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1

GATE 2015 –CE on 8th

February, 2015 – (Forenoon Session)

General Aptitude Questions

Q.No-1-5 Carry One Mark Each

1. Select the pair that best expresses a relationship similar to that expressed in the pair:

Children: Pediatrician

(A) Adult: Orthopaedist (B) Females: Gynaecologist

(C) Kidney: Nephrologist (D) Skin: Dermatologist

Answer: (B)

Exp: Community of people: Doctor

2. Extreme focus on syllabus and studying for test has become such a dominant concern of

Indian students that this has closed their minds to anything ________ to the requirements of

the exam

(A) related (B) extraneous (C) outside (D) useful

Answer: (B)

Exp: extraneous -irrelevant or unrelated to the subject being dealt with.

3. If ROAD is written as URDG, then SWAN should be written as:

(A) VXDQ (B) VZDQ (C) VZDP (D) UXDQ

Answer: (B)

Exp: R+3=U, O+3=R, A+3=D, D+3=G;

S+3=V, W+3=Z, A+3=D, N+3=Q

4. The Tamil version of __________ John Abraham-starrer Madras Café _____ cleared by the

censor board with no cuts last week, but the film’s distributors _______ no takers among the

exhibitors for a release in Tamil Nadu ________ this Friday.

(A) Mr., was, found, on (B) a, was found, at

(C) the, was, found, on (D) a, being, find, at

Answer: (C)

Exp: John-Abraham starrer Madras Café talks about the movie not the person, so Mr. is ruled out.

‘Find no takers’ is not the correct phrase. At this Friday is incorrect. So, option C is correct.

5. A function f(x) is linear and has a value of 29 at x = -2 and 39 at x = 3. Find its value at x = 5.

(A) 59 (B) 45 (C) 43 (D) 35

Answer: (C)

Exp: f(x)=2x+33



2

Q.No-6-10 Carry Two Marks Each

6. The head of a newly formed government desires to appoint five of the six selected members

P,Q,R,S,T and U to portfolios of Home, Power, Defense, Telecom and Finance. U does not

want any portfolio if S gets one of the five. R wants either Home or Finance or no portfolio.

Q says that if S gets either Power or Telecom, then she must get the other one. T insists on a

portfolio if P gets one.

Which is the valid distribution of portfolio?

(A) P-Home, Q-Power, R-Defense, S-Telecom, T-Finance

(B) R-Home, S-Power, P-Defense, Q-Telecom, T-Finance

(C) P-Home, Q-Power, T-Defense, S-Telecom, U-Finance

(D) Q-Home, U-Power, T-Defense, R-Telecom, P-Finance

Answer: (B)

Exp: Since U does not want any portfolio, (C) and (D) are ruled out. R wants Home, or Finance or

No portfolio, (A) is not valid. Hence option (B) is correct

7. The exports and imports (in crores of Rs.) of a country from the year 2000 to 2007 are given

in the following bar chart. In which year is the combined percentage increase in imports and

exports the highest?

Answer: 2006

Exp: Increase in exports in 2006=100 70

42.8%70

−=

Increase in imports in 2006=120 90

33.3%90

−=

which is more than any other year

Exports Imports

120

110

100

90

80

70

60

50

40

30

20

10

0

2000 2001 2002 2003 2004 2005 2006 2007



3

8. Most experts feel that in spite of possessing all the technical skills required to be a batsman of

the highest order., he is unlikely to be so due to lack of requisite temperament. He was guilty

of throwing away his wicket several times after working hard to lay a strong foundation. His

critics pointed out that until he addressed to this problem, success at the highest level will

continue to elude him.

Which of the statement (s) below is/are logically valid and can be inferred from the above

passage?

(i) He was already a successful batsman at the highest level

(ii) He has to improve his temperament in order to become a great batsman

(iii) He failed to make many of his good starts count

(iv) Improving his technical skills will guarantee success

(A) (iii) and (iv) (B) (ii) and (iii) (C) (i), (ii) and (iii) (D) (ii) only

Answer: (B)

9. Choose the most appropriate equation for the function drawn as a thick line, in the plot below.

(A) x = y-|y| (B) x = -(y-|y|) (C) x = y+|y| (D) x = -(y+|y|)

Answer: (B)

10. Alexander turned his attention towards India, since he had conquered Persia.

Which one of the statements below is logically valid and can be inferred from the above

sentence?

(A) Alexander would not have turned his attention towards India had he not conquered

Persia.

(B) Alexander was not ready to rest on his laurels, and wanted to march to India

(C) Alexander was completely in control of his army and could command it to move towards

India.

(D) Since Alexander’s kingdom extended to Indian borders after the conquest of Persia, he

was keen to move further.

Answer: (A)

y

π

( )0, 1−

( )2,0



4

Section Name: Civil Engineering

Q.No-1-25 Carry One Mark Each

1. Consider the following statements for air-entrained concrete:

(i) Air-entrainment reduces the water demand for a given level of workability

(ii) Use of air-entrained concrete is required in environments where cyclic freezing and

thawing is expected.

Which of the following is TRUE?

(A) Both (i) and (ii) are True (B) Both (i) and (ii) are False

(C) (i) is True and (ii) is False (D) (i) is False and (ii) is True

Answer: (A)

Exp: (i) Air-entrainment reduces the water demand for a given level of workability-True

(ii) Use of air-entrained concrete is required in environments where cyclic freezing and

thawing is expected. -True

2. Which of the following statements is TRUE for the relation between discharge velocity and

seepage velocity?

(A) Seepage velocity is always smaller than discharge velocity

(B) Seepage velocity can never be smaller than discharge velocity

(C) Seepage velocity is equal to the discharge velocity

(D) No relation between seepage velocity and discharge velocity can be established

Answer: (B)

Exp: s

VV n 1

n= <∵

So, VS > V always

So, seepage velocity (VS) can never by smaller than discharge velocity

3. The integral 2

1

x2

2 1x

x dx with x x 0> >∫ is evaluated analytically as well as numerically using a

single application of the trapezoidal rule. If I is the exact value of the integral obtained

analytically and J is the approximate value obtained using the trapezoidal rule, which of the

following statements is correct about their relationship?

(A) J > 1

(B) J<1

(C) J = 1

(D) Insufficient data to determine the relationship

Answer: (A)



5

Exp: We know that the approximated value of b

af (x)dx∫ obtained by trapezoidal rule is always

greater than the analytical value.

J I∴ > where J=approximate value

I=analytical value

4. A circular pipe has a diameter of 1m, bed slope of 1 in 1000, and Manning’s roughness

coefficient equal to 0.01. It may be treated as an open channel flow when it is flowing just

full, i.e., the water level just touches the crest. The discharge in this condition is denoted by

Qfull. Similarly, the discharge when the pipe is flowing half-full, i.e., with a flow depth of

0.5m, is denoted by Qhalf. The ratio Qfull/Qhalf is:

(A) 1 (B) 2 (C) 2 (D) 4

Answer: (C)

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 =

=

5. Which of the following statements is NOT correct?

(A) Loose sand exhibits contractive behavior upon shearing

(B) Dense sand when sheared under undrained condition, may lead to generation of negative

pore pressure

(C) Black cotton soil exhibits expansive behavior

(D) Liquefaction is the phenomenon where cohesionless soil near the downstream side of

dams or sheet-piles loses its shear strength due to high upward hydraulic gradient

Answer: (D)

Exp: Liquefaction is due to cyclic loads, not due to high hydraulic gradient

6. A fine-grained soil has 60% (by weight) silt content. The soil behaves as semi-solid when

water content is between 15% and 28%. The soil behaves fluid-like when the water content is

more than 40%. The ‘Activity’ of the soil is

(A) 3.33 (B) 0.42 (C) 0.30 (D) 0.20

Answer: (C)

Exp: IP = WL-WP = 40-28 = 12%

pI 12

Activity 0.3C 100 60

= = =−



6

7. For steady incompressible flow through a closed-conduit of uniform cross-section, the

direction of flow will always be:

(A) from higher to lower elevation (B) from higher to lower pressure

(C) from higher to lower velocity (D) from higher to lower piezometric head

Answer: (B)

8. Two triangular wedges are glued together as shown in the following figure. The stress acting

normal to the interface, σn is __________ MPa.

Answer: 0

Exp: x y x y

n cos22 2

σ + σ σ − σσ = + θ

100 100 100 ( 100)

cos90 02 2

− − −= + =

9. In a closed loop traverse of 1 km total length, the closing errors in departure and latitude are

0.3 m and 0.4 m, respectively. The relative precision of this traverse will be;

(A) 1:5000 (B) 1:4000 (C) 1:3000 (D) 1:2000

Answer: (D)

Exp: ( ) ( )5 22 2e d 0.3 0.4 0.5m

0.5Relativeprecision 1: 2000

1000

= + = + =

= =

�

10. Solid waste generated from an industry contains only two components, X and Y as shown in

the table below

( ) ( )3

1 1

2 2

Component Composition Density

% weight kg m

X c

Y c

ρρ

Assuming (c1+c2) = 100, the composite density of the solid waste (ρ) is given by:

(A) 1 2

1 2

100

c c + ρ ρ

(B) 1 2

1 2

100c c

ρ ρ+

(C) ( )1 1 2 2100 c cρ + ρ (D) oN77 50 E′

Answer: (A)

100MPa

100MPa

100MPa

100MPa

nσ

45°



7

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

11. The two columns below show some parameters and their possible values.

Parameter Value

P-Gross Command Area I-100 hectares/cumec

Q-Permanent Wilting Point II-6℃

R-Duty of canal water III-1000 hectares

S-Delta of wheat IV-1000 cm

V-40 cm

VI-0.12

Which of the following options matches the parameters and the values correctly?

(A) P-I, Q-II, R-III, S-IV (B) P-III, Q-VI, R-I, S-V

(C) P-I, Q-V, R-VI, S-II (D) P-III, Q-II, R-V, S-IV

Answer: (B)

Exp:

P-Gross Command Area=1000 ha

Q-Permanent Wilting Point=0.12

R-Duty of canal water=100 ha/cumec

S-Delta of wheat=40 cm

12. In an unconsolidated undrained triaxial test, it is observed that an increase in cell pressure

from 150 kPa to 250 kPa leads to a pore pressure increase of 80 kPa. It is further observed

that, an increase of 50 kPa in deviatoric stress results in an increase of 25 kPa in the pore

pressure. The value of Skempton’s pore pressure parameter B is;

(A) 0.5 (B) 0.625 (C) 0.8 (D) 1.0

Answer: (C)

Exp: 3

U 80B 0.8

100

∆= = =

∆σ



8

13. Which of the following statements is TRUE for degree of disturbance of collected soil

sample?

(A) Thinner the sampler wall, lower the degree of disturbance of collected soil sample

(B) Thicker the sampler wall, lower the degree of disturbance of collected soil sample

(C) Thickness of the sampler wall and the degree of disturbance of collected soil sample are

unrelated

(D) The degree of disturbance of collected soil sample is proportional to the inner diameter of

sampling tube

Answer: (A)

Exp: As thickness of sampler increases, disturbance increases

14. Which of the following statements is FALSE?

(A) Plumb line is along the direction of gravity

(B) Mean Sea Level (MSL) is used as a reference surface for establishing the horizontal

control

(C) Mean Sea Level (MSL) is a simplification of the Geoid

(D) Geoid is an equi-potential surface of gravity

Answer: (B)

Exp: Mean Sea Level (MSL) is used as a reference surface for establishing the vertical control and

not horizontal control

15. For what value of p the following set of equations will have no solution?

2x+3y = 5

3x+py = 10

Answer: 4.5

Exp: Given 2x+3y=5

3x py 10+ =

2 3 x 5

3 p y 10

AX B

⇒ =

=

Augmented matrix 2 3 5

[A / B]3 p 10

=

2 2 1R 2R 3R→ − 2 3 5

0 2p 9 5

−

system will have no solution if (A / B) (A)ρ ≠ ρ

2p 9 0

9p 4.5

2

⇒ − =

⇒ = =

16. In a two-dimensional steady flow field, in a certain region of the x-y plane, the velocity

component in the x-direction is given by 2

xv x= and the density varies as 1

.x

ρ = Which of

the following is a valid expression for the velocity component in the y-direction, vy?

(A) yv x / y= − (B) yv x / y= (C) yv xy= − (D) yv xy=



9

Answer: (C)

Exp: Continuity equation

( ) ( )

( )

Y V 0x y

1x .V 0

x y x

V V1 0 1

y x y x

V xy

∂ ∂ρ + ρ =

∂ ∂

∂ ∂ ⇒ + = ∂ ∂

∂ ∂ ⇒ + = ⇒ = − ∂ ∂

⇒ = −

17. Workability of concrete can be measured using slump, compaction factor and Vebe time.

Consider the following statements for workability of concrete:

(i) As the slump increases, the Vebe time increases

(ii) As the slum increases, the compaction factor increases

Which of the following is TRUE?

(A) Both (i) and (ii) are True (B) Both (i) and (ii) are False

(C) (i) is True and (ii) is False (D) (i) is False and (ii) is True

Answer: (D)

Exp: As the slump increases, the Vebe time decreases

18. Consider the following probability mass function (p.m.f) of a random variable X:

q if X 0

p(x,q) 1 q if X 1

0 otherwise

== − =

If q=0.4, the variance of X is ________ .

Answer: 0.24

Exp: p(x,q) q if X 0

1 q if X 1

0 otherwise

= == − =

given q = 0.4

( )p x,q 0.4 if X 0

0.6 if X 1

0 otherwise

⇒ = =

= ==

( )

X 0 1

p X x 0.4 0.6⇒

=

( ) ( ) ( ){ }( )( )( ) ( )

22

i i

2 2 2 2

i i

2

Required value= V X E X E X

E X x p 0 0.4 1 0.6 0.6

E X x p 0 0.4 1 0.6 0.6

V X 0.6 0.6

0.6 0.36

0.24

= −

= Σ = × + × =

= Σ = × + × =

= −

= −=



10

19. Which of the following statements CANNOT be used to describe free flow speed (uf) of a

traffic stream?

(A) uf is the speed when flow is negligible

(B) uf is the speed when density is negligible

(C) uf is affected by geometry and surface conditions of the road

(D) uf is the speed at which flow is maximum and density is optimum

Answer: (D)

Exp: Free flow speed → speed when flow is negligible

→ speed when density is negligible

→ affected by Geometry, deriver’s perception, roadway condition etc.

20. Consider the singly reinforced beam shown in the figure below:

At cross-section XX, which of the following statement is TRUE at the limit state?

(A) The variation of stress is linear and that of strain is non-linear

(B) The variation of strain is linear and that of stress is no-linear

(C) The variation of both stress and strain is linear

(D) The variation of both stress and strain is non-linear

Answer: (B)

Exp: At

Strain variation Stress variation

L L / 2 L

XP P

X



11

21. For the beam shown below, the stiffness coefficient K22 can be written as

(A) 2

6EI

L (B)

3

12EI

L (C)

3EI

L (D)

2

EI

6L

Answer: (B)

Exp:

22. The penetration value of a bitumen sample tested at o25 C is 80. When this sample is heated

to o60 C and tested again, the needle of the penetration test apparatus penetrates the bitumen

sample by d mm. The value of d CANNOT be less than ____ mm.

Answer: 8

23. The development length of a deformed reinforcement bar can be expressed as

s bd(1 / k)( / ).φσ τ From the IS:456-2000, the value of k can be calculated as ____ .

Answer: 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.

L

A, E, I

2

3

Note :1, 2 and 3

are the d.o.f

1

2

6EI

L

∆∆

2

31

3

12EI

L

∆

22 3

12EIK

L=



12

24. Total Kjeldahl Nitrogen (TKN) concentration (mg/L as N) in domestic sewage is the sum of

the concentrations of:

(A) organic and inorganic nitrogen in sewage

(B) organic nitrogen and nitrate is sewage

(C) organic nitrogen and ammonia is sewage

(D) ammonia and nitrate in sewage

Answer: (C)

Exp: Total Kjeldahl Nitrogen (TKN) = Ammonia (60%) + Organic Nitrogen (40%)

25. For the beam shown below, the value of the support moment M is ____ kN-m.

Answer: 5

Exp:

Q.No-26-55 Carry Two Marks Each

26. The directional derivative of the field u(x,y,z) 2x 3yz= − in the direction of the vector

ˆ ˆ ˆ(i j 2k) at point (2, 1,4)+ − − is ____ .

Answer: -5.72

3 m 1 m 1 m 3 m

20kN

M

EI EI EI

Internal hinge

10kN

1m3m

10 15kN m

2

×= −



13

Exp: Let u(x,y,z) = x2-3yz

( )

( ) ( )

( )

( ) ( )

2, 1,4

a i j 2k and P 2, 1,4

u u uu i j k

x y z

i2x j 3z k 3y

u 4i 12j 3k

a 1 1 4 6

directionalderivative u.a

i j 2k4i 12 j 3k .

6

4 12 6

6

145.72

6

−

= + − −

∂ ∂ ∂∇ = + +

∂ ∂ ∂

= + − + −

∇ = − +

= + + =

= ∇

+ −= − +

− −=

−= = −

�

�

�

27. For formation of collapse mechanism in the following figure, the minimum value of Pu is

cMp/L. p pM and 3M denote the plastic moment capacities of beam sections as shown in this

figure. The value of c is ____ .

Answer: 13.33

Exp: Mechanism-I

( )P P U

L3M . M 2 MP. P

4θ+ θ + θ = × ×θ

P U

L6M . P . .

4⇒ θ = θ

PU

MP 24

L⇒ =

2 m

p3 MpM

uP

1 m 1 m

uPPM

θ

2θ

PM

P3M θ



14

Mechanism-II

( )

( )

P P P U

P P P U

P U

P PU

1. 3. 3

L3M . M M . P

4

L3M M 3 M .3 P 3

4

L10M . P 3

4

M M40P . 13.33

3 L L

So, C 13.33

φ = θ ⇒ φ = θ

θ + θ + φ + φ = × φ

⇒ θ + θ + θ + θ = × θ×

⇒ θ = × θ×

⇒ = =

=

28. A tapered circular rod of diameter varying from 20 mm to 10 mm is connected to another

uniform circular rod of diameter 10 mm as shown in the following figure. Both bars are made

of same material with the modulus of elasticity, 5E 2 10 MPa.= × When subjected to a load

P 30 kN,= π the deflection at point A is ____ mm.

Answer: 15

Exp:

1

1 2

6

5

4P.L

d d E

4 30 2 10

20 10 2 10

6mm

∆ =π ×

× π× ×=

π× × × ×=

2m

1.5 m

2d 10 mm=

A

P 30 kN= π

1d 20mm=

30π

20mm

10mm

30π

uPPM

φ

θ + φ

PM

P3M θ



15

2

E

6

5

P L

A

4 30 1.5 10

10 10 2 10

9mm

×∆ =

× π× ×=

π× × × ×=

1 2

15mm∆ = ∆ + ∆ =

29. A water tank is to be constructed on the soil deposit shown in the figure below. A circular

footing of diameter 3m and depth of embedment 1m has been designed to support the tank.

The total vertical load to be taken by the footing is 1500 kN. Assume the unit weight of water

as 10kN/ 3m and the load dispersion pattern as 2V:1H. The expected settlement of the tank

due to primary consolidation of the clay layer is ____ mm.

Answer: 53.236

Exp:

( ) ( )

( )

c 00

0 0

0

2

2

02

CSettlement H log

1 e

15 2 18 10 6 18 10 *5

118kN m

15008.488kN m

3 6 64

σ + ∆σ= + σ

σ = × + − × + −

=

∆σ = =π + +

Silty Sand

Sand

Normally

consolidated

clay

Dense Sand

3Saturated unit weight 18kN / m .=

3Bulk unit weight 15 kN / m=

3

2

Saturated unit weight 18 kN / m

Compression index 0.3

Initial void ratio 0.7

Coefficient of consolidation 0.004cm / s

==

=

=

2m

6m

10m

30π

30π

2

6

10

31

6 615

12



16

10

0.3 118 8.488H 10log

1 0.7 118

0.0532m

H 53.236mm

+ ∆ = × +

=∆ =

30. Consider the following differential equation:

( )y yx(ydx xdy)cos y xdy ydx sin

x x+ = −

Which of the following is the solution of the above equation (c is an arbitrary constant)?

(A) x y

cos cy x

= (B) x y

sin cy x

= (C) y

xycos cx

= (D) y

xysin cx

=

Answer: (C)

Exp: Given D.E

( ) ( )

( ) ( )

( ) ( )

( ) ( )2

y yx ydx xdy cos y xdy ydx sin

x x

y yx ydx xdy cos sin y xdy ydx 0

x x

y xdy ydxy yydx xdy cos sin 0

x x x

y y xdy ydxydx xdy cos xy sin 0

x x x

yBy observing, the above equation is d (xy)cos

x

+ = −

⇒ + + − − =

− ⇒ + + − =

− ⇒ + + − =

0

yByintegrating,xycos c

x

=

=

31. The composition of an air-entrained concrete is given below:

3

3

3

3

:184 kg / mWater

Ordinary PortlandCement(OPC) :368 kg / m

Sand : 606kg / m

Coarse aggregate :1155 kg / m

Assume the specific gravity of OPC, sand and coarse aggregate to be 3.14, 2.67 and 2.74,

respectively, The air content is_________ liters/ 3m .

Answer: 51

Exp: C S aw a

C S a

M M MV V 1+ + + + =

ρ ρ ρ

V

368 606 1155 184V 1.0

3.14 1000 2.67 1000 2.74 1000 1000⇒ + + + + =

× × ×



17

V

0.117 0.227 0.421 0.184 V 1.0⇒ + + + + =

V

V 0.051⇒ =

30.051 1000 51 50.32 l m= × = �

32. An earth embankment is to be constructed with compacted cohesionless soil. The volume of

the embankment is 35000 m and the target dry unit weight is 16.2 3kN / m . Three nearby

sites (see figure below) have been identified from where the required soil can be transported

to the construction site. The void ratios (e) of different sites are shown in the figure. Assume

the specific gravity of soil to be 2.7 for all three sites. If the cost of transportation per km is

twice the cost of excavation per 3m of borrow pits, which site would you choose as the most

economic solution? (Use unit Weight of water 310kN / m )= .

(A) Site X (B) Site Y (C) Site Z (D) Any of the sites

Answer: (B)

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 4910.18m

V 5089.82 m

⇒ =

=

=

SiteX

e 0.6=

SiteY

e 0.7=

Site Z

e 0.64=

140 km

Construction

site



18

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

= × + × ×== × + × × =

= × + × × =

33. The concentration of Sulfur Dioxide 2

(SO ) is ambient atmosphere was measured as 330 g / m .µ Under the same conditions, the above

2SO concentration expressed in ppm is

___.

Given : 3P / (RT) 41.6mol / m ;= where P=Pressure; T=Temperature ; R=universal gas

constant; Molecular weight of 2

SO 64.=

Answer: 0.0133

Exp: 1 m3 of air has 30 mg SO2

6 3

2

2

3

3

2

10 m of air has 30g SO

30mol SO

64

nRT n 30 64 molV

P P RT 41.6 mol m

300.0113m

64 41.6

Concentration of SO in ppm 0.0113ppm

=

= = =

= =×

=

34. The 4-hr unit hydrograph for a catchment is given in the table below. What would be the

maximum ordinate of the S-curve 3(in m / s) derived from this hydrograph?

Time(hr) 0 2 4 6 8 10 12 14 16 18 20 22 24

Unit

hydrograph

ordinate(m3/s)

0

0.6

3.1

10

13

9

5

2

0.7

0.3

0.2

0.1

0

Answer: 22

Exp:

Time UHO S-curve Addition SA

0 0 0

2 0.6 0.6

4 3.1 0 3.1

6 10 0.6 10.6

8 13 3.1 16.1

10 9 10.6 19.6

12 5 16.1 21.1

14 2 19.6 21.6

16 0.7 21.1 21.8

18 0.3 21.6 21.9



19

20 0.2 21.8 22

22 0.1 21.9 22

24 0 22 22

Maximum S-curve ordinate is 22.

35. The drag force, FD, on a sphere kept in a uniform flow field depends on the diameter of the

sphere, D; flow velocity, V; fluid density, ;ρ and dynamic viscosity, µ . Which of the

following options represents the non-dimensional parameters which could be used to analyze

this problem?

(A) DFand

VD VD

µρ

(B) D

2

F VDand

VD

ρρ µ

(C) D

2 2

F VDand

V D

ρρ µ

(D) D

3 3

Fand

V D VD

µρ ρ

Answer: (C)

Exp: vD

Re dimensionles parameterρ

= →µ

( )( )

2

D

22 2 2

3 2

F kg m sdimensionless parameter

kg mV D m

m s

−→

ρ ×

36. Consider the singly reinforced beam section given below (left figure). The stress block

parameters for the cross-section from IS:456-2000 are also given below (right figure). The

moment of resistance for the given section by the limit state method is _________ kN-m.

Answer: 42.82

Exp: 2 2

stA 4 (12) 453 mm4

π= × × =

0.36 fck.b.xu = 0.87 fy Ast

4-12 Φ

Fe415

300 mm

M25

d

ux

u0.42x

ck u0.36 f x

u,maxx 0.4d

for Fe415

=

200 mm



20

y st

ck

0.87f A 0.87 415 453x

0.36f .b 0.36 25 200

90.86mm

ν× ×

⇒ = =× ×

=

( )( )

,max

, max

y st

x 0.48d

0.4 300 120mm

x x so U.R.section

M 0.87 f A d 0.42x

0.87 415 453 300 42 90.86 42.82kNm

ν

ν ν

ν ν

=

= × =<

= × × × −

= × × × − × =

37. Two reservoirs are connected through a 930 m long, 0.3 m diameter pipe, which has a gate

valve. The pipe entrances is sharp (loss coefficient = 0.5) and the valve is half-open (loss

coefficient = 5.5). The head difference between the two reservoirs is 20 m. Assume the

friction factor for the pipe as 0.03 and g = 10 m/s2. The discharge in the pipe accounting for

all minor and major losses is _________ m3/s.

Answer: 0.1413

Exp: Total loss = 20 m

( )

2 2 2 2

22 2 2

2

22 3

0.5 v f L v 5.5v v20

29 d 2g 2g 2g

0.03 930 v20 2 10 0.5v 5.5v v

0.3

400v 4

100

v 2m s

d v 0.3 2 0.1413 m s4 4

× ×⇒ = + × + +

× ×⇒ × × = + + +

⇒ = =

⇒ =π π

θ = × × = × × =

38. A sign is required to be put up asking drivers to slow down to 30 km/h before entering Zone

Y (see figure). On this road, vehicles require 174 m to slow down to 30 km/h (the distance of

174 m includes the distance travelled during the perception-reaction time of drivers). The sign

can be read by 6/6 vision drivers from a distance of 48 m. The sign is placed at distance of x

m from the start of Zone Y so that even a 6/9 vision driver can slow down to 30 km/h before

entering the zone. The minimum value of x is _________ m.

Direction of vehicle movement

Sign

Road

Start of Zone Y

Zone Yx



21

Answer: 142

Exp: For a 6/6 person, driver can see from a distance of 48 m.

For a 6/9 person, driver can see from distance6

48 32m9

= × =

The vehicle requires 174 m to slow down to 30 km/hr

So, minimum distance, X=174-32=142 m.

39. The quadric equation 2x 4x 4 0− + = is to be solved numerically, starting with the initial

guess 0

x 3.= The Newton-Raphson method is applied once to get a new estimate and then

the Secant method is applied once using the initial guess and this new estimate. The estimated

value of the root after the application of the Secant method is ___________.

Answer: 2.333

Exp: f(x) = x2-4x+4

x0 = 3

( )f ' x 2x 4= −

By Newton Raphson method ( )( )

0

1 0

0

f xx x

f ' x

13 2.5

2

= −

= − =

For secant method let x0 = 2.5 and x1 = 3

By secant method ( ) ( ) ( )1 0

2 1 1

1 0

x xx x f x

f x f x

−= −

−

( )

( ) ( ) ( )

( )

3 2.53 f 3

f 3 f 2.5

0.53 1

1 0.25

0.53

0.75

3 0.6667

2.333

−= −

−

= − ×−

= −

= −=

40. Consider the following complex function:

( )( )( )2

9f z

z 1 z 2=

− +

Which of the following one of the residues of the above function?

(A) 1− (B) 9/16 (C) 2 (D) 9

Answer: (A)



22

Exp: ( )( )( )2

9f 3

z 1 z 2=

− +

z = 1 is a simple pole

z = -2 is a pole of order 2

( ) ( )( )( )2z 1 z 1

9Resf z lim z 1

z 1 z 2

91

9

= → = − − +

= =

( ) ( )( )( )

( )

2z 2 z 2

2z 2

1 d 9Resf z lim z 2 .

1! dz z 1 z 2

9lim

z 1

91

9

2

=− →−

→−

= + − +

−=

−

−= = −

41. A short reach of a 2 m wide rectangular open channel has its bed level rising in the direction

of flow at a slope of 1 m in 10000. It carries a discharge of 4 m3/s and its Manning’s

roughness coefficient is 0.01. The flow in this reach is gradually varying. At a certain section

in this reach, the depth of flow was measured as 0.5m. The rate of change of the water depth

with distance, dy/dx, at this section is __________ (use g = 10 m/s2).

Answer: 0.0032

Exp: Adverse slope1

10000= −

3

0 f

2

r

r

2/3 1/2

f

1/2

f 2/32/3

3

f

3

3

2

4 m / s, n 0.01, y 0.5 m

S Sdy

dx 1 F

V Q 4F 1.79

gy By gy 2 0.5 10 5

1Q AR S

n

Q n 4 0.01S

A R 2 0.52 0.5

2 1

S 6.92 10

16.92 10

dy 10000 3.2 10 0.0032dx 1 (1.79)

−

−

−

θ = = =−

=−

= = = =× × ×

=

× ×= =

× × × × +

= ×

− ×= = × =

−



23

42. In a survey work, three independent angles X, Y and Z were observed with weights WX, WY,

WZ, respectively. The weight of the sum of angles X, Y and Z is given by:

(A) X Y Z

1 1 11

W W W

+ +

(B)

X Y Z

1 1 1

W W W

+ +

(C) X Y Z

W W W+ + (D) 2 2 2

X Y ZW W W+ +

Answer: (A)

43. A hydraulic jump is formed in a 2m wide rectangular channel which is horizontal and

frictionless. The post-jump depth and velocity are 0.8 m and 1 m/s, respectively. The pre-

jump velocity is ___________ m/s. (use = 10 m/s2).

Answer: 4.94

Exp: B=2m, 2 2

y 0.8m, U 1m / s= =

22

2

U 1F 0.35

g.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

= − + +

−⇒ = + + × =

1

y 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.

= =⇒ × = ×⇒ =

44. A 20 m thick clay layer is sandwiched between a silty sand layer and a gravelly sand layer.

The layer experiences 30 mm settlement in 2 years.

Given

( )

2

V

10

Ufor U 60%

T 4 100

1.781 0.933 log 100 U for U 60%

π ≤ = − − >

Where Tv is the time factor and U is the degree of consolidation in %.

If the coefficient of consolidation of the layer is 0.003 cm2/s, the deposit will experience a

total of 50 mm settlement in the next ________ years.

Answer: 4.43

Exp:

silty sand

20mclay

gravel



24

U 2

003 2 86400 365T 0.189

20100

2

× × ×= =

×

2U 0.189 U 0.49 60%4

30Consolidation 61.2.2mm

0.49

π= ⇒ = ≤

= =

Degree of consolidation for 50mm settlement

( )

( )

v 10

V

2

22

4 4

50U 0.817 81.7%

61.22

T 1.784 0.933 log 100 U

C t0.608

d

0.608 100.608 Ht s

0.003 10 0.003 10

202666667 s

6.43yr

Additional number of years 6.43 2 4.43 years

− −

= = =

⇒ = − −

×= =

××⇒ = =

× ×=

== − −

45. A bracket plate connected to a column flange transmits a load of 100 kN as shown in the

following figure. The maximum force for which the bolts should be designed is __________

kN.

Answer: 156.20

Exp: D

P 100F 20kN

n 5= = =

100 kN

600

75

75

75 75 All dimensions are in mm



25

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 =

46. Consider a primary sedimentation tank (PST) in a water treatment plant with surface

Overflow Rate (SOR) of 40 m3/m

2/d. The diameter of the spherical particle which will have

90 percent theoretical removal efficiency in this tank is ___________ m.µ Assume that

settling velocity of the particles in water is described by Stokes’s Law.

Given Density of water = 1000 kg/m3; Density of particle = 2650 kg/m

3; g = 9.81 m/s

2;

Kinematic viscosity of water ( ) 6 2v 1.10 10 m s−= ×

Answer: 22.58

Exp: s

s

V '% removal 100

V= ×

s s

V ' 0.9V=

0.9 40m s

86400

×=

θ

bFt

F

75

75

θ



26

( )2

S w

1 g 0.9 40d

18 86400

×⇒ × × ρ − ρ =

µ

w

S w

0.9 40 18 V.d

86480(G 1) g

× × × ρ⇒ =

− × ρ ×

d 22.58 m⇒ = µ

47. A non-homogenous oil deposit consists of a silt layer sandwiched between a fine-sand layer at

top and a clay layer below. Permeability of the silt layer is 10 times the permeability of the

clay layer and one-tenth of the permeability of the sand layer. Thickness of the silt layer is 2

time the thickness of the sand layer and two-third of the thickness of the clay layer. The ratio

of equivalent horizontal and equivalent vertical permeability of the deposit is ___________.

Answer: 10.967

Exp:

( )( )( )

1 1

2 2

3 3

H 1 K finesand

H 2 K silt

H 3 K clay

2 3 1

1 2

3

1 3

1 2

1k 10k k

10

k 10k

10 10k

k 100k

k 10k

= =

⇒ == ×

==

H2 = 2H1

2 3 3 2 1 1

3 1

1 1 1 1 1 11 1 2 2 3 3

x

1 2 3 1 1 1

1 1

x 1

1

1 2 3 1y

3 1 1 11 2

1 1 11 2 3

x

y

2 3 3H H H H 2H 3H

3 2 2

H 3H

1 1K H K 2H K 3H

K H K H K H 10 100KH H H H 2H 3H

2 31 K H

12310 100K K

6H 100 6

H H H 6HK

H H 2H 10 3H 100H H

K K KK K K

K 123 321

K 100 6 6

= ⇒ = = × =

=

+ × + ×+ += =

+ + + +

+ + = =

×+ +

= =× ×

+ ++ +

= ××

10.967=



27

48. In a region with magnetic declination of o2 E, the magnetic Fore bearing (FB) of a line AB

was measured as oN79 50 E.′ There was a local attraction at A. To determine the correct

magnetic bearing of the line, a point O was selected at which there was no local attraction.

The magnetic FB of line AO and OA were observed to be oS52 40 E′ and oN50 20 W,′

respectively. What is the true FB of line AB?

(A) oN81 50 E′ (B) oN82 10 E′ (C) oN84 10 E′ (D) oN77 50 E′

Answer: (C)

Exp: 2 Eδ = °

Magnetic F.B. of AB = N79O50’E = 79

O50.

Correct FB of OA = N50O20’W = 309

O40’

OCorrect B.B of OA 129 40'∴ =

observed F.B. of AO observed BB of OA=∵

O O552 40'E 127 20'= =

Error = M.V- T.V = -2O20’

Correction + 2O20’

T.B. of FB of AB N 79 50'E 2 2 20'= ° + + °

= N84 10'E°

49. For the 2D truss with the applied loads shown below, the strain energy in the member XY is

___________ kN-m. For member XY, assume AE = 30 kN, where A is cross-section area and

E is the modulus of elasticity.

5kN

3m

3m

YX

10 kN

3m

3m



28

Answer: 5

Exp:

RA×3 + 10×9 = 0

⇒ RA = -30 kN

RG = 35 kN

Taking joint A

Joint G

Joint B

Fx = 10 kN

2

E

F L 10 10 3U 5kN m

2A 2 30

× × ×= = = −

×

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



29

50. Two beam are connected by linear spring as shown in the following figure. For a load P as

shown in the figure, the percentage of the applied load P carried by the spring is

___________.

Answer: 33.33

Exp:

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

− =

⇒ = ⇒ = =

LP

EI

EI( )3

sK 3EI 2L=

P

R

R

R

R



30

51. The smallest and largest Eigen values of the following matrix are:

3 2 2

4 4 6

2 3 5

− − −

(A) 1.5 and 2.5 (B) 0.5 and 2.5 (C) 1.0 and 3.0 (D) 1.0 and 2.0

Answer: (D)

Exp:

3 2 2

Let A 4 4 6

2 3 5

− = − −

Characteristic equation is

|A-λI| = 0

( )( )( )( )( )

3 2

2

3 2 2

04 4 6

2 3 5

4 5 2 0

1 3 2 0

1 1 2 0

1,2

− λ −⇒ =− − λ

− − λ

⇒ λ − λ + λ − =

⇒ λ − λ − λ + =

λ − λ − λ − =

λ =

52. A square footing (2mx 2m) is subjected to an inclined point load, P as shown in the figure

below. The water table is located well below the base of the footing. Considering one-way

eccentricity, the net safe load carrying capacity of the footing for a factor of safety of 3.0 is

__________ kN.

The following factors may be used.

Bearing capacity factors: Nq = 33.3, N 37.16;γ = Shape factors: qs sF F 1.314;γ= = Depth

factors: qd dF F 1.113;γ= = Inclination factors: qi iF 0.444, F 0.02γ= =

0.85m

2m

o30

PGL

1m

3

o

Unit weight 18kN m

Cohesion 0

Friction angle 35

==

=



31

Answer: 450

Exp:

( )

nusafc

nu c q

nu q

qq

3

q cN qN 0.5 BN 8

C 0

q q N 1 0.5 BN

γ

γ

=

= + + γ − ∆

=

= − + γ

( )( )

( )

ns q qs qd qp s o p

ns

2

1q q N 1 F F F 0.5 BN F F F

3

118 1 33.3 1 1.314 1.113 0.444 2 181

q 23

37.16 1.314 1.113 0.02

397.03132.364kN m

3

γ γ γ γ= − × + + γ × × ×

× − × × × + × × × = × × ×

= =

For one way shear (eccentricity) area to be reduced

Reduced area of footing = 2×1.7 = 3.4m2

Load carrying capacity = 132.364×3.4 = 450.kN

53. In a catchment, there are four rain-gauge stations, P, Q, R, and S. Normal annual precipitation

values at these stations are 780 mm, 850 mm, 920 mm, and 980 mm, respectively. In the year

2013, stations Q, R, and S, were operative but P was not. Using the normal ratio method, the

precipitation at station P for the year 2013 has been estimated as 860 mm. If the observed

precipitation at stations Q and R for the year 2013 were 930 mm and 1010 mm, respectively;

what was the observed precipitation (in mm) at station S for that year?

Answer: 1076.2

Exp: p Qs R

s p Q R

s

s

P PP P1

N 3 N N N

P 1 860 930 1010

980 3 780 850 920

P 1076.20 mm

= + +

⇒ = + +

⇒ =

2

0.85 0.85

2



32

54. The acceleration-time relationship for a vehicle subjected to non-uniform acceleration is,

( ) t

0

dvv e

dt

−β= α − β

Where, v is the speed in m/s, t is the time in s, andα β are parameters, and 0

v is the initial

speed in m/s. If the accelerating behavior of a vehicle, whose drive intends to overtake a slow

moving vehicle ahead, is described as,

( )dvv

dt= α − β

Considering 22m s ,α = 10.05s−β = and 2dv1.3 m s

dt= at t = 3 s, the distance (in m)

travelled by the vehicle in 35 s is ____________.

Answer: 900.83

Exp: ( ) T

O

dVV e

dt

−β= α − β

( )( )

( )

( )

t

O

t

O

0

0

0

00

t

0

dv V e .dt

V e

t 0, V V

VV C

VC V C

V eV

−β

−β

−β

= α − β ×

α − β=

−β= =

α − β⇒ = +

−βα − β α

= + ⇒ =β β

α − αβ ×⇒ =

β

∫ ∫

( )

( )

( ) ( )

( )( ) ( )

0

0

t0 0

2

3

0

t 3

0 3

t0

2 3

35 0.05

2 3x0.05

t Vx e 1

dvV e 1.3

dt

1.3V

e

t 1.3x e 1

e

1.3 e 12 35

0.05 0.05 e

1400 499.17 900.83m

−β

− β

=

− β

−β− β

− ×

−

α α − β= + −

β β

= α − β =

⇒ α − β =

α= + −

β β

−×= +

= − =



33

55. On a circular curve, the rate of super elevation is e. While negotiating the curve a vehicle

comes to a stop. It is seen that the stopped vehicle does not slide inwards (in the radial

direction). The coefficient of side friction is f. Which of the following is true?

(A) e f≤ (B) f e 2f< <

(C) e 2f≥ (D) None of the above

Answer: (A)

Exp:

N

f mg sin≥ θ

( )f mgcos mgsin

f tan

f e

e f

⇒ θ = θ

⇒ ≥ θ⇒ ≥⇒ ≤

Nf

N

mg sin θ

θ

mgmgcosθ

ce-gate-2015 paper

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