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QUESTION: 1

Solution:

QUESTION: 2

Break : Piece

Solution:

QUESTION: 3

Replace the phrase printed in bold to make it grammatically correct ?

__ "Even though many companies"__ are now penetrating rural India, it would help to give India a real chance of witnessing a double digit GDP growth

Solution:

QUESTION: 4

Improve the sentence with suitable options by replacing the underlined word.

He is still in vigorous health although he is on the **" right"** side of sixty.

Solution:

QUESTION: 5

Complete the given sentence by choosing the correct phrase.

You cannot succeed unless

You cannot succeed unless

Solution:

QUESTION: 6

Chirag decided to give 12% of his salary to his younger brother as a pocket money.But he gave 1260 Rs which was 60% of what he had decided earlier. How much is Chirag’s salary?

Solution:
Let x be Chirag’s salary:

x = 17500 Rs

x = 17500 Rs

QUESTION: 7

Two pipes can fill a tank in 15 minutes and 25 minutes respectively. Both the pipes are opened together and after some time, the first pipe is closed and the tank is completely full in 15 minutes. For how many minutes is the first pipe opened?

Solution:

t = 6 min.

t = 6 min.

QUESTION: 8

A and B are required to solve a problem independently. If 1/2 and 1/3 are their respectively probabilities of solving the problem, then the probability that atleast one of them solves the problem.

Solution:
Probability that atleast one of them solves the problem = P

QUESTION: 9

What is the probability that a leap year has 53 Sundays and 52 Mondays?

Solution:
In leap year there are 366 days.

There are 52 weeks + 2 days

1. - Mon. + Tue.

2. - Tue. + Wed.

3. - Wed. + Thu.

4. - Thu. + Fri.

5. - Fri. + Sat.

6. - Sat. + Sun. = 53 Sundays + 52 Mondays

7. - Sun. + Mon.

Probability =1/7

There are 52 weeks + 2 days

1. - Mon. + Tue.

2. - Tue. + Wed.

3. - Wed. + Thu.

4. - Thu. + Fri.

5. - Fri. + Sat.

6. - Sat. + Sun. = 53 Sundays + 52 Mondays

7. - Sun. + Mon.

Probability =1/7

QUESTION: 10

A certain sum of money is invested for one year at a certain rate of simple interest. If the rate of interest is 3% higher, then the interest earned will be 25% more than the interest earned earlier. What is the earlier rate of interest ?

Solution:

r = 12% per annum

r = 12% per annum

QUESTION: 11

The rank of the matrix is 2, find the value of k?

Solution:
The rank of the matrix = 2

(-k+16+18) - (-12+4+6k) = 0

k = 6

(-k+16+18) - (-12+4+6k) = 0

k = 6

QUESTION: 12

How many solutions does the system of linear equations have:

-x + 5y = -1

x – y = 2

x + 3y = 3

-x + 5y = -1

x – y = 2

x + 3y = 3

Solution:
The augmented matrix is given by

Rank of [AB]=2, (Determinant of [AB]=0)

Rank of [A]=2

Therefore, unique solution

Rank of [AB]=2, (Determinant of [AB]=0)

Rank of [A]=2

Therefore, unique solution

QUESTION: 13

The polynomial has

Solution:
f(x) is polynomial of degree n with non zero constant terms:

- if f(x) has p changes of sign, then f(x) = 0 has atmost p positive real roots

- if f(-x) has q changes of sign, then f(x) = 0 has atmost q negative real roots

- f(x) = 0 has atleast (n-p-q) complex roots

p(x) has 1 negative real and 4 complex roots and no positive real root

- if f(x) has p changes of sign, then f(x) = 0 has atmost p positive real roots

- if f(-x) has q changes of sign, then f(x) = 0 has atmost q negative real roots

- f(x) = 0 has atleast (n-p-q) complex roots

p(x) has 1 negative real and 4 complex roots and no positive real root

QUESTION: 14

Find the value of

Solution:

QUESTION: 15

A long shaft of diameter d is fixed at one end and is subjected to twisting moment T at other end. The maximum normal stress acting at its cross-section is equal to:

Solution:

QUESTION: 16

Consider the I-section of a beam shown below:

If the shear stress at the level of junction in flange is 10 what will be shear stress in web at the level of junction?

Solution:

QUESTION: 17

If the difference in elevation of the edge of pavement of 2 lane divided highway(7m wide) and its crown is 7 cm, the camber of the pavement is:

Solution:

QUESTION: 18

In a bituminous concrete mix, bitumen and aggregates by weight are 8% and 92% respectively. Specific gravity of bitumen and aggregates are 1.1 and 2.5 respectively. Air void is 1%. Theoretical unit weight of the mix will be:

Solution:

QUESTION: 19

The standard project flood is

Solution:

QUESTION: 20

An irrigation canal has a steady discharge Q at a section where a cross regulation (gated) is provided for control purposes. If the gate of the regulator, which is normally fully open, is suddenly lowered down to a half open position, then a rapidly varied unsteady flow results. In such a case, it would take a form of :

Solution:

QUESTION: 21

For the network shown in the above figure (the number on each arrow denotes the time duration of activity in days), the earliest start time, in days for activity 5-6 is:

Solution:
Earliest start time of 5-6 is given activity 2-5

= 4 + 6 = 10 days

= 4 + 6 = 10 days

QUESTION: 22

The latitude and departure of line PQ are 46 m and 75 m respectively. Find the whole circle bearing of line PQ?

Solution:

Since, latitude is positive hence it corresponds to +Y axis and departure is negative hence it corresponds to –X axis.

Since, latitude is positive hence it corresponds to +Y axis and departure is negative hence it corresponds to –X axis.

QUESTION: 23

The liquid limit and plastic limit of a soil sample is 40% and 25%. In liquid limit test water content varies from 5% to 25% when the number of blows increased from 10 to 100. The toughness index of the soil is?

Solution:

QUESTION: 24

Degree of freedom for a given structure will be:

Solution:

QUESTION: 25

The slenderness ratio in a tension member as per IS code where reversal of stress is due to loads other than winds or seismic load should not exceed:

Solution:

QUESTION: 26

Separation of water or water sand cement from a freshly mixed concrete is known as :

Solution:

QUESTION: 27

Calcium chloride added in concrete acts as :

Solution:

QUESTION: 28

The increase in strength of concrete with time is :

Solution:

QUESTION: 29

A sewage sludge has a water content of 98%. What will be the concentration of suspended solids in the sludge? (Gsludge = 1)

Solution:
100 kg of sludge contains 2 kg of solids

QUESTION: 30

With what acceleration ‘a’ should the box descend so that the block of mass M exerts a force Mg/4 on the floor of the box?

Solution:
Forces on the block are:

i) Mg downwards (by the earth)

ii) N upwards (by the floor)

Mg – N = Ma

N = Mg/4

a = 3g/4

i) Mg downwards (by the earth)

ii) N upwards (by the floor)

Mg – N = Ma

N = Mg/4

a = 3g/4

QUESTION: 31

For sleeper density (n + 5), number of sleepers required for constructing a broad gauge (BG) track of length 768 m.

Solution:
Length of rail on BG track = 12.8

Sleeper density = 12.8 + 5 = 18 per rail

No. of rails = =60 rails

No. of Sleepers= = 1080

Sleeper density = 12.8 + 5 = 18 per rail

No. of rails = =60 rails

No. of Sleepers= = 1080

QUESTION: 32

Which one of the following is the correct relationship between the boundary layer thickness displacement thickness and the momentum thickness ?

Solution:

QUESTION: 33

Net safe bearing capacity for a raft (10×10)m if the depth is 5m and c = with a factor of safety as 2.5 will be:

Solution:

QUESTION: 34

Gumbel’s method is used for the prediction of:

Solution:

QUESTION: 35

A 3 hour unit hydrograph is parabolic in shape. The discharge rises from 0 to 72 in 6 hours and then falls to zero in next 6 hours. An average rainfall of 8 cm occurs during a period of 6 hours with uniform intensity over a catchment having index = 0.5 cm/hr. What is the peak discharge of resulting direct runoff hydrograph.

Solution:
Equation of parabola is given by:

Equation of 6 hour unit hydrograph is obtained by lagging the unit hydrograph by 3hour ,Hence; equation of 6 hour unit hydrograph becomes:

2 (x-6) + 2(x-9) = 0

x – 6 + x – 9 = 0

x = 7.5

Hence, peak discharge is given at 7.5 hours

Equation of 6 hour unit hydrograph is obtained by lagging the unit hydrograph by 3hour ,Hence; equation of 6 hour unit hydrograph becomes:

2 (x-6) + 2(x-9) = 0

x – 6 + x – 9 = 0

x = 7.5

Hence, peak discharge is given at 7.5 hours

QUESTION: 36

Chlorination with produces hypochlorous acid (HOCL), which may further dissociate as hypochlorite ion depending upon pH of water. The reaction is represented as:

What is the fraction of HOCL in the water at pH = 8?

What is the fraction of HOCL in the water at pH = 8?

Solution:

QUESTION: 37

Three weights are hanging by cables passing over smooth pulleys. Find out the mass m, such that the system is in equilibrium.

Solution:

QUESTION: 38

A cast insitu SOIL bored pile 0.5m diameter and 10m deep is placed in a purely cohesive soil. If the cohesion of the soil is 4t/m2 and adhesion between the pile and the soil is half the value of cohesion, then the ultimate bearing capacity of the pile is given by :

Solution:

QUESTION: 39

A school is proposed to be constructed in Delhi. The soil profile of construction site is shown in the figure. A square footing of carries a load of 200 ton and is laid with its base 1m below the ground surface. Clay is normally consolidated, use 1.25 V to 1H for load dispersion. The value of settlement of clay layer on account of construction (in mm)?

Solution:

Change in effective stress due to 200 tonnes

Change in effective stress due to 200 tonnes

QUESTION: 40

A survey line AB is obstructed by a high building. To prolong the line beyond the building, a perpendicular BC 115.45m long is set at B. From C, two lines CD and CE are set out at angles of and respectively. Determine the lengths (in m) CD and CE so that D and E are on the prolongations of AB.

Solution:

QUESTION: 41

The height of an inaccessible tower is to be determined by ranging rods. The two ranging rods of length 2.5m and 1.5m are placed in such a way that their tops are in line with the top of the tower. The distance between the ranging rods is 10m. The two ranging rods are then placed in a different setting on the same ranged out line such that the longer rod is placed 110m away from its first position and the distance between the ranging rods is 30m. If their tops are again in line with the top of the tower, determine the height of the tower.

Solution:

QUESTION: 42

The earliest date and latest date of the events 3 and 10 are given in the above figure. Activity C is connecting both the events and its duration is 12 weeks. The independent float of the activity is:

Solution:

QUESTION: 43

The flow in a 5m wide rectangular channel is 15 . The normal depth of flow is 2.5m. If at a certain section A, the depth of flow in the channel is 1.5m, the depth of flow at a section upstream of A would be:

Solution:

In profile, depth decreases in the direction of flow Depth upstream of A would be more than 1.5m

In profile, depth decreases in the direction of flow Depth upstream of A would be more than 1.5m

QUESTION: 44

The Thiessen weights of 4 raingauges A, B, C and D covering a river basin are 0.15, 0.25, 0.30 and 0.30 respectively. If the average depth of rainfall for the basin is 5 cm, the rainfall recorded at B, C and D are 5 cm, 4 cm and 5 cm respectively. What is the rainfall at A?

Solution:

QUESTION: 45

A rigid beam ABCD is hinged at D and supported by 2 springs at A and B as shown in the given figure. The beam carries a vertical load P at C. The stiffness of spring at A is 2k and that at B is 3k. The ratio of forces of spring B to that of spring A is:

Solution:

QUESTION: 46

Suppose that a book of 300 pages contains 30 printing mistakes. Assume that these errors are randomly distributed throughout the book. The number of errors per page has a Poisson’s distribution. What is the probability that 20 pages selected at random will be free from errors?

Solution:

QUESTION: 47

An examination paper has 150 MCQ’s of 1 mark each, with each equation having 4 choices. Each incorrect answer has -0.25 marks. Suppose 1000 students choose all their answers randomly with uniform probability. The sum total of expected marks obtained by all the students is:

Solution:
Let us define a random variable denoting the marks scored for a question

QUESTION: 48

Find the value of integrating factor for the differential equation given below:

Solution:

Integrating factor =

Integrating factor =

QUESTION: 49

A flat smooth rectangular plate is placed edgewise in a stream of fluid. At what fraction of the length from the leading edge would the drag force on the front portion be equal to the half of the total drag force? Assume the boundary layer to be laminar :

Solution:
Let x be the distance from the leading edge such that the drag force in the distance x is half of the total drag force

QUESTION: 50

An irrotational two-dimensional flow leaves a straight duct and enters a bend of the same width, in the horizontal plane. Find the velocity difference at the inner and outer wall of the bend.

Solution:
Consider a unit depth of the duct. For irrotational flow the velocity variation is :

Difference in velocity = 2.466 – 1.644 = 0.822 m/s

Difference in velocity = 2.466 – 1.644 = 0.822 m/s

QUESTION: 51

On a simply supported beam, a concentrated load F(x) kN passes from left to right, such that :

Where [ ] represents the greatest integer function. x is the distance of load from the left end A in meters.What is the value of vertical reaction at A, when the load is at a distance of 6.5m from Left end A ?

Where [ ] represents the greatest integer function. x is the distance of load from the left end A in meters.What is the value of vertical reaction at A, when the load is at a distance of 6.5m from Left end A ?

Solution:
Value of load at x = 6.5m

QUESTION: 52

A single stage filter is to treat a flow of 3.79 MLO of raw sewage with BOD of 240mg/L. It is to be designed for a loading of 11086 kg of BOD in raw sewage per hectare meter and recirculation is to be 1. Assume 35% of the BOD is removed in primary clarifier. Find the strength of effluent (that is BOD concentration in the effluent).

Solution:
Total BOD present in raw sewage =

QUESTION: 53

A sedimentation tank is treating 4.5 million liters of sewage per day containing 275 ppm of suspended solids. The tank removes 50% of the suspended solids. Calculate the quantity of sludge produced per day (in tonner) if the moisture content of the sludge is 98%

Solution:
Vol. of sewage treated = 4.5 ML/day

Wt. of suspended solids present in sewage = = 1237.5 kg/day

Since, 50% of solids are removed in sedimentation tank, we have

The mass of solids removed in sedimentation tank =

For sludge having 98% moisture content :

Wt. of sludge produced per day = 30.94 tones

Wt. of suspended solids present in sewage = = 1237.5 kg/day

Since, 50% of solids are removed in sedimentation tank, we have

The mass of solids removed in sedimentation tank =

For sludge having 98% moisture content :

Wt. of sludge produced per day = 30.94 tones

QUESTION: 54

Fineness test of cement gives an estimate of :

Solution:

QUESTION: 55

The early high strength of rapid hardening cement is due to its :

Solution:

QUESTION: 56

The flow of activities of a project is given in the following figure. The duration of activities are indicated along the arrows

The critical path of the activities is along :

The critical path of the activities is along :

Solution:

QUESTION: 57

Identify the critical path

Solution:

Critical path 1 – 2 – 4 – 6 – 7

Critical path 1 – 2 – 4 – 6 – 7

QUESTION: 58

The following are the details of estimated times of activities of a certain project

Calculate the expected project completion time ?

Calculate the expected project completion time ?

Solution:

QUESTION: 59

A flat smooth rectangular plates is placed edgewise in a stream of fluid. At what fraction of the length from the leading edge would the drag force on the front portion be equal to the half of the total drag force ? Assume the boundary layer to be laminar :

Solution:
Let x be the distance from the leading edge such that the drag force in the distance x is half of the total drag force

QUESTION: 60

A singly reinforced concrete beam of section is reinforced with Fe415 grade of steel having area of 900 .The ratio of depth of neutral axis with and without considering the partial factor of safety of materials will be ? Take Grade of concrete to be M20

Solution:
? By considering the partial factor of safety of materials

Total compression = Total tension

?Without considering the partial factor of safety of material

Total compression = Total tension

?Without considering the partial factor of safety of material

QUESTION: 61

Overtaking time required for a vehicle with design speed 50 kmph and overtaking acceleration of 12.5 to overtake a vehicle moving at a speed of 30 kmph is :

Solution:

T = 6.15 sec

T = 6.15 sec

QUESTION: 62

If the velocity of moving vehicles on a road is 24 kmph, stopping sight distance is 19 meters and average length of vehicle is 6 meters, the basic capacity of a lane is :

Solution:

= 960 Vehicles/hour

= 960 Vehicles/hour

QUESTION: 63

A cantilever beam AB shown in the figure has an extension BCD attached to the free end. A force P acts at the end of the extension. What is the ratio of so that vertical deflection at point B is zero ?

Solution:

QUESTION: 64

Calculate the elongation of copper bar of solid circular cross-section with tapered ends when it is stretched by axial loads of magnitude of 30 kN

Diameter at crosssection A, B, C and D are 0.5, 1, 1, and 0.5 cm respectively. Take E = 120 GPa

Diameter at crosssection A, B, C and D are 0.5, 1, 1, and 0.5 cm respectively. Take E = 120 GPa

Solution:

QUESTION: 65

While water passes through a given pipe at mean velocity V, the flow is found to change from laminar to turbulent. If another fluid of specific gravity 0.8 and coefficient of viscosity 20% of that of water, is passed through the same pipe, the transition of flow from laminar to turbulent is expected if the flow velocity is :

Solution:

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