The document provides instructions for a mock test paper on civil engineering. It consists of 65 multiple choice questions worth a total of 100 marks. Questions 1-25 and 56-60 carry 1 mark each, while questions 26-55 and 61-65 carry 2 marks each. Questions will cover both civil engineering topics and general aptitude. There are negative marks for incorrect answers. Calculators are allowed but no other aids. The purpose is to simulate exam conditions and help identify strengths and weaknesses to guide further preparation.

1. GATE MOCK TEST PAPER
CE : CIVIL ENGINEERING
Duration : Three Hours Maximum Marks : 100
Read the following instructions carefully.
1. All questions in this paper are of objective type.
2. There are a total of 65 questions carrying 100 marks.
3. Questions 1 through 25 are 1-mark questions, questions 26 through 55 are 2-mark questions.
4. Questions 48 and 51 (2 pairs) common data questions and question pairs (Q. 52 and Q.53) and (Q. 54 and
Q.55)are linked answer questions. The answer to the second question of the above pair depends on the
answer to the first question of the pair. If the first question in the linked pair is wrongly answered or is un-
attempted, then the answer to the second question in the pair will not be evaluated.
5. Questions 56 - 65 belong to general aptitude (GA). Questions 56 - 60 will carry 1-mark each, and questions
61-65 will carry 2-marks each. The GA questions will begin on a fresh page.
6. Un-attempted questions will carry zero marks.
7. Wrong answers will carry NEGATIVE marks. For Q.1 to Q.25 and Q.56 - Q.60, 1/3 mark will be deducted for
each wrong answer. For Q. 26 to Q. 51, and Q.61 - Q.65, 2/3 mark will be deducted for each wrong answer.
The question pairs (Q. 52, Q. 53) and (Q. 54, Q. 55) are questions with linked answers. There will be negative
marks only for wrong answer to the first question of the linked answer question pair i.e. for Q. 52 and Q.54,
2/3 mark will be deducted for each wrong answer. There is no negative marking for Q. 53 and Q.55.
8. Calculator (without data connectivity) is allowed.
9. Charts, graph sheets or tables are NOT allowed.
This set provides a Simulated Full-length Test for GATE. The purpose of this test is to provide you with
a fairly accurate evaluation of what your scores would be barring any special preparation.
Find a quiet place to work, in order to simulate examination conditions. Keep an accurate record of your
time.
Don't be worried, if you are not able to answer all questions in the allotted time. This may also occur on
the actual test. The paper is generally so broad based that it is difficult to expect that the examinee will
know answers to all questions.
No penalty is imposed for guessing. The score is determined by the number of correct answers. Therefore,
it is to your advantage to answer every question. Economy of time is of utmost concern. It is best to
work rapidly and carefully and not to waste time on questions that contain difficult or unfamiliar material.
Detailed explanatory answers are provided. After the rest is over, you may have self-evaluation of your
paper. Irrespective of whether you answer to a particular question is correct or wrong, you should go
through the explanatory answersprovided.
Based on your performance in this test, now you can identify strong and weak areas. Now you should be
in a position to approach your review program realistically and plan your time for study.

2. 2 GATE MOCK TEST PAPER (CIVIL ENGINEERING)
Q.1 – Q. 25 carry one mark each.
1. If z = x jy, where x and y are real, the value
of e jz
is
(a) 1 (b)
2 2
x y
e
(c) ey (d) e y
2. Given y = x2
+ 2x + 10, the value of
1x
dy
dx
is
equal to
(a) 0 (b) 4
(c) 12 (d) 13
3. Two independent random variables X and Y are
uniformly distributed in the interval [–1, 1].
The probability that max [X, Y] is less than 1/2
is
(a) 3/4 (b) 9/16
(c) 1/4 (d) 2/3
4. u(t) represents the unit step function. The Laplace
transform of u(t – ) is
(a)
1
s
(b)
1
s
(c)
s
e
s
(d) e–s
5. The contour integral
1/Z
C
e dz
with C as the counter-clockwise unit circle in the
z-plane is equal to
(a) 0 (b) 2
(c) 2 1 (d)
6. An elastic bar of length ‘l’, cross-sectional area A,
Young’s modulus of elasticity E and self-weight
W is hanging vertically. It is subjected to a load P
applied axially at the bottom end. The total
elongation of the bar is given by
(a)
W
AE
P
AE
l l
(b)
W
2AE
P
AE
l l
(c)
W
2AE
P
2AE
l l
(d)
W
AE
P
2AE
l l
7. The shear centre for the channel shown in the
given figure is located on axis of symmetry XX at a
distance equal to
b h t
4 I
2 2
to the
(a) right of CG (b) left of CG
(c) right of point B (d) left of point B
8. A bar 4 cm in diameter is subjected to an axial
load of 4t. The extension of the bar over a gauge
length of 20 cm is 0.03 cm. The decrease in
diameter is 0.0018 cm. The poisson’s ratio is
(a) 0.25 (b) 0.30
(c) 0.33 (d) 0.35
9. A steel cube of volume 8000 cc is subjected to an
all round stress of 1330 kg/cm2. The bulk modulus
of the material is 1.33 ×106 kg/cm2. The volumetric
change is
(a) 8 cc (b) 6 cc
(c) 0.8 cc (d) 10–3 cc
10. A beam has a triangular cross-section, having base
‘b’ and altitude ‘h’. If a section of the beam is
subjected to a shear force F, the shear stress at
the level of neutral axis in the cross-section is
given by
(a)
4
3
F
bh
(b)
3
4
F
bh
(c)
8
3
F
bh
(d)
3
8
F
bh
11. A long construction member of uniform section
is to be lifted using ropes at C and D (see figure).
This causes bending moments due to self-weight
as shown in figure given below. To minimise the
peak value of bending moment, the overhang ‘b’
shall be such, that
(a) M2 = 0 (b) M1 = M2
(c) M2 = 2 M1 (d) b =
l
4

3. GATE MOCK TEST PAPER (CIVIL ENGINEERING) 3
12. Given that for an element in a body of
homogeneous isotropic material subjected to
plane stress; x, y and z are normal strains in x,
y and z directions respectively and is the
poisson’s ratio, the magnitude of unit volume
change of the element is given by
(a) x + y + z (b) x – ( y + z)
(c) ( x + y + z) (d)
1 1 1
x y z
13. Which of the following condition will be satisfied
in the given portal frame ?
(a) Portal frame will sway towards left
(b) Portal frame will sway towards right
(c) There is no sway
(d) None of the above
14. Calculate ‘d’ with respect to D so that free end
deflection in both cases is same
(a) d = 1.682 D (b) d = 2 D
(c) d = 1.78 D (d) d = 1.5 D
15. Area of splice plates shall exceed the area of flange
element spliced by atleast
(a) 10%
(b) 20%
(c) 5%
(d) 2.5%
16. Centre to centre distance of adjacent rivet or bolt
holes measured in the direction of stress is known as
(a) Gauge (b) Pitch
(c) lap (d) edge distance
17. Calculate radius of curvature for a simply
supported beam having a moment of 100 kNm at
its end as shown in the figure EI = 10,000 kNm2
(a) 100 m (b) 400 m
(c) 10,000 m (d) 1000 m
18. I. In a two-hinged semi-circular arch, the
reaction locus is a straight line
II. The distance of reaction locus from abutment
is R/2
(a) Both I and II are true
(b) I is true but II is false
(c) I is false and II is true
(d) Both I and II are false
19. Which of the following statements is correct with
regard to the radius of curvature of an ideal
transition curve ?
(a) It is inversely proportional to the radius of
the main circular curve.
(b) It inversely proportional to its distance from
point of tangency.
(c) It is constant throughout the length of the
curve.
(d) It is directly proportional to the longitudinal
section of the curved portion of the road.
20. Which of the following parameters is NOT
necessary for the design of a sedimentation tank ?
(a) Volume of water to be treated per day
(b) Surface area of tank
(c) Depth of tank
(d) Detention period
21. A summit curve is formed at the intersection of a
3% up gradient and 5% down gradient. To provide
a stopping distance of 128 m, the length of summit
curve needed will be
(a) 271 m. (b) 298 m.
(c) 322 m. (d) 340 m.
22. According to Kozeny’s equation, the head loss in
the filter bed increases mainly due to decrease in
(a) viscosity of the fluid
(b) grain volume
(c) grain diameter
(d) density of third
23. The ratio of submerged unit weight of a soil to its
dry unit weight having specific gravity G = 2.5 is
(a) 0.4 (b) 0.33
(c) 0.6 (d) 0.25
24. For the load on inner and outer wheels to be equal
for a vehicle moving at a speed of 50 kmph
about a horizontal circular curve of radius 100 m
will be
(a)
25
127
(b)
25
225
(c)
25
125
(d)
25
227
25. A water treatment work treats 5000 cubic metres
of water per day. If it consumes 20 kg of chlorine
per day, then the chlorine dosage would be
(a) 0.25 mg/lt
(b) 4.0 mg/lt
(c) 0.40 mg/lt
(d) 10.0 mg/lt

4. 4 GATE MOCK TEST PAPER (CIVIL ENGINEERING)
Q. 26 – Q. 55 carry two marks each.
26. The box 1 contains chips numbered 3, 6, 9 ,12
and 15. The box 2 contains chips numbered 6, 11,
16, 21 and 26. Two chips, one from each box, are
drawn at random. The numbers written on these
chips are multiplied. The probability for the
product to be an even number is
(a) 6/25 (b) 2/5
(c) 3/5 (d) 19/25
27. The eigen values of a (2´2) matrix X are -2 and -3.
The eigen values of the matrix (X + I)-1
(X+5I) are
(a) – 3, – 4 (b) – 1, – 2
(c) –1, – 3 (d) – 2, – 4
28. The direction of vector A is radially outward from
t h e o r i g i n , w i t h A = krn
where r2
= x2
+ y2
+ z2
and k is a constant. The value of n for which
· A = 0 is
(a) – 2 (b) 2
(c) 1 (d) 0
29. Consider the function y = x2
– 6x + 9. The
maximum value of y obtained when x varies over
the interval 2 to 5 is
(a) 1
(b) 3
(c) 4
(d) 9
30. Consider the differential equation
dy
dx
+ y = ex
with y (0) = 1. The value of y(1) is
(a) e + e–1 (b)
1
2
(e – e–1)
(c)
1
2
(e + e–1) (d) 2(e – e–1)
31. The strain energy stored in member AB of the
pin-jointed truss shown in the figure, when E and
A are same for all members, is
(a)
2P L
AE
2
(b)
P L
AE
2
(c)
P L
2AE
2
(d) zero
32. The flexibility matrix of the beam shown in the
figure is
(a)
64
3
8
8 64
3
EI EI
EI EI
(b)
64
3
8
8 64
3
EI EI
EI EI
(c)
64
3
8
8 64
3
EI EI
EI EI
(d)
64
3
8
4 64
3
EI EI
EI EI
33. A frame ABCD is supported by a roller at A and is
on a hinge at C as shown in the figure.
The reaction at the roller end A is given by
(a) P (b) 2P
(c) P/2 (d) Zero
34. For the structure shown below, the vertical
deflection at point A is given by
3L
3L
3L
EI
EI
EI
P
A
L
(a)
PL
81EI
3
(b)
2
81
PL
EI
3
(c) Zero (d)
PL
EI
3
72
35. For a waste, the 5-day BOD at 20°C is found to be
200 mg/l. For the same waste, 5-day BOD at 30°C
will be
(a) less than 200 mg/l
(b) more than 200 mg/l
(c) 200 mg/l
(d) zero, as the bacteria cannot withstand such a
high temperature

5. GATE MOCK TEST PAPER (CIVIL ENGINEERING) 5
36. Along a straight stream line passing through the
origin the velocity is given by v = 2 2 2
x y , the
acceleration at a point (3, 4) will be
(a) 14 m/s2 (b) 10 m/s2
(c) 20 m/s2 (d) 0 m/s2
37. Given that plasticity Index (PI) of local soil = 15
and PI of sand = zero, for a desired PI of 6, the
percentage of sand in the mix should be
(a) 70 (b) 60
(c) 40 (d) 30
38. The figures given above show the state of a sample
of clay before and after consolidation. Based on
these figures, the settlement of a clay layer of initial
(a)
e
eo1
(b)
H e
ef1
Before
After
e
0
e
f
1
e
(c)
e
ef1
(d)
H e
e1 0
39. A soil sample tested in a triaxial compression
apparatus failed when the total maximum and
minimum principal stresses were 100 kPa and
40 kPa, respectively. The pore pressure measured
at failure was 10 kPa. The effective principal
stress ratio at failure is
(a) 2.5 (b) 3.0
(c) 2.75 (d) 2.0
40. A channel of bed slope 0.0009 carries a discharge
of 30 m3/s when the depth of flow is 1.0 m. What
is the discharge carried by an exactly similar
channel at the same depth of flow if the slope is
decreased to 0.0001 ?
(a) 10 m3/s (b) 15 m3/s
(c) 60 m3/s (d) 90 m3/s
41. In case of S2 water surface profile (y = depth of
flow, yo = normal depth and yc = critical depth)
(a) yo > yc > y (b) yc > yo > y
(c) yc > y > yo (d) y > yc > yo
42. When a particular discharge is flowing in a
horizontal pipe a mercurywater U-tube
manometer connected to the entrance and throat
of a venturimeter fitted in the pipe recorded a
deflection of 25 cm. If the same discharge flowed
through the same pipe kept at an angle of 45°to
the horizontal then the corresponding deflection
recorded by the U-tube manometer will be
(a) 25 2 cm (b) 25/ 2 cm
(c) 25/2 cm (d) 25 cm
43. A vane shear test on a soil sample gives a moment
of total resistance M. The shear stress at failure
‘S’ being more or less uniform at top, bottom and
surface of cylinder of soil is given by (where
H = height of vane, D = diameter of vane)
(a) s
2 M
D H2
(b) s
2 M
D H D2
(c) s
2 M
D H D/2
3 (d) s
2 M
DH
44. A pipe network consists of a pipe of 60 cm diameter
and branches out at a point F into two branches,
one of 30 cm diameter and the other of 45 cm
diameter. These branch pipes rejoin at a point B.
the velocity in the first branch (of 45 cm diameter)
is 1.5 m/sec. Which one of the following
statements is true ?
(a) The velocity in the second branch is 1.0 m/sec
(b) The velocity in the second branch is 2.25 m/sec
(c) The velocity in the second branch is
2
( 0.667)
3
m/sec
(d) The potential drop between F and B in both
branches is the same
45. The axial load carrying capacity of an R.C. column
of gross area of concrete Ac, area of steel As and
permissible stresses c in concrete and st in steel,
m-modular ratio is given as P =
(a) c c c smA A1 (b) c c c smA A
(c) c c s sA A (d) c c s s s(A A ) A
46. A prestressed concrete beam has a cross-section
with the following properties : are A = 46, 400 mm2,
I = 75.8 ×107 mm4, ybottom = 244 mm, ytop = 156 mm
It is subjected to a pre-stressing force at an
eccentricity ‘e’ so as to have a zero stress at the
top fibre. The value of ‘e’ is given by
(a) 66.66 mm (b) 66.75 mm
(c) 104.72 mm (d) 133.33 mm
47. Two steel plates each of 12 mm thickness are
connected by a double cover but joint by rivets
shown in the given figure. If the rivet diameter
is 22 mm with rivet force value of 53150 N
and permissible stress in tension of plate is
142 N/mm2, which one of the following section is
the most critical section?
(a) Section 1-1
(b) Section 2-2
(c) Section 3-3
(d) Both (a) and (b)

6. 6 GATE MOCK TEST PAPER (CIVIL ENGINEERING)
Common Data Questions
Common Data for Q. (48 – 49)
Ion concentration obtained for a groundwater sample (having pH = 8.1) are given below
Ion Ca2+
Mg2+
Na+
HCO3
–
SO4
2–
CI–
Ion concentration 100 6 15 250 45 39
(mg/L)
Atomic Weight Ca = 40 Mg = 24 Na = 23 H = 1, C = 12 S = 12 CI = 35.5
O = 16 O = 16
48. Total hardness (mg/L as CaCO3
) present in the
above water sample is
(a) 205 (b) 250
(c) 275 (d) 308
49. Carbonate hrdness (mg/L as CaCO3
) present in
the above water sample is
(a) 205 (b) 250
(c) 275 (d) 289
Common Data Questions (50 - 51) :
The ordinates of a 2-h unit hydrograph at 1 hour
intervals starting from time t = 0, are 0, 3, 8, 6, 3, 2
and 0 m3/s. Use trapzoidal rule for numerical
integration, if required.
50. What is the catchment area represented by the
unit hydrograph?
(a) 1.00 km2 (b) 2.00 km2
(c) 7.92 km2 (d) 8.64 km2
51. A storm of 6.6 cm occurs uniformly over the
catchment in 3 hours. If -index is equal to
2 mm/h and base flow is 5 m3/s, what is the peak
flow due to the storm?
(a) 41.0 m3/s (b) 43.4 m3/s
(c) 53.0 m3/s (d) 56.2 m3/s
Linked Answer Questions (52 - 53) :
A rigid beam is hinged at one end and supported on
linear elastic spring (both having a stiffness of ‘k’) at
points‘1’and ‘2’,and an inclined loadactsat‘2’,asshown
52. Which of the following options represents the
deflections 1 and 2 at point ‘1’ and ‘2’?
(a) 1 =
2
5
2P
k
and 2 =
4
5
2P
k
(b) 1 =
2
5
P
k
and 2 =
4
5
P
k
(c) 1 =
2
5
P
2k
and 2 =
4
5
P
2k
(d) 1 =
2
5
2P
k
and 2 =
4
5
2P
k
53. If the load P equals 100 kN, which of the following
options represents forces R1 and R2 in the springs
at points ‘1’ and ‘2’?
(a) R1 = 20 kN and R2 = 40 kN
(b) R1 = 50 kN and R2 = 50 kN
(c) R1 = 30 kN and R2 = 60 kN
(d) R1 = 40 kN and R2 = 80 kN
Linked Answer Question
Statement for Linked Answer Q. (54 – 55)
A doubly reinforced rectangular concrete beam has a
width of 300 mm and an effective depth of 500 mm.
The beam is reinforced with 2200 mm2
of steel in
tension and 628 mm2
of steel in compression. The
effective cover for compression steel is 50 mm.
Assume that both tension and compression steel yield.
The grades of concrete and steel used are M20 and
Fe250, respectively. The stress block parameters
(rounded off to first two decimal places) for concrete
shall be as per IS 456 : 2000.
54. The depth of neutral axis is
(a) 205.30 mm (b) 184.56 mm
(c) 160.91 mm (d) 145.30 mm
55. The moment of resistance of the section is
(a) 206.00 kN-m (b) 209.20 kN-m
(c) 236.80 kN-m (d) 251.90 kN-m
Section-II (General Aptitude)
56. Choose the words for each blank that best suit
for the meaning of the given sentence;
“While the disease in in ______ state it is almost
impossible to determine its existence by _____”.
(a) a critical ... examination
(b) an acute ... analysis
(c) a latent ... observation
(d) a suspended ... estimation

7. GATE MOCK TEST PAPER (CIVIL ENGINEERING) 7
57. SEXTENT : NAUTICAL : : ?
(a) octet : musical
(b) therapy : physical
(c) comet:astronomical
(d) forceps : surgical
58. Choose the lettered word that is most nearly
similar or opposite in meaning to the word in
capital letters.
‘SPASMODIC’
(a) Intermittent
(b) Inaccurate
(c) Violent
(d) Physical
59. Trace out the part (a, b, c, d) which has an error/
or No error.
The teacher advised the students
( )a
to work regularly and hardly
( )b
if they wanted to pass the examination
( )c
No error
( )d
60. The radii of three concentric circles are in the
ratio 1 : 2 : 3. The ratio of the area between the
two inner circles to that between the two outer
circles is
(a) 5 : 3
(b) 4 : 5
(c) 5 : 4
(d) 3 : 5
61. Two partners A and B invested Rs. 1, 250 and
Rs. 850 respectively in a business. Both the
partners distribute 60% of the profit equally and
distribute the rest 40% as the interest on their
capitals. If one partner received Rs. 30 more than
the other, the total profit is?
(a) Rs. 157.50
(b) Rs. 393.75
(c) Rs. 236.25
(d) Rs. 283.50
62. In the figure below, the seven identical circles
are tangent to each other. If the radius of the
circle is r, the area of the shaded region (in terms
of ‘r’) is equals
(a) 2 2
6 3 2r r
(b) 2 2
3 3 2r r
A B
C
DE
F
G
r
(c) 2 2
3 3 3r r
(d) 2 2
6 3 3r r
63. A train after travelling 60 km meets with an
accident and then proceeds at 3/4 of its former
rate and arrives at the terminus 40 minutes late.
Head the accident happends 25 km further on,
it would have arrived 10 minutes sooner. the
distance covered by the train and its speed given
by
(a) 150 km, 45 km/hr (b) 160 km, 50 km/hr
(c) 180 km, 60 km/hr (d) 200 km, 70 km/hr
64. Let ‘T’ be the set of integers {3, 11 19, 27,...,451,
459, 467} and ‘S’ be a subset of T such that the
sum of no two elements of S is 470. The maximum
possible number of elements S is ?
(a) 28 (b) 29
(c) 30 (d) 1
65. One of the legacies of the Roman legions was
discipline. In the legions, military law prevailed
and discipline was brutal. Discipline on the
battlefield kept units obedient, intact and fighting,
even when the odds and conditions were against
them.
Which one of the following statements best sums
up the meaning of the above passage?
(a) Thorough regimentation was the main reason
for the efficiency of the Roman legions even
in adverse circumstances.
(b) The legions were treated inhumanly as if the
men were animals.
(c) Discipline was the armies’ inheritance from
their seniors.
(d) The harsh discipline to which the legions were
subjected to led to the odds and conditions
being against them.

8. 8 GATE MOCK TEST PAPER (CIVIL ENGINEERING)
ANSWERS
1. (b) 2. (b) 3. (b) 4. (c) 5. (a) 6. (b) 7. (d) 8. (b) 9. (a) 10. (c)
11. (b) 12. (a) 13. (a) 14. (a) 15. (c) 16. (b) 17. (a) 18. (c) 19. (b) 20. (c)
21. (b) 22. (c) 23. (c) 24. (a) 25. (b) 26. (d) 27. (c) 28. (a) 29. (b) 30. (c)
31. (d) 32. (c) 33. (d) 34. (c) 35. (b) 36. (c) 37. (d) 38. (d) 39. (b) 40. (a)
41. (c) 42. (d) 43. (c) 44. (d) 45. (d) 46. (c) 47. (a) 48. (c) 49. (a) 50. (c)
51. (c) 52. (b) 53. (d) 54. (c) 55. (b) 56. (c) 57. (d) 58. (a) 59. (b) 60. (d)
61. (b) 62. (d) 63. (b) 64. (c) 65. (a)
1. z= x + iy
p = ejz
Taking log, loge
p = loge
ejz
loge
p = jz . loge
e = x y2 2
p = e
x y2 2
2. Given, y = x2
+ 2x + 10
dy
dx
= 2x + 2
dy
dx x 1
= 4
3. Uniform distribution X, Y on [1, 1];
f (x) = f (y) =
1
2
1
P max( , )
2
x y =
1 1
P X , 1 Y
2 2
.
1 1
P 1 X ,Y
2 2
=
1/2 1/2
–1 1
1 1
2 2
dx dy
=
3 3
4 4
=
9
16
4. f(t) = u(t – )
L{f(t)} = L{u(t – )}
F(s) =
s
e
s
EXPLANATIONS
27. Here, X =
–2
–3
0
0 , I =
1 0
0 1
A = (X + I)–1
( X + 5I)
A =
–1
–2
–1
0
0
3 0
0 2
=
–2
–1
0
0
3 0
0 2
2
=
–3
–1
0
0
Now I – A = 0
3 0
0 1 = 0
( + 3) ( + 1) = 0
= –1, –3
28. We know, .A = 2
1
rr
(r2
Ar)
=
H2)
2
1
(k r
r
rr
= 2
k
r
(n + 2)rn+1
= k(n + 2)rn+1
For .A = 0,
(n + 2) = 0
n = – 2
29. Given, y = x2
– 6x + 9
dy
dx
= 2x – 6 = 0
x = 3
or
dy
dx
2
2 = 2

9. GATE MOCK TEST PAPER (CIVIL ENGINEERING) 9
30. Given :
dy
y
dx
= ex
e–at
=
1
( )s a
s y(s) – y(0) + y(s) =
1
( 1)s
(s + 1) y(s) =
1
1
( 1) ( 1)
s
s s
y(s) =
1 1 1
( 1)( 1) 2 ( 1) ( 1)
s
s s s s
y(x) =
1
2
[e–x
+ ex
]
y(1) =
1
2
[e–1
+ e]
48. Total hardness
= ++ 3
++
Combined weight of CaCO
ca in mg/
Combined weight of Ca
l
+ 3
++
Combined weight of CaCO
mg in mg/
Combined weight of Mg
l
=
100(40 12 48)
100
22 6
40 24
2 2
= 250 + 25
= 275 mg/l
49. Alkalinity = HCO3
–
as CaCO3
= 3
50
HCO
61
=
50
250 205 mg /
61
l
Since Total hardness > Alkalinity
Carbonate hardess (as CaCO3
) = alkalinity
= 205 mg/l
50.
0 1 2 3 5 64
2
3
6
8
3
Time (hr)
Discharge
(m /sec)
3
Area of DRH (Direct Run-off Hydrograph)
= 1 60 60 [
1
2
3 +
1
2
(3 + 8) +
1
2
(8 + 6)
+
1
2
(6 + 3) +
1
2
(3 + 2) +
1
2
2]
= 79200 m3
As 1 cm depth of rainfall excess is considered,
area of the unit hydrograph is equal to a volume
given by 1 cm over the catchment.
1 10–2 A = 79200
A = 7.92 km2
Unit Hydrograph :
A unit hydrograph is defined as the hydrograph
of direct run-off resulting from one unit depth (1
cm) of rainfall excess occuring unifromly over the
basin and at a uniform rate for a specified duration
( hrs).
Alternative Answer
50. Run-off depth of UH = 1cm = 0.01m
8
6
3
2
3
0 1 2 3 4 5 6 7
1 UH
Discharge
(m /sec)
3
Time (hr)
Using trapezoidal rule for numerical
integration calculate the volume of 2-h UH.
Volume of run off hydrograph = (1 60 60)
0 3 3 8 8 6 6 3 3 2 2 0
2 2 2 2 2 2
= 1 60 60 [1.5 + 5.5 + 7.0 + 4.5 + 2.5
+ 1.0]
Run-off volume = 79,200 m3
Catchment Area =
Run-off volume
Run-off depth
=
79,200
0.01
m2
= 7.92 106
m2
=
6
6
7.92 10
10
km2
= 7.92 km2
So Ans. is (c)

10. 10 GATE MOCK TEST PAPER (CIVIL ENGINEERING)
51. index is the average rainfall volume which is
equal the run-off volum
Effective rainfall = 6.6 – 0.2 3 = 6cm.
Time Ordinate
Of Unit
Hydrog-
raph
RH
due to
6 cm
ER
Col 2
6
Base
flow
(m3
/sec)
Ordinates of
Flood
hydrograph
(m3
/sec.)
1 2 3 4 5
0 0 0 5 5
1 3 18 5 23
2 8 48 5 53
3 6 36 5 41
4 3 18 5 23
5 2 12 5 17
6 0 0 5 5
Peak flow due to sterm = 53 m3/sec,
54. Given : b = 300 mm, d = 500 mm,
Ast
= 2200 mm2
,
Asc
= 628 mm2
,
d = 50 mm, M 20, Fe 250
Depth of neutral axis in doubly reinforced beam,
xu
=
A ( 0.447 )A
0.362
st st sc ck sc
ck
f f f
f b
Here, fst
= fsc
= 0.87 250 = 217.5
xu
=
217.5 2200 (217.5 0.447 20)628
0.362 20 300
= 160 mm
55. Moment of resistance (under reinforced section),
Mu
= 0.362 fck
b xu
(d – 0.416 xu
)
+ (fsc
– 0.447 fck
) Asc
(d – d )
= 0.362 20 300 160.91 (500 – 0.416 160.91)
+ (217.5 – 0.447 20) 628 (500 – 50)
= 210.29 kN-m
57. By definition, a ‘SEXTANT’is a piece of equipment
that is nautical. Similarly, a forceps is a piece of
equipment that is surgical.
58. ‘SPASMODIC’ means happening at irregular
intervals or irregular bursts.
59. Write ‘hard’ in place of “hardly”.
60. Lt the radii of three concentric circles be R, 2R
and 3R.
=
Area between the two inner circles
Area between two outer circles
=
2 2
2 2
[ (2R) R ]
[ (3R) – (2R) ]
=
2
2
[4 1] R
[9 – 4] R
= 3 : 5
61. Since 60% of the profit is distributed equally so,
one partner receives Rs. 30 more than the other
only due to distribution of rest 40% of the basis of
their invested capitals.
A 40% profit
B 40% profit
s
s
=
1250
850
=
25
17
By using componendo and dividendo method,
A 40% profit + B 40% profit
A 40% profit – B 40% profit
s s
s s
=
25 17
25 17
Total 40% of profit
30
=
42
8
Total profit =
42 100
30
8 40
= Rs. 393.75
62. Since all circles (having radius = r) are identical.
Area of that part of all circles whose centres (A,
B, C, D, E and F) are the vertex of the Hexagon.
=
21
6
3
r
= 2 r2
also, area of circle whose centre ‘G’ = r2
There are six equilateral triangle formed in
the single hexagon having length of side,
AB = BC = ............ = EF = BG = ........... = 2r.
A B
F C
E D
G
2r

11. GATE MOCK TEST PAPER (CIVIL ENGINEERING) 11
Area of Hexagon
= 23
(2 ) 6
4
r
= 2
6 3 r
Area of shaded region
= 2 2 2
6 3 (2 )r r r
= 2 2
6 3 3r r
63.
60 km 25 km
A B
C D
Accident places
Let usual speed of train = V km/hr it takes time
to cover AB = t
Case I: When accident happen at C, then
convered distance by train after happening = CB.
Speed =
3
V
4
time (t1
) =
4
3
t
delay time = 40 minutes
Case I: When accident happens at D, then covered
distance by train after happening = DB.
delay time = (40 – 10)
= 30 minutes
Speed of train =
25km
(30/60)hr
= 50 km/hr
Now, 1/3 of usual time to cover CB
= 40 min
Usual time to cover CB
= 2 hr
CB = 50 km/hr 2 hr
= 100 km
Total distances = AB
= AC + CB
= 160 km
64. Total no. of terms in T = 59 ...(n) say
[tn
= a + (n – 1) d 467 = 3 + (n – 1)8]
Since, S is the subset of T we have following pairs
of terms whose addition is equals to 470.
467; 459451 443 ............. 227 , 235 3 11 19
27 ............. 243
Total 29 terms
S = {maximum possible no. of elements such that
sum of no two elements is 470}
(29 + 1) = 30
n n