced bearing is 90o NW.

(C) The boundary of water of a calm water pond will represent contour line.

(D) In the case of fixed hair stadia tachometry, the staff intercept will be larger, when
the staff is held nearer to the observation point.

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Q.18 – Q.25 Numerical Answer Type (NAT), carry ONE mark each (no negative
marks).

Q.18 Consider the limit:

𝟏 𝟏
𝐥𝐢𝐦 ( − )
𝒙→𝟏 𝐥𝐧 𝒙 𝒙 − 𝟏
The limit (correct up to one decimal place) is _____________

Q.19
The volume determined from ∭𝑽 𝟖 𝒙𝒚𝒛 𝒅𝑽 for V = [2, 3]× [1, 2] × [0,1]
will be (in integer) __________

Q.20 The state of stress in a deformable body is shown in the figure. Consider
transformation of the stress from the x-y coordinate system to the X-Y
coordinate system. The angle θ, locating the X-axis, is assumed to be positive
when measured from the x-axis in counter-clockwise direction.

y
X

σXX = 120 MPa

Y σxx = 40 MPa
σXY = 50 MPa

σxy
θ 30°
σxy x

σyy = 35.6 MPa

The absolute magnitude of the shear stress component  xy (in MPa, round off to
one decimal place) in x-y coordinate system is _____________________

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Q.21 The equation of deformation is derived to be y = x 2 − xL for a beam shown in
the figure.

y

x

L

The curvature of the beam at the mid-span (in units, in integer) will
be _______

Q.22 A truss EFGH is shown in the figure, in which all the members have the same
axial rigidity R. In the figure, P is the magnitude of external horizontal forces
acting at joints F and G.

F G
P P

L

E H

L

If R = 500×103 kN, P = 150 kN and L = 3 m, the magnitude of the horizontal
displacement of joint G (in mm, round off to one decimal place)
is _______________

Q.23 The cohesion (c), angle of internal friction (ϕ) and unit weight (γ) of a soil are 15
kPa, 20° and 17.5 kN/m3, respectively. The maximum depth of unsupported
excavation in the soil (in m, round off to two decimal places) is ______________

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Q.24 Two reservoirs are connected through a homogeneous and isotropic aquifer
having hydraulic conductivity (K) of 25 m/day and effective porosity () of 0.3
as shown in the figure (not to scale). Ground water is flowing in the aquifer at
the steady state.

Reservoir 1 Aquiclude
30 m

Reservoir 2
10 5m Aquifer K = 25 m/day 10 m
 = 0.3
Aquifuge
2 km

Datum

If water in Reservoir 1 is contaminated then the time (in days, round off to one
decimal place) taken by the contaminated water to reach to Reservoir 2 will be
__________

Q.25 A signalized intersection operates in two phases. The lost time is 3 seconds per
phase. The maximum ratios of approach flow to saturation flow for the two
phases are 0.37 and 0.40. The optimum cycle length using the Webster’s
method (in seconds, round off to one decimal place) is _________

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Q.26 – Q.35 Multiple Choice Question (MCQ), carry TWO mark each (for each wrong
answer: – 2/3).

Q.26 d2y dy
The solution of the second-order differential equation 2
+ 2 + y = 0 with
dx dx
boundary conditions y ( 0) = 1 and y (1) = 3 is

(A) e− x + ( 3e −1) xe− x

(B) e− x − ( 3e − 1) xe− x

(C)    x   −x
e − x + 3e sin   − 1 xe
  2  

(D)    x   −x
e − x − 3e sin   − 1 xe
  2  

Q.27 𝟏
The value of ∫𝟎 𝒆𝒙 𝒅𝒙 using the trapezoidal rule with four equal subintervals
is

(A) 1.718

(B) 1.727

(C) 2.192

(D) 2.718

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Q.28 A 50 mL sample of industrial wastewater is taken into a silica crucible. The
empty weight of the crucible is 54.352 g. The crucible with the sample is dried
in a hot air oven at 104 °C till a constant weight of 55.129 g. Thereafter, the
crucible with the dried sample is fired at 600 °C for 1 h in a muffle furnace,
and the weight of the crucible along with residue is determined as 54.783 g. The
concentration of total volatile solids is ______________ .

(A) 15540 mg/L

(B) 8620 mg/L

(C) 6920 mg/L

(D) 1700 mg/L

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Q.29 A wedge M and a block N are subjected to forces P and Q as shown in the
figure. If force P is sufficiently large, then the block N can be raised. The
weights of the wedge and the block are negligible compared to the forces P and
Q. The coefficient of friction (μ) along the inclined surface between the wedge
and the block is 0.2. All other surfaces are frictionless. The wedge angle is 30°.

Q

Surface 2
Surface 3 μ = 0.2
Block N

P
30° Wedge M

Surface 1

The limiting force P, in terms of Q, required for impending motion of block N
to just move it in the upward direction is given as P = Q . The value of the
coefficient ‘  ’ (round off to one decimal place) is

(A) 0.6

(B) 0.5

(C) 2.0

(D) 0.9

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Q.30 Contractor X is developing his bidding strategy against Contractor Y. The
ratio of Y’s bid price to X’s cost for the 30 previous bids in which Contractor
X has competed against Contractor Y is given in the Table

Ratio of Y’s bid Number of
price to X’s cost bids

1.02 6

1.04 12

1.06 3

1.10 6

1.12 3

Based on the bidding behaviour of the Contractor Y, the probability of winning
against Contractor Y at a mark up of 8% for the next project is

(A) 0%

(B) more than 0% but less than 50%

(C) more than 50% but less than 100%

(D) 100%

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Q.31 Based on drained triaxial shear tests on sands and clays, the representative
variations of volumetric strain (∆V/V) with the shear strain (γ) is shown in the
figure.
Expansion Curve P

Volumetric strain (ΔV/V)

Shear strain (γ)

Curve Q
Compression

Choose the CORRECT option regarding the representative behaviour
exhibited by Curve P and Curve Q.

(A) Curve P represents dense sand and overconsolidated clay, while Curve Q represents
loose sand and normally consolidated clay

(B) Curve P represents dense sand and normally consolidated clay, while Curve Q
represents loose sand and overconsolidated clay

(C) Curve P represents loose sand and overconsolidated clay, while Curve Q represents
dense sand and normally consolidated clay

(D) Curve P represents loose sand and normally consolidated clay, while Curve Q
represents dense sand and overconsolidated clay

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Q.32 A fluid flowing steadily in a circular pipe of radius R has a velocity that is
everywhere parallel to the axis (centerline) of the pipe. The velocity distribution
 r2 
along the radial direction is Vr = U 1 − 2  , where r is the radial distance as
 R 
measured from the pipe axis and U is the maximum velocity at r = 0. The
average velocity of the fluid in the pipe is

(A) U
2

(B) U
3

(C) U
4

(D) 5
 U
6

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Q.33 A water sample is analyzed for coliform organisms by the multiple-tube
fermentation method. The results of confirmed test are as follows:

Sample size Number of positive Number of negative
results out of 5 tubes results out of 5 tubes
(mL)

0.01 5 0

0.001 3 2

0.0001 1 4

The most probable number (MPN) of coliform organisms for the above results
is to be obtained using the following MPN Index.

MPN Index for Various Combinations of
Positive Results when Five Tubes used per
Dilution of 10.0 mL, 1.0 mL and 0.1 mL

Combination of positive MPN Index per
tubes 100 mL

0–2–4 11

1–3–5 19

4–2–0 22

5–3–1 110

The MPN of coliform organisms per 100 mL is

(A) 1100000

(B) 110000

(C) 1100

(D) 110

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Q.34 Ammonia nitrogen is present in a given wastewater sample as the ammonium
ion (NH4+) and ammonia (NH3). If pH is the only deciding factor for the
proportion of these two constituents, which of the following is a correct
statement?

(A) At pH above 9.25, only NH4+ will be present.

(B) At pH below 9.25, NH3 will be predominant.

(C) At pH 7.0, NH4+ and NH3 will be found in equal measures.

(D) At pH 7.0, NH4+ will be predominant.

Q.35 On a road, the speed – density relationship of a traffic stream is given by
u = 70 − 0.7k (where speed, u, is in km/h and density, k, is in veh/km). At the
capacity condition, the average time headway will be

(A) 0.5 s

(B) 1.0 s

(C) 1.6 s

(D) 2.1 s

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Q.36 – Q.55 Numerical Answer Type (NAT), carry TWO mark each (no negative marks).

Q.36 The values of abscissa (x) and ordinate (y) of a curve are as follows:

X y

2.0 5.00

2.5 7.25

3.0 10.00

3.5 13.25

4.0 17.00

By Simpson’s 1/3rd rule, the area under the curve (round off to two decimal
places) is ______________

Q.37 Vehicular arrival at an isolated intersection follows the Poisson distribution.
The mean vehicular arrival rate is 2 vehicle per minute. The probability
(round off to two decimal places) that at least 2 vehicles will arrive in any given
1-minute interval is ___________

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Q.38 Refer the truss as shown in the figure (not to scale).

Q R
E, 2A
E, A E, A E, A E, A

P T S

E, A E, A

L L

F

If load, F = 𝟏𝟎√𝟑 kN, moment of inertia, I = 8.33 × 106 mm4, area of cross-
section, A = 104 mm2, and length, L = 2 m for all the members of the truss, the
compressive stress (in kN/m2, in integer) carried by the member Q-R
is _______

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Q.39 A prismatic cantilever prestressed concrete beam of span length, L = 1.5 m has
one straight tendon placed in the cross-section as shown in the following figure
(not to scale). The total prestressing force of 50 kN in the tendon is applied at
dc = 50 mm from the top in the cross-section of width, b = 200 mm and depth,
d = 300 mm.

If the concentrated load, P = 5 kN, the resultant stress (in MPa, in integer)
experienced at point ‘Q’ will be ________

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Q.40 A column is subjected to a total load (P) of 60 kN supported through a bracket
connection, as shown in the figure (not to scale).

100 mm

40 mm 40 mm
P = 60 kN

30 mm
R
30 mm

The resultant force in bolt R (in kN, round off to one decimal place)
is __________________

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Q.41 Employ stiffness matrix approach for the simply supported beam as shown in
the figure to calculate unknown displacements/rotations. Take length, L = 8 m;
modulus of elasticity, E = 3×104 N/mm2; moment of inertia, I = 225×106 mm4.

P

A C

E, 2I B E, I
L L
2 2

The mid-span deflection of the beam (in mm, round off to integer) under
P = 100 kN in downward direction will be ________

Q.42 A square plate O-P-Q-R of a linear elastic material with sides 1.0 m is loaded
in a state of plane stress. Under a given stress condition, the plate deforms to a
new configuration O-P'-Q'-R' as shown in the figure (not to scale). Under the
given deformation, the edges of the plate remain straight.

y
10 mm

R' Q'
10 mm
Q
R

P'
10 mm
O P x
20 mm

The horizontal displacement of the point (0.5 m, 0.5 m) in the plate O-P-Q-R
(in mm, round off to one decimal place) is ______________

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Q.43 A small project has 12 activities – N, P, Q, R, S, T, U, V, W, X, Y, and Z. The
relationship among these activities and the duration of these activities are given
in the Table.

Activity Duration Depends
upon
(in weeks)

N 2 -

P 5 N

Q 3 N

R 4 P

S 5 Q

T 8 R

U 7 R, S

V 2 U

W 3 U

X 5 T, V

Y 1 W

Z 3 X, Y

The total float of the activity “V” (in weeks, in integer) is _______________

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Q.44 The soil profile at a construction site is shown in the figure (not to scale).
Ground water table (GWT) is at 5 m below the ground level at present. An old
well data shows that the ground water table was as low as 10 m below the
ground level in the past. Take unit weight of water, w = 9.81 kN/m3.

The overconsolidation ratio (OCR) (round off to two decimal places) at the
mid-point of the clay layer is _____________

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Q.45 A retaining wall of height 10 m with clay backfill is shown in the figure (not to
scale). Weight of the retaining wall is 5000 kN per m acting at 3.3 m from the
toe of the retaining wall. The interface friction angle between base of the
retaining wall and the base soil is 20. The depth of clay in front of the retaining
wall is 2.0 m. The properties of the clay backfill and the clay placed in front of
the retaining wall are the same. Assume that the tension crack is filled with
water. Use Rankine’s earth pressure theory. Take unit weight of water, w =
9.81 kN/m3.

The factor of safety (round off to two decimal places) against sliding failure of
the retaining wall after ignoring the passive earth pressure will be _________

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Q.46 A combined trapezoidal footing of length L supports two identical square
columns (P1 and P2) of size 0.5 m × 0.5 m, as shown in the figure. The columns
P1 and P2 carry loads of 2000 kN and 1500 kN, respectively.

L

5m 1.5 m
P1 P2

5m

If the stress beneath the footing is uniform, the length of the combined footing
L (in m, round off to two decimal places) is ______________

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Q.47 An unsupported slope of height 15 m is shown in the figure (not to scale), in
which the slope face makes an angle 50° with the horizontal. The slope material
comprises purely cohesive soil having undrained cohesion 75 kPa. A trial slip
circle KLM, with a radius 25 m, passes through the crest and toe of the slope
and it subtends an angle 60° at its center O. The weight of the active soil mass
(W, bounded by KLMN) is 2500 kN/m, which is acting at a horizontal distance
of 10 m from the toe of the slope. Consider the water table to be present at a
very large depth from the ground surface.

O
60°

N M

15 m
L
50°
W
K 10 m

Considering the trial slip circle KLM, the factor of safety against the failure
of slope under undrained condition (round off to two decimal places)
is ______________

Q.48 An unlined canal under regime conditions along with a silt factor of 1 has a
width of flow 71.25 m. Assuming the unlined canal as a wide channel, the
corresponding average depth of flow (in m, round off to two decimal places) in
the canal will be __________

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Q.49 A cylinder (2.0 m diameter, 3.0 m long and 25 kN weight) is acted upon by
water on one side and oil (specific gravity = 0.8) on other side as shown in the
figure.

1m

R
Water
2m Q
1 m Oil of sp gr 0.8
P

The absolute ratio of the net magnitude of vertical forces to the net magnitude
of horizontal forces (round off to two decimal places) is ___________

Q.50 A tube-well of 20 cm diameter fully penetrates a horizontal, homogeneous and
isotropic confined aquifer of infinite horizontal extent. The aquifer is of 30 m
uniform thickness. A steady pumping at the rate of 40 litres/s from the well
for a long time results in a steady drawdown of 4 m at the well face. The
subsurface flow to the well due to pumping is steady, horizontal and Darcian
and the radius of influence of the well is 245 m. The hydraulic conductivity of
the aquifer (in m/day, round off to integer) is ____________

Q.51 A baghouse filter has to treat 12 m3/s of waste gas continuously. The baghouse
is to be divided into 5 sections of equal cloth area such that one section can be
shut down for cleaning and/or repairing, while the other 4 sections continue
to operate. An air-to-cloth ratio of 6.0 m3/min-m2 cloth will provide sufficient
treatment to the gas. The individual bags are of 32 cm in diameter and 5 m in
length. The total number of bags (in integer) required in the baghouse is
___________

CE, Set-1 Copyright © GATE 2021 Page 35 of 36

Q.52 A secondary clarifier handles a total flow of 9600 m3/d from the aeration tank
of a conventional activated-sludge treatment system. The concentration of
solids in the flow from the aeration tank is 3000 mg/L. The clarifier is
required to thicken the solids to 12000 mg/L, and hence it is to be designed for
kg
a solid flux of 3.2 2 . The surface area of the designed clarifier for
m .h
2
thickening (in m , in integer) is _____________

Q.53 Spot speeds of vehicles observed at a point on a highway are 40, 55, 60, 65 and
80 km/h. The space-mean speed (in km/h, round off to two decimal places) of
the observed vehicles is ____________

Q.54 The longitudinal section of a runway provides the following data:

End-to-end runway (m) Gradient (%)

0 to 300 + 1.2

300 to 600 – 0.7

600 to 1100 + 0.6

1100 to 1400 – 0.8

1400 to 1700 – 1.0

The effective gradient of the runway (in %, round off to two decimal places)
is ________________

Q.55 Traversing is carried out for a closed traverse PQRS. The internal angles at
vertices P, Q, R and S are measured as 92°, 68°, 123°, and 77°, respectively. If
fore bearing of line PQ is 27°, fore bearing of line RS (in degrees, in integer)
is ______________

END OF THE QUESTION PAPER

CE, Set-1 Copyright © GATE 2021 Page 36 of 36