# Civil Engineering (CE) 2008 GATE Paper without solution Notes | Study GATE Past Year Papers for Practice (All Branches) - GATE

## GATE: Civil Engineering (CE) 2008 GATE Paper without solution Notes | Study GATE Past Year Papers for Practice (All Branches) - GATE

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``` Page 1

?CE?Civil Engineering: Gate 2008 Paper

1
GATE: 2008
CE: CIVIL ENGINEERING
Q.1 The product of matrices (PQ)
-
P is
(A) P
-1
(B) Q
-1
(C) P
-1
Q
-1
(D) PQP
-1
Q.2 The general solution of
2
2
0
d y
y
dx
+ = is
(A) y=P cos x + Q sin x (B) y=P cos x
(C) y = P six x  (D) y = P sin
2
x
Q.3 A mild steel specimen is under uni-axial tensile stress. Young’s modules and
yield stress for mild steel are 2 x 10
5
MPa respectively. The maximum amount of
strain energy per unit volume that can be stored in this specimen without
permanent set is
(A) 156 Nmm/mm
3
(B) 15.6 Nmm/mm
3
(C) 1.56 Nmm/mm
3
(D) 0.156 Nmm/mm
3
Q.4 A reinforced concrete structure has to be constructed along a sea coast. The
minimum grade of concrete to be used as per IS: 456-2000 is
(A) M 15 (B) M 20
(C) M 25 (D) M 30
Q.5 In the design of a reinforced concrete bean the requirement for bond is not getting
satisfied. The economical option to satisfy the requirement for bond is by
(A) bundling of bars
(B) providing smaller diameter bars more in number
(C) providing larger diameter bars less in number
(D) providing same diameter bars more in number
Q.6 The shape of the cross-section, which has a largest shape factor, is
(A) rectangular  (B) I-section
(C) diamond   (D) solid circular
Q.7 Group symbols assigned to silty sand and clayey sand are respectively
(A) SS and CS   (B) SM and CS
(C) SM and SC  (D) MS and CS
Q.8 When a retaining wall moves away from the back-fill, the pressure exerted on the
wall is termed as
(A) Passive earth pressure
(B) Swelling pressure
(C) Pore pressure
(D) Active earth pressure
Page 2

?CE?Civil Engineering: Gate 2008 Paper

1
GATE: 2008
CE: CIVIL ENGINEERING
Q.1 The product of matrices (PQ)
-
P is
(A) P
-1
(B) Q
-1
(C) P
-1
Q
-1
(D) PQP
-1
Q.2 The general solution of
2
2
0
d y
y
dx
+ = is
(A) y=P cos x + Q sin x (B) y=P cos x
(C) y = P six x  (D) y = P sin
2
x
Q.3 A mild steel specimen is under uni-axial tensile stress. Young’s modules and
yield stress for mild steel are 2 x 10
5
MPa respectively. The maximum amount of
strain energy per unit volume that can be stored in this specimen without
permanent set is
(A) 156 Nmm/mm
3
(B) 15.6 Nmm/mm
3
(C) 1.56 Nmm/mm
3
(D) 0.156 Nmm/mm
3
Q.4 A reinforced concrete structure has to be constructed along a sea coast. The
minimum grade of concrete to be used as per IS: 456-2000 is
(A) M 15 (B) M 20
(C) M 25 (D) M 30
Q.5 In the design of a reinforced concrete bean the requirement for bond is not getting
satisfied. The economical option to satisfy the requirement for bond is by
(A) bundling of bars
(B) providing smaller diameter bars more in number
(C) providing larger diameter bars less in number
(D) providing same diameter bars more in number
Q.6 The shape of the cross-section, which has a largest shape factor, is
(A) rectangular  (B) I-section
(C) diamond   (D) solid circular
Q.7 Group symbols assigned to silty sand and clayey sand are respectively
(A) SS and CS   (B) SM and CS
(C) SM and SC  (D) MS and CS
Q.8 When a retaining wall moves away from the back-fill, the pressure exerted on the
wall is termed as
(A) Passive earth pressure
(B) Swelling pressure
(C) Pore pressure
(D) Active earth pressure
?CE?Civil Engineering: Gate 2008 Paper

2
Q.9 Compaction by vibratory roller is the best method of compaction in case of
(A) moist silty sand
(B) well graded dry sand
(C) clay of medium compressibility
(D) silt of high compressibility
Q.10 A person standing on the bank of a canal drops a stone on the water surface. He
notices that the disturbance on the water in not traveling up-stream. This is
because the flow in the canal is
(A) sub-critical  (B) super-critical
(C) steady   (D) uniform
Q.11 A flood wave with a known inflow hydrograph is routed through a large reservoir.
The outflow hydrograph will have
(A) attenuated peak with reduced time-base
(B) attenuated peak with increased time-base
(C) increased peak with increased time-base
(D) increased peak with reduced time-base
Q.12 A stable channel is to be designed for a discharge of Q m
3
/s with silt factor f as
per Lacey’s method. The mean flow velocity (m/s) in the channel is obtained by
(A) (Q f
2
/ 140)
1/6
(B) (Qf / 140)
1/3
(C) (Q
2
f
2
/ 140)
1/6
(D) 0.48 (Q / f)
1/3
Q.13 The base width of an elementary profile of gravity dam of height H is b. The
specific gravity of the material of the dam is G and uplift pressure coefficient is
K. the correct relationship for no tension at the heel is given by
(A)
1
( )
b b
B G K
H H G K
= = -
-
(C)
1 1
( )
b b
D
H G K H K G K
= =
- -
Q.14 Two primary air pollutants are
(A) sulphur oxide and ozone (B) nitrogen oxide and peroxyacetylnitrate
(C) sulphur oxide and hydrocarbon (D) ozone and peroxyacetynitrate
Q.15 Two biodegradable components of municipal solid waste are
(A) plastics and wood  (B) cardboard and glass
(C) leather and tin cans (D) food wastes and garden trimmings
Q.16 The specific gravity of paving bitumen as per IS:73 – 1992 lies between
(A) 1.10 and 1.06   (B) 1.06 and 1.02
(C) 1.02 and 0.97   (D) 0.97 and 0.92
Page 3

?CE?Civil Engineering: Gate 2008 Paper

1
GATE: 2008
CE: CIVIL ENGINEERING
Q.1 The product of matrices (PQ)
-
P is
(A) P
-1
(B) Q
-1
(C) P
-1
Q
-1
(D) PQP
-1
Q.2 The general solution of
2
2
0
d y
y
dx
+ = is
(A) y=P cos x + Q sin x (B) y=P cos x
(C) y = P six x  (D) y = P sin
2
x
Q.3 A mild steel specimen is under uni-axial tensile stress. Young’s modules and
yield stress for mild steel are 2 x 10
5
MPa respectively. The maximum amount of
strain energy per unit volume that can be stored in this specimen without
permanent set is
(A) 156 Nmm/mm
3
(B) 15.6 Nmm/mm
3
(C) 1.56 Nmm/mm
3
(D) 0.156 Nmm/mm
3
Q.4 A reinforced concrete structure has to be constructed along a sea coast. The
minimum grade of concrete to be used as per IS: 456-2000 is
(A) M 15 (B) M 20
(C) M 25 (D) M 30
Q.5 In the design of a reinforced concrete bean the requirement for bond is not getting
satisfied. The economical option to satisfy the requirement for bond is by
(A) bundling of bars
(B) providing smaller diameter bars more in number
(C) providing larger diameter bars less in number
(D) providing same diameter bars more in number
Q.6 The shape of the cross-section, which has a largest shape factor, is
(A) rectangular  (B) I-section
(C) diamond   (D) solid circular
Q.7 Group symbols assigned to silty sand and clayey sand are respectively
(A) SS and CS   (B) SM and CS
(C) SM and SC  (D) MS and CS
Q.8 When a retaining wall moves away from the back-fill, the pressure exerted on the
wall is termed as
(A) Passive earth pressure
(B) Swelling pressure
(C) Pore pressure
(D) Active earth pressure
?CE?Civil Engineering: Gate 2008 Paper

2
Q.9 Compaction by vibratory roller is the best method of compaction in case of
(A) moist silty sand
(B) well graded dry sand
(C) clay of medium compressibility
(D) silt of high compressibility
Q.10 A person standing on the bank of a canal drops a stone on the water surface. He
notices that the disturbance on the water in not traveling up-stream. This is
because the flow in the canal is
(A) sub-critical  (B) super-critical
(C) steady   (D) uniform
Q.11 A flood wave with a known inflow hydrograph is routed through a large reservoir.
The outflow hydrograph will have
(A) attenuated peak with reduced time-base
(B) attenuated peak with increased time-base
(C) increased peak with increased time-base
(D) increased peak with reduced time-base
Q.12 A stable channel is to be designed for a discharge of Q m
3
/s with silt factor f as
per Lacey’s method. The mean flow velocity (m/s) in the channel is obtained by
(A) (Q f
2
/ 140)
1/6
(B) (Qf / 140)
1/3
(C) (Q
2
f
2
/ 140)
1/6
(D) 0.48 (Q / f)
1/3
Q.13 The base width of an elementary profile of gravity dam of height H is b. The
specific gravity of the material of the dam is G and uplift pressure coefficient is
K. the correct relationship for no tension at the heel is given by
(A)
1
( )
b b
B G K
H H G K
= = -
-
(C)
1 1
( )
b b
D
H G K H K G K
= =
- -
Q.14 Two primary air pollutants are
(A) sulphur oxide and ozone (B) nitrogen oxide and peroxyacetylnitrate
(C) sulphur oxide and hydrocarbon (D) ozone and peroxyacetynitrate
Q.15 Two biodegradable components of municipal solid waste are
(A) plastics and wood  (B) cardboard and glass
(C) leather and tin cans (D) food wastes and garden trimmings
Q.16 The specific gravity of paving bitumen as per IS:73 – 1992 lies between
(A) 1.10 and 1.06   (B) 1.06 and 1.02
(C) 1.02 and 0.97   (D) 0.97 and 0.92
?CE?Civil Engineering: Gate 2008 Paper

3
Q.17 A combined value of flakiness and elongation index is to be determined for a
sample of aggregates. The sequence in which the two tests are conducted is
(A) elongation index test followed by flakiness index test on the whole
sample.
(B) flakiness index test followed by elongation index test on the whole
sample.
(C)  flakiness index test followed by elongation index test on the non-flaky
aggregates.
(D) elongation index test followed by flakiness index test on non-elongated
aggregates.
Q.18 The capacities of “One-way 1.5m wide sidewalk (persons per hour)” and “One-
way 2-lane urban road (PCU per hour, with no frontage access, no standing
vehicles and very little cross traffic)” are respectively
(A) 1200 and 2400 (B) 1800 and 2000
(C) 1200 and 1500 (D) 2000 and 1200
Q.19 The shape of the STOP sign according to IRC: 67-2001 is
(A) circular (B) triangular
(C) octagonal (D) rectangular
Q.20 The type of surveying in which the curvature of the earth is taken into account is
called
(A) Geodetic surveying  (B) Plane surveying
(C) Preliminary surveying (D) Topographical surveying
Q.21 to Q.75 carry two marks each
Q.21 The equation
2 2
2 2
0
x z
h h
k k
x z
? ?
+ =
? ?
can be transformed to
2 2
2 2
1
0
h h
x z
? ?
+ =
? ?
by
substituting
(A)
1
z
x
k
x x
k
= (B)
1
x
z
k
x x
k
=
(C)
1
x
z
k
x x
k
= (D)
1
z
x
k
x x
k
=
Q.22 The value of
3
0 0
(6 )
x
x y dxdy - -
??
is
(A) 13.5 (B) 27.0 (C) 40.5 (D) 54.0
Q.23 Three values of x and y are to be fitted in a straight line in the form y=a+bx by the
method of least squares. Given: ?x=6, ?y=21, ?x
2
=14 and ?xy=46, the values of
a and b are respectively
(A) 2 and 3  (B) 1 and 2  (C) 2 and 1  (D) 3 and 2
Page 4

?CE?Civil Engineering: Gate 2008 Paper

1
GATE: 2008
CE: CIVIL ENGINEERING
Q.1 The product of matrices (PQ)
-
P is
(A) P
-1
(B) Q
-1
(C) P
-1
Q
-1
(D) PQP
-1
Q.2 The general solution of
2
2
0
d y
y
dx
+ = is
(A) y=P cos x + Q sin x (B) y=P cos x
(C) y = P six x  (D) y = P sin
2
x
Q.3 A mild steel specimen is under uni-axial tensile stress. Young’s modules and
yield stress for mild steel are 2 x 10
5
MPa respectively. The maximum amount of
strain energy per unit volume that can be stored in this specimen without
permanent set is
(A) 156 Nmm/mm
3
(B) 15.6 Nmm/mm
3
(C) 1.56 Nmm/mm
3
(D) 0.156 Nmm/mm
3
Q.4 A reinforced concrete structure has to be constructed along a sea coast. The
minimum grade of concrete to be used as per IS: 456-2000 is
(A) M 15 (B) M 20
(C) M 25 (D) M 30
Q.5 In the design of a reinforced concrete bean the requirement for bond is not getting
satisfied. The economical option to satisfy the requirement for bond is by
(A) bundling of bars
(B) providing smaller diameter bars more in number
(C) providing larger diameter bars less in number
(D) providing same diameter bars more in number
Q.6 The shape of the cross-section, which has a largest shape factor, is
(A) rectangular  (B) I-section
(C) diamond   (D) solid circular
Q.7 Group symbols assigned to silty sand and clayey sand are respectively
(A) SS and CS   (B) SM and CS
(C) SM and SC  (D) MS and CS
Q.8 When a retaining wall moves away from the back-fill, the pressure exerted on the
wall is termed as
(A) Passive earth pressure
(B) Swelling pressure
(C) Pore pressure
(D) Active earth pressure
?CE?Civil Engineering: Gate 2008 Paper

2
Q.9 Compaction by vibratory roller is the best method of compaction in case of
(A) moist silty sand
(B) well graded dry sand
(C) clay of medium compressibility
(D) silt of high compressibility
Q.10 A person standing on the bank of a canal drops a stone on the water surface. He
notices that the disturbance on the water in not traveling up-stream. This is
because the flow in the canal is
(A) sub-critical  (B) super-critical
(C) steady   (D) uniform
Q.11 A flood wave with a known inflow hydrograph is routed through a large reservoir.
The outflow hydrograph will have
(A) attenuated peak with reduced time-base
(B) attenuated peak with increased time-base
(C) increased peak with increased time-base
(D) increased peak with reduced time-base
Q.12 A stable channel is to be designed for a discharge of Q m
3
/s with silt factor f as
per Lacey’s method. The mean flow velocity (m/s) in the channel is obtained by
(A) (Q f
2
/ 140)
1/6
(B) (Qf / 140)
1/3
(C) (Q
2
f
2
/ 140)
1/6
(D) 0.48 (Q / f)
1/3
Q.13 The base width of an elementary profile of gravity dam of height H is b. The
specific gravity of the material of the dam is G and uplift pressure coefficient is
K. the correct relationship for no tension at the heel is given by
(A)
1
( )
b b
B G K
H H G K
= = -
-
(C)
1 1
( )
b b
D
H G K H K G K
= =
- -
Q.14 Two primary air pollutants are
(A) sulphur oxide and ozone (B) nitrogen oxide and peroxyacetylnitrate
(C) sulphur oxide and hydrocarbon (D) ozone and peroxyacetynitrate
Q.15 Two biodegradable components of municipal solid waste are
(A) plastics and wood  (B) cardboard and glass
(C) leather and tin cans (D) food wastes and garden trimmings
Q.16 The specific gravity of paving bitumen as per IS:73 – 1992 lies between
(A) 1.10 and 1.06   (B) 1.06 and 1.02
(C) 1.02 and 0.97   (D) 0.97 and 0.92
?CE?Civil Engineering: Gate 2008 Paper

3
Q.17 A combined value of flakiness and elongation index is to be determined for a
sample of aggregates. The sequence in which the two tests are conducted is
(A) elongation index test followed by flakiness index test on the whole
sample.
(B) flakiness index test followed by elongation index test on the whole
sample.
(C)  flakiness index test followed by elongation index test on the non-flaky
aggregates.
(D) elongation index test followed by flakiness index test on non-elongated
aggregates.
Q.18 The capacities of “One-way 1.5m wide sidewalk (persons per hour)” and “One-
way 2-lane urban road (PCU per hour, with no frontage access, no standing
vehicles and very little cross traffic)” are respectively
(A) 1200 and 2400 (B) 1800 and 2000
(C) 1200 and 1500 (D) 2000 and 1200
Q.19 The shape of the STOP sign according to IRC: 67-2001 is
(A) circular (B) triangular
(C) octagonal (D) rectangular
Q.20 The type of surveying in which the curvature of the earth is taken into account is
called
(A) Geodetic surveying  (B) Plane surveying
(C) Preliminary surveying (D) Topographical surveying
Q.21 to Q.75 carry two marks each
Q.21 The equation
2 2
2 2
0
x z
h h
k k
x z
? ?
+ =
? ?
can be transformed to
2 2
2 2
1
0
h h
x z
? ?
+ =
? ?
by
substituting
(A)
1
z
x
k
x x
k
= (B)
1
x
z
k
x x
k
=
(C)
1
x
z
k
x x
k
= (D)
1
z
x
k
x x
k
=
Q.22 The value of
3
0 0
(6 )
x
x y dxdy - -
??
is
(A) 13.5 (B) 27.0 (C) 40.5 (D) 54.0
Q.23 Three values of x and y are to be fitted in a straight line in the form y=a+bx by the
method of least squares. Given: ?x=6, ?y=21, ?x
2
=14 and ?xy=46, the values of
a and b are respectively
(A) 2 and 3  (B) 1 and 2  (C) 2 and 1  (D) 3 and 2
?CE?Civil Engineering: Gate 2008 Paper

4
Q.24 Solution of
dy x
dx y
=- at x =1 and y = 3 is
(A) x-y
2
= 2 (B) x+y
2
= 4 (C) x
2
-y
2
= -2 (D) x
2
+y
2
=4
Q.25 If probability density function of a random variable X is
f(x) = x
2
for -1= x = 1, and
= 0 for any other value of x
Then, the percentage probability
1 1
3 3
P x
? ?
- = =
? ?
? ?
is
(A) 0.247 (B) 2.47 (C) 24.7 (D) 247
Q.26 The Eigen values of the matrix
[ ]
4 5
2 5
P
? ?
=
? ?
-
? ?
are
(A) -7 and 8  (B) -6 and 5 (C) 3 and 4 (D) 1 and 2
Q.27 A person on a trip has a choice between private car and public transport. The
probability of using a private car is 0.45. While using the public transport, further
choices available are bus and metro, out of which the probability of commuting
by a bus is 0.55. In such a situation, the probability (rounded up to two decimals)
of using a car, bus and metro, respectively would be
(A) 0.45, 0.30 and 0.25 (B) 0.45, 0.25 and 0.30
(C) 0.45, 0.55 and 0.00 (D) 0.45, 0.35 and 0.20
Q.28 The following simultaneous equations
x+y+z=3
x+2y+3z=4
x+4y+kz=6
will NOT have a unique solution for k equal to
(A) 0   (B) 30 (C) 6 (D) 7
Q.29 The inner (dot) product of two vectors P
u v
and Q
uv
is zero. The angle (degrees)
between the two vectors is
(A) 0 (B) 5 (C) 90 (D) 120
Q.30 Cross-section of a column consisting of two steel strips, each of thickness t and width
b is shown in the figure below. The critical loads of the column with perfect bond and
without bond between the strips are P and P
0
respectively. The ration P/P
o
is
(A) 2   (B) 4  (C) 6  (D) 8
b
t
t
Page 5

?CE?Civil Engineering: Gate 2008 Paper

1
GATE: 2008
CE: CIVIL ENGINEERING
Q.1 The product of matrices (PQ)
-
P is
(A) P
-1
(B) Q
-1
(C) P
-1
Q
-1
(D) PQP
-1
Q.2 The general solution of
2
2
0
d y
y
dx
+ = is
(A) y=P cos x + Q sin x (B) y=P cos x
(C) y = P six x  (D) y = P sin
2
x
Q.3 A mild steel specimen is under uni-axial tensile stress. Young’s modules and
yield stress for mild steel are 2 x 10
5
MPa respectively. The maximum amount of
strain energy per unit volume that can be stored in this specimen without
permanent set is
(A) 156 Nmm/mm
3
(B) 15.6 Nmm/mm
3
(C) 1.56 Nmm/mm
3
(D) 0.156 Nmm/mm
3
Q.4 A reinforced concrete structure has to be constructed along a sea coast. The
minimum grade of concrete to be used as per IS: 456-2000 is
(A) M 15 (B) M 20
(C) M 25 (D) M 30
Q.5 In the design of a reinforced concrete bean the requirement for bond is not getting
satisfied. The economical option to satisfy the requirement for bond is by
(A) bundling of bars
(B) providing smaller diameter bars more in number
(C) providing larger diameter bars less in number
(D) providing same diameter bars more in number
Q.6 The shape of the cross-section, which has a largest shape factor, is
(A) rectangular  (B) I-section
(C) diamond   (D) solid circular
Q.7 Group symbols assigned to silty sand and clayey sand are respectively
(A) SS and CS   (B) SM and CS
(C) SM and SC  (D) MS and CS
Q.8 When a retaining wall moves away from the back-fill, the pressure exerted on the
wall is termed as
(A) Passive earth pressure
(B) Swelling pressure
(C) Pore pressure
(D) Active earth pressure
?CE?Civil Engineering: Gate 2008 Paper

2
Q.9 Compaction by vibratory roller is the best method of compaction in case of
(A) moist silty sand
(B) well graded dry sand
(C) clay of medium compressibility
(D) silt of high compressibility
Q.10 A person standing on the bank of a canal drops a stone on the water surface. He
notices that the disturbance on the water in not traveling up-stream. This is
because the flow in the canal is
(A) sub-critical  (B) super-critical
(C) steady   (D) uniform
Q.11 A flood wave with a known inflow hydrograph is routed through a large reservoir.
The outflow hydrograph will have
(A) attenuated peak with reduced time-base
(B) attenuated peak with increased time-base
(C) increased peak with increased time-base
(D) increased peak with reduced time-base
Q.12 A stable channel is to be designed for a discharge of Q m
3
/s with silt factor f as
per Lacey’s method. The mean flow velocity (m/s) in the channel is obtained by
(A) (Q f
2
/ 140)
1/6
(B) (Qf / 140)
1/3
(C) (Q
2
f
2
/ 140)
1/6
(D) 0.48 (Q / f)
1/3
Q.13 The base width of an elementary profile of gravity dam of height H is b. The
specific gravity of the material of the dam is G and uplift pressure coefficient is
K. the correct relationship for no tension at the heel is given by
(A)
1
( )
b b
B G K
H H G K
= = -
-
(C)
1 1
( )
b b
D
H G K H K G K
= =
- -
Q.14 Two primary air pollutants are
(A) sulphur oxide and ozone (B) nitrogen oxide and peroxyacetylnitrate
(C) sulphur oxide and hydrocarbon (D) ozone and peroxyacetynitrate
Q.15 Two biodegradable components of municipal solid waste are
(A) plastics and wood  (B) cardboard and glass
(C) leather and tin cans (D) food wastes and garden trimmings
Q.16 The specific gravity of paving bitumen as per IS:73 – 1992 lies between
(A) 1.10 and 1.06   (B) 1.06 and 1.02
(C) 1.02 and 0.97   (D) 0.97 and 0.92
?CE?Civil Engineering: Gate 2008 Paper

3
Q.17 A combined value of flakiness and elongation index is to be determined for a
sample of aggregates. The sequence in which the two tests are conducted is
(A) elongation index test followed by flakiness index test on the whole
sample.
(B) flakiness index test followed by elongation index test on the whole
sample.
(C)  flakiness index test followed by elongation index test on the non-flaky
aggregates.
(D) elongation index test followed by flakiness index test on non-elongated
aggregates.
Q.18 The capacities of “One-way 1.5m wide sidewalk (persons per hour)” and “One-
way 2-lane urban road (PCU per hour, with no frontage access, no standing
vehicles and very little cross traffic)” are respectively
(A) 1200 and 2400 (B) 1800 and 2000
(C) 1200 and 1500 (D) 2000 and 1200
Q.19 The shape of the STOP sign according to IRC: 67-2001 is
(A) circular (B) triangular
(C) octagonal (D) rectangular
Q.20 The type of surveying in which the curvature of the earth is taken into account is
called
(A) Geodetic surveying  (B) Plane surveying
(C) Preliminary surveying (D) Topographical surveying
Q.21 to Q.75 carry two marks each
Q.21 The equation
2 2
2 2
0
x z
h h
k k
x z
? ?
+ =
? ?
can be transformed to
2 2
2 2
1
0
h h
x z
? ?
+ =
? ?
by
substituting
(A)
1
z
x
k
x x
k
= (B)
1
x
z
k
x x
k
=
(C)
1
x
z
k
x x
k
= (D)
1
z
x
k
x x
k
=
Q.22 The value of
3
0 0
(6 )
x
x y dxdy - -
??
is
(A) 13.5 (B) 27.0 (C) 40.5 (D) 54.0
Q.23 Three values of x and y are to be fitted in a straight line in the form y=a+bx by the
method of least squares. Given: ?x=6, ?y=21, ?x
2
=14 and ?xy=46, the values of
a and b are respectively
(A) 2 and 3  (B) 1 and 2  (C) 2 and 1  (D) 3 and 2
?CE?Civil Engineering: Gate 2008 Paper

4
Q.24 Solution of
dy x
dx y
=- at x =1 and y = 3 is
(A) x-y
2
= 2 (B) x+y
2
= 4 (C) x
2
-y
2
= -2 (D) x
2
+y
2
=4
Q.25 If probability density function of a random variable X is
f(x) = x
2
for -1= x = 1, and
= 0 for any other value of x
Then, the percentage probability
1 1
3 3
P x
? ?
- = =
? ?
? ?
is
(A) 0.247 (B) 2.47 (C) 24.7 (D) 247
Q.26 The Eigen values of the matrix
[ ]
4 5
2 5
P
? ?
=
? ?
-
? ?
are
(A) -7 and 8  (B) -6 and 5 (C) 3 and 4 (D) 1 and 2
Q.27 A person on a trip has a choice between private car and public transport. The
probability of using a private car is 0.45. While using the public transport, further
choices available are bus and metro, out of which the probability of commuting
by a bus is 0.55. In such a situation, the probability (rounded up to two decimals)
of using a car, bus and metro, respectively would be
(A) 0.45, 0.30 and 0.25 (B) 0.45, 0.25 and 0.30
(C) 0.45, 0.55 and 0.00 (D) 0.45, 0.35 and 0.20
Q.28 The following simultaneous equations
x+y+z=3
x+2y+3z=4
x+4y+kz=6
will NOT have a unique solution for k equal to
(A) 0   (B) 30 (C) 6 (D) 7
Q.29 The inner (dot) product of two vectors P
u v
and Q
uv
is zero. The angle (degrees)
between the two vectors is
(A) 0 (B) 5 (C) 90 (D) 120
Q.30 Cross-section of a column consisting of two steel strips, each of thickness t and width
b is shown in the figure below. The critical loads of the column with perfect bond and
without bond between the strips are P and P
0
respectively. The ration P/P
o
is
(A) 2   (B) 4  (C) 6  (D) 8
b
t
t
?CE?Civil Engineering: Gate 2008 Paper

5
K
P
H
L
G
J H
G F E
I
Q.31 A rigid bar GH of length L is supported by a hinge and a spring of stiffness K as
shown in the figure below. The buckling load, P
cr’
for the bar will be
(A) 0.5 KL
(B) 0.8 KL
(C) 1.0KL
(D) 1.2KL
Q.32 The degree of static indeterminacy of the rigid frame having two internal hinges
as shown in the figure below, is
(A) 8
(B) 7
(C) 6
(D) 5
Q.33 The members EJ and IJ of a steel truss shown in the figure below are subjected to
a temperature rise of 30
0
C. The coefficient of thermal expansion of steel is
0.000012 per
0
C per unit length. The displacement (mm) of joint E relative to
joint H along the direction HE of truss, is
(A) 0.255
(B) 0.589
(C) 0.764
(D) 1.026
Q.34 The maximum shear stress in a solid shaft of circular cross-section having
diameter subjected to a torque T is t . If the torque is increased by four times and
the diameter of the shaft is increased by two times, the maximum shear stress in
the shaft will be
3000mm 3000mm
E
G
3000mm
H
I
J
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## GATE Past Year Papers for Practice (All Branches)

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