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GATE (Graduate Aptitude Test in Engineering) Civil Engineering is an online examination conducted to get admission in M-Tech (Masters in Technology), ME (Master of Engineering ) and PhD at IITs (Indian Institutes of Technology), NITs (National Institutes of Technology), IIITs (Indian Institutes of Information Technology) and other universities in India. GATE exam is jointly conducted by IIT Bombay, IIT Delhi, IIT Guwahati, IIT Kanpur, IIT Kharagpur, IIT Madras, IIT Roorkee and Indian Institute for Science, Bangalore (IISC Bangalore). The exam is divided into two different parts General Aptitude (GA) and Candidate’s Selected Subject (Core Subjects). GATE Civil Engineering online mock tests help candidates in preparing for the GATE exam. By attempting GATE online mock tests candidates get familiar with the pattern of actual question paper. BrPaper provides all GATE question papers completely free. Here you can practice free online mock tests of Main exam of GATE Civil Engineering. We advise candidates to solve the online GATE Civil Engineering mock tests to get good marks in the exam. Start practicing CivilGATE 2020 Mock tests here online for free

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Category: GATE Civil Engineering 2020 set 1

Question 1:

In the following partial differential equation,

θ

is a function of t and z, and D and K are functions of

θ

D (θ) \frac{\partial^{2} θ}{\partial z^{2}} + \frac{\partial K (θ)}{\partial z} - \frac{\partial θ}{\partial t} = 0

The above equation is

a second order linear equation

a second degree linear equation

a second order non-linear equation

a second degree non-linear equation

Category: GATE Civil Engineering 2020 set 1

Question 2:

The value of

\lim_{x \to \infty} \frac{x^{2} - 5 x + 4}{4 x^{2} + 2 x} is

A	0	B	$\frac{1}{4}$
C	$\frac{1}{2}$	D	1

Category: GATE Civil Engineering 2020 set 1

Question 3:

The true value of In(2) is 0.69. If the value of In (2) is obtained by linear interpolation between ln(1) and ln(6), the percentage of absolute error (round off to the nearest integer), is

Category: GATE Civil Engineering 2020 set 1

Question 4:

The area of an ellipse represented by an equation

\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1 is

A	$\frac{πab}{4}$	B	$\frac{πab}{2}$
C	$πab$	D	$\frac{4 πab}{3}$

Category: GATE Civil Engineering 2020 set 1

Question 5:

Consider the planner truss shown in the figure (not drawn to the scale)

Neglecting self-weight of the members, the number of zero-force members in the truss under the action of the P, is

Category: GATE Civil Engineering 2020 set 1

Question 6:

A reinforcing steel bar, partially embedded in concrete, is subjected to a tensile force P. The figure that appropriately represents the distribution of the magnitude of band stress (repressed as hatched as hatched region), along the embedded length of the bar, is

A		B
C		D

Category: GATE Civil Engineering 2020 set 1

Question 7:

In a two-dimensional stress analysis, the state of stress at a point P is

[σ] = [\begin{matrix} σ_{xx} & τ_{xy} \\ τ_{xy} & σ_{yy} \end{matrix}]

The necessary and sufficient condition for the existence of the state of pure shear at the point P is

A	$σ_{xx} σ_{yy} - τ_{xy}^{2} = 0$	B	$τ_{xy} = 0$
C	$σ_{xx} + σ_{yy} = 0$	D	$(σ_{xx} - σ_{yy}) + 4 τ_{xy}^{2} = 0$

Category: GATE Civil Engineering 2020 set 1

Question 8:

During the process of hydration of cement, due to an increase in Dicalcium Silicate

(C_{2} S)

content clinker, the heat of hydration

increases

decreases

intially decreases and then increases

does not change

Category: GATE Civil Engineering 2020 set 1

Question 9:

The Los Angeles test for stone aggregates is used to examine

abrasion resistance

crushing strength

soundness

specific gravity

Category: GATE Civil Engineering 2020 set 1

Question 10:

Which one of the following statements is NOT correct?

A clay deposit with a liquidity index greater than unity is in a state of plastic consistency.

The cohesion of normally consolidated clay is zero when triaxial test is conducted under consolidated underained condition.

The ultimate bearing capacity of a strip foundation supported on the surface of sandy soil increases in direct proportion to the width of footing.

In case of a point load, Boussinesq\'s equation predicts higher value of vertical stress at a point directly beneath the load as compared to Westergaard\'s equation

Category: GATE Civil Engineering 2020 set 1

Question 11:

In a soil investigation work at a site, the Standard Penetration Test (STP) was conducted at every 1.5 m interval up to 30 m depth. At 3 m depth, the observed number of hammer blows for three successive 150 mm penetrations were 8, 6, and 9, respectively. The SPT N-value at 3m depth, is

Category: GATE Civil Engineering 2020 set 1

Question 12:

The velocity of flow is proportional to the first power of hydraulic gradient in Darcy's law. This law is applicable to

laminar flow in porous media

transitional flow in porous media

turbulent flow in porous media

laminar as well as turbulent flow in porous media

Category: GATE Civil Engineering 2020 set 1

Question 13:

A body floating in a liquid is in a stable state of equilibrium if its

metacentre lies above its centre of gravity

metacentre lies below its centre of gravity

metacentre coincides with its centre of gravity

centre of gravity is below its centre of buyancy

Category: GATE Civil Engineering 2020 set 1

Question 14:

Uniform flow with velocity U makes an angle

θ

with the y-axis, as shown in the figure

The velocity potential

A	undefined	B	undefined
C	undefined	D	undefined

Category: GATE Civil Engineering 2020 set 1

Question 15:

The data for an agricultural field for a specific month is given below:

Pan Evaporation = 100 m Effective Rainfall = 20 mm (after deducting losses due to runoff and deep percolation) Crop Coefficient = 0.4 Irrigation Efficiency = 0.5

The amount of irrigation water (in mm) to be applied to the field in that moth, is

Category: GATE Civil Engineering 2020 set 1

Question 16:

During the chlorination process, aqueous

(aq)

chlorine reacts rapidly with water to form

C l, HOCL, and H^{+}

as shown below

{Cl}_{2} (aq) + H_{2} O \Leftrightarrow HOCl + C l + H^{+}

The most active disinfectant in the chlorination process from amongst the following, is

A	$H^{+}$	B	$HOCl$
C	${Cl}^{-}$	D	$H_{2} O$

Category: GATE Civil Engineering 2020 set 1

Question 17:

An amount of 35.67 mg HCl is added to distilled water and the total solution volume is made to one liter. The atomic weights of H and Cl are 1 and 35.5, respectively. Neglecting the dissociation of water, the pH of the solution, is

3.50

3.01

2.50

2.01

Category: GATE Civil Engineering 2020 set 1

Question 18:

The probability that a 50 year flood may Not occur at all during the 25-year life of a project (round off to two decimal places), is______________

0.55 to 0.57

0.57 to 0.59

0.59 to 0.61

0.61 to 0.63

Category: GATE Civil Engineering 2020 set 1

Question 19:

A planar elastic structure is subjected to uniformly load, as shown in the figure (not drawn to the scale)

Neglecting self-weight, the maximum bending moment generated in the structure (in k.N.m, round off to the nearest interger), is ____________.

89 to 91

91 to 93

93 to 95

95 to 97

Category: GATE Civil Engineering 2020 set 1

Question 20:

In an urban area, a median is provided to separate the opposing streams of traffic. As per IRC: 86-1983, the desirable minimum width (in m, expressed as integers) of the median, is________.

5 to 5

6 to 6

7 to 7

8 to 8

Category: GATE Civil Engineering 2020 set 1

Question 21:

A road in hilly terrain is to be laid at a gradient of 4.5%. A horizontal curve of radius 100 m is laid at a location on this road. Gradient needs to be eased due to a combination of curved horizontal and vertical profiles of the road. As per IRC, the compensated of curved horizontal and vertical profiles of the road. As per IRC, the compensated gradient (in%, round off to one decimal place), is ___________.

3.9 to 4.0

4.0 to 4.0

4.0 to 4.1

4.1 to 4.1

Category: GATE Civil Engineering 2020 set 1

Question 22:

In a drained triaxial compression test, a sample of sand fails at deviator stress of 150 kph under confining pressure of 50 kph. The angle of internal friction (in degree, round off to the nearest integer) of the sample, is_____________

32 to 34

34 to 36

36 to 38

38 to 40

Category: GATE Civil Engineering 2020 set 1

Question 23:

A fully submerged infinite sandy slope has an inclination

30 °

with the horizontal. The saturated unit weight and effective angle of internal friction of sand are

18 kN / m^{3} and 38 °, respectively .

the unit weight of water is

10 kN / m^{3}

. Assume that the seepage is parallel to the slope. Against shear failure of the slope, the factor of safety ( round off to two decimal places) is ____________.

0.59 to 0.61

0.61 to 0.63

0.63 to 0.65

0.65 to 0.67

Category: GATE Civil Engineering 2020 set 1

Question 24:

A 4 wide rectangular channel carries

6 m^{3} / s

of water. The meaning's 'n' of the open channel is 0.02. Considering g = 9.81

m / s^{2},

the critical velocity of flow ( in m/s, round off to two decimal places) in the channel, is _________.

2.15 to 2.35

2.25 to 2.45

2.35 to 2.55

2.45 to 2.65

Category: GATE Civil Engineering 2020 set 1

Question 25:

A river has a flow of 1000 million litres per day (MLD),

{BOD}_{5}

of mg/litre before receiving the wastewater discharge at a location. For the existing ev=nvironmental conditions, the saturation DO level is 10 mg/litre in the river. Wastewater discharge of 100 MLD with the

{BOD}_{5} of 200 mg / litre

and DO level of 2 mg/litre falls at that location. Assuming complete mixing of wastewater and river water, the immediate DO deficit (in mg/liter, round off to two decimal places), is____________.

2.15 to 2.35

2.25 to 2.45

2.35 to 2.55

2.45 to 2.65

Category: GATE Civil Engineering 2020 set 1

Question 26:

For the Ordinary Differential Equation

\frac{d^{2} x}{{dt}^{2}} - 5 \frac{dx}{dt} + 6 x = 0,

with initial conditions x(0) = 0 and

\frac{dx}{dt} (0) = 10,

the solution

A	$- 5 e^{2 t} - 6 e^{3 t}$	B	$5 e^{2 t} + 6 e^{3 t}$
C	$- 10 e^{2 t} + 10 e^{3 t}$	D	$10 e^{2 t} + 10 e^{3 t}$

Category: GATE Civil Engineering 2020 set 1

Question 27:

A continuous function f(x) is defined. If the third derivative at

x_{i}

to be computed by using the fourth-order central finite-divided-differences scheme (with step length = h), the correct formula is

A	$f''' (x_{i}) = \frac{- f (x_{i + 3}) + 8 f (x_{i + 2}) - 13 f (x_{i + 1}) + 13 f (x_{i - 1}) - 8 f (x_{i - 2}) + f (x_{i - 3})}{8 h^{3}}$
B	$f''' (x_{i}) = \frac{- f (x_{i + 3}) - 8 f (x_{i + 2}) - 13 f (x_{i + 1}) + 13 f (x_{i - 1}) + 8 f (x_{i - 2}) + f (x_{i - 3})}{8 h^{3}}$
C	$f''' (x_{i}) = \frac{- f (x_{i + 3}) - 8 f (x_{i + 2}) - 13 f (x_{i + 1}) + 13 f (x_{i - 1}) + 8 f (x_{i - 2}) - f (x_{i - 3})}{8 h^{3}}$
D	$f''' (x_{i}) = \frac{f (x_{i + 3}) - 8 f (x_{i + 2}) + 13 f (x_{i + 1}) + 13 f (x_{i - 1}) - 8 f (x_{i - 2}) - f (x_{i - 3})}{8 h^{3}}$

Category: GATE Civil Engineering 2020 set 1

Question 28:

Distributed load (s) of 50 kN/m may occupy any position (s) (either continuously or in patches) on the girder PQRST as shown in the figure (not drawn to the scale)

The maximum negative (hogging) bending moment (in kN,m) that occurs at point R, is

22.50

56.25

93.75

150.00

Category: GATE Civil Engineering 2020 set 1

Question 29:

A rigid weightless platform PQRS shown in the figure (not drawn to the scale) can slide freely in the vertical direction. The platform is held in position by the weightless member OJ and four weightless, frictionless rollers. Points O and J are pin connections. A block of 90kN rests on the platform as shown in the figure

The magnitude of horizontal component of the reaction (in kN) at pin O, is

120

150

180

Category: GATE Civil Engineering 2020 set 1

Question 30:

A cantilever beam PQ of uniform flexural rigidity (El) is subject to a concentrated moment M at R as shown in the figure

The deflection at free end Q is

A	undefined	B	undefined
C	undefined	D	undefined

Category: GATE Civil Engineering 2020 set 1

Question 31:

A dowel bar is placed at a contraction joint. When contraction occurs, the concrete slab cracks at a predetermined location(s). Identify the arrangement, which shows the correct placement of the dowel bar and the place of occurrence of the contraction crack (s).

A		B
C		D

Category: GATE Civil Engineering 2020 set 1

Question 32:

The relationship between traffic flow (q) and density (D) is shown in the figure

A	flow with respect to pint 1 undefined
B	flow with respect to pint 2 undefined
C	flow with respect to pint 3 undefined
D	flow with respect to pint 4 undefined

A to B

B to C

C to D

None of this above

Category: GATE Civil Engineering 2020 set 1

Question 33:

The appropriate design length of a clearway is calculated on the basis of the 'Normal Take-off' condition. Which one of the following options correctly depicts the length of the clearway? (Note: None of the options are drawn to scale)

A		B
C		D

Category: GATE Civil Engineering 2020 set 1

Question 34:

The total stress path corresponding to different loading conditions, for a soil specimen under the isotropically consolidated stress state (O), is shown below

The correct match between the stress paths and the listed loading conditions is

A	OP - I, OQ - II, OR - IV, OS - III	B	OP - IV, OQ - III, OR - I, OS - II
C	OP - III, OQ - II, OR - IVI, OS - IV	D	OP - I, OQ - III, OR - II, OS - IV

Category: GATE Civil Engineering 2020 set 1

Question 35:

The soil profile at a site up to a depth of 10 m is shown in the figure (not drawn to the scale). The soil is preloaded with a uniform surcharge (q) of 70 kN/

m^{2}

at the ground level. The water table is at depth of 3 m below ground level. The soil unit weight of the respective layers as shown in the figure. Consider unit weight of water a undefine and assume that the surcharge (q) is applied instantaneously.

Immediately after preloading, the effective stress (in kPa) at points P and Q, respectively, are

124 and 204

36 and 90

36 and 126

54 and 95

Category: GATE Civil Engineering 2020 set 1

Question 36:

Water flows at the rate of

12 m^{3} / s

in a 6m wide rectangular channel. A hydraulic jump is formed in the channel at a point where the upstream depth is 30 cm (just before the jump). Considering acceleration due to gravity as

9.81 m / s^{2}

and density of water as

1000 kg / m^{3},

the energy loss in the jump is

114.2 kW

114.2 MW

141.2 h.p.

141.2 J/s

Category: GATE Civil Engineering 2020 set 1

Question 37:

A water supply scheme transports 10 MLD (Million Litres per Day) water through a 450 mm diameter pipeline for a distance of 2.5 km. A chlorine dose of 3.50 mg/litre is applied at the starting point of the pipeline to attain a certain level of disinfection at the downstream end. It is decided to increase the flow rate from 10 MLD to 13 MLD in the pipeline. Assume exponent for concentration, n = 0.86. With this increased flow, in order to attain the same level of disinfection, the chlorine dose (in mg/litre) to be applied at the starting point should be

3.95

4.40

4.75

5.55

Category: GATE Civil Engineering 2020 set 1

Question 38:

An open traverse PQRST is surveyed using a theodolite and the consecutive coordinates obtained are given in the table

If the independent coordinates (Nortjing Easting) of station P are (400m, 200m), the independent coordinates (in m) of station T, are

194.7, 370.1

205.3, 429.9

394.7, 170.1

405.3, 229.9

Category: GATE Civil Engineering 2020 set 1

Question 39:

If C represents a line segment between (0, 0, 0) and (1, 1, 1) in a Cartesian coordinate system, the value (expressed as an integer) of the line integral

\int_{c} [(y + z) dx + (x + z) dy + (x + y) dz]

is_____________.

0 to 3

1 to 3

2 to 3

3 to 3

Category: GATE Civil Engineering 2020 set 1

Question 40:

Consider the system of equation

[\begin{matrix} 1 & 3 & 2 \\ 2 & 2 & - 3 \\ 4 & 4 & - 6 \\ 2 & 5 & 2 \end{matrix}] [\begin{matrix} x_{1} \\ x_{2} \\ x_{3} \end{matrix}] = [\begin{matrix} 1 \\ 1 \\ 2 \\ 1 \end{matrix}]

The value of

x_{3}

(round off to the nearest interger), is _____________.

3 to 3

3 to 4

3 to 5

3 to 6

Category: GATE Civil Engineering 2020 set 1

Question 41:

A rigid, uniform, weightless, horizontal bar is connected to three vertical members P, Q, and R as shown in the figure (not drawn to the scale), All three members have identical axial stiffness of kN/mm. The lower ends of bars P and R rest on a rigid horizontal surface. When NO load is applied, a gap of 2 mm exists between the lower end of the bar Q and the rigid horizontal surface. When a vertical load W is placed on the horizontal bar in the downward direction, the bar still remains horizontal and gets displaced by 5 mm in the vertically downward direction.

The magnitude of the load W (in kN, round off to the nearest integer), is _______________.

129 to 131

130 to 131

131 to 131

non of these

Category: GATE Civil Engineering 2020 set 1

Question 42:

The flange and web plates of the doubly symmetric built-up section are connected by a continuous 10 mm thick weld as shown in the figure (not drawn to the scale). The moment of inertia of the section about its principal axis X - X is undefined The permissible shear stress in the fillet welds is undefined . The design shear strength of the section is governed by the capacity of the fillet welds.

Themaximum shear force (in kN, round off to one decimal place) that can be carried by the section, is_____________.

393.3 to 399.1

393.4 to 399.1

393.5 to 399.1

393.6 to 399.1

Category: GATE Civil Engineering 2020 set 1

Question 43:

The single reinforced concrete beam section shown in the figure (not drawn to the scale) is made of M25 grade concrete and Fe500 grade reinforcing steel. The total cross-sectional area of the tension steel is undefined

As per Limit State Design of IS 456:2000, the design moment capacity (in kN.m, round off to two decimal places) of the beam section, is _________________.

158.00 to 158.20

158.00 to 158.40

158.00 to 158.60

158.00 to 158.80

Category: GATE Civil Engineering 2020 set 1

Question 44:

A simply supported prismatic concrete beam of rectangular cross-section, having a span of 8 m, is prestressed with an effective force of 600 kN. The eccentricity of the prestressing tendon is zero at supports and varies linearly to a value of e at the mid-span. In order to balance an external concentrated loadof 12 kN applied at the mid-span, the required value of e (in mm, round off to the nearest integer) of the tendon, is__________.

39 to 41

40 to 42

41 to 43

42 to 44

Category: GATE Civil Engineering 2020 set 1

Question 45:

Traffic volume count has been collected on a 2-lane road section which needs upgradation due to severe traffic flow condition. The maximum service flow rate per lane is observed as 1280 veh/h at the level of service 'C'. The Peak Hour Factor is reported as 0.78125. Historical traffic volume count provides Annual Average Daily Traffic as 12270 veh/day. The directional split of the traffic flow is observed to be 60:40. Assuming that the traffic stream consists of 'All Cars' and all drives are 'Regular Commuters', The number of the extra lanes (s) (round off to the next higher integer) to be provided, is ______________.

A to B

B to C

C to D

None of this above

Category: GATE Civil Engineering 2020 set 1

Question 46:

A vertical retaining wall of 5 m height has to support soil having a unit weight of 18

kN / m^{2}

, effective cohesion

12 kN / m^{2}

, and effective friction angle of

30 °

. As per Rankine's earth pressure theory and assuming that a tension crack has occurred, the lateral active thrust on the wall per meter length ( in kN/m, round off to two decimal places), is______________.

21.00 to 23.00

23.00 to 25.00

25.00 to 27.00

27.00 to 29.00

Category: GATE Civil Engineering 2020 set 1

Question 47:

Water flows in the upward direction in a tank through a 2.5 m thick sand layer as shown in the figure. The void ratio and specific gravity of sand are 0.58 and 2.7, respectively. The sand is fully saturated. Unit weight of water undefined

The effective stress (in kPa, round off to two decimal places) at point A, located 1m above the base of tank, is ________________.

8.70 to 9.10

8.70 to 9.20

8.70 to 9.30

8.70 to 9.40

Category: GATE Civil Engineering 2020 set 1

Question 48:

A 10 m thick clay layer is resting over a 3 thick sand layer and is submerged. A fill of 2 m thick sand with a unit weight of undefined is placed above the clay layer to accelerate the rate of consolidation of the clay layer. The coefficient of consolidation of clay is undefined and coefficient of volume compressibility of clay is undefined Assume Taylor's relation between time factor and average degree of consolidation.

18.40 to 19.40

18.40 to 19.50

18.40 to 19.60

18.40 to 19.70

Category: GATE Civil Engineering 2020 set 1

Question 49:

Three reservoirs P, Q, and R are interconnected by pipes as shown in the figure (not drawn to the scale). The piezometric head at the junction S of the pipes is 100m. Assume acceleration due to due to gravity as 9.81 undefinedm and density of water as 1000 undefined The length of the pipe from junction S to the inlet of reservoir R is 180 m.

Considering head loss only due to friction (with friction os 0.03 for all the pipes), the height of water level in the lowermost reservoir R (in m, round off to one decimal place) with respect to the datum, is _________.

97.0 to 97.8

97.1 to 97.8

97.2 to 97.8

97.3 to 97.8

Category: GATE Civil Engineering 2020 set 1

Question 50:

In a homogeneous unconfined aquifer of area,

3.00 {km}^{2},

the water table was at an elevation of 102.00 m. After a natural recharge of volume 0.90 million cubic meters

({Mm}^{3}),

the water table rose to 103.20 m. After this recharge, groundwater pumping took place and the water table dropped down to 101.20 m. The volume of groundwater pumped after the natural recharge expressed (in

{Mm}^{3}

and round off to two decimal places), is___________.

1.20 to 1.40

1.40 to 1.60

1.60 to 1.80

1.80 to 2.00

Category: GATE Civil Engineering 2020 set 1

Question 51:

A circular water tank of 2 diameters has a circular orifice of diameter 0.1 m at the bottom. Water enters the tank steadily at a flow rate of 20 litre/s and escapes through the orifice. The coefficient of discharge of the orifice is 0.8. Consider the acceleration due to gravity as 9.81

m / s^{2}

and neglect frictional losses. The height of the water level (in m, round off two decimal places) in the tank at the steady-state, is ________________.

0.50 to 0.51

0.50 to 0.52

0.50 to 0.53

0.50 to 0.54

Category: GATE Civil Engineering 2020 set 1

Question 52:

The surface Overflow Rate (SOR) of a primary settling tank (discrete setting) is 20000

litre / m^{2}

per day. The kinematic viscosity of water in the tank is

1.01 \times 10^{- 2} {cm}^{2} / s .

Specific gravity of the settling particles is 2.64. Acceleration due to gravity is

9.81 m / s^{2} .

The minimum diameter (in

μm

, round off to one decimal place) of the particles that will be removed with 80% efficiency in the tank, is_____________.

10.0 to 11.0

12.0 to 13.0

14.0 to 15.0

16.0 to 17.0

Category: GATE Civil Engineering 2020 set 1

Question 53:

A gaseous chemical has a concentration of

41.6 μmol / m^{3}

in air at 1 atm pressure and temperature 293 K. The universal gas constant R is

82.05 \times 10^{- 6} (m^{3} atm) / (mol K) .

Assuming that ideal gas law is valid, the concentration of the gaseous chemical (in ppm, round off to one decimal place), is _____________.

0.9 to 1.1

1.1 to 1.3

1.3 to 1.5

1.5 to 1.7

Category: GATE Civil Engineering 2020 set 1

Question 54:

A stream with a flow rate of

5 m^{3} / s

is having an ultimate BOD of 30 mg/liter. A wastewater discharge of

0.20 m^{3} / s

having

{BOD}_{5} of 500 mg / litre

joins the stream at a location and instantaneously gets mixed up completely. The cross-sectional area of the stream is

40 m^{2}

which remains constant. BOD (in mg/litre, round off to two decimal places) remaining at 3 km downstream from the mixing location, is ____________.

46.00 to 47.00

47.00 to 48.00

48.00 to 49.00

49.00 to 50.00

Category: GATE Civil Engineering 2020 set 1

Question 55:

The lengths and bearings of a traverse PQRS are:

Segment	Length (m)	Bearing
PQ	40	$80 °$
QR	50	$10 °$
RS	30	$210 °$

The length of the line segment SP (in m, round off to two decimal places), is ___________.

42.00 to 43.00

44.00 to 45.00

46.00 to 47.00

48.00 to 49.00

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Question 1:

In the following partial differential equation,

θ

is a function of t and z, and D and K are functions of

θ

D (θ) \frac{\partial^{2} θ}{\partial z^{2}} + \frac{\partial K (θ)}{\partial z} - \frac{\partial θ}{\partial t} = 0

The above equation is

Correct Answer : a second order non-linear equation

Question 2:

The value of

\lim_{x \to \infty} \frac{x^{2} - 5 x + 4}{4 x^{2} + 2 x} is

A	0	B	$\frac{1}{4}$
C	$\frac{1}{2}$	D	1

Correct Answer : B

Question 3:

The true value of In(2) is 0.69. If the value of In (2) is obtained by linear interpolation between ln(1) and ln(6), the percentage of absolute error (round off to the nearest integer), is

Correct Answer : 48

Question 4:

The area of an ellipse represented by an equation

\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1 is

A	$\frac{πab}{4}$	B	$\frac{πab}{2}$
C	$πab$	D	$\frac{4 πab}{3}$

Correct Answer : C

Question 5:

Consider the planner truss shown in the figure (not drawn to the scale)

Neglecting self-weight of the members, the number of zero-force members in the truss under the action of the P, is

Correct Answer : 8

Question 6:

A		B
C		D

Correct Answer : C

Question 7:

In a two-dimensional stress analysis, the state of stress at a point P is

[σ] = [\begin{matrix} σ_{xx} & τ_{xy} \\ τ_{xy} & σ_{yy} \end{matrix}]

The necessary and sufficient condition for the existence of the state of pure shear at the point P is

A	$σ_{xx} σ_{yy} - τ_{xy}^{2} = 0$	B	$τ_{xy} = 0$
C	$σ_{xx} + σ_{yy} = 0$	D	$(σ_{xx} - σ_{yy}) + 4 τ_{xy}^{2} = 0$

Correct Answer : C

Question 8:

During the process of hydration of cement, due to an increase in Dicalcium Silicate

(C_{2} S)

content clinker, the heat of hydration

Correct Answer : decreases

Question 9:

The Los Angeles test for stone aggregates is used to examine

Correct Answer : abrasion resistance

Question 10:

Which one of the following statements is NOT correct?

Correct Answer : A clay deposit with a liquidity index greater than unity is in a state of plastic consistency.

Question 11:

Correct Answer : 15

Question 12:

The velocity of flow is proportional to the first power of hydraulic gradient in Darcy's law. This law is applicable to

Correct Answer : laminar flow in porous media

Question 13:

A body floating in a liquid is in a stable state of equilibrium if its

Correct Answer : metacentre lies above its centre of gravity

Question 14:

Uniform flow with velocity U makes an angle

θ

with the y-axis, as shown in the figure

The velocity potential

A	undefined	B	undefined
C	undefined	D	undefined

Correct Answer : A

Question 15:

The data for an agricultural field for a specific month is given below:

Pan Evaporation = 100 m Effective Rainfall = 20 mm (after deducting losses due to runoff and deep percolation) Crop Coefficient = 0.4 Irrigation Efficiency = 0.5

The amount of irrigation water (in mm) to be applied to the field in that moth, is

Correct Answer : 40

Question 16:

During the chlorination process, aqueous

(aq)

chlorine reacts rapidly with water to form

C l, HOCL, and H^{+}

as shown below

{Cl}_{2} (aq) + H_{2} O \Leftrightarrow HOCl + C l + H^{+}

The most active disinfectant in the chlorination process from amongst the following, is

A	$H^{+}$	B	$HOCl$
C	${Cl}^{-}$	D	$H_{2} O$

Correct Answer : B

Question 17:

Correct Answer : 3.01

Question 18:

The probability that a 50 year flood may Not occur at all during the 25-year life of a project (round off to two decimal places), is______________

Correct Answer : 0.59 to 0.61

Question 19:

A planar elastic structure is subjected to uniformly load, as shown in the figure (not drawn to the scale)

Neglecting self-weight, the maximum bending moment generated in the structure (in k.N.m, round off to the nearest interger), is ____________.

Correct Answer : 95 to 97

Question 20:

In an urban area, a median is provided to separate the opposing streams of traffic. As per IRC: 86-1983, the desirable minimum width (in m, expressed as integers) of the median, is________.

Correct Answer : 5 to 5

Question 21:

Correct Answer : 4.0 to 4.0

Question 22:

Correct Answer : 36 to 38

Question 23:

A fully submerged infinite sandy slope has an inclination

30 °

with the horizontal. The saturated unit weight and effective angle of internal friction of sand are

18 kN / m^{3} and 38 °, respectively .

the unit weight of water is

10 kN / m^{3}

. Assume that the seepage is parallel to the slope. Against shear failure of the slope, the factor of safety ( round off to two decimal places) is ____________.

Correct Answer : 0.59 to 0.61

Question 24:

A 4 wide rectangular channel carries

6 m^{3} / s

of water. The meaning's 'n' of the open channel is 0.02. Considering g = 9.81

m / s^{2},

the critical velocity of flow ( in m/s, round off to two decimal places) in the channel, is _________.

Correct Answer : 2.35 to 2.55

Question 25:

A river has a flow of 1000 million litres per day (MLD),

{BOD}_{5}

{BOD}_{5} of 200 mg / litre

and DO level of 2 mg/litre falls at that location. Assuming complete mixing of wastewater and river water, the immediate DO deficit (in mg/liter, round off to two decimal places), is____________.

Correct Answer : 2.45 to 2.65

Question 26:

For the Ordinary Differential Equation

\frac{d^{2} x}{{dt}^{2}} - 5 \frac{dx}{dt} + 6 x = 0,

with initial conditions x(0) = 0 and

\frac{dx}{dt} (0) = 10,

the solution

A	$- 5 e^{2 t} - 6 e^{3 t}$	B	$5 e^{2 t} + 6 e^{3 t}$
C	$- 10 e^{2 t} + 10 e^{3 t}$	D	$10 e^{2 t} + 10 e^{3 t}$

Correct Answer : C

Question 27:

A continuous function f(x) is defined. If the third derivative at

x_{i}

to be computed by using the fourth-order central finite-divided-differences scheme (with step length = h), the correct formula is

A	$f''' (x_{i}) = \frac{- f (x_{i + 3}) + 8 f (x_{i + 2}) - 13 f (x_{i + 1}) + 13 f (x_{i - 1}) - 8 f (x_{i - 2}) + f (x_{i - 3})}{8 h^{3}}$
B	$f''' (x_{i}) = \frac{- f (x_{i + 3}) - 8 f (x_{i + 2}) - 13 f (x_{i + 1}) + 13 f (x_{i - 1}) + 8 f (x_{i - 2}) + f (x_{i - 3})}{8 h^{3}}$
C	$f''' (x_{i}) = \frac{- f (x_{i + 3}) - 8 f (x_{i + 2}) - 13 f (x_{i + 1}) + 13 f (x_{i - 1}) + 8 f (x_{i - 2}) - f (x_{i - 3})}{8 h^{3}}$
D	$f''' (x_{i}) = \frac{f (x_{i + 3}) - 8 f (x_{i + 2}) + 13 f (x_{i + 1}) + 13 f (x_{i - 1}) - 8 f (x_{i - 2}) - f (x_{i - 3})}{8 h^{3}}$

Correct Answer : A

Question 28:

Distributed load (s) of 50 kN/m may occupy any position (s) (either continuously or in patches) on the girder PQRST as shown in the figure (not drawn to the scale)

The maximum negative (hogging) bending moment (in kN,m) that occurs at point R, is

Correct Answer : 56.25

Question 29:

The magnitude of horizontal component of the reaction (in kN) at pin O, is

Correct Answer : 120

Question 30:

A cantilever beam PQ of uniform flexural rigidity (El) is subject to a concentrated moment M at R as shown in the figure

The deflection at free end Q is

A	undefined	B	undefined
C	undefined	D	undefined

Correct Answer : C

Question 31:

A		B
C		D

Correct Answer : B

Question 32:

The relationship between traffic flow (q) and density (D) is shown in the figure

A	flow with respect to pint 1 undefined
B	flow with respect to pint 2 undefined
C	flow with respect to pint 3 undefined
D	flow with respect to pint 4 undefined

Correct Answer : None of this above

Question 33:

A		B
C		D

Correct Answer : C

Question 34:

The total stress path corresponding to different loading conditions, for a soil specimen under the isotropically consolidated stress state (O), is shown below

The correct match between the stress paths and the listed loading conditions is

A	OP - I, OQ - II, OR - IV, OS - III	B	OP - IV, OQ - III, OR - I, OS - II
C	OP - III, OQ - II, OR - IVI, OS - IV	D	OP - I, OQ - III, OR - II, OS - IV

Correct Answer : B

Question 35:

The soil profile at a site up to a depth of 10 m is shown in the figure (not drawn to the scale). The soil is preloaded with a uniform surcharge (q) of 70 kN/

m^{2}

Immediately after preloading, the effective stress (in kPa) at points P and Q, respectively, are

Correct Answer : 54 and 95

Question 36:

Water flows at the rate of

12 m^{3} / s

in a 6m wide rectangular channel. A hydraulic jump is formed in the channel at a point where the upstream depth is 30 cm (just before the jump). Considering acceleration due to gravity as

9.81 m / s^{2}

and density of water as

1000 kg / m^{3},

the energy loss in the jump is

Correct Answer : 114.2 kW

Question 37:

Correct Answer : 4.75

Question 38:

An open traverse PQRST is surveyed using a theodolite and the consecutive coordinates obtained are given in the table

If the independent coordinates (Nortjing Easting) of station P are (400m, 200m), the independent coordinates (in m) of station T, are

Correct Answer : 394.7, 170.1

Question 39:

If C represents a line segment between (0, 0, 0) and (1, 1, 1) in a Cartesian coordinate system, the value (expressed as an integer) of the line integral

\int_{c} [(y + z) dx + (x + z) dy + (x + y) dz]

is_____________.

Correct Answer : 3 to 3

Question 40:

Consider the system of equation

[\begin{matrix} 1 & 3 & 2 \\ 2 & 2 & - 3 \\ 4 & 4 & - 6 \\ 2 & 5 & 2 \end{matrix}] [\begin{matrix} x_{1} \\ x_{2} \\ x_{3} \end{matrix}] = [\begin{matrix} 1 \\ 1 \\ 2 \\ 1 \end{matrix}]

The value of

x_{3}

(round off to the nearest interger), is _____________.

Correct Answer : 3 to 3

Question 41:

The magnitude of the load W (in kN, round off to the nearest integer), is _______________.

Correct Answer : 129 to 131

Question 42:

Themaximum shear force (in kN, round off to one decimal place) that can be carried by the section, is_____________.

Correct Answer : 393.5 to 399.1

Question 43:

As per Limit State Design of IS 456:2000, the design moment capacity (in kN.m, round off to two decimal places) of the beam section, is _________________.

Correct Answer : 158.00 to 158.80

Question 44:

Correct Answer : 39 to 41

Question 45:

Correct Answer : None of this above

Question 46:

A vertical retaining wall of 5 m height has to support soil having a unit weight of 18

kN / m^{2}

, effective cohesion

12 kN / m^{2}

, and effective friction angle of

30 °

Correct Answer : 21.00 to 23.00

Question 47:

The effective stress (in kPa, round off to two decimal places) at point A, located 1m above the base of tank, is ________________.

Correct Answer : 8.70 to 9.30

Question 48:

Correct Answer : 18.40 to 19.50

Question 49:

Correct Answer : 97.2 to 97.8

Question 50:

In a homogeneous unconfined aquifer of area,

3.00 {km}^{2},

the water table was at an elevation of 102.00 m. After a natural recharge of volume 0.90 million cubic meters

({Mm}^{3}),

{Mm}^{3}

and round off to two decimal places), is___________.

Correct Answer : 1.40 to 1.60

Question 51:

m / s^{2}

and neglect frictional losses. The height of the water level (in m, round off two decimal places) in the tank at the steady-state, is ________________.

Correct Answer : 0.50 to 0.54

Question 52:

The surface Overflow Rate (SOR) of a primary settling tank (discrete setting) is 20000

litre / m^{2}

per day. The kinematic viscosity of water in the tank is

1.01 \times 10^{- 2} {cm}^{2} / s .

Specific gravity of the settling particles is 2.64. Acceleration due to gravity is

9.81 m / s^{2} .

The minimum diameter (in

μm

, round off to one decimal place) of the particles that will be removed with 80% efficiency in the tank, is_____________.

Correct Answer : 14.0 to 15.0

Question 53:

A gaseous chemical has a concentration of

41.6 μmol / m^{3}

in air at 1 atm pressure and temperature 293 K. The universal gas constant R is

82.05 \times 10^{- 6} (m^{3} atm) / (mol K) .

Assuming that ideal gas law is valid, the concentration of the gaseous chemical (in ppm, round off to one decimal place), is _____________.

Correct Answer : 0.9 to 1.1

Question 54:

A stream with a flow rate of

5 m^{3} / s

is having an ultimate BOD of 30 mg/liter. A wastewater discharge of

0.20 m^{3} / s

having

{BOD}_{5} of 500 mg / litre

joins the stream at a location and instantaneously gets mixed up completely. The cross-sectional area of the stream is

40 m^{2}

which remains constant. BOD (in mg/litre, round off to two decimal places) remaining at 3 km downstream from the mixing location, is ____________.

Correct Answer : 49.00 to 50.00

Question 55:

The lengths and bearings of a traverse PQRS are:

Segment	Length (m)	Bearing
PQ	40	$80 °$
QR	50	$10 °$
RS	30	$210 °$

The length of the line segment SP (in m, round off to two decimal places), is ___________.

Correct Answer : 44.00 to 45.00

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