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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 Caf _____ cleared by the censor board with no cuts last week, but the films 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 Caf 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 Imports120110

10090

80

706050

40

30

20

100

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 Alexanders kingdom extended to Indian borders after the conquest of Persia, he

was keen to move further. Answer: (A)

y

pi

( )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: sVV n 1n

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

3. The integral 21

x 22 1

xx 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



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 Mannings 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: 2

2 1 1323 2 2full

1 1 DQ .AR S Q . .D . sn n 4 4

pi = =

212 32

half

full

half

1 D DQ . . sn 8 4

Q 2Q

pi =

=

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 12Activity 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, n is __________ MPa.

Answer: 0

Exp: x y x yn cos22 2 +

= +

100 100 100 ( 100)cos90 0

2 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: 20001000

= + = + =

= =

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

( ) ( )31 1

2 2

Component Composition Density% weight kg m

X cY c

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

(A) 1 2

1 2

100c c

+

(B) 1 21 2

100c c

+

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

Answer: (A)

100MPa

100MPa

100MPa

100MPa

n

45



7

Exp: Let density of sludge is

1 2 1 2

1 2

1 2

1 2

c c c c

100c c

+= +

=+

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 Skemptons pore pressure parameter B is;

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

Exp: 3

U 80B 0.8100

= = =



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 53 p y 10

AX B

=

=

Augmented matrix 2 3 5[A / B]3 p 10

=

2 2 1R 2R 3R 2 3 50 2p 9 5

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

2p 9 09p 4.52

=

= =

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 2x

v x= and the density varies as 1 .x

= 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 xV V1 0 1

y x y xV xy

+ =

+ =

+ = = =

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 0p(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 10 otherwise

= =

= =

given q = 0.4

( )p x,q 0.4 if X 00.6 if X 10 otherwise

= =

= =

=

( )X 0 1

p X x 0.4 0.6

=

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

22

i i

2 2 2 2i 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 0.60.6 0.360.24

=

= = + =

= = + =

=

=

=



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, derivers 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) 26EIL

(B) 312EI

L (C) 3EI

L (D) 2

EI6L

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

Answer: 6.4

Exp: sdbd

L4

=

But for deformed bars bd is increased by 60%.

So,

st s

bd bd

Ld4 1.6 6.4

= =

So, k=6.4.

L

A, E, I

2

3

Note :1, 2 and 3are the d.o.f

1

26EI

L

2

31

312EI

L

22 312EIK

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

(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 1 5kN m2

=



13

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

( )

( ) ( )( )

( ) ( )

2, 1,4

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

u i j kx y z

i2x j 3z k 3yu 4i 12j 3k

a 1 1 4 6

directionalderivative u.ai j 2k

4i 12 j 3k .6

4 12 66

14 5.726

= +

= + +

= + +

= +

= + + =

= +

= +

=

= =

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 4+ + =

P UL6M . P . .4

=

PU

MP 24L

=

2 m

p3 MpM

uP1 m 1 m

uPPM

2PM

P3M



14

Mechanism-II

( )( )

P P P U

P P P U

P U

P PU

1. 3. 3L3M . M M . P4

L3M M 3 M .3 P 34

L10M . P 34

M M40P . 13.333 L L

So, C 13.33

= = + + + =

+ + + =

=

= =

=

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,= pi the deflection at point A is ____ mm.

Answer: 15 Exp:

11 2

6

5

4P.Ld d E

4 30 2 1020 10 2 10

6mm

=pi

pi =

pi =

2m

1.5 m

2d 10 mm=

A

P 30 kN= pi

1d 20mm=

30pi

20mm

10mm

30pi

uPPM

+ PM

P3M



15

2E

6

5

P LA

4 30 1.5 1010 10 2 10

9mm

=

pi =

pi =

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

20

2

CSettlement H log1 e15 2 18 10 6 18 10 *5118kN m

1500 8.488kN m3 6 6

4

+ =

+

= + +

=

= =pi

+ +

Silty Sand

Sand

Normallyconsolidated

clay

Dense Sand

3Saturated unit weight 18kN / m .=

3Bulk unit weight 15 kN / m=

3

2

Saturated unit weight 18 kN / mCompression index 0.3Initial void ratio 0.7Coefficient of consolidation 0.004cm / s

=

=

=

=

2m

6m

10m

30pi

30pi

2

6

10

31

6 615

12



16

100.3 118 8.488H 10log

1 0.7 1180.0532m

H 53.236mm

+ = + =

=

30. Consider the following differential equation:

( )y yx(ydx xdy)cos y xdy ydx sinx x

+ =

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

(A) x ycos cy x

= (B) x ysin cy x

= (C) yxycos cx

= (D) yxysin 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 0x x x

y y xdy ydxydx xdy cos xy sin 0x x x

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

+ =

+ + =

+ + =

+ + =

0

yByintegrating,xycos cx

=

=

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

3

3

3

3

:184 kg / mWaterOrdinary PortlandCement(OPC) :368 kg / mSand : 606kg / mCoarse 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 a w aC S a

M M M V V 1+ + + + =

V368 606 1155 184 V 1.0

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



17

V0.117 0.227 0.421 0.184 V 1.0 + + + + =

VV 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 z1 2 3

VV VV1 e 1 e 1 e 1 e

= = =

+ + + +

d wG 2.67

. 16 101 e 1 e

e 0.67

= = + +

=

yx zVV V50001.67 1.6 1.64 1.7

= = =

3x

3y

3z

V 4790.42 mV 4910.18m

V 5089.82 m

=

=

=

SiteXe 0.6=

SiteYe 0.7=

Site Ze 0.64=

140 km

Constructionsite



18

x

y

z

C C 479042 2 C 1405070.42 C

C C 4910.18 2 C 80 5070.18CC 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 . 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 2SO 64.=

Answer: 0.0133 Exp: 1 m3 of air has 30 mg SO2

6 32

2

3

3

2

10 m of air has 30g SO30

mol SO64

nRT n 30 64 molVP P RT 41.6 mol m

30 0.0113m64 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, ; and dynamic viscosity, . Which of the following options represents the non-dimensional parameters which could be used to analyze this problem?

(A) DF andVD VD

(B) D 2F VD

andVD

(C) D2 2F VD

andV D

(D) D3 3F

andV D VD

Answer: (C)

Exp: vD Re dimensionles parameter =

( )( )

2D

22 2 2

3 2

F kg m sdimensionless parameter

kg mV D mm s

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 2stA 4 (12) 453 mm4pi

= =

0.36 fck.b.xu = 0.87 fy Ast

4-12 Fe415

300 mm

M25

d

ux

u0.42x

ck u0.36 f x

u,maxx 0.4dfor Fe415

=

200 mm



20

y st

ck

0.87f A 0.87 415 453x

0.36f .b 0.36 25 20090.86mm

= =

=

( )( )

,max

, max

y st

x 0.48d0.4 300 120mm

x x so U.R.section

M 0.87 f A d 0.42x0.87 415 453 300 42 90.86 42.82kNm

=

= =

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 2003 2 86400 365T 0.189

20 1002

= =

2U 0.189 U 0.49 60%4

30Consolidation 61.2.2mm0.49

pi= =

= =

Degree of consolidation for 50mm settlement

( )

( )

v 10

V2

22

4 4

50U 0.817 81.7%61.22

T 1.784 0.933 log 100 UC t0.608

d0.608 100.608 H

t s0.003 10 0.003 10

202666667 s6.43yr

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: DP 100F 20kNn 5

= = =

100 kN

600

75

75

75 75 All dimensions are in mm



25

t 2 2

(P.d)r 100 600 75 2F 141.42kNr 4 (75 2)

= = =

2 2R D t D t

2 2

F F F 2 F F cos

1(20) (141.42) 2 20 141.422

156.20kN

= + +

= + +

=

o

1cos

245 .

=

=

46. Consider a primary sedimentation tank (PST) in a water treatment plant with surface Overflow Rate (SOR) of 40 m3/m2/d. The diameter of the spherical particle which will have 90 percent theoretical removal efficiency in this tank is ___________ m. Assume that settling velocity of the particles in water is described by Stokess Law.

Given Density of water = 1000 kg/m3; Density of particle = 2650 kg/m3; g = 9.81 m/s2; Kinematic viscosity of water ( ) 6 2v 1.10 10 m s=

Answer: 22.58

Exp: ss

V '% removal 100V

=

s sV ' 0.9V=

0.9 40m s

86400

=

bFtF

75

75



26

( )2 S w1 g 0.9 40d18 86400

=

w

S w

0.9 40 18 V.d86480(G 1) g

=

d 22.58 m =

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 finesandH 2 K siltH 3 K clay

2 3 1

1 2

3

1 3

1 2

1k 10k k10

k 10k10 10k

k 100kk 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 11

1 2 3 1y

3 1 1 11 2

1 1 11 2 3

x

y

2 3 3H H H H 2H 3H3 2 2

H 3H1 1K H K 2H K 3HK H K H K H 10 100K

H H H H 2H 3H2 31 K H

12310 100K K6H 100 6

H H H 6HK H H 2H 10 3H 100H HK K KK K K

K 123 321K 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 E = Magnetic F.B. of AB = N79O50E = 79O50.

Correct FB of OA = N50O20W = 309O40

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:

RA3 + 109 = 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 m2A 2 30

= = =

10kN

5kN

3m

3m

3m

D

E

F

G

AR

B

C

3m GR

A10kN

30kN

10kN

30kN

10kN

35kN10kN

10 2

10 230

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

RKR 2L

3EI2R.L3EI

=

=

=

3 3 3

3 3

PL RL 2RL3EI 3EI 3EI

PL 3RL PR 33.33%.3EI 3EI 3

=

= = =

LP

EI

EI( )3sK 3EI 2L=

P

R

R

R

R



30

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

3 2 24 4 62 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 62 3 5

=

Characteristic equation is |A-I| = 0

( )( )( )( )( )

3 2

2

3 2 204 4 6

2 3 54 5 2 01 3 2 0

1 1 2 01,2

=

+ = + =

= =

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; = Shape factors: qs sF F 1.314;= = Depth

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

0.85m

2m

o30

PGL

1m

3

o

Unit weight 18kN mCohesion 0Friction angle 35

=

=

=



31

Answer: 450

Exp:

( )

nusafc

nu c q

nu q

qq3

q cN qN 0.5 BN 8C 0

q q N 1 0.5 BN

=

= + + =

= +

( )( )( )

ns q qs qd qp s o p

ns

2

1q q N 1 F F F 0.5 BN F F F3

118 1 33.3 1 1.314 1.113 0.444 2 181q 23 37.16 1.314 1.113 0.02397.03 132.364kN m

3

= + +

+

=

= =

For one way shear (eccentricity) area to be reduced

Reduced area of footing = 21.7 = 3.4m2 Load carrying capacity = 132.3643.4 = 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 Rs p Q R

s

s

P PP P1N 3 N N N

P 1 860 930 1010980 3 780 850 920P 1076.20 mm

= + +

= + +

=

2

0.85 0.852



32

54. The acceleration-time relationship for a vehicle subjected to non-uniform acceleration is, ( ) t0dv v edt

=

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

( )dv vdt

=

Considering 22m s , = 10.05s = and 2dv 1.3 m sdt

= at t = 3 s, the distance (in m) travelled by the vehicle in 35 s is ____________.

Answer: 900.83

Exp: ( ) TOdV V edt

=

( )( )

( )

( )

tO

tO

0

00

00

t0

dv V e .dt

V e

t 0, V VV

V C

VC V C

V eV

=

=

= =

= +

= + =

=

( )( )

( ) ( )( )

( ) ( )

0

0

t0 02

30

t 3

0 3

t02 3

35 0.05

2 3x0.05

t Vx e 1

dv V e 1.3dt

1.3Ve

t 1.3x e 1

e

1.3 e 12 350.05 0.05 e

1400 499.17 900.83m

=

= +

= =

=

= +

= +

= =



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:

Nf mg sin

( )f mgcos mgsinf tanf ee f

=

NfN

mg sin

mgmgcos

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