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GATE 2015 – A Brief Analysis
(Based on student test experiences in the stream of CE on 8th
February, 2015 – (Forenoon Session))
Section wise analysis of the paper
3
1 3
2 2
2
0 1 1
3 2
2 3
&
2 3
0 2 2 1 0 1
3 2
2 3
2 2
3 2
2 3
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Questions from the Paper
1. Find maximum ordinate of S-curve of the 4-hr unit hydrograph given below.
0 2 4 6 8 10 12 14 16 18 20 22 24
0 0.6 3.1 10 13 9 5 2 0.7 0.3 0.2 0.1 0
2. Find maximum moment carrying capacity of concrete (in kNm)
Key: (42.82)
Exp:( )
2
st
2
A 4 124
453mm
π= × ×
=
0.36 f ck .b.xu = 0.87 f y Ast
( )
( )
y st
u
ck
u,max
u u,max
u y st u
0.87f A 0.87 415 453x
0.36f .b 0.36 25 200
90.86mmx 0.48d
0.48 300 144 mm
x x so Under Reinf orced section
M 0.87 f A d 0.42 x
0.87 415 453 300 42 90.86
42.82kNm
× ×⇒ = =
× ×
==
= × =
<
= × × × −
= × × × − ×
=
Capacity
u maxx 0.48d=4 12× φ
300 mm
M25
Fe415
200 mm
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3.
Find maximum strength (in kN) for which bolt has to be designed
Key: (156.20)
Exp:D
P 100F 20kN
n 5= = =
t 2 2
(P.d)r 100 600 75 2F 141.42kN
r 4 (75 2)
× ×= = =
×∑
2 2
R D t D t
2 2
F F F 2 F F cos
1(20) (141.42) 2 20 141.42
2
156.20kN
= + + × × θ
= + + × × ×
=
o
1cos
2
45 .
θ =
⇒ θ =
P 100kN=
600
75
75
75 75
θ
bFtF
75
75
θ
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4.( )( )
2
9f(z)
z 1 z 2=
− + which of the following is one of the residues of the given function
(A)
-1 (B) 9/16 (C) 2 (D) 9
5.
3 2 2
4 4 6
2 3 3
− − −
Which one of the following are its smallest and largest eigen values?(A)
1.5,2.5 (B) 0.5,2.5 (C) 1,3 (D) (1,2)
6. For 2m wide rectangular channel n = 0.01, s = 1/10000, discharge 4m3 /s in GVF profile,
find rate of change of slopedy
dx at y = 0.2 m
7. Find directional derivative of x2
-3yz in direction ˆi j 2k + −ɵ ɵ
at (2,-1,4)
8. Find the value of x2+4x-4 = 0 by Newton Raphson method, after second approximation
9. Compound Composition(%) Density
1C 1ρ
2C 2ρ
If the combined composition is 100%, what is the equivalent density of sludge?
(A)1 2
1 2
100
C C+ρ ρ
(B) 1 2
1 2
100C C
ρ ρ+
(C) ( )
1 1 2 2
100 C Cρ + ρ (D)
( )
1 2
1 1 2 2
100C C
ρ ρ
ρ + ρ
Key: (A)
Exp: Let density of sludge is ρ
1 2 1 2
1 2
1 2
1 2
c c c c
100
c c
+= +
ρ ρ ρ
⇒ ρ =
+ρ ρ
10. ( ) t0dv
t edt
−β= α − β for slow vehicle, whose acceleration varies with this equation and V0
is initial velocity.dv
vdt
= α + β for vehicle that is overtaking. Ifdv
2dt
= at 3sec. α =
0.005, β = 0.01 at t = 45s find distance
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11.
If x=48 m is the distance where sign should be placed for 6/6 eyes, what would be x for
6/9 vision?
12. Solve ( ) ( )y y
xdx ydy cos xy ydx xdy sinx x
+ = −
Key: (y
xycos cx
= )
13. SO2 - 30µg/m3 at ambient pressure and temperature, Find its volume in ppm. If weight of
SO2 = 64, andPR
41.6molT
=
14. A circular footing of 3m diameter is placed at 1m depth.
Find compression of clay layer if a load of 1500 kN is applied from top. Stress
distribution is of 2 vertical to 1 horizontal. Unit weight of water is 10.
15. Find ratio of horizontal and vertical permeability
If tsand = 3 times tclay tsilt = 2 time tclay
permeability of sand is 10 times of silt and permeability of clay is 1/10th of silt
16.
Find k 22 (stiffness)
x
2m
6m
10m
Dense
Sand−
Silt
c
0
C 0.3
e 0.7
=
=
318 kN m
Clay
318 kN m
315 kN m
GWT=
A,E,I
3
L
2
1
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17. Concentration of SO2 is 303
g / mµ
Under same condition above 2SO concentration expressed in ppm is _________
32P / RT 41.6 mol / m Mol. wt. of SO 64= =
18. Which of the following is true?
(A) Thinner the soil sampler wall, lower the degree of disturbance.
(B) Thicker the soil sampler wall, lower the degree of disturbance.
(C) No relation between thickness and degree of disturbance
(D) None of these
Key: (A)
Exp: Degree of disturbance decreases with decrease in thickness of wall.
19. Development length of a deformed reinforcement bar is given by s
bdk.
φσ
τ . As per IS 456,
value of k is ____ .Key: (6.4)
Exp: sd
bd
L4
φσ=
τ But for deformed bars bdτ is increased by 60%.
So,
st s
bd bd
Ld4 1.6 6.4
φσ φσ= =
× × τ τ
So, k=6.4.
20. Although the tamil version of _________ John Abraham starrer Madras Café _________
cleared by the censor board with no cuts, film distributors ________ no takers forreleasing __________ this Friday
(Mr., was, found, on)
21. Children: Pediatrician
(A) Kidney: Nephrologist (B) Female: Gynecologist
(C) Skin dermatologist (D) ..
22. ROAD – URDG: SWAN – ________
Key: (VZDQ)
23. f(x) = 29,at x = -2 f(x) = 39,at x = 3
Find f(x) ,at x = 5
Key: (43)
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24. Extreme focus on syllabus and studying for test has become such a dominant concern ofIndian students that this has closed their minds to anything ________ to the requirements
of the exam
(A) related (B) extraneous (C) outside (D) useful
25.
For a simply reinforced beam shown above
(A) Variation of stress is linear and strain non-linear
(B) Variation of strain is linear and stress non-linear
(C) Both linear
(D) Both non-linear
26. What is the relationship between seepage velocity and discharge velocity?
Key: (B)
Exp: SV
Vn
= VS never be smaller than discharge velocity
27. Penetration of bitumen sample tested at 25°C is 80. When heated to 60°C, penetration is
measured as ‘d’mm – d value cannot be lesser than ____ mm.
Key: (8)
28. A vehicle is moving in a circular curve and it has a super elevation of e when it does notslide inwards. When friction factor is f
(A) e f ≤ (B) e f ≥ (C) e f = (D) Cannot be determined
Key: (A)
29. Which of these are non dimensional parameters?
Key: d2
F VD,
VD
ρ
µρ
30. Which of these statements is false?
(1) Plumb line is along direction of gravity(2) Mean Sea Level in reference surface for establishing horizontal control
(3) Mean Sea Level is simplification of geoid
(4) Geoid is an equi potential surface of gravity.
Key: (B)
L L 2 L
y
x
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31. For a wide rectangular channel of width 2m, post jump depth and velocity are 0.8, 1 m/s,respectively. Find velocity before jump (in m/s).
Key: (4.94)
Exp: B=2m,2 2y 0.8m, U 1m / s= =
22
2
U 1F 0.35g.y 10 0.8
= = =×
212
2
21
y 1 1. 1 8F
y 2 2
y 1 1. 1 8 (3.5) 0.203
0.8 2 2
= − + +
−⇒ = + + × =
1y 0.203 0.8 0.162 m⇒ = × =
2 2 1 1
1
1
Q B.y .V B.y V
0.8 1 0.162 V
V 4.94 m / s.
= =
⇒ × = ×
⇒ =
32. Selection incorrect statement.
(A) Shear strength of loose soil increases on shearing
(B) Dense sand develops negative pore pressure
(C) Cotton soil is collapsible soil.
(D) Liquefaction of sheet pile occurs at downstream due to hydraulic gradient.
33.
For the structure shown in figure, calculate the displacement of point P ________ mm (E
= 2×105 MPa)
Key: (15)
20mm
2m
1.5m 10mm
P
30 kNπ
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Exp:
1
1 2
6
5
4P.L
d d E
4 30 2 10
20 10 2 10
6mm
∆ =π ×
× π × ×=
π × × × ×
=
2
6
5
P L
AE
4 30 1.5 10
10 10 2 10
9mm
×∆ =
× π × ×=
π × × × ×
=
∆ = ∆1+∆2 = 15 mm
34. In a survey work, three independent angles x,y,z were observed with weights Wx, Wy, Wz respectively the weight of sum of angles x,y,z is
(A)
x y z
1
1 1 1
W W W
+ +
(B)x y z
1 1 1
W W W
+ +
(C) Wx+Wy+Wz (D)
2 2 2x y zW W W+ +
35. A=o
N77 50', magnetic bearing, binary magnetic declinationo
2 , Due to local attrition,error in AO is free from local attrition OA, magnetic bearing oS52 20'W, AO=55
o40’,
Find true Bearing of A.
Key: o oN84 10 E
30π
20mm
10mm
30π
30π
30π
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36. For what values of ‘p’ the set of equations2x 3y 5, 3x py 10+ = + = has no solution
37. P.M.F of random variable x if ( )
q if x 0
P x,q 1 q x 1
0 otherwise
=
= − =
If q=0.4, the variance of x is ________.
38. 1. As slump increases, the vebe time increases.
2. As slump increases, the compaction factor increases.
(A) 1 is correct (B) 2 is correct (C) Both are correct (D) None
Key: (B)
Exp: As vebe time increases, slump decreases
39. Which of these can not be used to describe free flow speed of traffic stream?
(A) Uf is speed when flow is negligible(B) Uf is speed when density is negligible
(C) Affected by geometry and surface condition of road
(D) Flow is maximum and density is optimum
40. Which of the following is not correct?
Key: (B) Dense sand when sheared under undrained condition may lead to generation ofnegative pore pressure
41. Kjeldahl Nitrogen is combination of
(A) Ammonia + nitrate (B) Ammonia + organic nitrogen
(C) Organic Nitrogen + nitrate (D) Nitrate + nitrite
Key: (B)
42.
Find n ,σ normal stress on planeo
45 to major principal axis
Key: (0)
100
100
100
100
nσ
o45
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Exp: x y x y
n cos22 2
σ + σ σ − σσ = + θ
100 100 100 ( 100)cos90 0
2 2
− − −= + =
43. 60% of silt is fine-grained. The soil is semisolid at water content of 15% & 28% and fluidlike when water content when water content is greater than 40%. What is the activity?
(A) 6 (B) 4 (C) 2 (D) 0.2
Key: (D)
Exp: IP = WL. WP = 40-28 = 12%
PI 12A 0.2c 60
= = =
44. 20 m thick soil is between silty sand and gravel sand and found 30 mm settlement in 2
years.
2
VC 0.003 cm s,− total settlement – 50mm. What is the time required (in years) for final
settlement?
45.
46. For steady incompressible flow through a closed conduit of uniform c/s the direction of
flow will always be
(A) Higher to lower elevation (B) Higher to lower pressure
(C) Higher to lower velocity (D) Higher to lower piezometric head
Key: (B)
47. In closed loop traverse of 1 km total length, the closing error in departure and latitude are0.3 m and 0.4 m respectively. The relative precision of this traverse is
(A) 1:5000 (B) 1:4000 (A) 1:3000 (A) 1:2000Key: (D)
Exp: ( ) ( )5 22 2e d 0.3 0.4 0.5m
0.5Relative precision 1: 2000
1000
= + = + =
= =
ℓ
M ?=
3 31 1
(EI)
20 kN
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48. In an x-y plane, the velocity in x- direction is x2, and the fluid density is
1,
x then what is
the velocity in y-direction?
(A)x
y
− (B) x / y (C) xy− (D) xy
Key: (C)
Exp: Continuity equation
( ) ( )
( )
U V 0x y
1x .V 0
x y x
V V1 0 1
y x y x
V xy
∂ ∂ρ + ρ =
∂ ∂
∂ ∂ ⇒ + =
∂ ∂
∂ ∂ ⇒ + = ⇒ = −
∂ ∂
⇒ = −
49. Match the following
P Graph Command Area 1-100 ha/cumec
Q Permanent Wilting Point 2. o6 C
R Duty 3. 1000 ha
S Delta 4. 1000 cm
5. 40 cm
6. 0.12
Key: P-3, Q-6, R-1, S-5
50. In a soil test, confined pressure is increased from-150 to 250 kPa, its pore pressure is
increased by 80 kPa, and its deviatory stress is increased by 25 kPa. Skempton’s porepressure parameter B is ___________.
(A) 0.5 (B) 0.625 (C) 0.8 (D) 1
Key: (C)
Exp:3
U 80B 0.8
100
∆= = =
∆σ
51. A circular pipe of 1 m diameter is laid on a bed slope 1 in 1000. Its Manning’s coefficientis 0.01 and the flow is upto its crest and the discharge is referred as Q full. If Qhalf is thedischarge in water at 0.5 m depth, then find the ratio of Qfull / Qhalf
(A) 1 (B) 2 (C) 2 (D) 4
Key: (A)
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Exp:
22 1 1
323 2 2
full
1 1 DQ .AR S Q . .D . s
n n 4 4
π = ⇒ =
212
32
half
full
half
1 D DQ . . s
n 8 4
Q2
Q
π =
=
52. The below statements are related to air entrained concrete
(1) They reduce water demand at given workability
(2) They are used in an environment where cyclic freezing and thawing take place
(A) 1 is correct (B) 2 is correct (C) Both are correct (D) None
Key: (C)
53.
Find percentage load taken by springKey: (33.33)
Exp:
EI, L
EI, L
P
s 3 3
3EI 3EIK
2L 2L
=
P
R
R
R
R
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3
3
R
K
R2L
3EI
2R.L
3EI
∆ =
= ×
∆ =
3 3 3
3 3
PL RL 2RL
3EI 3EI 3EI
PL 3RL PR 33.33%.
3EI 3EI 3
− =
⇒ = ⇒ = =
54.
dl dr
si sr
i ir
F F 1.134
F F 1.113
Fq 0.444 F 0.2
= =
=
= =
3
FOS 3
18kN/m
=
γ =
Find maximum eccentric load at net safe criteria.
55.
Find the strain energy in member X (in kN-m)
Take AE = 30 kN-m
2
0.85
1
P
10kN
5kN
3m
3m
3m
D
E
F
G
A
B
C
3m
X
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Key: (5)
Exp:
RA×3 + 10×9 = 0
⇒ RA = -30 kN
RG = 35 kN
Taking joint A
Joint G
Joint B
Fx = 10 kN
10kN
5kN
3m
3m
3m
D
E
F
G
AR
B
C
3m GR
A
10kN
30kN
10kN
30kN
10kN
35kN10kN
10 2
10 2
30
10
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2F L 10 10 3
U 5kN m2AE 2 30
× × ×= = = −
×
56. Excavation is to be obtained either from x,y or z,
5000 m3 sand. Unit weight 17.6. Cost of transportation per km is double of cost of
excavation per3
m . Find economical option.
Key: (y)
Exp: yx z
1 2 3
VV VV
1 e 1 e 1 e 1 e= = =
+ + + +
d w
G 2.67. 16 10
1 e 1 e
e 0.67
γ = γ ⇒ = ×+ +
⇒ =
yx z
VV V5000
1.67 1.6 1.64 1.7= = =
3
x
3
y
3
z
V 4790.42 m
V 4910.18 m
V 5089.82 m
⇒ =
=
=
x
y
z
C C 479042 2 C 140
5070.42 C
C C 4910.18 2 C 80 5070.18C
C C 5089.82 2 C 100 5289.82C
= × + × ×
=
= × + × × =
= × + × × =
e0.164z
e
0.7y
e
0.6x
Construct
site
140 km
80 km 100 km
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