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QUESTION: 1

There was no doubt that their work was __thorough__.

Which of the words below is closest in meaning to the underlined word above?

Solution:

QUESTION: 2

Four cards lie on a table. Each card has a number printed on one side and a colour on the other. The faces visible on the cards are 2, 3, red, and blue.

Proposition: If a card has an even value on one side, then its opposite face is red. The cards which MUST be turned over to verify the above proposition are

Solution:

In order to verify this propositions we have to turn to card 2 and blue from given 4 cards as proposition says it has even an one side opposite is red. Vice-verse might or might not be true so, answer (C) as all other options are eliminated.

QUESTION: 3

Two dice are thrown simultaneously. The probability that the product of the numbers appearing on the top faces of the dice is a perfect square is

Solution:

Required probability

QUESTION: 4

What is the value of x when

Solution:

QUESTION: 5

The event would have been successful if you ______ able to come.

Solution:

QUESTION: 6

P,Q,R,S,T and U are seated around a circular table. R is seated two places to the right of Q.P is seated three places to the left of R. S is seated opposite U. If P and U now switch seats. Which of the following must necessarily be true?

Solution:

P ↔ U Now, P & U switch seats; then there are 2 possibilities

QUESTION: 7

Bhaichung was observing the pattern of people entering and leaving a car service centre. There was a single window where customers were being served. He saw that people inevitably came out of the centre in the order that they went in. However, the time they spent inside seemed to vary a lot: some people came out in a matter of minutes while for others it took much longer.

From this, what can one conclude?

Solution:

People coming out in the same order in which they enter indicates that the centre operates on a first come first serve basis.

QUESTION: 8

A map shows the elevations of Darjeeling, Gangtok, Kalimpong, pelling, and Siliguri. Kalimpong is at a lower elevation than Gangtok. Pelling is at a lower elevation than Gangtok. Pelling is at a higher elevation that siliguri. Darjeeling is at a higher elevation than Gangtok. Which of the following statements can be inferred from the paragraph above?

i. Pelling is at a higher elevation than Kalimpong

ii. Kalimpong is at a lower elevation than Darjeeling

iii. Kalimpong is at a higher elevation than siliguri

iv. Siliguri is at a lower elevation than Gangtok

Solution:

QUESTION: 9

Budhan covers a distance of 19 km in 2 hours by cycling one fourth of the time and walking the rest. The next day he cycles (at the same speed as before) for half the time and walks the rest (at the same speed as before) and covers 26 km in 2 hours. The speed in km/h at which Budhan walks is

Solution:

Let cycling speed = C; and walking speed = W

On solving (1) & (2), we get W = 6 km/hr

QUESTION: 10

The points in the graph below represent the halts of a lift for duration of 1 minute, over a period of 1 hour.

Which of the following statements are correct?

i. The elevator never moves directly from any non-ground floor to another non-ground floor over the one hour period

ii. The elevator stays on the fourth floor for the longest duration over the one hour period

Solution:

(i). is incorrect as its has more directly.

(ii). is incorrect as it stayed for maximum duration on ground floor.

QUESTION: 11

Consider a rigid retaining wall with partially submerged cohesionless backfill with a surcharge. Which one of the following diagrams closely represents the Rankine’s active earth pressure distribution against this wall?

Solution:

*Answer can only contain numeric values

QUESTION: 12

The VPI (vertical point of intersection) is 100 m away (when measured along the horizontal) from the VPC (vertical point of curvature). If the vertical curve is parabolic, the length of the curve (in meters and measured along the horizontal) is ______

Solution:

VPI is horizontally midway between VPC and VPT

VPC = VPI – L/2

⇒ O = 100 – L/2

⇒ L = 200m

*Answer can only contain numeric values

QUESTION: 13

For a construction project. The mean and standard deviation of the completion time are 200 days and 6.1 days, respectively. Assume normal distribution and use the value of standard normal deviate Z = 1.64 for the 95% confidence level. The maximum time required (in days) for the completion of the project would be __________

Solution:

For 95% confidence level z = 1.64

T_{E} = 200 days

σ = 6.1days

T_{S} = T_{E} + zσ = 200 + 1.64 × 6.1 = 200 + 10.004 = 210.004 days

QUESTION: 14

Given that the scope of the construction work is well-defined with all its drawings, specifications, quantities and estimates, which one of the following types of contract would be most preferred?

Solution:

*Answer can only contain numeric values

QUESTION: 15

The divergence of the vector field V = x^{2}i + 2y^{3}j + z^{4}k at x = 1, y = 2, z = 3 is_______

Solution:

Given

QUESTION: 16

Consider the frame shown in the figure:

If the axial and shear deformations in different members of the frame are assumed to be negligible, the reduction in the degree of kinematical indeterminacy would be equal to

Solution:

Total degree of freedom = 3j-R

J = no. of joints = 6

R = no.of reactions = 2 + 2 = 4

DOF = 3×6 − 4 = 18 − 4 = 14

When axial deformation are neglected total axial deformations = 8

Reduction in D_{k} = 14 − 8 = 6

QUESTION: 17

As per Noise Pollution (Regulation and Control) Rules 2000 of India, the day time noise limit for a residential zone, expressed in dB (A) L_{eq}, is

Solution:

QUESTION: 18

Let G be the specific gravity of soil solids, w the water content in the soil sample, γ_{w} the unit weight of water, and γ_{d} the dry unit weight of the soil. The equation for the zero air voids line in a compaction test plot is

Solution:

From zero air void line

QUESTION: 19

The safety within a roundabout and the efficiency of a roundabout can be increased, respectively, by

Solution:

QUESTION: 20

In a material under a state of plane strain, a 10 × 10 mm square centered at a point gets deformed as shown in the figure.

If the shear strain γ_{xy} at this point is expressed as 0.001k (in rad), the value of k is

Solution:

Shear strain in an element is positive when the angle between two faces is reduced and negative when angle is increased.

Here since angle has increased, so shear strain should be negative.

Y_{xy} = -0.0056 rad = 0.001k

So, -0.005 = 0.001 K

⇒ K = -0.50

QUESTION: 21

The method of orientation used, when the plane table occupies a position not yet located on the map, is called as

Solution:

Resection is the method of orientation used when the table occupies a position not yet located in the map.

QUESTION: 22

If a centrifugal pump has an impeller speed of N (in rpm), discharge Q (in m^{3}/s) and the total head H (in m), the expression for the specific speed Ns of the pump is given by

Solution:

The specific speed of pump

QUESTION: 23

Following observations have been made for the elevation and temperature to ascertain the stability of the atmosphere:

The atmosphere is classified as

Solution:

So, Neutral

*Answer can only contain numeric values

QUESTION: 24

During a storm event in a certain period, the rainfall intensity is 3.5 cm/hour and the is 1.5 cm/hour. The intensity of effective rainfall (in cm/hour, up to one decimal place) for this period is ______

Solution:

QUESTION: 25

For a broad gauge railway track on a horizontal curve of radius R (in m), the equilibrium cant e required for a train moving at a speed of V (in km per hour) is

Solution:

QUESTION: 26

Consider the following simultaneous equations (with c_{1} and c_{2} being constants):

3x_{1} + 2x_{2} = c_{1}

4x_{1} + x_{2} = c_{2}

The characteristic equation for these simultaneous equations is

Solution:

given systems

3x_{1} + 2x_{2} = c_{1}

4x_{1} + x_{2} = c_{2}

Characteristic equations of above systems is

By expanding λ^{2} − 4λ − 5 = 0

*Answer can only contain numeric values

QUESTION: 27

A sheet pile has an embedment depth of 12 m in a homogeneous soil stratum. The coefficient of permeability of soil is 10^{−6} m s. Difference in the water levels between the two sides of the sheet pile is 4 m. The flow net is constructed with five number of flow lines and eleven number of equipotential lines. The quantity of seepage (in cm^{3}/s per m, up to one decimal place) under the sheet pile is _____

Solution:

N^{f} = No. of flow channels = No. of flow lines -1 = 5 - 1 = 4

N_{d} = No. of equipotential drops= no. of equipotenial lines-1 = 11 - 1 = 10

*Answer can only contain numeric values

QUESTION: 28

While aligning a hill road with a ruling gradient of 6 %, a horizontal curve of radius 50 m is encountered. The grade compensation (in percentage, up to two decimal places) to be provided for this case would be______

Solution:

The grade compensation

Maximum grade compensation

Grade compensation = 1.5

QUESTION: 29

Consider the following statements related to the pore pressure parameters, A and B:

P. A always lies between 0 and 1.0

Q. A can be less than 0 or greater than 1.0

R. B always lies between 0 and 1.0

S. B can be less than 0 or greater than 1.0

For these statements, which one of the following options is correct?

Solution:

QUESTION: 30

Let the characteristic strength be defined as that value, below which not more than 50% of the results are expected to fall. Assuming a standard deviation of 4 MPa, the target mean strength (in MPa) to be considered in the mix design of a M25 concrete would be

Solution:

For the given condition,

Target mean strength = characteristic strength = 25 MPa

QUESTION: 31

The plate load test was conducted on a clayey strata by using a plate of 0.3m × 0.3 m dimensions, and the ultimate load per unit area for the plate was found to be 180 kPa. The ultimate bearing capacity (in kPa) of a 2 m wide square footing would be

Solution:

In plate load test,

The ultimate bearing capacity does not depends upon width of footing

q_{uf} = q_{up} = 180 kPa

*Answer can only contain numeric values

QUESTION: 32

The infiltration capacity of a soil follows the Horton’s exponential model, f = c_{1} + c_{2}e^{−kt}.

During and experiment, the initial infiltration capacity was observed to be 200 mm/h. After a long time, the infiltration capacity was reduced to 25 mm/h. If the infiltration capacity after 1 hour was 90 mm/h, the value of the decay rate constant, k (in h^{-1}, up to two decimal places) is_______

Solution:

Horton’s infiltration capacity f = f_{e} + (f_{o} − f_{e}) e^{−∝t}

f_{e} = ultimate infiltration capacity = 25 mm/hr

f_{o} = Initial infiltration capacity = 200 mm/hr

f = Infiltration capacity = 90 mm/hr

90 = 25 + (200 − 25) e^{−∝×1}

*Answer can only contain numeric values

QUESTION: 33

A two-faced fair coin has its faces designated as head (H) and tail (T). This coin is tossed three times in succession to record the following outcomes: H, H, H. If the coin is tossed one more time, the probability (up to one decimal place) of obtaining H again, given the previous realizations of H, H and H, would be_______

Solution:

Given first three are already heads. If the coin is tossed again, the outcome does not depends on previous outcomes.

Probability of fourth time head is

Given condition is that ( H.H.H) is already realized

QUESTION: 34

The most important type of species involved in the degradation of organic matter in the case of activated sludge process is

Solution:

QUESTION: 35

Let w = f (x,y), where x and y are functions of t. Then, according to the chain rule equal to

Solution:

w = f (x, y) where x and y are functions of t.

By Chain Rule

*Answer can only contain numeric values

QUESTION: 36

Consider the portal frame shown in the figure and assume the modulus of elasticity E = 2.5 × 10^{4} MPa and the moment of inertial, I = 8 × 10^{8} mm^{4} for all the members of the frame.

The rotation (in degrees, up to one decimal place) at the rigid joint Q would be_______

Solution:

*Answer can only contain numeric values

QUESTION: 37

The radii of relative stiffness of the rigid pavements P and Q are denoted by ℓ_{p} and ℓ_{Q} , respectively. The geometric and material properties of the concrete slab and underlying soil are given below:

The ratio (up to one decimal place) of ℓ_{p} / ℓ_{Q} is__________

Solution:

Radius of relative stiffness

*Answer can only contain numeric values

QUESTION: 38

A 1 m wide rectangular channel carries a discharge of 2m^{3}s. The specific energy-depth diagram is prepared for the channel. It is observed in this diagram that corresponding to a particular specific energy, the subcritical depth is twice the supercritical depth. The subcritical depth (in meters, up to two decimal places) is equal to _______

Solution:

Given sub critical depth = 2 × super critical depth

y= super critical depth

Sub critical depth = 2 y

Super critical depth (y) = 0.5347

Sub critical depth = 2y = 2 × 0.5347 = 1.0694 m

*Answer can only contain numeric values

QUESTION: 39

A hollow circular shaft has an outer diameter of 100 mm and inner diameter of 50 mm. If the allowable shear stress is 125 MPa, the maximum torque (in kN-m) that the shaft can resist is_______

Solution:

QUESTION: 40

Consider the following statements:

P. Walls of one brick thick are measured in square meters.

Q. Walls of one brick thick are measured in cubic meters.

R. No deduction in the brickwork quantity is made for openings in walls up to 0.1 m^{2} area.

S. For the measurement of excavation from the borrow pit in a fairly uniform ground, dead men are left at suitable intervals.

For the above statements, the correct option is

Solution:

QUESTION: 41

Following are the statements related to the stress paths in a triaxial testing of soils:

P. If σ_{1} = σ_{3} , the stress point lies at the origin of the p-q plot

Q. If σ_{1} = σ_{3} , the stress point lies on the p-axis of the p-q plot.

R. If σ_{1} > σ_{3} , both the stress points p and q are positive.

For the above statements, the correct combination is

Solution:

∴ lies on P.ax is

p & q are positive

*Answer can only contain numeric values

QUESTION: 42

A simply supported rectangular concrete beam of span 8m has to be prestressed with a force of 1600kN. The tendon is of parabolic profile having zero eccentricity at the supports. The beam has to carry an external uniformly distributed load of intensity 30 kN/m. Neglecting the self-weight of the beam, the maximum dip (in meters, up to two decimal places) of the tendon at the mid-span to balance the external load should be________

Solution:

Maximum moment = Pe

*Answer can only contain numeric values

QUESTION: 43

An observer standing on the deck of a ship just sees the top of a lighthouse. The top of the lighthouse is 40 m above the sea level and the height of the observer’s eye is 5 m above the sea level. The distance (in km, up to one decimal place) of the observer form the lighthouse is

Solution:

Therefore distance of observer from light house

d = d_{1} + d_{2}

= 8.62 + 24.38

= 33 km

QUESTION: 44

Solution:

*Answer can only contain numeric values

QUESTION: 45

A 2 m long, axially loaded mild steel rod of 8 mm diameter exhibits the load-displacement (p − δ) behavior as shown in the figure.

Assume the yield stress of steel as 250 Mpa. The complementary energy (in N-mm) stored in the bar up to its linear elastic behavior will be_______

Solution:

Strain up to linear elastic behaviour is

QUESTION: 46

Two cars P and Q are moving in a racing track continuously for two hour. Assume that no other vehicles are using the track during this time. The expressions relating the distance travelled d (in km) and time t (in hour) for both the vehicles are given as

P:d = 60t

Q:d = 60t^{2}

Within the first one hour, the maximum space headway would be

Solution:

P: d = 60t , Q : d = 60t^{2}

Distance at any time t between P and Q is given by d(t) = 60t - 60t^{2}

For space headway to be maximum

So, space headway would be max at t = 30 minutes

QUESTION: 47

Consider the following definite integral:

The value of the integral is

Solution:

*Answer can only contain numeric values

QUESTION: 48

A municipal corporation is required to treat 1000 m^{3}/day of water. It is found that an overflow rate of 20 m/day will produce a satisfactory removal of the discrete suspended particles at a depth of 3 m. The diameter (in meters, rounded to the nearest integer) of a circular settling tank designed for the removal of these particles would be______

Solution:

Detention time of a circular tank is given by

(rounded to nearest integer)

QUESTION: 49

For the construction of a highway. A cut is to be made as shown in the figure.

The soil exhibits and the undrained shear strength = 80 kPa. The unit weight of water is 9.81 kN/m^{3}. The unit weights of the soil above and below the ground water table are 18 and 20 kN/m^{3}, respectively. If the shear stress at Point A is 50 kPa, the factors of safety against the shear failure at this point, considering the undrained and drained conditions, respectively, would be

Solution:

Case-I: Undrained condition

Case-I: Drained condition

*Answer can only contain numeric values

QUESTION: 50

A catchment is idealized as a 25 km × 25 km square. It has five rain gauges, one at each corner and one at the center, as shown in the figure.

During a month, the precipitation at these gauges is measured as G_{1} = 300 mm, G_{2} = 285 mm, G_{3} = 272 mm, G_{4} = 290 mm and G_{5} = 288 mm. The average precipitation (in mm, up to one decimal place) over the catchment during this month by using the Thiessen polygon method is_______

Solution:

By thiesen polygon method

QUESTION: 51

The tangent to the curve represented by y = x ln x is required to have 45° inclination with the x-axis. The coordinates of the tangent point would be

Solution:

y = x ln x

*Answer can only contain numeric values

QUESTION: 52

Water is pumped at a steady uniform flow rate of 0.01 m^{3}/s through a horizontal smooth circular pipe of 100 mm diameter. Given that the Reynolds number is 800 and g is 9.81 m/s^{2} , the head loss (in meters, up to one decimal place) per km length due to friction would be____

Solution:

QUESTION: 53

Group I given a list of test methods and test apparatus for evaluating some of the properties of ordinary Portland cement (OPC) and concrete. Group II gives the list of these properties.

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

Solution:

P - Le chattier test - soundness of OPC

Q - Vee-Bee test - consistency or workability of concrete

R - Blaine air permeability test - Fineness of OPC

S - The vicat apparatus - consistency and setting time of OPC

*Answer can only contain numeric values

QUESTION: 54

The figure shows a U-tube having a 5 mm × 5 mm square cross-section filled with mercury (specific gravity = 13.6) up to a height of 20 cm in each limb (open to the atmosphere).

If 5cm^{3} of water is added to the right limb, the new height (in cm, up to two decimal places) of mercury in the LEFT limb will be______

Solution:

*Answer can only contain numeric values

QUESTION: 55

The analysis of a water sample produces the following results:

The total hardness (in mg/L as CaCO_{3}) of the water sample is_____

Solution:

QUESTION: 56

Consider the three prismatic beams with the clamped supports P, Q, and R as shown in the figures.

Given that the modulus of elasticity, E is 2.5×10^{4} MPa; and the moment of inertia, I is 8 × 10^{8} mm^{4} , the correct comparison of the magnitudes of the shear forces S and the bending moment M developed at the supports is

Solution:

S_{P} < S_{Q} > S_{R} M_{P} = M_{Q} = M_{R}

*Answer can only contain numeric values

QUESTION: 57

Consider a square-shaped area ABCD on the ground with its centre at M as shown in the figure. Four concentrated vertical load of P = 5000 kN are applied on this area, at each corner.

The vertical stress increment (in kPa, up to one decimal place) due to these loads according to the Boussinesq’s equation, at a point 5 m right below M, is______

Solution:

*Answer can only contain numeric values

QUESTION: 58

For a given water sample, the ratio between BOD_{5-day, 20°C} and the ultimate BOD is 0.68. The value of the reaction rate constant k (on base e)( in day-1, up to two decimal places) is ______

Solution:

QUESTION: 59

Two identical concrete piles having the plan dimensions 50 cm × 50 cm are driven into a homogeneous sandy layer as shown in the figures. Consider the bearing capacity factor Nq for

If Q_{P1} and Q_{P2} represent the ultimate point bearing resistance of the piles under dry and submerged conditions, respectively, which one of the following statements is correct ?

Solution:

*Answer can only contain numeric values

QUESTION: 60

The culturable command area of a canal is 10,000 ha. The area grows only two crops-rice in the Kharif season and wheat in the Rabi season. The design discharge of the canal is based on the rice requirements, which has an irrigated area of 2500 ha, base period of 150 days and delta of 130 cm. The maximum permissible irrigated area (in ha) for wheat, with a base period of 120 days and delta of 50 cm, is_______

Solution:

For rice,

*Answer can only contain numeric values

QUESTION: 61

The composition of a municipal solid waste sample is given below:

The difference between the energy content of the waste sample calculated on dry basis and as- discarded basis (in kJ/kg) would be______

Solution:

Dry weight = Total weight –m.c

QUESTION: 62

Consider the following second-order differential equation:

The particular solution of the differential equations is

Solution:

By the definition of particular solution

verifying options, option (a) satisfies,

∴ (A) is correct

__Alternate solution__

Given

*Answer can only contain numeric values

QUESTION: 63

Two plates of 8 mm thickness each are connected by a fillet weld of 6 mm thickness as shown in the figure.

The permissible stresses in the plate and the weld are 150 MPa and 110 MPa, respectively. Assuming the length of the weld shown in the figure to be the effective length, the permissible load P (in KN) is______

Solution:

Maximum load taken by plate = 150 × 50 × 8 = 60KN

QUESTION: 64

Two prismatic beams having the same flexural rigidity of 1000 kN-m^{2} are shown in the figures.

If the mid-span deflections of these beams are denoted by δ_{1 }and δ_{2} (as indicated in the figures). The correct option is

Solution:

*Answer can only contain numeric values

QUESTION: 65

Two towers A and B, standing vertically on a horizontal ground, appear in a vertical aerial photograph as shown in the figure.

The length of the image of the tower A on the photograph is1.5 cm and of the tower B is 2.0 cm. The distance of the top the tower A (as shown by the arrowhead) is 4.0 cm and the distance of the top of the tower B is 6.0 cm, as measured form the principal point p of the photograph. If the height of the tower B is 80 m, the height (in meters) of the tower A is

Solution:

For Tower B,

Radial distance of top of tower, r = 6 cm

Length of image, d = 2 cm

Height of tower, h_{2} = 80 m

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