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QUESTION: 1

Consider the following sentences: All benches are beds. No bed is a bulb. Some bulbs are lamps. Which of the following can be inferred?

i. Some beds are lamps.

ii. Some lamps are beds.

Solution:

(D)

Since there is no direct relation given between lamps and beds. So, neither will be correct

QUESTION: 2

The following sequence of numbers is arranged in increasing order: 1, x, x, x, y, y, 9,16,18.

Given that the mean and median are equal, and are also equal to twice the mode, the value of y is

Solution:

(D)

Exp: Given, Mean = Median = 2Mode

⇒ Mean = Median = 2x

∴ y = 2x→ (4) [∵Median = 2 Mode]

From (2);11x = 44 x = 4; ∴ y = 8

QUESTION: 3

The bacteria in milk are destroyed when it _________ heated to 80 degree Celsius.

Solution:

Since “are” is used in the statement and the statement is talking general information, therefore, present tense will be used.

Thus, the statement will be- The bacteria in milk are destroyed when it is heated to 80 degree Celsius.

QUESTION: 4

If the radius of a right circular cone is increased by 50%, its volume increases by

Solution:

(C)

Exp : Given, radius of a right circular cone is increased by 50%.

Let, height of the circular cone = (h) Initially, Volume of the cone(V) =(1/3)πR^{2}h .......(1)

New volume of the cone(V') = =(1/3)πr^{2}(1.5R)^{2}h .......(2)

From (1) and (2);= 2.25v

Hence increases by 125% as

100 = 125%

QUESTION: 5

__________ with someone else’s email account is now very serious offence.

Solution:

Involving means getting indulged in a work.

Assisting means helping others to do a work.

Tampering means interfering with (something) in order to cause damage or make unauthorized alterations.

Incubating means developing an infectious disease before symptoms appear.

Thus, here tampering is most suitable word.

QUESTION: 6

The last digit of (2171)^{7} + (2172)^{9} + (2173)^{11} + (2174)^{13} is

Solution:

The last digit of (2171)^{7} = 1

The last digit of (2172)^{9} = (2172)^{8}(2172)

QUESTION: 7

Two machines M1 and M2 are able to execute any of four jobs P, Q, R and S. The machines can perform one job on one object at a time. Jobs P, Q, R and S take 30 minutes, 20 minutes, 60 minutes and 15 minutes each respectively. There are 10 objects each requiring exactly 1 job. Job P is to be performed on 2 objects. Job Q on 3 objects. Job R on 1 object and Job S on 4 objects. What is the minimum time needed to complete all the jobs?

Solution:

QUESTION: 8

Students applying for hostel rooms are allotted rooms in order of seniority. Students already staying in a room will move if they get a room in their preferred list. Preferences of lower ranked applicants are ignored during allocation.

Given the data below, which room will Ajit stay in?

Solution:

**(B) **

As per their preferences given

QUESTION: 9

The bar graph below shows the output of five carpenters over one month, each of whom made different items of furniture: Chairs, tables, and beds.

Consider the following statements.

i. The number of beds made by carpenter C2 is exactly the same as the same as the number of tables made by carpenter C3.

ii. The total number of chairs made by all carpenters is less than the total number of tables. Which one of the following is true?

Solution:

(C) Exp:

(i) The number of beds made by carpenter C_{2} is exactly the same as the number of tables made by carpenter C_{3}

i.e., beds made by carpenter

C_{2} = 8 = tables made by carpenter C_{3}

[∵ From the bar graph ]

So,(i) is correct. (ii) Total Number of tables made by all carpenters=31.

Total Number of chairs made by all carpenters=23

∴23 < 31

∵ (ii) is correct

QUESTION: 10

The old concert hall was demolished because of fears that the foundation would be affected by the construction tried to mitigate the impact of pressurized air pockets created by the excavation of large amounts of soil. But even with these safeguards, it was feared that the soil below the concert hall would not be stable.

From this, one can infer that

Solution:

QUESTION: 11

The ordinates of a 2 – h unit hydrograph at 1 hour intervals starting from time t = 0, are 0, 3, 8, 6, 3, 2 and 0 m3/s. Use trapezoidal rule for numerical integration, if required.

What is the catchment area represented by the unit hydrograph?

Solution:

QUESTION: 12

A uniformly distributed line load of 500 kN/m is acting on the ground surface. Based on Boussinesq’s theory, the ratio of vertical stress at a depth 2 m to that at 4 m, right below the line of loading, is

Solution:

(C)

Exp: Due to UDL

Vertical stress =

at x 0; veritcal stress

QUESTION: 13

According to IS 456-2000, which one of the following statements about the depth of neutral axis χ_{u,bal} for a balanced reinforced concrete section is correct?

Solution:

(B) Exp: By limit state method

For balanced section

∴ χ_{u ,bal} depends upon grade of steel only.

QUESTION: 14

Group I lists the type of gain or loss of strength in soils.

Group II lists the property or process responsible for the loss or gain of strength in soils.

Group I Group II

P. Regain of strength with time 1. Boiling

Q. Loss of strength due to cyclic loading 2. Liquefaction

R. Loss of strength due to upward seepage 3. Thixotropy

S. Loss of strength due to remolding 4. Sensitivity

The correct match between Group I and Group II is

Solution:

QUESTION: 15

A runway is being constructed in a new airport as per the International Civil Aviation Organization (ICAO) recommendations. The elevation and the airport reference temperature of this airport are 535 m above the mean sea level and 22.65°C, respectively. Consider the effective gradient of runway as 1%. The length of runway required for a design-aircraft under the standard conditions is 2000 m. Within the framework of applying sequential corrections as per the ICAO recommendations, the length of runway corrected for the temperature is

Solution:

Correction for elevation : 7 % increase per 300 m height

∴ Corrected length = 2000 + 249.7 = 2249.7 m

Correction for temperature :

std. Atm temp 15 - 0.0065 *535 + 11.52°C

ΔT = 22.65 -11.52 = 11.13°C

∴ Corrected length 2249.74 250.32

= 2500.02m

QUESTION: 16

A soil sample is subjected to a hydrostatic pressure, σ. The Mohr circle for any point in the soil sample would be

Solution:

σx = σy = σz = σ,

For Mohr’s Circle

QUESTION: 17

The figure shows a two-hinged parabolic arch of span load of intensity q per unit length.

The maximum bending moment in the arch is equal to

Solution:

Bending moment at any point for two-hinged parabolic arch with uniformly distributed load is zero.

QUESTION: 18

For a steady incompressible laminar flow between two infinite parallel stationary plates, the shear stress variation is

Solution:

We know that velocity variation,

QUESTION: 19

Solution:

QUESTION: 20

The number of parameters in the univariate exponential and Gaussian distributions, respectively, are

Solution:

Probability density functions of univariable exponential distributes

For Gaussian distribution

where µ and σ are parameters

QUESTION: 21

The wastewater form a city, containing a high concentration of biodegradable organics, is being steadily discharged into a flowing river at a location S. If the rate of aeration of the river water is lower than the rate of degradation of the organics, then the dissolved oxygen of the river water

Solution:

Since, currently the rate of aeration is less than the rate of degradation of the organics. Therefore, at downstream the oxygen level will continue to deplete until the rate of aeration = rate of degradation of organics.

QUESTION: 22

The reaction rate involving reactants A and B is given by −k [A]^{α} [B]^{β}. Which one of the following statements is valid for the reaction to be first –order reaction?

Solution:

In chemical kinetics, the order of reaction with respect to given substance is defined as the index or exponent to which its concentration term in the rate equation is raised.

r = k.[A]^{α} [B]^{β}

Order of reaction = α + β

For first order reaction, α + β = 1

QUESTION: 23

A strip footing is resting on the ground surface of a pure clay bed having an undrained cohesion C_{u}. The ultimate bearing capacity of the footing is equal to

Solution:

Ultimate bearing capacity = c.N_{c}

For pure clay N_{c} = 5.14 = (π + 2)

UBC = (π + 2) C

QUESTION: 24

A simply supported beam is subjected to a uniformly distributed load. Which one of the following statements is true?

Solution:

QUESTION: 25

A triangular pipe network is shown in the figure.

The head loss in each pipe is given by h_{f} = rQ^{1.8}, with the variables expressed in a consistent set of units. The value of r for the pipe AB is 1 and for the pipe BC is 2. If the discharge supplied at the point A (i.e., 100) is equally divided between the pipes AB and AC, the value of r (up to two decimal places) for the pipe AC should be_______.

Solution:

If the discharge supplied at point A is equally divided so Q_{AB }= Q_{AC} = 50m^{3}/s

*Answer can only contain numeric values

QUESTION: 26

Solution:

QUESTION: 27

A super-elevation e is provided on a circular horizontal curve such that a vehicle can be stopped on the curve without sliding. Assuming a design speed v and maximum coefficient of side friction f_{max}, which one of the following criteria should be satisfied?

Solution:

θ = tan θ = e

For no sliding

For stopped vehicle v = 0

f ≥ −e

QUESTION: 28

Which one of the following is NOT present in the acid rain?

Solution:

Acid rain is caused due to a mixture of gases like sulphur, nitrogen dioxide and carbon dioxide with water. Thus, Nitric acid, sulphuric acid and carbonic acid are formed.

However, acetic acid is not present in the acid rain.

QUESTION: 29

The accuracy of an Electronic Distance Measuring Instrument (EDMI) is specified as ± (a mm + b ppm). Which one of the following statements is correct?

Solution:

Accuracy of EDMI is generally stated in terms of constant instrument error and measuring error proportional to distance being measured.

± (a mm + b ppm)

The first part in this expression indicates a constant instrument error that is independent of length of line measured. Second component is distance related error.

*Answer can only contain numeric values

QUESTION: 30

Consider the following partial differential equation:

Solution:

By comparing with general form

Condition for parabolic is

B^{2} - 4AC = 0

QUESTION: 31

The matrix P is the inverse of a matrix Q. If I denotes the identity matrix, which one of the following options is correct ?

Solution:

Given P is inverse of Q

⇒ PQ = QP = I

*Answer can only contain numeric values

QUESTION: 32

Vehicles arriving at an intersection from one of the approach road follow the Poisson distribution. The mean rate of arrival is 900 vehicles per hour. If a gap is defined as the time difference between two successive vehicle arrivals (with vehicles assumed to be points), the probability (up to four decimal places) that the gap is greater than 8 seconds is _____

Solution:

By Poission’s distribution

QUESTION: 33

Let x be a continuous variable defined over the interval

The integral

Solution:

QUESTION: 34

The number of spectral bands in the Enhanced Thematic satellite Landsat-7 is

Solution:

*Answer can only contain numeric values

QUESTION: 35

A 3 m thick clay layer is subjected to an initial uniform pore pressure of 145 kPa as shown in the figure.

For the given ground conditions, the time (in days, rounded to the nearest integer) required for 90% consolidation would be ________

Solution:

It is single drainage

QUESTION: 36

A planar truss tower structure is shown in the figure.

Consider the following statements about the external and internal determinacies of the truss.

(P) Externally Determinate

(Q) External Static Indeterminacy = 1

(R) External Static Indeterminacy = 2

(S) Internally Determinate

(T) Internal Static Indeterminacy = 1

(U) Internal Static Indeterminacy = 2

**Which one of the following options is correct?**

Solution:

D_{se} = r - 3

r = number if sup port reactions = 4

D_{se } = 4 - 3 = 1

D_{si} = number of double diagonals 2

*Answer can only contain numeric values

QUESTION: 37

Consider the stepped bar made with a linear elastic material and subjected to an axial load of 1 kN, as shown in the figure.

Segments 1 and 2 have cross-sectional are of 100 mm^{2} and 60 mm^{2}, Young’s modulus of 2 × 10^{5} MPa and 3 × 10^{5} MPa, and length of 400 mm and 900 mm, respectively. The strain energy (in N-mm, up to one decimal place) in the bar due to the axial load is_____

Solution:

*Answer can only contain numeric values

QUESTION: 38

Consider the beam ABCD shown in the figure.

For a moving concentrated load of 50 kN on the beam, the magnitude of the maximum bending moment (in kN-m) obtained at the support C will be equal to______

Solution:

By muller Breslau principle

ILD for moment at C

x - 0 = 4

x = 4

Load is acting at point B

B.M = 50 × 4 = 200kN − m

*Answer can only contain numeric values

QUESTION: 39

A column is subjected to a load through a bracket as shown in the figure.

The resultant force (in kN, up to one decimal place) in the bolt 1 is_____

Solution:

P = 10KN, e = 15cm, r_{1} = r_{2} = r_{3} = r_{4} = 5 cm

Force in bolt 1 due to moment

*Answer can only contain numeric values

QUESTION: 40

The activity details of a project are given below :

Solution:

Activity on arrow (AoA) diagram:

Time along path 1- 2- 4- 6- 7

= 6+15+14+16 = 51 day

*Answer can only contain numeric values

QUESTION: 41

The value of M in the beam ABC shown in the figure is such that the joint B does not rotate.

The value of support reaction (in kN) at B should be equal to______

Solution:

*Answer can only contain numeric values

QUESTION: 42

Two wastewater streams A and B, having an identical ultimate BOD are getting mixed to form the stream C. The temperature of the stream A is 20°C and the temperature of the stream C is 10°C. It is given that

• The 5-day BOD of the stream A measured at 20°C=50 mg/l

• BOD rate constant (base 10) at 20°C=0.115 per day

• Temperature coefficient = 1.135

The 5 –day BOD (in mg/l, up to one decimal place) of the stream C, calculated at 10°C, is______

Solution:

*Answer can only contain numeric values

QUESTION: 43

A particle of mass 2 kg is travelling at a velocity of 1.5 m/s. A force f(t) = 3t^{2} (in N) is applied to it in the direction of motion for a duration of 2 seconds, where t denotes time in seconds. The velocity (in m/s, up to one decimal place) of the particle immediately after the removal of the force is________

Solution:

f (t) = 3t^{2}

m.Q = 3t^{2}

QUESTION: 44

The queue length (in number of vehicles) versus time (in seconds) plot for an approach to a signalized intersection with the cycle length of 96 seconds is shown in the figure scale).

At time t = 0, the light has just turned red. The effective green time is 36 seconds, during which vehicles discharge at the saturation flow rate, vph). Vehicles arrive at a uniform rate, v (in vph), throughout the cycle. Which one of the following statements is TRUE?

Solution:

QUESTION: 45

For the function to be a valid probability density function, which one of the following statements is correct?

Solution:

f (x) = a + bx 0 ≤ x ≤ 1 is a valid probability density function

a = 0.5, b = 1 satisfies the above relation

*Answer can only contain numeric values

QUESTION: 46

The infinite sand slope shown in the figure is on the verge of sliding failure. The ground water table coincides with the ground surface. Unit weight of water γ_{w} = 9.81kN m^{3} .

The value of the effective angle of internal friction (in degrees, up to one decimal place) of the sand is

Solution:

*Answer can only contain numeric values

QUESTION: 47

A sluice gate used to control the flow in a horizontal channel of unit width is shown in figure.

It is observed that the depth of flow is 1.0 m upstream of the gate, while the depth is 0.2 m downstream of the gate. Assuming a smooth flow transition across the sluice gate, i.e., without any energy loss, and the acceleration due to gravity as 10 m/s^{2}, the discharge (in m^{3}/s, up to two decimal places) passing under the sluice gate is_______

Solution:

Given Energy loss is zero ⇒ = E_{1} = E_{2}

QUESTION: 48

Group I contains three broad classes of irrigation supply canal outlets. Group II presents hydraulic performance attributes.

The correct match of the items in Group I with the items in Group II is

Solution:

QUESTION: 49

Consider the matrix Which one of the following statements is TRUE for the

eigenvalues and eigenvectors of this matrix?

Solution:

Let A =

Characteristic equations is λ^{2} − 6λ + 9 = 0 ⇒ λ = 3, 3

Eigen value 3 has multiplicity 2. Eigen vectors corresponding to λ = 3 is (A − 3I) X = 0

e(A) = 1

Number of linearly independent eigen vectors corresponding to eigen value λ = 3 is n - r = 2 - 1 = 1 where n = no. of unknowns, r= rank of (A − λI)

∴ One linearly independent eigen vector exists corresponding to λ = 3

QUESTION: 50

The laboratory test on a soil sample yields the following results: natural moisture content = 18%, liquid limit = 60%, plastic limit = 25%, percentage of clay sized fraction = 25%. The liquidity index and activity (as per the expression proposed by skempton) of the soil, respectively, are

Solution:

Liquidity Index (I_{L}) = 1 − I_{C}

QUESTION: 51

The solution of the equation with Q = 0 at t = 0 is

Solution:

Comparing with first order linear differential equations

*Answer can only contain numeric values

QUESTION: 52

Water flows through a 90° bend in a horizontal plane as depicted in the figure.

A pressure of 140 kPa is measured at section 1-1. The inlet diameter marked at section 1-1 is cm, while the nozzle diameter marked at section 2-2 iscm. Assume the following:

(i) Acceleration due to gravity = 10 m/s^{2}.

(ii) Weights of both the bent pipe segment as well as water are negligible.

(iii) Friction across the bend is negligible.

The magnitude of the force (in kN, up to two decimal places) that would be required to hold the pipe section is______

Solution:

*Answer can only contain numeric values

QUESTION: 53

A pre-tensioned rectangular concrete beam 150 mm wide and 300 mm depth is prestressed with three straight tendons, each having a cross-sectional area of 50 mm2, to an initial stress of 1200 N/mm2. The tendons are located at 100 mm from the soffit of the beam. If the modular ratio is 6, the loss of prestressing force (in kN, up to one decimal place) due to the elastic deformation of concrete only is ______.

Solution:

Stress = 1200 N / mm^{2}

Loss due to elastic deformation = m.f _{c} = 6 × 5.33 = 31.98

Prestress force = 31.98 × 3 × 50 = 4797 N = 4.8 KN

*Answer can only contain numeric values

QUESTION: 54

The spherical grit particles, having a radius of 0.01mm and specific gravity of 3.0, need to be separated in a settling chamber. It is given that

• g = 9.81 m/s^{2}

• the density of the liquid in the settling chamber = 1000 kg/m^{3}

• the kinematic viscosity of the liquid in the settling chamber = 10^{-6} m^{2}/s

Assuming laminar conditions, the settling velocity (in mm/s, up to one decimal place) is_____

Solution:

Kinematic viscocity = 10^{−6} m^{2} / s

*Answer can only contain numeric values

QUESTION: 55

The equivalent sound power level (in dB) of the four sources with the noise levels of 60 dB, 69 dB, 70 dB and 79 dB is_______

Solution:

Equivalent sound power level

*Answer can only contain numeric values

QUESTION: 56

Consider the equation This is numerically solved by using the forward Euler method with a step size. ∆t = 2. The absolute error in the solution at the end of the first time step is_________

Solution:

__Approximation value by Euler's Method__:

__Exact value__:

u = t^{3} + t

u (2) = 8 + 2 = 10

∴ absolute error = |10 − 2| = 8

*Answer can only contain numeric values

QUESTION: 57

It is proposed to drive H-piles up to a depth of 7 m at a construction site. The average surface area of the H-pile is 3 m^{2} per meter length. The soil at the site is homogeneous sand, having an effective friction angle of 32°. The ground water table (GWT) is at a depth of 2 m below the ground surface. The unit weights of the soil above and below the GWT are 16 kN/m^{3} and 19 kN/m^{3}, respectively. Assume the earth pressure coefficient, K= 1.0, and the angle of wall friction, δ = 23°. The total axial frictional resistance (in kN, up to one decimal place) mobilized on the pile against the driving is________

Solution:

__BC__:

Effective stress variation

Total axial frictional resistance = 350+40.75 = 390.75KN

*Answer can only contain numeric values

QUESTION: 58

The wastewater having an organic concentration of 54 mg/l is flowing at a steady rate of 0.8m^{3}/day through a detention tank of dimensions 2m × 4m × 2m. If the contents of the tank are well mixed and the decay constant is 0.1 per day, the outlet concentration (in mg/l, up to one decimal place) is ______

Solution:

QUESTION: 59

The radius of a horizontal circular curve on a highway is 120 m. The design speed is 60 km/hour, and the design coefficient of lateral friction between the tyre and the road surface is 0.15. The estimated value of superelevation required (if full lateral friction is assumed to develop), and the value of coefficient of friction needed (if no superelevation is provided) will, respectively, be

Solution:

*Answer can only contain numeric values

QUESTION: 60

Consider two axially loaded columns, namely, 1 and 2, made of a linear elastic material with Young’s modulus 2 × 105 MPa, square cross-section with side 10 mm, and length 1 m. For Column 1, one end is fixed and the other end is free. For Column 2, one end is fixed and the other end is pinned. Based on the Euler’s theory, the ratio (up to one decimal place) of the buckling load of Column 2 to the buckling load of Column 1 is ________

Solution:

For column -1; One end is fixed and other is free

One end is fixed and other is pinned.

QUESTION: 61

The observed bearings of a traverse are given below:

The stations(s) most likely to be affected by the local attraction is/are

Solution:

So, local attraction at only R

QUESTION: 62

A 1 m wide rectangular channel has a bed slope of 0.0016 and the Manning’s roughness coefficient is 0.04. Uniform flow takes place in the channel at a flow depth of 0.5 m. At a particular section, gradually varied flow (GVF) is observed and the flow depth is measured as 0.6 m. The GVF profile at that section is classified as

Solution:

y_{n} = 0.5m

*Answer can only contain numeric values

QUESTION: 63

A consolidated undrained (CU) triaxial compression test is conducted on a normally consolidated clay at a confining pressure of 100 kPa. The deviator stress at failure is 80 kPa, and the pore-water pressure measured at failure is 50 kPa. The effective angle of internal friction (in degrees, up to one decimal place) of the soil is_________

Solution:

For normally consolidated clay c = 0

*Answer can only contain numeric values

QUESTION: 64

An effective rainfall of 2-hour duration produced a flood hydrograph peak of 200 m^{3}/s. The flood hydrograph has a base flow of 20 m^{3}/s. If the spatial average rainfall in the watershed for the duration of storm is 2 cm and the average loss rate is 0.4 cm/hour, the peak of 2-hour unit hydrograph (in m^{3}/s-cm, up to one decimal place) is_________

Solution:

Food hydrograph peak = 200 m^{3}/s

Base flow 20 m^{3}/s

QUESTION: 65

The following observations are made while testing aggregate for its suitability in pavement construction:

i. Mass of oven-dry aggregate in air = 1000 g

ii. Mass of saturated surface-dry aggregate in air = 1025 g

iii. Mass of saturated surface-dry aggregate under water = 625 g

Based on the above observations, the correct statement is

Solution:

Mass of oven dry aggregate w_{a} = 1000g

Mass of water in saturated surface dry aggregate = w_{w}

So, w_{a} + w_{w} = 1025

Mass of saturated surface dry aggregate under water = 625 g

∴ Bulk specific gravity of aggregate

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