Download GATE 2015 CE Civil Engineering CE01 Question Paper

Download Graduate Aptitude Test in Engineering (GATE) 2015 CE Civil Engineering CE01 Question Paper

GATE 2015 SET-2 CIVIL - CE
CE 1/8
Q. 1 ? Q. 25 carry one mark each.
Q.1 While minimizing the function f(x), necessary and sufficient conditions for a point, x
0
to be a
minima are:
(A) 0 ) ( " and 0 ) ( '
0 0
? ? x f x f (B) 0 ) ( " and 0 ) ( '
0 0
? ? x f x f
(C) 0 ) ( " and 0 ) ( '
0 0
? ? x f x f (D) 0 ) ( " and 0 ) ( '
0 0
? ? x f x f

Q.2 In Newton-Raphson iterative method, the initial guess value (x
ini
) is considered as zero while
finding the roots of the equation:
3 2
5 . 0 4 6 2 ) ( x x x x f ? ? ? ? ? . The correction, ?x, to be added to
x
ini
in the first iteration is ________________.


Q.3
Given, 1 ? ? i , the value of the definite integral, I =
?
?
?
2
0
sin cos
sin cos
?
dx
x i x
x i x
is:
(A) 1 (B) ?1 (C) i (D) ?i


Q.4
x
x
x
2
1
1 lim ?
?
?
?
?
?
?
? ?
is equal to
(A)
2 ?
e
(B) e
(C) 1 (D)
2
e

Q.5
Let n j i a
ij
? ? ? , 1 , ] [ A with 3 ? n and j i a
ij
. ? . The rank of A is:
(A) 0 (B) 1 (C) n ?1 (D) n

Q.6 A horizontal beam ABC is loaded as shown in the figure below. The distance of the point of
contraflexure from end A (in m) is ____________________.








Q.7 For the plane stress situation shown in the figure, the maximum shear stress and the plane on which
it acts are:








(A) ?50 MPa, on a plane 45
0
clockwise w.r.t. x-axis
(B) ?50 MPa, on a plane 45
0
anti-clockwise w.r.t. x-axis
(C) 50 MPa, at all orientations
(D) Zero, at all orientations

?
x
= 50 MPa
?
y
= 50 MPa
?
y
= 50 MPa
?
x
= 50 MPa
x
y
A
B
10 kN
1 m
0.75 m
C
FirstRanker.com - FirstRanker's Choice
GATE 2015 SET-2 CIVIL - CE
CE 1/8
Q. 1 ? Q. 25 carry one mark each.
Q.1 While minimizing the function f(x), necessary and sufficient conditions for a point, x
0
to be a
minima are:
(A) 0 ) ( " and 0 ) ( '
0 0
? ? x f x f (B) 0 ) ( " and 0 ) ( '
0 0
? ? x f x f
(C) 0 ) ( " and 0 ) ( '
0 0
? ? x f x f (D) 0 ) ( " and 0 ) ( '
0 0
? ? x f x f

Q.2 In Newton-Raphson iterative method, the initial guess value (x
ini
) is considered as zero while
finding the roots of the equation:
3 2
5 . 0 4 6 2 ) ( x x x x f ? ? ? ? ? . The correction, ?x, to be added to
x
ini
in the first iteration is ________________.


Q.3
Given, 1 ? ? i , the value of the definite integral, I =
?
?
?
2
0
sin cos
sin cos
?
dx
x i x
x i x
is:
(A) 1 (B) ?1 (C) i (D) ?i


Q.4
x
x
x
2
1
1 lim ?
?
?
?
?
?
?
? ?
is equal to
(A)
2 ?
e
(B) e
(C) 1 (D)
2
e

Q.5
Let n j i a
ij
? ? ? , 1 , ] [ A with 3 ? n and j i a
ij
. ? . The rank of A is:
(A) 0 (B) 1 (C) n ?1 (D) n

Q.6 A horizontal beam ABC is loaded as shown in the figure below. The distance of the point of
contraflexure from end A (in m) is ____________________.








Q.7 For the plane stress situation shown in the figure, the maximum shear stress and the plane on which
it acts are:








(A) ?50 MPa, on a plane 45
0
clockwise w.r.t. x-axis
(B) ?50 MPa, on a plane 45
0
anti-clockwise w.r.t. x-axis
(C) 50 MPa, at all orientations
(D) Zero, at all orientations

?
x
= 50 MPa
?
y
= 50 MPa
?
y
= 50 MPa
?
x
= 50 MPa
x
y
A
B
10 kN
1 m
0.75 m
C
GATE 2015 SET-2 CIVIL - CE
CE 2/8
Q.8 A guided support as shown in the figure below is represented by three springs (horizontal, vertical
and rotational) with stiffness k
x
, k
y
and k
?
respectively. The limiting values of k
x
, k
y
and k
?
are:




(A) ?, 0, ? (B) ?, ?, ? (C) 0, ?, ? (D) ?, ?, 0

Q.9 A column of size 450 mm ? 600 mm has unsupported length of 3.0 m and is braced against side
sway in both directions. According to IS 456: 2000, the minimum eccentricities (in mm) with
respect to major and minor principal axes are:
(A) 20.0 and 20.0 (B) 26.0 and 21.0 (C) 26.0 and 20.0 (D) 21.0 and 15.0

Q.10 Prying forces are:
(A) shearing forces on the bolts because of the joints
(B) tensile forces due to the flexibility of connected parts
(C) bending forces on the bolts because of the joints
(D) forces due the friction between connected parts

Q.11 A steel member ?M? has reversal of stress due to live loads, whereas another member ?N? has
reversal of stress due to wind load. As per IS 800: 2007, the maximum slenderness ratio permitted
is:
(A) less for member ?M? than that of member ?N?
(B) more for member ?M? than for member ?N?
(C) same for both the members
(D) not specified in the Code

Q.12 If the water content of a fully saturated soil mass is 100%, the void ratio of the sample is:
(A) less than specific gravity of soil
(B) equal to specific gravity of soil
(C) greater than specific gravity of soil
(D) independent of specific gravity of soil

Q.13 In friction circle method of slope stability analysis, if r defines the radius of the slip circle, the
radius of friction circle is:
(A) r sin ? (B) r (C) r cos ? (D) r tan ?

Q.14 Net ultimate bearing capacity of a footing embedded in a clay stratum
(A) increases with depth of footing only
(B) increases with size of footing only
(C) increases with depth and size of footing
(D) is independent of depth and size of footing

Q.15 Surcharge loading required to be placed on the horizontal backfill of a smooth retaining vertical
wall so as to completely eliminate tensile crack is:
(A) 2 c (B) 2 c k
a

(C)
a
k c 2 (D)
a
k c 2

Q.16 The relationship between the length scale ratio (
) and the velocity scale ratio ( ) in hydraulic
models, in which Froude dynamic similarity is maintained, is:
(A) =
(B) =
(C) = .
(D) =

FirstRanker.com - FirstRanker's Choice
GATE 2015 SET-2 CIVIL - CE
CE 1/8
Q. 1 ? Q. 25 carry one mark each.
Q.1 While minimizing the function f(x), necessary and sufficient conditions for a point, x
0
to be a
minima are:
(A) 0 ) ( " and 0 ) ( '
0 0
? ? x f x f (B) 0 ) ( " and 0 ) ( '
0 0
? ? x f x f
(C) 0 ) ( " and 0 ) ( '
0 0
? ? x f x f (D) 0 ) ( " and 0 ) ( '
0 0
? ? x f x f

Q.2 In Newton-Raphson iterative method, the initial guess value (x
ini
) is considered as zero while
finding the roots of the equation:
3 2
5 . 0 4 6 2 ) ( x x x x f ? ? ? ? ? . The correction, ?x, to be added to
x
ini
in the first iteration is ________________.


Q.3
Given, 1 ? ? i , the value of the definite integral, I =
?
?
?
2
0
sin cos
sin cos
?
dx
x i x
x i x
is:
(A) 1 (B) ?1 (C) i (D) ?i


Q.4
x
x
x
2
1
1 lim ?
?
?
?
?
?
?
? ?
is equal to
(A)
2 ?
e
(B) e
(C) 1 (D)
2
e

Q.5
Let n j i a
ij
? ? ? , 1 , ] [ A with 3 ? n and j i a
ij
. ? . The rank of A is:
(A) 0 (B) 1 (C) n ?1 (D) n

Q.6 A horizontal beam ABC is loaded as shown in the figure below. The distance of the point of
contraflexure from end A (in m) is ____________________.








Q.7 For the plane stress situation shown in the figure, the maximum shear stress and the plane on which
it acts are:








(A) ?50 MPa, on a plane 45
0
clockwise w.r.t. x-axis
(B) ?50 MPa, on a plane 45
0
anti-clockwise w.r.t. x-axis
(C) 50 MPa, at all orientations
(D) Zero, at all orientations

?
x
= 50 MPa
?
y
= 50 MPa
?
y
= 50 MPa
?
x
= 50 MPa
x
y
A
B
10 kN
1 m
0.75 m
C
GATE 2015 SET-2 CIVIL - CE
CE 2/8
Q.8 A guided support as shown in the figure below is represented by three springs (horizontal, vertical
and rotational) with stiffness k
x
, k
y
and k
?
respectively. The limiting values of k
x
, k
y
and k
?
are:




(A) ?, 0, ? (B) ?, ?, ? (C) 0, ?, ? (D) ?, ?, 0

Q.9 A column of size 450 mm ? 600 mm has unsupported length of 3.0 m and is braced against side
sway in both directions. According to IS 456: 2000, the minimum eccentricities (in mm) with
respect to major and minor principal axes are:
(A) 20.0 and 20.0 (B) 26.0 and 21.0 (C) 26.0 and 20.0 (D) 21.0 and 15.0

Q.10 Prying forces are:
(A) shearing forces on the bolts because of the joints
(B) tensile forces due to the flexibility of connected parts
(C) bending forces on the bolts because of the joints
(D) forces due the friction between connected parts

Q.11 A steel member ?M? has reversal of stress due to live loads, whereas another member ?N? has
reversal of stress due to wind load. As per IS 800: 2007, the maximum slenderness ratio permitted
is:
(A) less for member ?M? than that of member ?N?
(B) more for member ?M? than for member ?N?
(C) same for both the members
(D) not specified in the Code

Q.12 If the water content of a fully saturated soil mass is 100%, the void ratio of the sample is:
(A) less than specific gravity of soil
(B) equal to specific gravity of soil
(C) greater than specific gravity of soil
(D) independent of specific gravity of soil

Q.13 In friction circle method of slope stability analysis, if r defines the radius of the slip circle, the
radius of friction circle is:
(A) r sin ? (B) r (C) r cos ? (D) r tan ?

Q.14 Net ultimate bearing capacity of a footing embedded in a clay stratum
(A) increases with depth of footing only
(B) increases with size of footing only
(C) increases with depth and size of footing
(D) is independent of depth and size of footing

Q.15 Surcharge loading required to be placed on the horizontal backfill of a smooth retaining vertical
wall so as to completely eliminate tensile crack is:
(A) 2 c (B) 2 c k
a

(C)
a
k c 2 (D)
a
k c 2

Q.16 The relationship between the length scale ratio (
) and the velocity scale ratio ( ) in hydraulic
models, in which Froude dynamic similarity is maintained, is:
(A) =
(B) =
(C) = .
(D) =

GATE 2015 SET-2 CIVIL - CE
CE 3/8
Q.17 A nozzle is so shaped that the average flow velocity changes linearly from 1.5 m/s at the beginning
to 15 m/s at its end in a distance of 0.375 m. The magnitude of the convective acceleration (in
m/s
2
) at the end of the nozzle is ___________.

Q.18 A hydraulic jump takes place in a frictionless rectangular channel. The pre-jump depth is . The
alternate and sequent depths corresponding to are and respectively. The correct
relationship among , and is:
(A) < < (B) < <
(C) < = (D) = =

Q.19 The relationship between porosity ( ?), specific yield (S
y
) and specific retention (S
r
) of an
unconfined aquifer is:
(A) S
y
+ S
r
= ? (B) S
y
+ ? = S
r

(C) S
r
+ ? = S
y
(D) S
y
+ S
r
+ ? = 1

Q.20 A groundwater sample was found to contain 500 mg/L total dissolved solids (TDS). TDS (in %)
present in the sample is ____________.

Q.21 SO
2
and CO adversely affect
(A) oxygen carrying capacity of blood and functioning of lungs respectively
(B) functioning of the respiratory system and brain respectively
(C) functioning of the respiratory system and oxygen carrying capacity of blood respectively
(D) functioning of air passages and chest respectively

Q.22 A superspeedway in New Delhi has among the highest super-elevation rates of any track on the
Indian Grand Prix circuit. The track requires drivers to negotiate turns with a radius of 335 m and
33 ? banking. Given this information, the coefficient of side friction required in order to allow a
vehicle to travel at 320 km/h along the curve is:
(A) 1.761 (B) 0.176 (C) 0.253 (D) 2.530

Q.23 The following statements are made related to the lengths of turning lanes at signalised intersections:
(i) 1.5 times the average number of vehicles (by vehicle type) that would store in turning lane per
cycle during the peak hour
(ii) 2 times the average number of vehicles (by vehicle type) that would store in turning lane per
cycle during the peak hour
(iii) Average number of vehicles (by vehicle type) that would store in the adjacent through lane per
cycle during the peak hour
(iv) Average number of vehicles (by vehicle type) that would store in all lanes per cycle during the
peak hour
As per the IRC recommendations, the correct choice for design length of storage lanes is:
(A) Maximum of (ii and iii) (B) Maximum of (i and iii)
(C) Average of (i and iii) (D) Only (iv)

Q.24 In a leveling work, sum of the Back Sight (B.S.) and Fore Sight (F.S.) have been found to be 3.085
m and 5.645 m respectively. If the Reduced Level (R.L.) of the starting station is 100.000 m, the
R.L. (in m) of the last station is ___________.

Q.25 The combined correction due to curvature and refraction (in m) for a distance of 1 km on the
surface of Earth is:
(A) 0.0673 (B) 0.673 (C) 7.63 (D) 0.763
FirstRanker.com - FirstRanker's Choice
GATE 2015 SET-2 CIVIL - CE
CE 1/8
Q. 1 ? Q. 25 carry one mark each.
Q.1 While minimizing the function f(x), necessary and sufficient conditions for a point, x
0
to be a
minima are:
(A) 0 ) ( " and 0 ) ( '
0 0
? ? x f x f (B) 0 ) ( " and 0 ) ( '
0 0
? ? x f x f
(C) 0 ) ( " and 0 ) ( '
0 0
? ? x f x f (D) 0 ) ( " and 0 ) ( '
0 0
? ? x f x f

Q.2 In Newton-Raphson iterative method, the initial guess value (x
ini
) is considered as zero while
finding the roots of the equation:
3 2
5 . 0 4 6 2 ) ( x x x x f ? ? ? ? ? . The correction, ?x, to be added to
x
ini
in the first iteration is ________________.


Q.3
Given, 1 ? ? i , the value of the definite integral, I =
?
?
?
2
0
sin cos
sin cos
?
dx
x i x
x i x
is:
(A) 1 (B) ?1 (C) i (D) ?i


Q.4
x
x
x
2
1
1 lim ?
?
?
?
?
?
?
? ?
is equal to
(A)
2 ?
e
(B) e
(C) 1 (D)
2
e

Q.5
Let n j i a
ij
? ? ? , 1 , ] [ A with 3 ? n and j i a
ij
. ? . The rank of A is:
(A) 0 (B) 1 (C) n ?1 (D) n

Q.6 A horizontal beam ABC is loaded as shown in the figure below. The distance of the point of
contraflexure from end A (in m) is ____________________.








Q.7 For the plane stress situation shown in the figure, the maximum shear stress and the plane on which
it acts are:








(A) ?50 MPa, on a plane 45
0
clockwise w.r.t. x-axis
(B) ?50 MPa, on a plane 45
0
anti-clockwise w.r.t. x-axis
(C) 50 MPa, at all orientations
(D) Zero, at all orientations

?
x
= 50 MPa
?
y
= 50 MPa
?
y
= 50 MPa
?
x
= 50 MPa
x
y
A
B
10 kN
1 m
0.75 m
C
GATE 2015 SET-2 CIVIL - CE
CE 2/8
Q.8 A guided support as shown in the figure below is represented by three springs (horizontal, vertical
and rotational) with stiffness k
x
, k
y
and k
?
respectively. The limiting values of k
x
, k
y
and k
?
are:




(A) ?, 0, ? (B) ?, ?, ? (C) 0, ?, ? (D) ?, ?, 0

Q.9 A column of size 450 mm ? 600 mm has unsupported length of 3.0 m and is braced against side
sway in both directions. According to IS 456: 2000, the minimum eccentricities (in mm) with
respect to major and minor principal axes are:
(A) 20.0 and 20.0 (B) 26.0 and 21.0 (C) 26.0 and 20.0 (D) 21.0 and 15.0

Q.10 Prying forces are:
(A) shearing forces on the bolts because of the joints
(B) tensile forces due to the flexibility of connected parts
(C) bending forces on the bolts because of the joints
(D) forces due the friction between connected parts

Q.11 A steel member ?M? has reversal of stress due to live loads, whereas another member ?N? has
reversal of stress due to wind load. As per IS 800: 2007, the maximum slenderness ratio permitted
is:
(A) less for member ?M? than that of member ?N?
(B) more for member ?M? than for member ?N?
(C) same for both the members
(D) not specified in the Code

Q.12 If the water content of a fully saturated soil mass is 100%, the void ratio of the sample is:
(A) less than specific gravity of soil
(B) equal to specific gravity of soil
(C) greater than specific gravity of soil
(D) independent of specific gravity of soil

Q.13 In friction circle method of slope stability analysis, if r defines the radius of the slip circle, the
radius of friction circle is:
(A) r sin ? (B) r (C) r cos ? (D) r tan ?

Q.14 Net ultimate bearing capacity of a footing embedded in a clay stratum
(A) increases with depth of footing only
(B) increases with size of footing only
(C) increases with depth and size of footing
(D) is independent of depth and size of footing

Q.15 Surcharge loading required to be placed on the horizontal backfill of a smooth retaining vertical
wall so as to completely eliminate tensile crack is:
(A) 2 c (B) 2 c k
a

(C)
a
k c 2 (D)
a
k c 2

Q.16 The relationship between the length scale ratio (
) and the velocity scale ratio ( ) in hydraulic
models, in which Froude dynamic similarity is maintained, is:
(A) =
(B) =
(C) = .
(D) =

GATE 2015 SET-2 CIVIL - CE
CE 3/8
Q.17 A nozzle is so shaped that the average flow velocity changes linearly from 1.5 m/s at the beginning
to 15 m/s at its end in a distance of 0.375 m. The magnitude of the convective acceleration (in
m/s
2
) at the end of the nozzle is ___________.

Q.18 A hydraulic jump takes place in a frictionless rectangular channel. The pre-jump depth is . The
alternate and sequent depths corresponding to are and respectively. The correct
relationship among , and is:
(A) < < (B) < <
(C) < = (D) = =

Q.19 The relationship between porosity ( ?), specific yield (S
y
) and specific retention (S
r
) of an
unconfined aquifer is:
(A) S
y
+ S
r
= ? (B) S
y
+ ? = S
r

(C) S
r
+ ? = S
y
(D) S
y
+ S
r
+ ? = 1

Q.20 A groundwater sample was found to contain 500 mg/L total dissolved solids (TDS). TDS (in %)
present in the sample is ____________.

Q.21 SO
2
and CO adversely affect
(A) oxygen carrying capacity of blood and functioning of lungs respectively
(B) functioning of the respiratory system and brain respectively
(C) functioning of the respiratory system and oxygen carrying capacity of blood respectively
(D) functioning of air passages and chest respectively

Q.22 A superspeedway in New Delhi has among the highest super-elevation rates of any track on the
Indian Grand Prix circuit. The track requires drivers to negotiate turns with a radius of 335 m and
33 ? banking. Given this information, the coefficient of side friction required in order to allow a
vehicle to travel at 320 km/h along the curve is:
(A) 1.761 (B) 0.176 (C) 0.253 (D) 2.530

Q.23 The following statements are made related to the lengths of turning lanes at signalised intersections:
(i) 1.5 times the average number of vehicles (by vehicle type) that would store in turning lane per
cycle during the peak hour
(ii) 2 times the average number of vehicles (by vehicle type) that would store in turning lane per
cycle during the peak hour
(iii) Average number of vehicles (by vehicle type) that would store in the adjacent through lane per
cycle during the peak hour
(iv) Average number of vehicles (by vehicle type) that would store in all lanes per cycle during the
peak hour
As per the IRC recommendations, the correct choice for design length of storage lanes is:
(A) Maximum of (ii and iii) (B) Maximum of (i and iii)
(C) Average of (i and iii) (D) Only (iv)

Q.24 In a leveling work, sum of the Back Sight (B.S.) and Fore Sight (F.S.) have been found to be 3.085
m and 5.645 m respectively. If the Reduced Level (R.L.) of the starting station is 100.000 m, the
R.L. (in m) of the last station is ___________.

Q.25 The combined correction due to curvature and refraction (in m) for a distance of 1 km on the
surface of Earth is:
(A) 0.0673 (B) 0.673 (C) 7.63 (D) 0.763
GATE 2015 SET-2 CIVIL - CE
CE 4/8

Q. 26 ? Q. 55 carry two marks each.

Q.26 The probability density function of a random variable, x is
? ?
otherwise 0
2 0 for 4
4
) (
2
?
? ? ? ? x x
x
x f

The mean, ?
x
of the random variable is _______________.

Q.27 Consider the following second order linear differential equation
20 24 12
2
2
2
? ? ? ? x x
dx
y d

The boundary conditions are: at x = 0, y = 5 and at x = 2, y = 21
The value of y at x = 1 is ____________.

Q.28 The two Eigen values of the matrix 2 1
1 have a ratio of 3:1 for p = 2. What is another value of p
for which the Eigen values have the same ratio of 3:1?
(A) ?2 (B) 1 (C) 7/3 (D) 14/3


Q.29 For step-size, ?x =0.4, the value of following integral using Simpson?s 1/3 rule is _____________.
? ?
?
? ? ? ? ?
8 . 0
0
5 4 3 2
400 900 675 200 25 2 . 0 dx x x x x x

Q.30 In a system, two connected rigid bars AC and BC are of identical length, L with pin supports at A
and B. The bars are interconnected at C by a frictionless hinge. The rotation of the hinge is
restrained by a rotational spring of stiffness, k. The system initially assumes a straight line
configuration, ACB. Assuming both the bars as weightless, the rotation at supports, A and B, due to
a transverse load, P applied at C is:
(A)
k
PL
4
(B)
k
PL
2
(C)
k
P
4
(D)
L
Pk
4


Q.31 A simply supported reinforced concrete beam of length 10 m sags while undergoing shrinkage.
Assuming a uniform curvature of 0.004 m
?1
along the span, the maximum deflection (in m) of the
beam at mid-span is ______________.

FirstRanker.com - FirstRanker's Choice
GATE 2015 SET-2 CIVIL - CE
CE 1/8
Q. 1 ? Q. 25 carry one mark each.
Q.1 While minimizing the function f(x), necessary and sufficient conditions for a point, x
0
to be a
minima are:
(A) 0 ) ( " and 0 ) ( '
0 0
? ? x f x f (B) 0 ) ( " and 0 ) ( '
0 0
? ? x f x f
(C) 0 ) ( " and 0 ) ( '
0 0
? ? x f x f (D) 0 ) ( " and 0 ) ( '
0 0
? ? x f x f

Q.2 In Newton-Raphson iterative method, the initial guess value (x
ini
) is considered as zero while
finding the roots of the equation:
3 2
5 . 0 4 6 2 ) ( x x x x f ? ? ? ? ? . The correction, ?x, to be added to
x
ini
in the first iteration is ________________.


Q.3
Given, 1 ? ? i , the value of the definite integral, I =
?
?
?
2
0
sin cos
sin cos
?
dx
x i x
x i x
is:
(A) 1 (B) ?1 (C) i (D) ?i


Q.4
x
x
x
2
1
1 lim ?
?
?
?
?
?
?
? ?
is equal to
(A)
2 ?
e
(B) e
(C) 1 (D)
2
e

Q.5
Let n j i a
ij
? ? ? , 1 , ] [ A with 3 ? n and j i a
ij
. ? . The rank of A is:
(A) 0 (B) 1 (C) n ?1 (D) n

Q.6 A horizontal beam ABC is loaded as shown in the figure below. The distance of the point of
contraflexure from end A (in m) is ____________________.








Q.7 For the plane stress situation shown in the figure, the maximum shear stress and the plane on which
it acts are:








(A) ?50 MPa, on a plane 45
0
clockwise w.r.t. x-axis
(B) ?50 MPa, on a plane 45
0
anti-clockwise w.r.t. x-axis
(C) 50 MPa, at all orientations
(D) Zero, at all orientations

?
x
= 50 MPa
?
y
= 50 MPa
?
y
= 50 MPa
?
x
= 50 MPa
x
y
A
B
10 kN
1 m
0.75 m
C
GATE 2015 SET-2 CIVIL - CE
CE 2/8
Q.8 A guided support as shown in the figure below is represented by three springs (horizontal, vertical
and rotational) with stiffness k
x
, k
y
and k
?
respectively. The limiting values of k
x
, k
y
and k
?
are:




(A) ?, 0, ? (B) ?, ?, ? (C) 0, ?, ? (D) ?, ?, 0

Q.9 A column of size 450 mm ? 600 mm has unsupported length of 3.0 m and is braced against side
sway in both directions. According to IS 456: 2000, the minimum eccentricities (in mm) with
respect to major and minor principal axes are:
(A) 20.0 and 20.0 (B) 26.0 and 21.0 (C) 26.0 and 20.0 (D) 21.0 and 15.0

Q.10 Prying forces are:
(A) shearing forces on the bolts because of the joints
(B) tensile forces due to the flexibility of connected parts
(C) bending forces on the bolts because of the joints
(D) forces due the friction between connected parts

Q.11 A steel member ?M? has reversal of stress due to live loads, whereas another member ?N? has
reversal of stress due to wind load. As per IS 800: 2007, the maximum slenderness ratio permitted
is:
(A) less for member ?M? than that of member ?N?
(B) more for member ?M? than for member ?N?
(C) same for both the members
(D) not specified in the Code

Q.12 If the water content of a fully saturated soil mass is 100%, the void ratio of the sample is:
(A) less than specific gravity of soil
(B) equal to specific gravity of soil
(C) greater than specific gravity of soil
(D) independent of specific gravity of soil

Q.13 In friction circle method of slope stability analysis, if r defines the radius of the slip circle, the
radius of friction circle is:
(A) r sin ? (B) r (C) r cos ? (D) r tan ?

Q.14 Net ultimate bearing capacity of a footing embedded in a clay stratum
(A) increases with depth of footing only
(B) increases with size of footing only
(C) increases with depth and size of footing
(D) is independent of depth and size of footing

Q.15 Surcharge loading required to be placed on the horizontal backfill of a smooth retaining vertical
wall so as to completely eliminate tensile crack is:
(A) 2 c (B) 2 c k
a

(C)
a
k c 2 (D)
a
k c 2

Q.16 The relationship between the length scale ratio (
) and the velocity scale ratio ( ) in hydraulic
models, in which Froude dynamic similarity is maintained, is:
(A) =
(B) =
(C) = .
(D) =

GATE 2015 SET-2 CIVIL - CE
CE 3/8
Q.17 A nozzle is so shaped that the average flow velocity changes linearly from 1.5 m/s at the beginning
to 15 m/s at its end in a distance of 0.375 m. The magnitude of the convective acceleration (in
m/s
2
) at the end of the nozzle is ___________.

Q.18 A hydraulic jump takes place in a frictionless rectangular channel. The pre-jump depth is . The
alternate and sequent depths corresponding to are and respectively. The correct
relationship among , and is:
(A) < < (B) < <
(C) < = (D) = =

Q.19 The relationship between porosity ( ?), specific yield (S
y
) and specific retention (S
r
) of an
unconfined aquifer is:
(A) S
y
+ S
r
= ? (B) S
y
+ ? = S
r

(C) S
r
+ ? = S
y
(D) S
y
+ S
r
+ ? = 1

Q.20 A groundwater sample was found to contain 500 mg/L total dissolved solids (TDS). TDS (in %)
present in the sample is ____________.

Q.21 SO
2
and CO adversely affect
(A) oxygen carrying capacity of blood and functioning of lungs respectively
(B) functioning of the respiratory system and brain respectively
(C) functioning of the respiratory system and oxygen carrying capacity of blood respectively
(D) functioning of air passages and chest respectively

Q.22 A superspeedway in New Delhi has among the highest super-elevation rates of any track on the
Indian Grand Prix circuit. The track requires drivers to negotiate turns with a radius of 335 m and
33 ? banking. Given this information, the coefficient of side friction required in order to allow a
vehicle to travel at 320 km/h along the curve is:
(A) 1.761 (B) 0.176 (C) 0.253 (D) 2.530

Q.23 The following statements are made related to the lengths of turning lanes at signalised intersections:
(i) 1.5 times the average number of vehicles (by vehicle type) that would store in turning lane per
cycle during the peak hour
(ii) 2 times the average number of vehicles (by vehicle type) that would store in turning lane per
cycle during the peak hour
(iii) Average number of vehicles (by vehicle type) that would store in the adjacent through lane per
cycle during the peak hour
(iv) Average number of vehicles (by vehicle type) that would store in all lanes per cycle during the
peak hour
As per the IRC recommendations, the correct choice for design length of storage lanes is:
(A) Maximum of (ii and iii) (B) Maximum of (i and iii)
(C) Average of (i and iii) (D) Only (iv)

Q.24 In a leveling work, sum of the Back Sight (B.S.) and Fore Sight (F.S.) have been found to be 3.085
m and 5.645 m respectively. If the Reduced Level (R.L.) of the starting station is 100.000 m, the
R.L. (in m) of the last station is ___________.

Q.25 The combined correction due to curvature and refraction (in m) for a distance of 1 km on the
surface of Earth is:
(A) 0.0673 (B) 0.673 (C) 7.63 (D) 0.763
GATE 2015 SET-2 CIVIL - CE
CE 4/8

Q. 26 ? Q. 55 carry two marks each.

Q.26 The probability density function of a random variable, x is
? ?
otherwise 0
2 0 for 4
4
) (
2
?
? ? ? ? x x
x
x f

The mean, ?
x
of the random variable is _______________.

Q.27 Consider the following second order linear differential equation
20 24 12
2
2
2
? ? ? ? x x
dx
y d

The boundary conditions are: at x = 0, y = 5 and at x = 2, y = 21
The value of y at x = 1 is ____________.

Q.28 The two Eigen values of the matrix 2 1
1 have a ratio of 3:1 for p = 2. What is another value of p
for which the Eigen values have the same ratio of 3:1?
(A) ?2 (B) 1 (C) 7/3 (D) 14/3


Q.29 For step-size, ?x =0.4, the value of following integral using Simpson?s 1/3 rule is _____________.
? ?
?
? ? ? ? ?
8 . 0
0
5 4 3 2
400 900 675 200 25 2 . 0 dx x x x x x

Q.30 In a system, two connected rigid bars AC and BC are of identical length, L with pin supports at A
and B. The bars are interconnected at C by a frictionless hinge. The rotation of the hinge is
restrained by a rotational spring of stiffness, k. The system initially assumes a straight line
configuration, ACB. Assuming both the bars as weightless, the rotation at supports, A and B, due to
a transverse load, P applied at C is:
(A)
k
PL
4
(B)
k
PL
2
(C)
k
P
4
(D)
L
Pk
4


Q.31 A simply supported reinforced concrete beam of length 10 m sags while undergoing shrinkage.
Assuming a uniform curvature of 0.004 m
?1
along the span, the maximum deflection (in m) of the
beam at mid-span is ______________.

GATE 2015 SET-2 CIVIL - CE
Q.32 A steel strip of length, L = 200 mm is fixed at end A and rests at B on a vertical spring of stiffness,
k = 2 N/mm. The steel strip is 5 mm wide and 10 mm thick. A vertical load, P = 50 N is applied at
B, as shown in the figure. Considering E = 200 GPa, the force (in N) developed in the spring is
__________.










Q.33 A simply supported beam AB of span, L = 24 m is subjected to two wheel loads acting at a
distance, d = 5 m apart as shown in the figure below. Each wheel transmits a load, P = 3 kN and
may occupy any position along the beam. If the beam is an I-section having section modulus, S =
16.2 cm
3
, the maximum bending stress (in GPa) due to the wheel loads is
_______________________.









Q.34 According to the concept of Limit State Design as per IS 456: 2000, the probability of failure of a
structure is _____________.

Q.35 In a pre-stressed concrete beam section shown in the figure, the net loss is 10% and the final pre-
stressing force applied at X is 750 kN. The initial fiber stresses (in N/mm
2
) at the top and bottom of
the beam were:







(A) 4.166 and 20.833 (B) ?4.166 and ?20.833
(C) 4.166 and ?20.833 (D) ?4.166 and 20.833

Q.36 A fixed end beam is subjected to a load, W at 1/3rd span from the left support as shown in the
figure. The collapse load of the beam is:







(A) 16.5 M
P
/L (B) 15.5 M
P
/L (C) 15.0 M
P
/L (D) 16.0 M
P
/L
b
d
1
d
1
d
2
X
b = 250 mm
d
1
= 200 mm
d
2
= 100 mm
A
P
B
L
k
L
d
P P
A
B
L/3
X
W
Z
L/2
Y
2M
P
M
P

L/2
FirstRanker.com - FirstRanker's Choice
GATE 2015 SET-2 CIVIL - CE
CE 1/8
Q. 1 ? Q. 25 carry one mark each.
Q.1 While minimizing the function f(x), necessary and sufficient conditions for a point, x
0
to be a
minima are:
(A) 0 ) ( " and 0 ) ( '
0 0
? ? x f x f (B) 0 ) ( " and 0 ) ( '
0 0
? ? x f x f
(C) 0 ) ( " and 0 ) ( '
0 0
? ? x f x f (D) 0 ) ( " and 0 ) ( '
0 0
? ? x f x f

Q.2 In Newton-Raphson iterative method, the initial guess value (x
ini
) is considered as zero while
finding the roots of the equation:
3 2
5 . 0 4 6 2 ) ( x x x x f ? ? ? ? ? . The correction, ?x, to be added to
x
ini
in the first iteration is ________________.


Q.3
Given, 1 ? ? i , the value of the definite integral, I =
?
?
?
2
0
sin cos
sin cos
?
dx
x i x
x i x
is:
(A) 1 (B) ?1 (C) i (D) ?i


Q.4
x
x
x
2
1
1 lim ?
?
?
?
?
?
?
? ?
is equal to
(A)
2 ?
e
(B) e
(C) 1 (D)
2
e

Q.5
Let n j i a
ij
? ? ? , 1 , ] [ A with 3 ? n and j i a
ij
. ? . The rank of A is:
(A) 0 (B) 1 (C) n ?1 (D) n

Q.6 A horizontal beam ABC is loaded as shown in the figure below. The distance of the point of
contraflexure from end A (in m) is ____________________.








Q.7 For the plane stress situation shown in the figure, the maximum shear stress and the plane on which
it acts are:








(A) ?50 MPa, on a plane 45
0
clockwise w.r.t. x-axis
(B) ?50 MPa, on a plane 45
0
anti-clockwise w.r.t. x-axis
(C) 50 MPa, at all orientations
(D) Zero, at all orientations

?
x
= 50 MPa
?
y
= 50 MPa
?
y
= 50 MPa
?
x
= 50 MPa
x
y
A
B
10 kN
1 m
0.75 m
C
GATE 2015 SET-2 CIVIL - CE
CE 2/8
Q.8 A guided support as shown in the figure below is represented by three springs (horizontal, vertical
and rotational) with stiffness k
x
, k
y
and k
?
respectively. The limiting values of k
x
, k
y
and k
?
are:




(A) ?, 0, ? (B) ?, ?, ? (C) 0, ?, ? (D) ?, ?, 0

Q.9 A column of size 450 mm ? 600 mm has unsupported length of 3.0 m and is braced against side
sway in both directions. According to IS 456: 2000, the minimum eccentricities (in mm) with
respect to major and minor principal axes are:
(A) 20.0 and 20.0 (B) 26.0 and 21.0 (C) 26.0 and 20.0 (D) 21.0 and 15.0

Q.10 Prying forces are:
(A) shearing forces on the bolts because of the joints
(B) tensile forces due to the flexibility of connected parts
(C) bending forces on the bolts because of the joints
(D) forces due the friction between connected parts

Q.11 A steel member ?M? has reversal of stress due to live loads, whereas another member ?N? has
reversal of stress due to wind load. As per IS 800: 2007, the maximum slenderness ratio permitted
is:
(A) less for member ?M? than that of member ?N?
(B) more for member ?M? than for member ?N?
(C) same for both the members
(D) not specified in the Code

Q.12 If the water content of a fully saturated soil mass is 100%, the void ratio of the sample is:
(A) less than specific gravity of soil
(B) equal to specific gravity of soil
(C) greater than specific gravity of soil
(D) independent of specific gravity of soil

Q.13 In friction circle method of slope stability analysis, if r defines the radius of the slip circle, the
radius of friction circle is:
(A) r sin ? (B) r (C) r cos ? (D) r tan ?

Q.14 Net ultimate bearing capacity of a footing embedded in a clay stratum
(A) increases with depth of footing only
(B) increases with size of footing only
(C) increases with depth and size of footing
(D) is independent of depth and size of footing

Q.15 Surcharge loading required to be placed on the horizontal backfill of a smooth retaining vertical
wall so as to completely eliminate tensile crack is:
(A) 2 c (B) 2 c k
a

(C)
a
k c 2 (D)
a
k c 2

Q.16 The relationship between the length scale ratio (
) and the velocity scale ratio ( ) in hydraulic
models, in which Froude dynamic similarity is maintained, is:
(A) =
(B) =
(C) = .
(D) =

GATE 2015 SET-2 CIVIL - CE
CE 3/8
Q.17 A nozzle is so shaped that the average flow velocity changes linearly from 1.5 m/s at the beginning
to 15 m/s at its end in a distance of 0.375 m. The magnitude of the convective acceleration (in
m/s
2
) at the end of the nozzle is ___________.

Q.18 A hydraulic jump takes place in a frictionless rectangular channel. The pre-jump depth is . The
alternate and sequent depths corresponding to are and respectively. The correct
relationship among , and is:
(A) < < (B) < <
(C) < = (D) = =

Q.19 The relationship between porosity ( ?), specific yield (S
y
) and specific retention (S
r
) of an
unconfined aquifer is:
(A) S
y
+ S
r
= ? (B) S
y
+ ? = S
r

(C) S
r
+ ? = S
y
(D) S
y
+ S
r
+ ? = 1

Q.20 A groundwater sample was found to contain 500 mg/L total dissolved solids (TDS). TDS (in %)
present in the sample is ____________.

Q.21 SO
2
and CO adversely affect
(A) oxygen carrying capacity of blood and functioning of lungs respectively
(B) functioning of the respiratory system and brain respectively
(C) functioning of the respiratory system and oxygen carrying capacity of blood respectively
(D) functioning of air passages and chest respectively

Q.22 A superspeedway in New Delhi has among the highest super-elevation rates of any track on the
Indian Grand Prix circuit. The track requires drivers to negotiate turns with a radius of 335 m and
33 ? banking. Given this information, the coefficient of side friction required in order to allow a
vehicle to travel at 320 km/h along the curve is:
(A) 1.761 (B) 0.176 (C) 0.253 (D) 2.530

Q.23 The following statements are made related to the lengths of turning lanes at signalised intersections:
(i) 1.5 times the average number of vehicles (by vehicle type) that would store in turning lane per
cycle during the peak hour
(ii) 2 times the average number of vehicles (by vehicle type) that would store in turning lane per
cycle during the peak hour
(iii) Average number of vehicles (by vehicle type) that would store in the adjacent through lane per
cycle during the peak hour
(iv) Average number of vehicles (by vehicle type) that would store in all lanes per cycle during the
peak hour
As per the IRC recommendations, the correct choice for design length of storage lanes is:
(A) Maximum of (ii and iii) (B) Maximum of (i and iii)
(C) Average of (i and iii) (D) Only (iv)

Q.24 In a leveling work, sum of the Back Sight (B.S.) and Fore Sight (F.S.) have been found to be 3.085
m and 5.645 m respectively. If the Reduced Level (R.L.) of the starting station is 100.000 m, the
R.L. (in m) of the last station is ___________.

Q.25 The combined correction due to curvature and refraction (in m) for a distance of 1 km on the
surface of Earth is:
(A) 0.0673 (B) 0.673 (C) 7.63 (D) 0.763
GATE 2015 SET-2 CIVIL - CE
CE 4/8

Q. 26 ? Q. 55 carry two marks each.

Q.26 The probability density function of a random variable, x is
? ?
otherwise 0
2 0 for 4
4
) (
2
?
? ? ? ? x x
x
x f

The mean, ?
x
of the random variable is _______________.

Q.27 Consider the following second order linear differential equation
20 24 12
2
2
2
? ? ? ? x x
dx
y d

The boundary conditions are: at x = 0, y = 5 and at x = 2, y = 21
The value of y at x = 1 is ____________.

Q.28 The two Eigen values of the matrix 2 1
1 have a ratio of 3:1 for p = 2. What is another value of p
for which the Eigen values have the same ratio of 3:1?
(A) ?2 (B) 1 (C) 7/3 (D) 14/3


Q.29 For step-size, ?x =0.4, the value of following integral using Simpson?s 1/3 rule is _____________.
? ?
?
? ? ? ? ?
8 . 0
0
5 4 3 2
400 900 675 200 25 2 . 0 dx x x x x x

Q.30 In a system, two connected rigid bars AC and BC are of identical length, L with pin supports at A
and B. The bars are interconnected at C by a frictionless hinge. The rotation of the hinge is
restrained by a rotational spring of stiffness, k. The system initially assumes a straight line
configuration, ACB. Assuming both the bars as weightless, the rotation at supports, A and B, due to
a transverse load, P applied at C is:
(A)
k
PL
4
(B)
k
PL
2
(C)
k
P
4
(D)
L
Pk
4


Q.31 A simply supported reinforced concrete beam of length 10 m sags while undergoing shrinkage.
Assuming a uniform curvature of 0.004 m
?1
along the span, the maximum deflection (in m) of the
beam at mid-span is ______________.

GATE 2015 SET-2 CIVIL - CE
Q.32 A steel strip of length, L = 200 mm is fixed at end A and rests at B on a vertical spring of stiffness,
k = 2 N/mm. The steel strip is 5 mm wide and 10 mm thick. A vertical load, P = 50 N is applied at
B, as shown in the figure. Considering E = 200 GPa, the force (in N) developed in the spring is
__________.










Q.33 A simply supported beam AB of span, L = 24 m is subjected to two wheel loads acting at a
distance, d = 5 m apart as shown in the figure below. Each wheel transmits a load, P = 3 kN and
may occupy any position along the beam. If the beam is an I-section having section modulus, S =
16.2 cm
3
, the maximum bending stress (in GPa) due to the wheel loads is
_______________________.









Q.34 According to the concept of Limit State Design as per IS 456: 2000, the probability of failure of a
structure is _____________.

Q.35 In a pre-stressed concrete beam section shown in the figure, the net loss is 10% and the final pre-
stressing force applied at X is 750 kN. The initial fiber stresses (in N/mm
2
) at the top and bottom of
the beam were:







(A) 4.166 and 20.833 (B) ?4.166 and ?20.833
(C) 4.166 and ?20.833 (D) ?4.166 and 20.833

Q.36 A fixed end beam is subjected to a load, W at 1/3rd span from the left support as shown in the
figure. The collapse load of the beam is:







(A) 16.5 M
P
/L (B) 15.5 M
P
/L (C) 15.0 M
P
/L (D) 16.0 M
P
/L
b
d
1
d
1
d
2
X
b = 250 mm
d
1
= 200 mm
d
2
= 100 mm
A
P
B
L
k
L
d
P P
A
B
L/3
X
W
Z
L/2
Y
2M
P
M
P

L/2
GATE 2015 SET-2 CIVIL - CE
CE 6/8

Q.37 A 588 cm
3
volume of moist sand weighs 1010 gm. Its dry weight is 918 gm and specific gravity of
solids, G is 2.67. Assuming density of water as 1 gm/cm
3
, the void ratio is ___________.

Q.38 A 4 m thick layer of normally consolidated clay has an average void ratio of 1.30. Its compression
index is 0.6 and coefficient of consolidation is 1 m
2
/yr. If the increase in vertical pressure due to
foundation load on the clay layer is equal to the existing effective overburden pressure, the change
in the thickness of the clay layer is _______________ mm

Q.39 A pile of diameter 0.4 m is fully embedded in a clay stratum having 5 layers, each 5 m thick as
shown in the figure below. Assume a constant unit weight of soil as 18 kN/m
3
for all the layers.
Using ?-method ( ? = 0.15 for 25 m embedment length) and neglecting the end bearing component,
the ultimate pile capacity (in kN) is ________________.


Q.40
Stress path equation for tri-axial test upon application of deviatoric stress is, p q 5 . 0 3 10 ? ? .
The respective values of cohesion, c (in kPa) and angle of internal friction, ? are:
(A) 20 and 20 ? (B) 20 and 30 ?
(C) 30 and 30 ? (D) 30 and 20 ?

Q.41 A 6 m high retaining wall having a smooth vertical back face retains a layered horizontal backfill.
Top 3 m thick layer of the backfill is sand having an angle of internal friction, ? = 30 ? while the
bottom layer is 3 m thick clay with cohesion, c = 20 kPa. Assume unit weight for both sand and
clay as 18 kN/m
3
. The total active earth pressure per unit length of the wall (in kN/m) is:
(A) 150 (B) 216 (C) 156 (D) 196

Q.42 A field channel has cultivable commanded area of 2000 hectares. The intensities of irrigation for
gram and wheat are 30% and 50% respectively. Gram has a kor period of 18 days, kor depth of 12
cm, while wheat has a kor period of 18 days and a kor depth of 15 cm. The discharge (in m
3
/s)
required in the field channel to supply water to the commanded area during the kor period is
_______________.

Q.43 A triangular gate with a base width of 2 m and a height of 1.5 m lies in a vertical plane. The top
vertex of the gate is 1.5 m below the surface of a tank which contains oil of specific gravity 0.8.
Considering the density of water and acceleration due to gravity to be 1000 kg/m
3
and 9.81 m/s
2

respectively, the hydrostatic force (in kN) exerted by the oil on the gate is _________________.

FirstRanker.com - FirstRanker's Choice
GATE 2015 SET-2 CIVIL - CE
CE 1/8
Q. 1 ? Q. 25 carry one mark each.
Q.1 While minimizing the function f(x), necessary and sufficient conditions for a point, x
0
to be a
minima are:
(A) 0 ) ( " and 0 ) ( '
0 0
? ? x f x f (B) 0 ) ( " and 0 ) ( '
0 0
? ? x f x f
(C) 0 ) ( " and 0 ) ( '
0 0
? ? x f x f (D) 0 ) ( " and 0 ) ( '
0 0
? ? x f x f

Q.2 In Newton-Raphson iterative method, the initial guess value (x
ini
) is considered as zero while
finding the roots of the equation:
3 2
5 . 0 4 6 2 ) ( x x x x f ? ? ? ? ? . The correction, ?x, to be added to
x
ini
in the first iteration is ________________.


Q.3
Given, 1 ? ? i , the value of the definite integral, I =
?
?
?
2
0
sin cos
sin cos
?
dx
x i x
x i x
is:
(A) 1 (B) ?1 (C) i (D) ?i


Q.4
x
x
x
2
1
1 lim ?
?
?
?
?
?
?
? ?
is equal to
(A)
2 ?
e
(B) e
(C) 1 (D)
2
e

Q.5
Let n j i a
ij
? ? ? , 1 , ] [ A with 3 ? n and j i a
ij
. ? . The rank of A is:
(A) 0 (B) 1 (C) n ?1 (D) n

Q.6 A horizontal beam ABC is loaded as shown in the figure below. The distance of the point of
contraflexure from end A (in m) is ____________________.








Q.7 For the plane stress situation shown in the figure, the maximum shear stress and the plane on which
it acts are:








(A) ?50 MPa, on a plane 45
0
clockwise w.r.t. x-axis
(B) ?50 MPa, on a plane 45
0
anti-clockwise w.r.t. x-axis
(C) 50 MPa, at all orientations
(D) Zero, at all orientations

?
x
= 50 MPa
?
y
= 50 MPa
?
y
= 50 MPa
?
x
= 50 MPa
x
y
A
B
10 kN
1 m
0.75 m
C
GATE 2015 SET-2 CIVIL - CE
CE 2/8
Q.8 A guided support as shown in the figure below is represented by three springs (horizontal, vertical
and rotational) with stiffness k
x
, k
y
and k
?
respectively. The limiting values of k
x
, k
y
and k
?
are:




(A) ?, 0, ? (B) ?, ?, ? (C) 0, ?, ? (D) ?, ?, 0

Q.9 A column of size 450 mm ? 600 mm has unsupported length of 3.0 m and is braced against side
sway in both directions. According to IS 456: 2000, the minimum eccentricities (in mm) with
respect to major and minor principal axes are:
(A) 20.0 and 20.0 (B) 26.0 and 21.0 (C) 26.0 and 20.0 (D) 21.0 and 15.0

Q.10 Prying forces are:
(A) shearing forces on the bolts because of the joints
(B) tensile forces due to the flexibility of connected parts
(C) bending forces on the bolts because of the joints
(D) forces due the friction between connected parts

Q.11 A steel member ?M? has reversal of stress due to live loads, whereas another member ?N? has
reversal of stress due to wind load. As per IS 800: 2007, the maximum slenderness ratio permitted
is:
(A) less for member ?M? than that of member ?N?
(B) more for member ?M? than for member ?N?
(C) same for both the members
(D) not specified in the Code

Q.12 If the water content of a fully saturated soil mass is 100%, the void ratio of the sample is:
(A) less than specific gravity of soil
(B) equal to specific gravity of soil
(C) greater than specific gravity of soil
(D) independent of specific gravity of soil

Q.13 In friction circle method of slope stability analysis, if r defines the radius of the slip circle, the
radius of friction circle is:
(A) r sin ? (B) r (C) r cos ? (D) r tan ?

Q.14 Net ultimate bearing capacity of a footing embedded in a clay stratum
(A) increases with depth of footing only
(B) increases with size of footing only
(C) increases with depth and size of footing
(D) is independent of depth and size of footing

Q.15 Surcharge loading required to be placed on the horizontal backfill of a smooth retaining vertical
wall so as to completely eliminate tensile crack is:
(A) 2 c (B) 2 c k
a

(C)
a
k c 2 (D)
a
k c 2

Q.16 The relationship between the length scale ratio (
) and the velocity scale ratio ( ) in hydraulic
models, in which Froude dynamic similarity is maintained, is:
(A) =
(B) =
(C) = .
(D) =

GATE 2015 SET-2 CIVIL - CE
CE 3/8
Q.17 A nozzle is so shaped that the average flow velocity changes linearly from 1.5 m/s at the beginning
to 15 m/s at its end in a distance of 0.375 m. The magnitude of the convective acceleration (in
m/s
2
) at the end of the nozzle is ___________.

Q.18 A hydraulic jump takes place in a frictionless rectangular channel. The pre-jump depth is . The
alternate and sequent depths corresponding to are and respectively. The correct
relationship among , and is:
(A) < < (B) < <
(C) < = (D) = =

Q.19 The relationship between porosity ( ?), specific yield (S
y
) and specific retention (S
r
) of an
unconfined aquifer is:
(A) S
y
+ S
r
= ? (B) S
y
+ ? = S
r

(C) S
r
+ ? = S
y
(D) S
y
+ S
r
+ ? = 1

Q.20 A groundwater sample was found to contain 500 mg/L total dissolved solids (TDS). TDS (in %)
present in the sample is ____________.

Q.21 SO
2
and CO adversely affect
(A) oxygen carrying capacity of blood and functioning of lungs respectively
(B) functioning of the respiratory system and brain respectively
(C) functioning of the respiratory system and oxygen carrying capacity of blood respectively
(D) functioning of air passages and chest respectively

Q.22 A superspeedway in New Delhi has among the highest super-elevation rates of any track on the
Indian Grand Prix circuit. The track requires drivers to negotiate turns with a radius of 335 m and
33 ? banking. Given this information, the coefficient of side friction required in order to allow a
vehicle to travel at 320 km/h along the curve is:
(A) 1.761 (B) 0.176 (C) 0.253 (D) 2.530

Q.23 The following statements are made related to the lengths of turning lanes at signalised intersections:
(i) 1.5 times the average number of vehicles (by vehicle type) that would store in turning lane per
cycle during the peak hour
(ii) 2 times the average number of vehicles (by vehicle type) that would store in turning lane per
cycle during the peak hour
(iii) Average number of vehicles (by vehicle type) that would store in the adjacent through lane per
cycle during the peak hour
(iv) Average number of vehicles (by vehicle type) that would store in all lanes per cycle during the
peak hour
As per the IRC recommendations, the correct choice for design length of storage lanes is:
(A) Maximum of (ii and iii) (B) Maximum of (i and iii)
(C) Average of (i and iii) (D) Only (iv)

Q.24 In a leveling work, sum of the Back Sight (B.S.) and Fore Sight (F.S.) have been found to be 3.085
m and 5.645 m respectively. If the Reduced Level (R.L.) of the starting station is 100.000 m, the
R.L. (in m) of the last station is ___________.

Q.25 The combined correction due to curvature and refraction (in m) for a distance of 1 km on the
surface of Earth is:
(A) 0.0673 (B) 0.673 (C) 7.63 (D) 0.763
GATE 2015 SET-2 CIVIL - CE
CE 4/8

Q. 26 ? Q. 55 carry two marks each.

Q.26 The probability density function of a random variable, x is
? ?
otherwise 0
2 0 for 4
4
) (
2
?
? ? ? ? x x
x
x f

The mean, ?
x
of the random variable is _______________.

Q.27 Consider the following second order linear differential equation
20 24 12
2
2
2
? ? ? ? x x
dx
y d

The boundary conditions are: at x = 0, y = 5 and at x = 2, y = 21
The value of y at x = 1 is ____________.

Q.28 The two Eigen values of the matrix 2 1
1 have a ratio of 3:1 for p = 2. What is another value of p
for which the Eigen values have the same ratio of 3:1?
(A) ?2 (B) 1 (C) 7/3 (D) 14/3


Q.29 For step-size, ?x =0.4, the value of following integral using Simpson?s 1/3 rule is _____________.
? ?
?
? ? ? ? ?
8 . 0
0
5 4 3 2
400 900 675 200 25 2 . 0 dx x x x x x

Q.30 In a system, two connected rigid bars AC and BC are of identical length, L with pin supports at A
and B. The bars are interconnected at C by a frictionless hinge. The rotation of the hinge is
restrained by a rotational spring of stiffness, k. The system initially assumes a straight line
configuration, ACB. Assuming both the bars as weightless, the rotation at supports, A and B, due to
a transverse load, P applied at C is:
(A)
k
PL
4
(B)
k
PL
2
(C)
k
P
4
(D)
L
Pk
4


Q.31 A simply supported reinforced concrete beam of length 10 m sags while undergoing shrinkage.
Assuming a uniform curvature of 0.004 m
?1
along the span, the maximum deflection (in m) of the
beam at mid-span is ______________.

GATE 2015 SET-2 CIVIL - CE
Q.32 A steel strip of length, L = 200 mm is fixed at end A and rests at B on a vertical spring of stiffness,
k = 2 N/mm. The steel strip is 5 mm wide and 10 mm thick. A vertical load, P = 50 N is applied at
B, as shown in the figure. Considering E = 200 GPa, the force (in N) developed in the spring is
__________.










Q.33 A simply supported beam AB of span, L = 24 m is subjected to two wheel loads acting at a
distance, d = 5 m apart as shown in the figure below. Each wheel transmits a load, P = 3 kN and
may occupy any position along the beam. If the beam is an I-section having section modulus, S =
16.2 cm
3
, the maximum bending stress (in GPa) due to the wheel loads is
_______________________.









Q.34 According to the concept of Limit State Design as per IS 456: 2000, the probability of failure of a
structure is _____________.

Q.35 In a pre-stressed concrete beam section shown in the figure, the net loss is 10% and the final pre-
stressing force applied at X is 750 kN. The initial fiber stresses (in N/mm
2
) at the top and bottom of
the beam were:







(A) 4.166 and 20.833 (B) ?4.166 and ?20.833
(C) 4.166 and ?20.833 (D) ?4.166 and 20.833

Q.36 A fixed end beam is subjected to a load, W at 1/3rd span from the left support as shown in the
figure. The collapse load of the beam is:







(A) 16.5 M
P
/L (B) 15.5 M
P
/L (C) 15.0 M
P
/L (D) 16.0 M
P
/L
b
d
1
d
1
d
2
X
b = 250 mm
d
1
= 200 mm
d
2
= 100 mm
A
P
B
L
k
L
d
P P
A
B
L/3
X
W
Z
L/2
Y
2M
P
M
P

L/2
GATE 2015 SET-2 CIVIL - CE
CE 6/8

Q.37 A 588 cm
3
volume of moist sand weighs 1010 gm. Its dry weight is 918 gm and specific gravity of
solids, G is 2.67. Assuming density of water as 1 gm/cm
3
, the void ratio is ___________.

Q.38 A 4 m thick layer of normally consolidated clay has an average void ratio of 1.30. Its compression
index is 0.6 and coefficient of consolidation is 1 m
2
/yr. If the increase in vertical pressure due to
foundation load on the clay layer is equal to the existing effective overburden pressure, the change
in the thickness of the clay layer is _______________ mm

Q.39 A pile of diameter 0.4 m is fully embedded in a clay stratum having 5 layers, each 5 m thick as
shown in the figure below. Assume a constant unit weight of soil as 18 kN/m
3
for all the layers.
Using ?-method ( ? = 0.15 for 25 m embedment length) and neglecting the end bearing component,
the ultimate pile capacity (in kN) is ________________.


Q.40
Stress path equation for tri-axial test upon application of deviatoric stress is, p q 5 . 0 3 10 ? ? .
The respective values of cohesion, c (in kPa) and angle of internal friction, ? are:
(A) 20 and 20 ? (B) 20 and 30 ?
(C) 30 and 30 ? (D) 30 and 20 ?

Q.41 A 6 m high retaining wall having a smooth vertical back face retains a layered horizontal backfill.
Top 3 m thick layer of the backfill is sand having an angle of internal friction, ? = 30 ? while the
bottom layer is 3 m thick clay with cohesion, c = 20 kPa. Assume unit weight for both sand and
clay as 18 kN/m
3
. The total active earth pressure per unit length of the wall (in kN/m) is:
(A) 150 (B) 216 (C) 156 (D) 196

Q.42 A field channel has cultivable commanded area of 2000 hectares. The intensities of irrigation for
gram and wheat are 30% and 50% respectively. Gram has a kor period of 18 days, kor depth of 12
cm, while wheat has a kor period of 18 days and a kor depth of 15 cm. The discharge (in m
3
/s)
required in the field channel to supply water to the commanded area during the kor period is
_______________.

Q.43 A triangular gate with a base width of 2 m and a height of 1.5 m lies in a vertical plane. The top
vertex of the gate is 1.5 m below the surface of a tank which contains oil of specific gravity 0.8.
Considering the density of water and acceleration due to gravity to be 1000 kg/m
3
and 9.81 m/s
2

respectively, the hydrostatic force (in kN) exerted by the oil on the gate is _________________.

GATE 2015 SET-2 CIVIL - CE
CE 7/8
Q.44
The velocity components of a two dimensional plane motion of a fluid are: =
+ 2 ? and
= ? 2 ?
.
The correct statement is:
(A) Fluid is incompressible and flow is irrotational
(B) Fluid is incompressible and flow is rotational
(C) Fluid is compressible and flow is irrotational
(D) Fluid is compressible and flow is rotational

Q.45 The average surface area of a reservoir in the month of June is 20 km
2
. In the same month, the
average rate of inflow is 10 m
3
/s, outflow rate is 15 m
3
/s, monthly rainfall is 10 cm, monthly
seepage loss is 1.8 cm and the storage change is 16 million m
3
. The evaporation (in cm) in that
month is:
(A) 46.8 (B) 136.0 (C) 13.6 (D) 23.4

Q.46 A pipe of 0.7 m diameter has a length of 6 km and connects two reservoirs A and B. The water
level in reservoir A is at an elevation 30 m above the water level in reservoir B. Halfway along the
pipe line, there is a branch through which water can be supplied to a third reservoir C. The friction
factor of the pipe is 0.024. The quantity of water discharged into reservoir C is 0.15 m
3
/s.
Considering the acceleration due to gravity as 9.81 m/s
2
and neglecting minor losses, the discharge
(in m
3
/s) into the reservoir B is ______________.

Q.47 A landfill is to be designed to serve a population of 200000 for a period of 25 years. The solid
waste (SW) generation is 2 kg/person/day. The density of the un-compacted SW is 100 kg/m
3
and a
compaction ratio of 4 is suggested. The ratio of compacted fill (i.e., SW + cover) to compacted SW
is 1.5. The landfill volume (in million m
3
) required is ____________.

Q.48 A water treatment plant of capacity, 1 m
3
/s has filter boxes of dimensions 6 m ? 10 m. Loading rate
to the filters is 120 m
3
/day/m
2
. When two of the filters are out of service for back washing, the
loading rate (in m
3
/day/m
2
) is ______________.

Q.49 Ultimate BOD of a river water sample is 20 mg/L. BOD rate constant (natural log) is 0.15 day
?1
.
The respective values of BOD (in %) exerted and remaining after 7 days are:
(A) 45 and 55 (B) 55 and 45
(C) 65 and 35 (D) 75 and 25

Q.50 In a wastewater treatment plant, primary sedimentation tank (PST) designed at an overflow rate of
32.5 m
3
/day/m
2
is 32.5 m long , 8.0 m wide and liquid depth of 2.25 m. If the length of the weir is
75 m, the weir loading rate (in m
3
/day/m) is ______________.

Q.51 The relation between speed u (in km/h) and density k (number of vehicles / km) for a traffic stream
on a road is u = 70 ? 0.7k. The capacity on this road is _______________ vph (vehicles/hour).

FirstRanker.com - FirstRanker's Choice
GATE 2015 SET-2 CIVIL - CE
CE 1/8
Q. 1 ? Q. 25 carry one mark each.
Q.1 While minimizing the function f(x), necessary and sufficient conditions for a point, x
0
to be a
minima are:
(A) 0 ) ( " and 0 ) ( '
0 0
? ? x f x f (B) 0 ) ( " and 0 ) ( '
0 0
? ? x f x f
(C) 0 ) ( " and 0 ) ( '
0 0
? ? x f x f (D) 0 ) ( " and 0 ) ( '
0 0
? ? x f x f

Q.2 In Newton-Raphson iterative method, the initial guess value (x
ini
) is considered as zero while
finding the roots of the equation:
3 2
5 . 0 4 6 2 ) ( x x x x f ? ? ? ? ? . The correction, ?x, to be added to
x
ini
in the first iteration is ________________.


Q.3
Given, 1 ? ? i , the value of the definite integral, I =
?
?
?
2
0
sin cos
sin cos
?
dx
x i x
x i x
is:
(A) 1 (B) ?1 (C) i (D) ?i


Q.4
x
x
x
2
1
1 lim ?
?
?
?
?
?
?
? ?
is equal to
(A)
2 ?
e
(B) e
(C) 1 (D)
2
e

Q.5
Let n j i a
ij
? ? ? , 1 , ] [ A with 3 ? n and j i a
ij
. ? . The rank of A is:
(A) 0 (B) 1 (C) n ?1 (D) n

Q.6 A horizontal beam ABC is loaded as shown in the figure below. The distance of the point of
contraflexure from end A (in m) is ____________________.








Q.7 For the plane stress situation shown in the figure, the maximum shear stress and the plane on which
it acts are:








(A) ?50 MPa, on a plane 45
0
clockwise w.r.t. x-axis
(B) ?50 MPa, on a plane 45
0
anti-clockwise w.r.t. x-axis
(C) 50 MPa, at all orientations
(D) Zero, at all orientations

?
x
= 50 MPa
?
y
= 50 MPa
?
y
= 50 MPa
?
x
= 50 MPa
x
y
A
B
10 kN
1 m
0.75 m
C
GATE 2015 SET-2 CIVIL - CE
CE 2/8
Q.8 A guided support as shown in the figure below is represented by three springs (horizontal, vertical
and rotational) with stiffness k
x
, k
y
and k
?
respectively. The limiting values of k
x
, k
y
and k
?
are:




(A) ?, 0, ? (B) ?, ?, ? (C) 0, ?, ? (D) ?, ?, 0

Q.9 A column of size 450 mm ? 600 mm has unsupported length of 3.0 m and is braced against side
sway in both directions. According to IS 456: 2000, the minimum eccentricities (in mm) with
respect to major and minor principal axes are:
(A) 20.0 and 20.0 (B) 26.0 and 21.0 (C) 26.0 and 20.0 (D) 21.0 and 15.0

Q.10 Prying forces are:
(A) shearing forces on the bolts because of the joints
(B) tensile forces due to the flexibility of connected parts
(C) bending forces on the bolts because of the joints
(D) forces due the friction between connected parts

Q.11 A steel member ?M? has reversal of stress due to live loads, whereas another member ?N? has
reversal of stress due to wind load. As per IS 800: 2007, the maximum slenderness ratio permitted
is:
(A) less for member ?M? than that of member ?N?
(B) more for member ?M? than for member ?N?
(C) same for both the members
(D) not specified in the Code

Q.12 If the water content of a fully saturated soil mass is 100%, the void ratio of the sample is:
(A) less than specific gravity of soil
(B) equal to specific gravity of soil
(C) greater than specific gravity of soil
(D) independent of specific gravity of soil

Q.13 In friction circle method of slope stability analysis, if r defines the radius of the slip circle, the
radius of friction circle is:
(A) r sin ? (B) r (C) r cos ? (D) r tan ?

Q.14 Net ultimate bearing capacity of a footing embedded in a clay stratum
(A) increases with depth of footing only
(B) increases with size of footing only
(C) increases with depth and size of footing
(D) is independent of depth and size of footing

Q.15 Surcharge loading required to be placed on the horizontal backfill of a smooth retaining vertical
wall so as to completely eliminate tensile crack is:
(A) 2 c (B) 2 c k
a

(C)
a
k c 2 (D)
a
k c 2

Q.16 The relationship between the length scale ratio (
) and the velocity scale ratio ( ) in hydraulic
models, in which Froude dynamic similarity is maintained, is:
(A) =
(B) =
(C) = .
(D) =

GATE 2015 SET-2 CIVIL - CE
CE 3/8
Q.17 A nozzle is so shaped that the average flow velocity changes linearly from 1.5 m/s at the beginning
to 15 m/s at its end in a distance of 0.375 m. The magnitude of the convective acceleration (in
m/s
2
) at the end of the nozzle is ___________.

Q.18 A hydraulic jump takes place in a frictionless rectangular channel. The pre-jump depth is . The
alternate and sequent depths corresponding to are and respectively. The correct
relationship among , and is:
(A) < < (B) < <
(C) < = (D) = =

Q.19 The relationship between porosity ( ?), specific yield (S
y
) and specific retention (S
r
) of an
unconfined aquifer is:
(A) S
y
+ S
r
= ? (B) S
y
+ ? = S
r

(C) S
r
+ ? = S
y
(D) S
y
+ S
r
+ ? = 1

Q.20 A groundwater sample was found to contain 500 mg/L total dissolved solids (TDS). TDS (in %)
present in the sample is ____________.

Q.21 SO
2
and CO adversely affect
(A) oxygen carrying capacity of blood and functioning of lungs respectively
(B) functioning of the respiratory system and brain respectively
(C) functioning of the respiratory system and oxygen carrying capacity of blood respectively
(D) functioning of air passages and chest respectively

Q.22 A superspeedway in New Delhi has among the highest super-elevation rates of any track on the
Indian Grand Prix circuit. The track requires drivers to negotiate turns with a radius of 335 m and
33 ? banking. Given this information, the coefficient of side friction required in order to allow a
vehicle to travel at 320 km/h along the curve is:
(A) 1.761 (B) 0.176 (C) 0.253 (D) 2.530

Q.23 The following statements are made related to the lengths of turning lanes at signalised intersections:
(i) 1.5 times the average number of vehicles (by vehicle type) that would store in turning lane per
cycle during the peak hour
(ii) 2 times the average number of vehicles (by vehicle type) that would store in turning lane per
cycle during the peak hour
(iii) Average number of vehicles (by vehicle type) that would store in the adjacent through lane per
cycle during the peak hour
(iv) Average number of vehicles (by vehicle type) that would store in all lanes per cycle during the
peak hour
As per the IRC recommendations, the correct choice for design length of storage lanes is:
(A) Maximum of (ii and iii) (B) Maximum of (i and iii)
(C) Average of (i and iii) (D) Only (iv)

Q.24 In a leveling work, sum of the Back Sight (B.S.) and Fore Sight (F.S.) have been found to be 3.085
m and 5.645 m respectively. If the Reduced Level (R.L.) of the starting station is 100.000 m, the
R.L. (in m) of the last station is ___________.

Q.25 The combined correction due to curvature and refraction (in m) for a distance of 1 km on the
surface of Earth is:
(A) 0.0673 (B) 0.673 (C) 7.63 (D) 0.763
GATE 2015 SET-2 CIVIL - CE
CE 4/8

Q. 26 ? Q. 55 carry two marks each.

Q.26 The probability density function of a random variable, x is
? ?
otherwise 0
2 0 for 4
4
) (
2
?
? ? ? ? x x
x
x f

The mean, ?
x
of the random variable is _______________.

Q.27 Consider the following second order linear differential equation
20 24 12
2
2
2
? ? ? ? x x
dx
y d

The boundary conditions are: at x = 0, y = 5 and at x = 2, y = 21
The value of y at x = 1 is ____________.

Q.28 The two Eigen values of the matrix 2 1
1 have a ratio of 3:1 for p = 2. What is another value of p
for which the Eigen values have the same ratio of 3:1?
(A) ?2 (B) 1 (C) 7/3 (D) 14/3


Q.29 For step-size, ?x =0.4, the value of following integral using Simpson?s 1/3 rule is _____________.
? ?
?
? ? ? ? ?
8 . 0
0
5 4 3 2
400 900 675 200 25 2 . 0 dx x x x x x

Q.30 In a system, two connected rigid bars AC and BC are of identical length, L with pin supports at A
and B. The bars are interconnected at C by a frictionless hinge. The rotation of the hinge is
restrained by a rotational spring of stiffness, k. The system initially assumes a straight line
configuration, ACB. Assuming both the bars as weightless, the rotation at supports, A and B, due to
a transverse load, P applied at C is:
(A)
k
PL
4
(B)
k
PL
2
(C)
k
P
4
(D)
L
Pk
4


Q.31 A simply supported reinforced concrete beam of length 10 m sags while undergoing shrinkage.
Assuming a uniform curvature of 0.004 m
?1
along the span, the maximum deflection (in m) of the
beam at mid-span is ______________.

GATE 2015 SET-2 CIVIL - CE
Q.32 A steel strip of length, L = 200 mm is fixed at end A and rests at B on a vertical spring of stiffness,
k = 2 N/mm. The steel strip is 5 mm wide and 10 mm thick. A vertical load, P = 50 N is applied at
B, as shown in the figure. Considering E = 200 GPa, the force (in N) developed in the spring is
__________.










Q.33 A simply supported beam AB of span, L = 24 m is subjected to two wheel loads acting at a
distance, d = 5 m apart as shown in the figure below. Each wheel transmits a load, P = 3 kN and
may occupy any position along the beam. If the beam is an I-section having section modulus, S =
16.2 cm
3
, the maximum bending stress (in GPa) due to the wheel loads is
_______________________.









Q.34 According to the concept of Limit State Design as per IS 456: 2000, the probability of failure of a
structure is _____________.

Q.35 In a pre-stressed concrete beam section shown in the figure, the net loss is 10% and the final pre-
stressing force applied at X is 750 kN. The initial fiber stresses (in N/mm
2
) at the top and bottom of
the beam were:







(A) 4.166 and 20.833 (B) ?4.166 and ?20.833
(C) 4.166 and ?20.833 (D) ?4.166 and 20.833

Q.36 A fixed end beam is subjected to a load, W at 1/3rd span from the left support as shown in the
figure. The collapse load of the beam is:







(A) 16.5 M
P
/L (B) 15.5 M
P
/L (C) 15.0 M
P
/L (D) 16.0 M
P
/L
b
d
1
d
1
d
2
X
b = 250 mm
d
1
= 200 mm
d
2
= 100 mm
A
P
B
L
k
L
d
P P
A
B
L/3
X
W
Z
L/2
Y
2M
P
M
P

L/2
GATE 2015 SET-2 CIVIL - CE
CE 6/8

Q.37 A 588 cm
3
volume of moist sand weighs 1010 gm. Its dry weight is 918 gm and specific gravity of
solids, G is 2.67. Assuming density of water as 1 gm/cm
3
, the void ratio is ___________.

Q.38 A 4 m thick layer of normally consolidated clay has an average void ratio of 1.30. Its compression
index is 0.6 and coefficient of consolidation is 1 m
2
/yr. If the increase in vertical pressure due to
foundation load on the clay layer is equal to the existing effective overburden pressure, the change
in the thickness of the clay layer is _______________ mm

Q.39 A pile of diameter 0.4 m is fully embedded in a clay stratum having 5 layers, each 5 m thick as
shown in the figure below. Assume a constant unit weight of soil as 18 kN/m
3
for all the layers.
Using ?-method ( ? = 0.15 for 25 m embedment length) and neglecting the end bearing component,
the ultimate pile capacity (in kN) is ________________.


Q.40
Stress path equation for tri-axial test upon application of deviatoric stress is, p q 5 . 0 3 10 ? ? .
The respective values of cohesion, c (in kPa) and angle of internal friction, ? are:
(A) 20 and 20 ? (B) 20 and 30 ?
(C) 30 and 30 ? (D) 30 and 20 ?

Q.41 A 6 m high retaining wall having a smooth vertical back face retains a layered horizontal backfill.
Top 3 m thick layer of the backfill is sand having an angle of internal friction, ? = 30 ? while the
bottom layer is 3 m thick clay with cohesion, c = 20 kPa. Assume unit weight for both sand and
clay as 18 kN/m
3
. The total active earth pressure per unit length of the wall (in kN/m) is:
(A) 150 (B) 216 (C) 156 (D) 196

Q.42 A field channel has cultivable commanded area of 2000 hectares. The intensities of irrigation for
gram and wheat are 30% and 50% respectively. Gram has a kor period of 18 days, kor depth of 12
cm, while wheat has a kor period of 18 days and a kor depth of 15 cm. The discharge (in m
3
/s)
required in the field channel to supply water to the commanded area during the kor period is
_______________.

Q.43 A triangular gate with a base width of 2 m and a height of 1.5 m lies in a vertical plane. The top
vertex of the gate is 1.5 m below the surface of a tank which contains oil of specific gravity 0.8.
Considering the density of water and acceleration due to gravity to be 1000 kg/m
3
and 9.81 m/s
2

respectively, the hydrostatic force (in kN) exerted by the oil on the gate is _________________.

GATE 2015 SET-2 CIVIL - CE
CE 7/8
Q.44
The velocity components of a two dimensional plane motion of a fluid are: =
+ 2 ? and
= ? 2 ?
.
The correct statement is:
(A) Fluid is incompressible and flow is irrotational
(B) Fluid is incompressible and flow is rotational
(C) Fluid is compressible and flow is irrotational
(D) Fluid is compressible and flow is rotational

Q.45 The average surface area of a reservoir in the month of June is 20 km
2
. In the same month, the
average rate of inflow is 10 m
3
/s, outflow rate is 15 m
3
/s, monthly rainfall is 10 cm, monthly
seepage loss is 1.8 cm and the storage change is 16 million m
3
. The evaporation (in cm) in that
month is:
(A) 46.8 (B) 136.0 (C) 13.6 (D) 23.4

Q.46 A pipe of 0.7 m diameter has a length of 6 km and connects two reservoirs A and B. The water
level in reservoir A is at an elevation 30 m above the water level in reservoir B. Halfway along the
pipe line, there is a branch through which water can be supplied to a third reservoir C. The friction
factor of the pipe is 0.024. The quantity of water discharged into reservoir C is 0.15 m
3
/s.
Considering the acceleration due to gravity as 9.81 m/s
2
and neglecting minor losses, the discharge
(in m
3
/s) into the reservoir B is ______________.

Q.47 A landfill is to be designed to serve a population of 200000 for a period of 25 years. The solid
waste (SW) generation is 2 kg/person/day. The density of the un-compacted SW is 100 kg/m
3
and a
compaction ratio of 4 is suggested. The ratio of compacted fill (i.e., SW + cover) to compacted SW
is 1.5. The landfill volume (in million m
3
) required is ____________.

Q.48 A water treatment plant of capacity, 1 m
3
/s has filter boxes of dimensions 6 m ? 10 m. Loading rate
to the filters is 120 m
3
/day/m
2
. When two of the filters are out of service for back washing, the
loading rate (in m
3
/day/m
2
) is ______________.

Q.49 Ultimate BOD of a river water sample is 20 mg/L. BOD rate constant (natural log) is 0.15 day
?1
.
The respective values of BOD (in %) exerted and remaining after 7 days are:
(A) 45 and 55 (B) 55 and 45
(C) 65 and 35 (D) 75 and 25

Q.50 In a wastewater treatment plant, primary sedimentation tank (PST) designed at an overflow rate of
32.5 m
3
/day/m
2
is 32.5 m long , 8.0 m wide and liquid depth of 2.25 m. If the length of the weir is
75 m, the weir loading rate (in m
3
/day/m) is ______________.

Q.51 The relation between speed u (in km/h) and density k (number of vehicles / km) for a traffic stream
on a road is u = 70 ? 0.7k. The capacity on this road is _______________ vph (vehicles/hour).

GATE 2015 SET-2 CIVIL - CE
CE 8/8
Q.52 Match the information related to tests on aggregates given in Group-I with that in Group-II.
Group-I Group-II
P. Resistance to impact 1. Hardness
Q. Resistance to wear 2. Strength
R. Resistance to weathering action 3. Toughness
S. Resistance to crushing 4. Soundness
(A) P-1, Q-3, R-4, S-2 (B) P-3, Q-1, R-4, S-2
(C) P-4, Q-1, R-3, S-2 (D) P-3, Q-4, R-2, S-1

Q.53 In Marshall method of mix design, the coarse aggregate, fine aggregate, fines and bitumen having
respective values of specific gravity 2.60, 2.70, 2.65 and 1.01, are mixed in the relative proportions
(% by weight) of 55.0, 35.8, 3.7 and 5.5 respectively. The theoretical specific gravity of the mix
and the effective specific gravity of the aggregates in the mix respectively are:
(A) 2.42 and 2.63 (B) 2.42 and 2.78 (C) 2.42 and 2.93 (D) 2.64 and 2.78

Q.54 The bearings of two inaccessible stations, S
1
(Easting 500 m, Northing 500 m) and S
2
(Easting 600
m, Northing 450 m) from a station S
3
were observed as 225
0
and 153
0
26 ? respectively. The
independent Easting (in m) of station S
3
is:
(A) 450.000 (B) 570.710 (C) 550.000 (D) 650.000

Q.55 Two Pegs A and B were fixed on opposite banks of a 50 m wide river. The level was set up at A
and the staff readings on Pegs A and B were observed as 1.350 m and 1.550 m, respectively.
Thereafter the instrument was shifted and set up at B. The staff readings on Pegs B and A were
observed as 0.750 m and 0.550 m, respectively. If the R.L. of Peg A is 100.200 m, the R.L. (in m)
of Peg B is ___________________.


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