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QUESTION: 1

Q. 1 – Q. 5 carry one mark each.

A number is as much greater than 75 as it is smaller than 117. The number is:

Solution:

Let the number be N.

Then we know that N - 75 = 117 - N

Add N to both sides to get this:

2N - 75 = 117

Add 75 to both sides to get this:

2N = 117 + 75 = 192

Divide both sides by 2 to get this:

N = 96

QUESTION: 2

Which of the above underlined parts of the sentence is grammatically incorrect?

Solution:

The correction needs to be done in the second part by excluding to from it. It should be-

The professor ordered the students to go out of the class.

Here, “to” is implied in the word “ordered”.

QUESTION: 3

Which of the following options is the closest in meaning to the word given below:

Primeval

Solution:

Primeval pertains to the first age or ages, especially of the world. E.g.: primeval forms of life

QUESTION: 4

Friendship, no matter how _________it is, has its limitations.

Solution:

Friendship, No matter how intimate it is, has its limitation. Intimate refers to close personal relations, e.g. an intimate friend. It is also characterized by or involving warm friendship or a personally close or familiar association or feeling.

QUESTION: 5

The pair that best express a relationship similar to that expression in the pair:

Medicine: Health

Solution:

Medicine leads to good health. Similarly, Education leads to Knowledge. Science does not lead to experiment. Wealth may not necessarily lead to peace. Also money may not also lead to happiness all the time

*Answer can only contain numeric values

QUESTION: 6

Q. 6 to Q. 10 carry two marks each.

A reduction of 5% in price of sugar enables a housewife to buy 3 kg more for Rs.280. Find the reduced price

Solution:

QUESTION: 7

x and y are two positive real numbers, such that equation 2x + y ≤ 6; x + 2y ≤ 8 For which values of (x, y), the function f (x, y) = 3x + 6y will give maximum value

Solution:

QUESTION: 8

A firm is selling it product at Rs. 60/unit. The total cost of production is Rs. 100 and firm is earning total profit of Rs. 500. Later, the total cost increased by 30%. By what percentage the price should be increased to maintain the same profit level

Solution:

Profit= Earned money after selling- Cost of Production

500= Earned money after selling-100

Earned money after selling = 600

Therefore, firm sold 600/60= 10 units.

New cost of production= 130

Profit=500

Earned money after selling=500+130=630

Therefore, new price of each unit = 630/10 = 63

Therefore % increase in price= 100*(63-60)/60=5

QUESTION: 9

Abhishek is elder to Savan, Savan is younger to Anshul. The correct relations is

Solution:

Abhishek > Savan

Anshul> Savan

Thus, no conclusion can be drawn b/w ages of Abhishek and Anshul

QUESTION: 10

Which one of the following increased by same percentage in year 2010-2011?

Solution:

*Answer can only contain numeric values

QUESTION: 11

Q. No. 11 – 35 Carry One Mark Each

A pin-jointed 2-D truss is loaded with a horizontal force of 15 kN at joint S and another 15 kN vertical force at joint U as shown in figure. Find the force in member RS (in kN) and report your answer taking tension as +ve and compression as –ve

Solution:

.

If two members meet at a joint which are not collinear and also there is no external forces acting on that joint then both members will carry zero forces

So, force is member is “RS” will be zero

QUESTION: 12

The latitude and departure of a line AB are +78m and −45.1m respectively. The whole circle bearing of the line AB is

Solution:

Since the latitude of line is positive and departure is negative, the line lies in Fourth quadrant.

QUESTION: 13

For two major-roads with divided carriage way crossing at right angle, a full clover leaf interchange with four indirect ramps is provided. Following statements are made on turning movement of vehicles to all direction from both roads. Identity the correct statement

Solution:

QUESTION: 14

For subcritical flow in an open channel, the control section for gradually varied flow profile is

Solution:

In an open channel flow, a section where depth is known for a given discharge is known is known as control section. Hence, the control section for subcritical flow is downstream end and for supercritical flow is upstream end.

QUESTION: 15

Creep strain is

Solution:

Creep means when the length of bar keeps on changing at a constant load.

Therefore, creep strain will be caused by a static load.

Since, out of dead load, live load and cyclic load, constant and static load is only dead load and other loads application keeps on changing, hence, creep strain is caused due to dead load only.

*Answer can only contain numeric values

QUESTION: 16

A water treatment plant, having discharge 1m^{3} / sec, has 14 filters to treat the water. Each filter is having 50m^{2 }area, but due to backwashing activity, 2 filters are non operational. Calculate hydraulic loading rate in

Solution:

QUESTION: 17

In its natural condition a soil sample has a mass of 1.980 kg and a volume of 0.001m^{3} . After being completely dried in an oven, the mass of the sample is 1.800 kg. Specific gravity is 2.7. Unit weight of water is 10kN /m^{3} . The degree of saturation of soil is

Solution:

QUESTION: 18

Group-I contains dimensionless parameter and Group-II contains ratio

Correct match of the dimensionless parameter in Group-I with Group-II is

Solution:

Mach Number - Ratio of fluid velocity and velocity of sound.

Reynold Number- Ratio of inertial force and viscous force.

Weber Number- Ratio of Inertial force and surface tension force

Froude Number- Ratio of Inertial force and gravity force

Euler Number- Ratio of inertial force and pressure force.

QUESTION: 19

For a 2-D flow field, the stream function ψ is given as

The magnitude of discharge occurring between the stream line passing through points (0, 3) and (3, 4) is

Solution:

QUESTION: 20

Select the strength parameter of concrete used in design of plain jointed cement pavement from the following choices:

Solution:

Pavement made up of cement acts as a beam, even though the soil below the pavement settles at some sections, the whole beam will either not settle or settlement will take place as a whole, similar to a beam. Thus, plain jointed cement pavement will be designed for appropriate flexural strength.

QUESTION: 21

Four columns of building are to be located within a plot size of 10m×10m. The expected load on each column is 400 kN. Allowable bearing capacity of soil deposit is 100kN /m^{2} . The type of foundation to be used is

Solution:

Load on each column = 400kN

Bearing capacity of soil= 100 kN /m^{2}

If the foundation area is less than 40% of plot area, then isolated foundation is suitable.

QUESTION: 22

Following statement are made on compacted soil, where DS stands for soil compaction on Dry Side of OMC and WS stands for soil compacted on Wet Side of OMC. Identify incorrect statement

Solution:

For a given compacting effort, the soil tends to have a flocculated structure on the wet side of optimum whereas the wet side of optimum, the structure tends to be more dispersed.

Construction of pore water pressure is low on dry side and high on wet side, due to presence of more water on wet side (which will be exerted to normal and shear stresses) which leads to higher pore water pressure.

Soil compacted on wet of optimum tends to exhibit more shrinkage upon drying than those compacted dry side of optimum. The more orderly, nearly parallel orientation of particles allows the particles to pack more efficiently as compared to randomly oriented particles on the dry side of optimum.

A soil on the dry side of optimum has a higher water deficiency and a more random arrangement. It can therefore, imbibe more water than a soil on the wet of optimum and in the process swells more.

*Answer can only contain numeric values

QUESTION: 23

It was observed that 150 vehicle crossed a particular location of highway in 30 minutes. Assume that vehicle arrival follow a negative exponential distribution. The number of time headways greater than 5 seconds in above observation is

Solution:

QUESTION: 24

As per IS 800: 2007 the cross-section in which extreme fibre can reach the yield stress but cannot develop the plastic moment of resistance due to local buckling is classified as

Solution:

As per clause 3.7.2 of IS 800:2007

QUESTION: 25

The “Plane section remain plane” assumption in bending theory implies

Solution:

QUESTION: 26

The ratio N_{f} / N_{d} is known as shape-factor where N_{f} is the number of flow channels and N_{d} is the equipotential drop. The flownet always drawn with a constant b/ a ratio where b and a are distance between two consecutive flow lines and equipotential lines respectively. Assuming that b/a ratio remains same, the shape factor of a flow net will change if the

Solution:

The shape of flow net character depends only on the type of soil available at the site. Similarly, flow-net once formed is only on the basis of type of soil and its properties. It has no influence in the upstream and downstream heads, dimension of flow space and head difference causing the flow.

QUESTION: 27

Match the given water properties in Group-I to the given titrants shown in Group-II

Solution:

Alkalinity is measured by titrating solution against N/50 H_{2}SO_{4} with indicator methyl orange and phenolphthalein.

Hardness is measured by titrating solution against N/50 EDTA with indicator EBT (Erichrome Black T).

Chlorine is measured by titrating the solution against N/35.5 Silver Nitrate Solution and Potassium Chromate as an indicator.

Dissolved Oxygen is measured by titrating it against N/40 Sodium Thiosulphate and starch indicator.

QUESTION: 28

Two steel column P (length L and yield strength y_{f} = 250MPa) and Q (length 2L and yield strength y_{f} = 500MPa ) have the same cross-section and end condition. The ratio of buckling load of column P to that of column Q is

Solution:

*Answer can only contain numeric values

QUESTION: 29

As per IS 456 : 2000, bond strength of concrete = 1.2 for M20 . It is increased by 60% for HYSD bar. The development length d L in terms of is ( σ_{st} = 360 MPa)

Solution:

QUESTION: 30

A 1 hour rainfall of 10 cm has return period of 50 year. The probability that 1 hour of rainfall 10 cm or more will occur in each of two successive years is

Solution:

Return period of rainfall, T = 50 years

Probability of occurrence once in 50 years, p=1/50 =0.02

Probability of occurrence in each of 2 successive years

*Answer can only contain numeric values

QUESTION: 31

A symmetric I-section (with width of each flange = 50 mm, thickness of web = 10 mm) of steel is subjected to a shear force of 100 kN. Find the magnitude of the shear stress (in N/mm^{2}) in the web at its junction with the top flange

Solution:

QUESTION: 32

Maximum possible value of compaction factor for fresh (green) concrete is

Solution:

QUESTION: 33

In a setting chamber, what is the minimum dimension of particle which can be completely removed, if rate of overflow is 30m^{3} / d /m^{2} . Take G = 2.65;

Solution:

QUESTION: 34

An isohyet is a line joining points of

Solution:

QUESTION: 35

If |4x − 7| = 5 then the value of 2 |x| − |−x| is

Solution:

*Answer can only contain numeric values

QUESTION: 36

Q. No. 36 – 65 Carry Two Marks Each

A rectangular concrete beam 250 mm wide and 600 mm deep is prestressed by means of 16 wire of high tensile steel wires, each of 7 mm diameter located at 200 mm from the bottom face of the beam at a given section. If the effective pre-stress in the wires is 700 MPa, what is the maximum sagging B.M (in kN-m)

due to live load which this section of the beam can with stand without causing tensile stresses at the bottom face of the beam. Neglect the self weight of the beam

Solution:

Since the tensile stress at bottom face of the beam is zero,

Since the prestressing force is located at 200 mm from the bottom face of the beam. Ecentricity = 300 − 200 = 100mm

QUESTION: 37

In compacted cylindrical bituminous mix,

The magnitude of VFB (void filled bituminous) is

Solution:

*Answer can only contain numeric values

QUESTION: 38

The magnitude as the error (correct to two decimal places) in the estimation of integral using Simpson 1/3 rule is ___. [Take the step length as 1]

Solution:

Using Simpson’s Rule

Magnitude of error = 245.33 − 244.8 = 0.53

QUESTION: 39

The normal depth in a wide rectangular channel is increased by 10%. The percentage increase in discharge in the channel is

Solution:

The discharge in the channel is given by

QUESTION: 40

Elevation and temperature data for places are tabulated below

Based on this data, lapse rate can be referred as

Solution:

Ambient lapse rate=

When the ambient lapse rate exceeds the adiabatic lapse rate, the ambient lapse rate is said to be super adiabatic.

QUESTION: 41

2D stress at a point is given by a matrix, The maximum shear stress in MPa is

Solution:

*Answer can only contain numeric values

QUESTION: 42

Find the value of l such that function f(x) is valid probability density function

Solution:

QUESTION: 43

The value of

Solution:

Alternative Method:

*Answer can only contain numeric values

QUESTION: 44

Laplace equation for water flow in soil is given by Head H does not vary in y and z-direction. Boundary condition What is the value of H at x = 1.2?

Solution:

At x = 1.2m, H= 5 - 1.2 = 3.8m

*Answer can only contain numeric values

QUESTION: 45

A student began an experiment of 5 day 20°C BOD on Monday. Since the 5th day fell on Saturday, the final DO reading was taken on Monday. On calculation BOD (i.e. 7 day 20° C) was found to be 150 mg/L. What would be the 5 day, 20°C BOD (in mg/L)? Assume value of BOD rate constant (K) at standard temperature of 20°C as 0.23/day (base e).

Solution:

QUESTION: 46

A 2 km pipe of 0.2 m diameter connects two reservoirs. The difference between the water levels in the reservoir is 8 m. The Darcy Weisbach friction factor of the pipe is 0.04. Accounting for frictional entry and exit losses, the velocity in the pipe in (m/sec) is

Solution:

QUESTION: 47

Bearing of the given system is shown below:

Applying correction due to local attraction, the correct bearing of line BC will be

Solution:

The difference between back bearing and fore bearing of line DE

QUESTION: 48

Two soil profile are used as backfill behind a retaining wall as shown in the figure, where γ_{t} g is total unit weight and c’ & ' ‘ are effective shear parameters. Find the resultant active earth pressure in kN/m

Solution:

QUESTION: 49

The soil profile above the rock surface at 25° infinite slope is shown in figure where S_{u} is undrain shear stress and γ_{t} is total unit weight. The slip will occur at a depth of

Solution:

The slip will occur when shear stress is greater than or equal to shear strength

*Answer can only contain numeric values

QUESTION: 50

A Theodolite is placed at A and a 3 m long vertical staff is held at B. The depression angle made at reading of 2.5m marking on staff is o 6 10'.The horizontal distance between A and B is 2200 m. The height of instrument at A is 1.2 m and reduced level of point A is 880.88 m. Using curvature correction and refraction correction determine the R.L. of point B (in m).

Solution:

R.L. of A = 880.88m

R.L. of Plane of Collimation = 880.88 + 1.2 = 882.08m

QUESTION: 51

A settling tank is designed for a surface overflow rate of . Assuming

specific gravity of sediment particles = 2.65, Density of water, r_{w} = 1000 kg /m^{3} , dynamic viscosity of water m_{water} = 0.001 Ns /m and stokes law is valid. The approximate minimum size of particles which can be completely removed is

Solution:

To calculate minimum size of particles equating settling velocity to overflow rate, we get

*Answer can only contain numeric values

QUESTION: 52

A uniform beam weighing 1800 N is supported at E & F by cable ABCD. Determine the tension force in segment AB at this cable (correct to 1 decimal place). Assume the cable ABCD, BE and CF are weightless

Solution:

Taking bending moment about point (1) [as we know that bending moment at every point in the cable is zero] Hy_{1} = M_{1,beam} = 1350

*Answer can only contain numeric values

QUESTION: 53

A uniform beam (EI = constant) PQ in the form of a quarter circle of radius R is fixed at end P and free at the end Q, where a load W is applied as shown. The vertical downward displacement δ_{Q} at the loaded point Q is given by Find the value of b correct to 4-decimal place

Solution:

QUESTION: 54

The transplantation of rice requires 10 days and total depth of water required during transplantation is 48 cm. During transplantation there is an effective rainfall (useful for irrigation) of 8 cm. The duty of irrigation water in hectare/ cumecs is

Solution:

*Answer can only contain numeric values

QUESTION: 55

All members in the rigid-jointed frame shown are prismatic and have the same flexural stiffness EI. Find the magnitude of the B.M. at Q (in kN-m) due to given loading

Solution:

*Answer can only contain numeric values

QUESTION: 56

There are three matrixes The minimum of multiplication required to compute the matrix PQR is

Solution:

If we multiply QR first then

QUESTION: 57

Beam subjected to moving distributed load of 4 kN/m maximum shear force that can occur just to right of Q is

Solution:

When a cut is made just to the right of Q and displacements are given such that A’B’ is parallel to B’C’, as B’ is very close to Q, displacement of B’ to the left will be zero and that to the right will be 1.

*Answer can only contain numeric values

QUESTION: 58

Common Data Questions: 58 & 59

For a portion of highway descending gradient 1 in 25 meets an ascending gradient 1 in 20. A valley curve needs to be designed at a velocity of 90 kmph based on

(i) Head light sight distance equal to stopping sight distance of a level terrain. Consider length of curve > SSD

(ii) Comfort condition if rate of change of acceleration is 0.5 m / s^{3}

Reaction time = 2.5 sec, coefficient of longitudinal friction μ = 0.35. Height of head light = 0.75 m, and beam angle= 1°

What is the length of valley curve as per headlight sight distance?

Solution:

*Answer can only contain numeric values

QUESTION: 59

For a portion of highway descending gradient 1 in 25 meets an ascending gradient 1 in 20. A valley curve needs to be designed at a velocity of 90 kmph based on

(i) Head light sight distance equal to stopping sight distance of a level terrain. Consider length of curve > SSD

(ii) Comfort condition if rate of change of acceleration is 0.5 m / s^{3}

Reaction time = 2.5 sec, coefficient of longitudinal friction μ = 0.35. Height of head light = 0.75 m, and beam angle= 1°

What is the length of valley curve (in m)based on the comfort condition? __________

Solution:

QUESTION: 60

Common Data Questions: 50 & 51

Storm-I of duration 5 hours gives a direct run-off of 4 cm and has an average intensity of 2cm / hr

Storm-II of 8 hour duration gives a run-off of 8.4 cm.

(Assume -index is same for both the storms.)

The value of − index is

Solution:

c

QUESTION: 61

Storm-I of duration 5 hours gives a direct run-off of 4 cm and has an average intensity of 2cm / hr

Storm-II of 8 hour duration gives a run-off of 8.4 cm.

(Assume -index is same for both the storms.)

Intensity of storm-II in cm/hr is

Solution:

*Answer can only contain numeric values

QUESTION: 62

Linked Answer Questions: Q.62 to Q.65 Carry Two Marks Each

Statement for Linked Answer Questions: 62 & 63

The magnitude of load P is increased till collapse and the plastic moment carrying capacity of steel beam section is 90 kNm

What is the value of R (in kN) if value of P is 80 kN by elastic theory?

Solution:

*Answer can only contain numeric values

QUESTION: 63

The magnitude of load P is increased till collapse and the plastic moment carrying capacity of steel beam section is 90 kNm

The value of R (in kN), using plastic analysis is (upto 1 decimal place).

Solution:

QUESTION: 64

Statement for Linked Answer Questions: 64 & 65

A multistorey building with a basement is to be constructed. The top 4 m contains loose silt below which dense sand layer is present upto a great depth. Ground water table is at the ground surface. The foundation consists of the basement slab of 6 m width which will rest on the top of dense sand as shown in figure. For dense sand saturated unit weight is 20kN /m^{3} and bearing capacity factor, N_{q} =40, N_{λ}= 45, g for loose silt saturated unit

weight =18kN /m^{3} , N_{q}=15, N_{λ} =20 g . Effective cohesion is 0. Neglect depth factor average elastic modulus E, and Poisson ratio μ of dense sand is 60 ×10^{3} kN /m^{2} and 0.3 respectively, using factor of safety = 3. (Take influence factor = 2)

The net safe bearing capacity (in kN /m^{3}) of foundation is

Solution:

QUESTION: 65

A multistorey building with a basement is to be constructed. The top 4 m contains loose silt below which dense sand layer is present upto a great depth. Ground water table is at the ground surface. The foundation consists of the basement slab of 6 m width which will rest on the top of dense sand as shown in figure. For dense sand saturated unit weight is 20kN /m^{3} and bearing capacity factor, N_{q} =40, N_{λ}= 45, g for loose silt saturated unit

weight =18kN /m^{3} , N_{q}=15, N_{λ} =20 g . Effective cohesion is 0. Neglect depth factor average elastic modulus E, and Poisson ratio μ of dense sand is 60 ×10^{3} kN /m^{2} and 0.3 respectively, using factor of safety = 3. (Take influence factor = 2)

The immediate settlement of foundation is

Solution:

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