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QUESTION: 1

“Wanted a two bedroom flat in the court area for immediate possession” - An Advertisement.

Assumptions:

I. Flats are available in the court area

II. Some people will respond to the advertisement

III. It is a practice to give such an advertisement

Solution:

The person needs a flat in court area. It may be or may not be possible to have a court area.

The person hopes that he will get the room because if available people will respond to the advertisement.

It may or may not be practice to give such an advertisement and nothing can be said because of insufficient information in the question.

QUESTION: 2

DIRE

Solution:

QUESTION: 3

The famous playwright has been in the sick bed from the last one week

Solution:

QUESTION: 4

He always _________ you in his letters

Solution:

QUESTION: 5

His health ____________ under the pressure of work

Solution:

QUESTION: 6

A, B and C shoots to hit a target. If A hits the target 4 times in 5 trials, B hits in 3 times in 4 trials and C hits it 2 times in 3 trials. What is the probability that the target is hit by at least 2 persons?

Solution:
Probability that A hits the target = 4/5

Probability that B hits the target = 3/4

Probability that C hits the target = 2/3

P (at least 2) = P(2) + P(3)

Probability that B hits the target = 3/4

Probability that C hits the target = 2/3

P (at least 2) = P(2) + P(3)

QUESTION: 7

Two liquids are mixed in the ratio 4:3 and the mixture is sold at Rs 20 with a profit of % If the first liquid is costlier than the second by Rs 7. Find the sum of costs of both the liquids.

Solution:
Profit =%

Cost of 1 unit of liquid 1 = x+7

Cost of 1 unit of liquid 2 = x

x = 11

x+7 = 18

Total value of the prices = 11+18 = 29

Cost of 1 unit of liquid 1 = x+7

Cost of 1 unit of liquid 2 = x

x = 11

x+7 = 18

Total value of the prices = 11+18 = 29

QUESTION: 8

Henry and Ford worked together to complete a task in 10 days. Had Henry worked with half of his efficiency and Ford at 5 times of his efficiency it would have taken them to finish the job in 50% of the scheduled time. In how many days can Ford complete the job working alone?

Solution:
Let henryâ€™s one day work be x

Let fordâ€™s one day work be y

Solving 2 equations we get, y = 1/30

Hence, Ford can complete the job working alone in 30 days

Let fordâ€™s one day work be y

Solving 2 equations we get, y = 1/30

Hence, Ford can complete the job working alone in 30 days

QUESTION: 9

A new flag is to be designed with six vertical stripes using some or all of the colours- yellow, green, blue and red. Then the number of ways this can be done such that no two adjacent stripes have the same colour out is:

Solution:
There are 6 stripes. The stripe can be coloured in 4ways, in 3, in 3 and so on.Thus, total number of ways =

QUESTION: 10

Find the value of

Solution:

y(y-3) = 0

y = 3

y(y-3) = 0

y = 3

QUESTION: 11

In laboratory compaction tests, the optimum moisture content of soil decreases:

Solution:
Optimum moisture content of soil decreases:

(1) With increase in compaction energy

(2) With increase in coarse grains in the soil

(1) With increase in compaction energy

(2) With increase in coarse grains in the soil

QUESTION: 12

For a matrix =6. The eigen vectors for the matrix are:

Solution:

QUESTION: 13

The equation is to be solved using the Newton Raphson Method. If x = 2is taken as initial approximation of the solution, then the next approximation using this method is:

Solution:

QUESTION: 14

A bag contains 5 white and 8 black balls and a second bag contains 3 white and 7 black balls. A ball is drawn at random from the first bag and placed in the second bag. Find the probability that drawn ball is white.

Solution:

QUESTION: 15

The non destructive test on fresh concrete is done using:

Solution:

Pull out Test

The test measures the force required to pull out a previously cast in steel insert with an embedded enlarged end in the concrete. Thus, it is a type of destructible test.

Ultrasonic Test

An ultrasonic pulse velocity (UPV) test is an in-situ, nondestructive test to check the quality of concrete. In this test, the strength and quality of concrete is assessed by measuring the velocity of an ultrasonic pulse passing through a concrete structure.

Radioactive Test

Radioactive methods of testing concrete can be used to detect the location of reinforcement, measure density and perhaps establish whether honeycombing has occurred in structural concrete units. It is a non-destructible test and is used for hardened concrete rather for fresh concrete.

QUESTION: 16

Curing of concrete by stream under pressure:

1) Increases the compressive strength of concrete

2) Reduces the shear strength of concrete

3) Increases the speed of chemical reaction

Select the correct answer using the codes given below

1) Increases the compressive strength of concrete

2) Reduces the shear strength of concrete

3) Increases the speed of chemical reaction

Select the correct answer using the codes given below

Solution:

QUESTION: 17

The presence of entrained air in concrete results in:

i) Reduced bleeding

ii) Lowering density of concrete

iii) Decrease in strength at all ages

The correct answer is:

i) Reduced bleeding

ii) Lowering density of concrete

iii) Decrease in strength at all ages

The correct answer is:

Solution:

QUESTION: 18

According to Whitneyâ€™s theory of ultimate load method of concrete, the ultimate strain of concrete is assumed to be:

Solution:

QUESTION: 19

A rigid cantilever frame ABC is fixed at C, It carries a point load P at A. Neglecting the axial deformation, the horizontal deflection of the point A will be:

Solution:

QUESTION: 20

For a circular curve of radius 200m, the coefficient of lateral friction is 0.15 and the design speed is 40 kmph. The equilibrium super elevation would be

Solution:
The super elevation at which pressure on outer and inner wheels is same is called equilibrium super elevation.

Friction force = 0

Friction force = 0

QUESTION: 21

The composite sleeper index used for wooden sleepers is the index of:

Solution:

QUESTION: 22

A ball kept in a closed box moves in the box making collisions with the walls. The box is kept on a smooth surface. The velocity of the centre of mass:

Solution:

QUESTION: 23

The area on which crops are grown in a particular reason is called:

Solution:
The area on which crops are grown in a particular season is called as seasonal cropped area or seasonal sown area such as Rabi or Kharif area. Net sown area is the total cropped area in the entire year i.e. both the seasons.

QUESTION: 24

If a shaft is subjected to pure torsion, it will fail along the plane:

Solution:
If shaft is subjected to pure torsion it will fail along to longitudinal axis in brittle material and to longitudinal axis inductile material.

QUESTION: 25

A 12 hour unit hydrograph of a catchment is triangular in shape with a base width of 64 hours and a peak ordinate of 30 If a 2 cm rainfall excess occurs in 12 hour in the catchment, the resulting surface runoff will have:

Solution:
Surface runoff = Area under DRH

6.912 ha m

6.912 ha m

QUESTION: 26

In Marshall mix design test, the relationship between voids in mineral aggregates and % Bitumen content (BT) is the best illustrated by

Solution:

QUESTION: 27

Difference between airport and highway pavement thickness arises due to:

1. Magnitude of wheel load

2. Tyre pressure

3. Size of vehicle

4. Number of repetition

Which of the statement given above are correct?

1. Magnitude of wheel load

2. Tyre pressure

3. Size of vehicle

4. Number of repetition

Which of the statement given above are correct?

Solution:

QUESTION: 28

One end of a two dimensional water tank has the shape of a quadrant of a circle of radius 2m. When the tank is full the vertical component of the force per unit length on the curved surface will be?

Solution:
Vertical component of force = weight of liquid enclosed above the circular surface

QUESTION: 29

A lysimeter is used to measure :

Solution:

QUESTION: 30

When the recirculation ratio in a high rate trickling filter is unity, then what is the value of recirculation factor?

Solution:
Recirculation factor

QUESTION: 31

Presence of nitrogen in a waste sample is due to the decomposition of:

Solution:
The presence of nitrogen in waste sample is due to the decomposition of proteins

QUESTION: 32

Consider the following activities:

1. Pouring of concrete

2. Erection of formwork

3. Curing of concrete

4. Removal of formwork

What is the correct sequence on a network of these activities?

1. Pouring of concrete

2. Erection of formwork

3. Curing of concrete

4. Removal of formwork

What is the correct sequence on a network of these activities?

Solution:
Correct sequence of activities is:

a) Erection of formwork

b) Placing of reinforcement

c) Pouring of concrete

d) Compaction of concrete

e) Removal of formwork

f) Curing

a) Erection of formwork

b) Placing of reinforcement

c) Pouring of concrete

d) Compaction of concrete

e) Removal of formwork

f) Curing

QUESTION: 33

Match List-I (contract types) with List-II (Characteristics):

List-I

a. Labour contract

b.Item rate contract

c. Piecework contract

d.Lump sum contract

List-II

1.Petty works and regular maintenance work

2.Adopted for buildings, roads, bridges and electrical works

3.Payment made by detailed measurement of different time

4.Not practiced in government

List-I

a. Labour contract

b.Item rate contract

c. Piecework contract

d.Lump sum contract

List-II

1.Petty works and regular maintenance work

2.Adopted for buildings, roads, bridges and electrical works

3.Payment made by detailed measurement of different time

4.Not practiced in government

Solution:

QUESTION: 34

The angle of intersections of the mirrors in an optical square is:

Solution:

QUESTION: 35

Prying forces can be reduced by:

1) Increasing the end distance

2) Decreasing the end distance

3) Increasing the distance of the bolt from half the root radius for the rolled section Of the above

1) Increasing the end distance

2) Decreasing the end distance

3) Increasing the distance of the bolt from half the root radius for the rolled section Of the above

Solution:

QUESTION: 36

A bracket carries a load of 120 kN, it is connected to column by means of 2 horizontal fillet welds each of 150 mm effective length and 10mm thickness. The load acts at 80mm from the face of the column as shown in the figure. Find the resultant stress on weld.

Solution:

QUESTION: 37

A septic tank for a hospital is designed for 250 persons. The flow into the tank may be assumed to be at the rate of 65 lpcd. What would be the surface over loading if following date are given:

Detention period = 20 hours

Depth = 0.9 m

Length: width =1.5

Percolation rate = 15 minutes

Detention period = 20 hours

Depth = 0.9 m

Length: width =1.5

Percolation rate = 15 minutes

Solution:
Quantity of sewage applied = 250Ã—65 = 16250 litres/day

t = 20 hours

B = 3.16 (Since L/B = 1.5)

L = 4.75

t = 20 hours

B = 3.16 (Since L/B = 1.5)

L = 4.75

QUESTION: 38

A digestion tank of the primary sludge is designed with the help of following data:

I. Average flow = 20MLD

II. Total suspended solids in raw sewage = 300 mg/L

III. Moisture content of the raw sewage =95%

IV. Moisture content of the digested sludge =85%

V. 65% of solids removed in primary tanks

VI. Specific gravity of sludge = 1.02

VII. Digested period = 30 days

Volume of raw sewage produced per day is:

I. Average flow = 20MLD

II. Total suspended solids in raw sewage = 300 mg/L

III. Moisture content of the raw sewage =95%

IV. Moisture content of the digested sludge =85%

V. 65% of solids removed in primary tanks

VI. Specific gravity of sludge = 1.02

VII. Digested period = 30 days

Volume of raw sewage produced per day is:

Solution:

QUESTION: 39

What will be the value of limiting depth of neutral axis in a singly reinforced beam of section 300mm Ã— 500mm (effective depth), if strain in concrete at limit state of collapse was found to be 0.0030? Use M20 grade of concrete and Fe 415 grade of steel.

Solution:

d = 500mm

Xulim = 220.70mm

d = 500mm

Xulim = 220.70mm

QUESTION: 40

A concrete beam is pre-stressed by a cable carrying an initial pre-stressing force of 300kN. The cross â€“ sectional area of the wires in the cable is 300 mm2. Calculate the ratio of percentage loss of stress in cable only due to shrinkage of concrete due to pre-tensioning and post â€“ tensioning

Assume

Age of concrete at transfer = 8 days

Assume

Age of concrete at transfer = 8 days

Solution:

QUESTION: 41

Find the critical path for the following data:

Solution:

QUESTION: 42

Which of the following is not correct?

Solution:

QUESTION: 43

In the influence line diagram for member AF in the given truss:

Solution:
When unit load is at A

F = 0

When unit load is at B

F = -1.25

When unit load is at C

F sin? + 1/2 = 0

F = -5/6 = -0.83

F = 0

When unit load is at B

F = -1.25

When unit load is at C

F sin? + 1/2 = 0

F = -5/6 = -0.83

QUESTION: 44

Find the magnitude of horizontal displacement at joint E of the truss shown in the figure below due to temperature increase of in member AC and CE is ________ mm

Solution:

Forces in the members are computed:

= 0.0096 m

= 9.6mm

Forces in the members are computed:

= 0.0096 m

= 9.6mm

QUESTION: 45

For the frame shown below:

Solution:

QUESTION: 46

A taxiway is to be designed for a supersonic aircraft with a wheel base of 30 m and tread of main loading gear as 6m for a design turning speed of 50 kmph. Assume coefficient of friction between tyre and pavement surface as 0.13 and width of taxiway pavement as 22.5m. Assume oleo distance as 6m. The turning radius of taxiway is:

Solution:
Radius of taxiway will be maximum if

III. For supersonic aircraft radius of taxiway should not be less than 180m.

Therefore radius of taxiway will be 180m

III. For supersonic aircraft radius of taxiway should not be less than 180m.

Therefore radius of taxiway will be 180m

QUESTION: 47

An irrigation canal proposed to be excavated in an incoherent alluvial soil of minimum size 0.4mm, for carrying a discharge of 40 cumecs, should have a bed slope of:

Solution:

QUESTION: 48

A block P of mass 200 g is placed on a block Q of mass 300 g as shown in the figure. Block P is tied to the wall by a massless and inextensible string AB. If the coefficient of static friction for all the surfaces is 0.5, find the minimum force F (in kN) needed to move the block Q is:

Solution:

QUESTION: 49

A light spring of spring constant K is kept compressed between two blocks of masses m and M on a smooth horizontal surface. When released, the blocks acquire velocities in opposite directions. The spring loses contact with the blocks when it acquires natural length. If the spring was initially compressed through a distance x, find the final speeds of the block having mass M?

Solution:
No external force acts on the system hence linear momentum is constant

Initial momentum is zero as blocks are released from rest

MV - mv = 0

Initial momentum is zero as blocks are released from rest

MV - mv = 0

QUESTION: 50

Delta (Δ) in cm. Duty (*D*) in hectare Cumec and Base period (*B*) in days are related as

Solution:

QUESTION: 51

Extra widening required at a horizontal curve on a single lane road of radius 100m for a design speed of 60 kmph and for a vehicle with wheel base 6m is:

Solution:
For a single lane road we provide only mechanical widening

QUESTION: 52

The following metrological data pertains to a large reservoir with a watershed area of The data represents the average values for the day.

Water temperature =

Air temperature =

Relative humidity = 46%

Find the actual vapour pressure (in mm of Hg)

Water temperature =

Air temperature =

Relative humidity = 46%

Find the actual vapour pressure (in mm of Hg)

Solution:

QUESTION: 53

Find the directional derivative of the function at a point (1, -2, -1) in the direction of

Solution:

QUESTION: 54

Find the value of:

Solution:

QUESTION: 55

A bag contains 5 white, 6 red and 7 black balls, 4 balls are drawn at random. Find the probability that at least 3 balls are black balls.

Solution:
Atleast 3 are black balls = 3 black balls + 4 black balls

QUESTION: 56

A hollow shaft having outer diameter equal to 3 times the inner diameter. It transmits 40 kW power at 2500 RPM. If the maximum permissible shear stress is 32 MPa, then outer diameter is

Solution:

QUESTION: 57

The microbial quality of treated piped water supplies is monitored by

Solution:

QUESTION: 58

A rectangular channel carries a flow of 3.5 the depth of flow being 1.5m and width of channel is 2m. Maximum rise in floor at a section so that upstream flow condition does not change is given as?

Solution:

QUESTION: 59

The stream function for a 2-D flow is given by .The resultant velocity at a point P(2, 3) is:

Solution:
=-2x=-4 units

= 7.21 units/sec

= 7.21 units/sec

QUESTION: 60

In a laminar boundary layer, the velocity distribution can be assumed to be given, in usual notation as Which of the following is the correct expression for the displacement thickness for this boundary layer?

Solution:

QUESTION: 61

A vertical photograph was taken from a height of 3500 m above mean sea level with a camera of focal length 120 mm. IT contains 2 points a and b corresponding to ground points A and B.

For out horizontal length AB

For out horizontal length AB

Solution:
Scale for point A:

Scale for point B:

AB=608.37 m

Scale for point B:

AB=608.37 m

QUESTION: 62

For a reciprocal leveling, following readings were taken:

If R.L. of point A is 200m and the distance between A and B is 300m. Calculate the angular error in instrument. Neglect effect of curvature and refraction.

If R.L. of point A is 200m and the distance between A and B is 300m. Calculate the angular error in instrument. Neglect effect of curvature and refraction.

Solution:
(2.82 - e) â€“ 1.62 = 1.95 â€“ (0.81 - e)

e = 0.03

Angular error in inclination =

e = 0.03

Angular error in inclination =

QUESTION: 63

In an insitu vane shear test on saturated clay, a torque of 35 Nm was required to shear the soil. The diameter of the vane was 50mm and length 100mm.When the soil was remoulded, the torque required to shear the soil in the remoulded state was 5 Nm. Determine the sensitivity of the clay

Solution:

QUESTION: 64

A footing 4m Ã— 2mm in plan, transmits a pressure of 150 on a cohesive soil having E= and ==0.5. Determine the immediate settlement of the footing at the center assuming the footing to be rigid footing. Influence factor for flexible footing is 1.52

Solution:

QUESTION: 65

A clay sample originally 25mm thick and at a void ratio of 1.120, was subjected to a compressive load. After the clay sample was completely consolidated, its thickness was measured to be 24 mm .Compute the final void ratio.

Solution:

Final void ratio = 1.120-0.0848 = 1.0352

Final void ratio = 1.120-0.0848 = 1.0352

### Civil Engineering (CE) 2006 GATE Paper without solution

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