CE Forenoon-Final New

8/9/2019 CE Forenoon-Final New

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CE-GATE-2015

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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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