Gate Mock Test Civil Engineering (CE)- 5

# Gate Mock Test Civil Engineering (CE)- 5 - Civil Engineering (CE)

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## 65 Questions MCQ Test GATE Civil Engineering (CE) 2023 Mock Test Series - Gate Mock Test Civil Engineering (CE)- 5

Gate Mock Test Civil Engineering (CE)- 5 for Civil Engineering (CE) 2023 is part of GATE Civil Engineering (CE) 2023 Mock Test Series preparation. The Gate Mock Test Civil Engineering (CE)- 5 questions and answers have been prepared according to the Civil Engineering (CE) exam syllabus.The Gate Mock Test Civil Engineering (CE)- 5 MCQs are made for Civil Engineering (CE) 2023 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Gate Mock Test Civil Engineering (CE)- 5 below.
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Gate Mock Test Civil Engineering (CE)- 5 - Question 1

### A rectangular sheet made of cardboard has a size of 4cm x 2cm. If a circle of greatest diameter is cut from it what is the area of the remaining portion of the rectangular sheet in cm2 ?

Detailed Solution for Gate Mock Test Civil Engineering (CE)- 5 - Question 1
Area of rectangular sheet = 4 x 2 = 8cm2

Circle of Maximum diameter is obtained when circle has diameter of the rectangle width = 2 cm

Area of circle = (π x 22)/4 = π cm2

Remaining area = (8 - π) cm2

Gate Mock Test Civil Engineering (CE)- 5 - Question 2

### Select the suitable figure from the answer figures that would replace the question mark (?).

Detailed Solution for Gate Mock Test Civil Engineering (CE)- 5 - Question 2
As, second figure is mirror image of first one horizontally.

Similarly, figure given in answer figure (1) is the mirror image of third figure horizontally.

Gate Mock Test Civil Engineering (CE)- 5 - Question 3

### Select the word or phrase which is close to the OPPOSITE in the meaning of the bold word or phrase.The habit of squandering money should not be encouraged.

Detailed Solution for Gate Mock Test Civil Engineering (CE)- 5 - Question 3
Squandering is opposite in meaning to saving
Gate Mock Test Civil Engineering (CE)- 5 - Question 4

Directions: Fill in the blank with the most suitable option.

He is such a miser that he can never part ___________ his money.

Detailed Solution for Gate Mock Test Civil Engineering (CE)- 5 - Question 4
'Part with' is a phrasal verb, which means 'to give up or let go of'. It fits in context of a 'miser' who does not give up his money.
Gate Mock Test Civil Engineering (CE)- 5 - Question 5

There are Six friends Arya, Janvi, Pratik, Tirtha, Saloni and Divya, with distinct heights, compare their heights and make the following observations.

Observation I: Pratik is taller than Tirtha.

Observation II: Janvi is the shortest of all.

Observation III: Divya is taller than only one person.

Observation IV: Saloni is taller than Pratik but she is not the tallest

The number of persons that are taller than Tirtha is the same as the number of persons shorter than_________

Detailed Solution for Gate Mock Test Civil Engineering (CE)- 5 - Question 5
Arya>Saloni>Pratik>Tirtha>Divya>Janvi
Gate Mock Test Civil Engineering (CE)- 5 - Question 6

In a certain code, BUILDER is written as JVCKSFE. How is SEALING written in that code?

Detailed Solution for Gate Mock Test Civil Engineering (CE)- 5 - Question 6

Gate Mock Test Civil Engineering (CE)- 5 - Question 7

Nikhil aspires to buy a bike worth Rs. 200000 after 7 years. what is the minimum amount in Rupees that he should deposit now in a bank which offers 5.5% annual rate of interest, if the interest was compounded annually ?

Detailed Solution for Gate Mock Test Civil Engineering (CE)- 5 - Question 7
CI = P(1 + r/100)n

200000 = P(1 + 5.5/100)7

P = 137487

Gate Mock Test Civil Engineering (CE)- 5 - Question 8

Directions: Study the given graph carefully and answer the following question.

The graph below shows the numbers of students appearing for and qualifying in a scholarship exam from various schools:

Q. What is the difference between the average number of students appearing and qualifying in the exam from all the given schools?

Detailed Solution for Gate Mock Test Civil Engineering (CE)- 5 - Question 8
Average number of students appearing for the exam from all the given schools,

= (3000 + 2250 + 3250 + 2500 + 3000)/5 = 2800

The average number of students qualifying in the exam from all the given schools,

= (1750 + 1250 + 2250 + 2000 + 2000)/5 = 1850

Difference = 2800 – 1850 = 950

Gate Mock Test Civil Engineering (CE)- 5 - Question 9

Statements:

1. All boys are genius.

2. All girls are boys.

Conclusions:

I. All girls are genius.

II. Some boys are girls

Based on the above statements and conclusions, which one of the following options is logically CORRECT?

Detailed Solution for Gate Mock Test Civil Engineering (CE)- 5 - Question 9

from the above imaginary diagram we can conclude that both conclusion I and II are follows

Gate Mock Test Civil Engineering (CE)- 5 - Question 10

In the sequence of the terms AD CG FK JP, the next term is

Detailed Solution for Gate Mock Test Civil Engineering (CE)- 5 - Question 10
Observe the first letters: A, C, F, J; the difference between each consecutive letter is incrementing by one letter. Or if we number the letters, the sequence is 1, 3, 6, 10 and the difference of the consecutive numbers in order is 2, 3, 4. Hence, the next difference is 5 and so the next number is 10 + 5 = 15, i.e. letter 'O'.

Observe the second letters: D, G, K, P; if we number these letters, they are 4, 7, 11, 16 and the difference of the consecutive numbers in order is 3, 4, 5. Hence, the next difference is 6 and so the next number is 16 + 6 = 22, i.e. letter 'V'.

Hence, the next term is 'OV'.

Gate Mock Test Civil Engineering (CE)- 5 - Question 11

Zero hardness of water is achieved by

Detailed Solution for Gate Mock Test Civil Engineering (CE)- 5 - Question 11
Zero hardness, other than ion exchange or base exchange or zeolite method, leaves behind a substantial amount of hardness or alkalinity. Zero hardness of water can be achieved only by means of zeolite process.
Gate Mock Test Civil Engineering (CE)- 5 - Question 12

The value of is

Detailed Solution for Gate Mock Test Civil Engineering (CE)- 5 - Question 12

Gate Mock Test Civil Engineering (CE)- 5 - Question 13

There is a free overfall at the end of a long open channel. For a given flow rate, the critical depth is less than the normal depth. What gradually varied flow profile will occur in the channel for this flow rate?

Detailed Solution for Gate Mock Test Civil Engineering (CE)- 5 - Question 13

Here, yn > yc . So, the mild sloped channel.

For free flow at the end of long channel on the mild sloped surface. There will be draw down and depth of flow decreases from yn tp yc but not below the yc . So, appropriate answer will be M2 only.

Gate Mock Test Civil Engineering (CE)- 5 - Question 14

The solution at x = 1, t = 1 of the partial differential equation subject to initial conditions of u(0) = 3x and = 3 is ____________.

Detailed Solution for Gate Mock Test Civil Engineering (CE)- 5 - Question 14
By D Alembert's formula

Solution to IVP for wave equation

utt = C2Uxx

u(x, 0) = f(x)

ut (x, 0) = g(x)

Given: f(x) = 3x

g(x) = 3 & c2 = 1/25

= 3x + 3t

At x = 1, t = 1; u(x, t) = 6

Gate Mock Test Civil Engineering (CE)- 5 - Question 15

Match the following:

Detailed Solution for Gate Mock Test Civil Engineering (CE)- 5 - Question 15
Rainfall intensity versus time is provided by a hydrograph.

Rainfall excess: Provides the direct run-off hydrograph over the infiltration index.

Rainfall average: Isohyets provide the time on the map having equal rainfall depth and used to measure the average rainfall across a particular area.

Mass curve is a mass curve of inflow or mass curve is a plot of accumulated flow in a stream against time. Cumulative rainfall is denoted by mass curve.

Gate Mock Test Civil Engineering (CE)- 5 - Question 16

The slenderness ratio of a column is zero when its length is

Detailed Solution for Gate Mock Test Civil Engineering (CE)- 5 - Question 16
Slenderness ratio means the ratio of the length of a column to the least radius of gyration of its cross-section. It is denoted by λ.

The slenderness ratio of a column is zero when its length is between the points of zero moments.

Gate Mock Test Civil Engineering (CE)- 5 - Question 17

For a saturated sand deposit, the void ratio and the specific gravity of solids are 0.70 and 2.67, respectively. The critical (upward) hydraulic gradient for the deposit would be

Detailed Solution for Gate Mock Test Civil Engineering (CE)- 5 - Question 17

e = 0.70, G = 2.67

Critical hydraulic gradient causes effective stress to zero and

Gate Mock Test Civil Engineering (CE)- 5 - Question 18

For concreting of shallow sections with vibrations, the workability should be ______.

Detailed Solution for Gate Mock Test Civil Engineering (CE)- 5 - Question 18

For concreting of shallow sections with vibrations, the workability should be very low.

Gate Mock Test Civil Engineering (CE)- 5 - Question 19

To provide safety against piping failure, with a factor of safety of 5, what should be the maximum permissible exit gradient for soil with a specific gravity of 2.5 and porosity of 0.35?

Detailed Solution for Gate Mock Test Civil Engineering (CE)- 5 - Question 19
Exit gradient = seepage pressure per unit volume

Critical ic = when n = 0.35

= (G - 1)(1 - n)

= (2.5 - 1)(1 - 0.35) = 0.975

Maximum possible exit gradient with factor of safety

of 5 = 0.975/5 = 0.195

Gate Mock Test Civil Engineering (CE)- 5 - Question 20

The solution of the equation xdy/dx+ y = 0 passing through the point (1, 1) is

Detailed Solution for Gate Mock Test Civil Engineering (CE)- 5 - Question 20

= loge (c/x)

⇒ y = c/x

(1, 1) ⇒ c = 1

∴ y = 1/x = x-1

Gate Mock Test Civil Engineering (CE)- 5 - Question 21

A stable channel is to be designed for a discharge of Q m3/s with silt factor f as per Lacey's method. The mean flow velocity (m/s) in the channel is obtained by

Detailed Solution for Gate Mock Test Civil Engineering (CE)- 5 - Question 21
According to Lacey’s, the design formulas to build a canal is as follows:
1. Silt factor ⇒ f = size of particle(mm)
2. Velocity of flow ⇒
3. Hydraulic mean depth ⇒
4. Wetted perimeter ⇒
5. Bed slope ⇒

Hence, the correct relationship between the parameter given in the option as per Lacey’s silt theory is the velocity of flow,

Gate Mock Test Civil Engineering (CE)- 5 - Question 22

In the formula a + bk used in the calculation of the net effective section of single angles in tension connected by one leg only, the value of k is

Detailed Solution for Gate Mock Test Civil Engineering (CE)- 5 - Question 22
In the calculation of the net effective section of single angles in tension connected by one leg only, the formula used is a + bk, in which the value of k is .
Gate Mock Test Civil Engineering (CE)- 5 - Question 23

From among the following sewage treatment options, largest land requirements for a given discharge will be needed for

Detailed Solution for Gate Mock Test Civil Engineering (CE)- 5 - Question 23
Oxidation pond - Standing pond with minimum depth, so the sunlight can penetrate into the tank for photosynthesis at the bottom of the tank and provide oxygen for aerobic oxidation. For less depth, more surface area and large detention time is required.
Gate Mock Test Civil Engineering (CE)- 5 - Question 24

Neglecting gravitational effects, for steady, fully developed flow inside a straight pipe of diameter 2.24 m, the pressure drop is 80 kPa. If the wall shear stress τw is 250 N/m2, then the length of the pipe will be _____________ m.

Detailed Solution for Gate Mock Test Civil Engineering (CE)- 5 - Question 24
Wall shear stress is

Gate Mock Test Civil Engineering (CE)- 5 - Question 25

The presence of hardness in excess of permissible limit causes

Detailed Solution for Gate Mock Test Civil Engineering (CE)- 5 - Question 25
Hardness of water means the presence of carbonate and bicarbonate of Ca and Mg in water as such does not cause any health related problem, but on precipitation when reacting with fatty acid (soap) and scale formation in boiler. So, hardness will increase the expenses on laundry materials like soap and shampoo, etc.
Gate Mock Test Civil Engineering (CE)- 5 - Question 26

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 (not drawn to 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, s (in vph). Vehicles arrive at a uniform rate, v (in vph), throughout the cycle. Which one of the following statements is TRUE?

Detailed Solution for Gate Mock Test Civil Engineering (CE)- 5 - Question 26
Vehicle arrived up to 60 sec (Red time) = 10

Arrival rate = 1060 × 3600 = 600 V/hV = 600 V/h

Departure at vehicle starts at 60 seconds and ends at 90 seconds.

So, between 60 second to 90 second

Total vehicle departed = Vehicle arrived up to 60 sec + Vehicle arriving between 60 sec and 90 sec = 10 + 600/3600 × 30 = 10 + 5 = 15

So, departure rate = saturation flow = S = 1530 × 3600

S = 1800 vph

Average delay time is given by: td = (C/2(1 − gc)2)/(1 − V/S)C = 96 seconds

g = 96 - 60 = 36 seconds

V = 600 vph

S = 1800 vph

td = 96/2(1 − 36/96)21 − 600/1800

td = 28.125 seconds

Gate Mock Test Civil Engineering (CE)- 5 - Question 27

The shape of the cross section which has the largest shape factor is

Detailed Solution for Gate Mock Test Civil Engineering (CE)- 5 - Question 27
Largest shape factor also depends upon lowest value of section modulus and diamond section of equal area will have least section modulus (Z). Hence, diamond has shape factor as 2, whereas circle has 1.7, Rectangle-1.3.
*Answer can only contain numeric values
Gate Mock Test Civil Engineering (CE)- 5 - Question 28

If the sleeper density for a B.G. track is n + 5 and the length of one rail is 12.8 m, then number of sleepers required per km length of the track is (Answer up to the nearest integer)

Detailed Solution for Gate Mock Test Civil Engineering (CE)- 5 - Question 28

Length of one rail is 12.8 m ≈ 13 m

Sleeper density is n + 5 = 13 + 5 = 18

Number of sleepers required is

Gate Mock Test Civil Engineering (CE)- 5 - Question 29

If xSin (a + y) = Sin y, then dy/dx is equal to

Detailed Solution for Gate Mock Test Civil Engineering (CE)- 5 - Question 29

Differentiating w.r.t. y, we have.

*Answer can only contain numeric values
Gate Mock Test Civil Engineering (CE)- 5 - Question 30

The extra widening required in a 6 lane carriage when the length of the vehicle is 10 m, radius of curve is 450 m and speed is 72 kmph is ________ m. (Answer up to three decimal places)

Detailed Solution for Gate Mock Test Civil Engineering (CE)- 5 - Question 30
Given: n = 6, l = 10 m, R = 450 m and V = 72 km/h

Extra widening is given by

= 1.006 m

*Answer can only contain numeric values
Gate Mock Test Civil Engineering (CE)- 5 - Question 31

For f(z) = the residue of the pole at z = 0 is ___________.(Answer up to the nearest integer)

Detailed Solution for Gate Mock Test Civil Engineering (CE)- 5 - Question 31

Residue = coefficient of 1/z = 1

*Answer can only contain numeric values
Gate Mock Test Civil Engineering (CE)- 5 - Question 32

The figure shows the geometry of a strip footing supporting the load bearing walls of a three-storeyed building and the properties of clay layer.

If the pressure acting on the footing is 40 kPa, the consolidation settlement of the footing will be (Answer up to the nearest integer)

Detailed Solution for Gate Mock Test Civil Engineering (CE)- 5 - Question 32

Consolidation statement

Effective initial overburden pressure at the centre of clay layer.

Increase in pressure acting on the footing

= 40 KN/m2

*Answer can only contain numeric values
Gate Mock Test Civil Engineering (CE)- 5 - Question 33

In the limit state design method of concrete structures, the recommended partial material safety factor for steel according to IS:456-2000 is

(Answer up to two decimal places)

Detailed Solution for Gate Mock Test Civil Engineering (CE)- 5 - Question 33
The Acceptable limit for safety and service ability requirements before failure occurs is called a limit state.

It is further divided into two parts:

Limit state of collapse: It deals with strength and stability of the structure under maximum design load.

As per Clause 36.4.2 of IS 456, the material partial safety factor (γm) for concrete and steel should be taken as 1.5 and 1.15, respectively when assessing the strength of the structures or structural members employing limit state of collapse.

Limit state of serviceability: It deals with the deflection and cracking under service loads, durability, stability, fire resistance etc.

*Answer can only contain numeric values
Gate Mock Test Civil Engineering (CE)- 5 - Question 34

A lift of weight 500 kg is moving upwards with a uniform acceleration of 2 m/s2. The tension in the cable supporting the lift is _________ kgf. (Answer up to the nearest integer)

Detailed Solution for Gate Mock Test Civil Engineering (CE)- 5 - Question 34
Given: W = 500 kg and f = 2 m/s2

g = 9.81 m/s2

Tension in the cable supporting the lift is

*Answer can only contain numeric values
Gate Mock Test Civil Engineering (CE)- 5 - Question 35

The undrained cohesion of a remoulded clay soil is 10 kN/m2. If the sensitivity of the clay is 20, then the corresponding remoulded compressive strength (in kN/m2) is (Answer up to the nearest integer)

Detailed Solution for Gate Mock Test Civil Engineering (CE)- 5 - Question 35
Undrained cohesion of the remolded clay = Cu = 10 kN/m2

Remoulded compressive strength qu = 2Cu

= 2 × 10 = 20 kN/m2

Gate Mock Test Civil Engineering (CE)- 5 - Question 36

Which one of the following matrices is singular?

Detailed Solution for Gate Mock Test Civil Engineering (CE)- 5 - Question 36
A square matrix 'A' is said to be singular if |A| = 0

is singular matrix.

Gate Mock Test Civil Engineering (CE)- 5 - Question 37

For the matrix , one of the eigen values is - 2. Which of the following is an eigen vector?

Detailed Solution for Gate Mock Test Civil Engineering (CE)- 5 - Question 37
We know that AX = λX

AX − λX = [0]

(A − λI)X = [0] ----> (1) where I= Identity matrix.

Given that λ = −2

Now, from the equation (1),

(A − λI)X = [0]

Now, we can apply some operation on matrix

Again apply some operation on matrix

In R3, we create Nullity. So Rank of this matrix is 2 [Rank: Maximum number of independent Rows/Colums]

r = 2, and number of unknowns (Variables = 3)

Here clearly see, r < />

So, there are Infinitely many solution are possible, and n − r = 3 − 2 = 1 variable give some value and other will be evaluate accordingly.

Let say y = k

z = 0 ----> (2)

5x − 2k + 2z = 0

5x − 2k + 0 = 0

5x = 2k

Finally we got the Eigen Vector, X =

Put the Value of k = 5

and we get, X =

Actually, we get Infinitely many number of solutions.

So, we can get Infinte number of Eigen Vector, but for k = 5, we got one Eigen Vector.

Gate Mock Test Civil Engineering (CE)- 5 - Question 38

The rank of the following matrix is

Detailed Solution for Gate Mock Test Civil Engineering (CE)- 5 - Question 38

Reducing into Echelon form

Rank = No of non-zero rows

= 2

Gate Mock Test Civil Engineering (CE)- 5 - Question 39

A three-phase traffic signal at an intersection is designed for flows shown in the figure below. There are six groups of flows identified by the numbers 1 to 6. Among these 1, 3, 4 and 6 are through flows, and 2 and 5 are right turning. Which phasing scheme is not feasible?

Detailed Solution for Gate Mock Test Civil Engineering (CE)- 5 - Question 39

Under combination choice R, in phase II, 1 and 3 cannot move simultaneously. Also in phase III, 4 and 6 cannot move simultaneously.

Gate Mock Test Civil Engineering (CE)- 5 - Question 40

The solution of dy/dx – y tan x – y2 sec x = 0 is given by

Detailed Solution for Gate Mock Test Civil Engineering (CE)- 5 - Question 40

Substituting in the given equation, we get

Gate Mock Test Civil Engineering (CE)- 5 - Question 41

While applying the Rational formula for computing the design discharge, the rainfall duration is stipulated as the time of concentration because

Detailed Solution for Gate Mock Test Civil Engineering (CE)- 5 - Question 41
Time of concentration (tc) is the time when entire catchment starts contributing to surface run-off at channel and this is the minimum time required.
Gate Mock Test Civil Engineering (CE)- 5 - Question 42

If q is the average sewage flow from a city of population P, the expression for maximum flow of sewage is ________. Here, q is the average sewage flow and P is the population.

Detailed Solution for Gate Mock Test Civil Engineering (CE)- 5 - Question 42
The maximum sewage flow Q and average flow q is related by the empirical formula by population P as

Gate Mock Test Civil Engineering (CE)- 5 - Question 43

Match the following groups:

Detailed Solution for Gate Mock Test Civil Engineering (CE)- 5 - Question 43
Constant head permeability test is used for the soil bearing and high permeability coefficient, that is used for sand.

Consolidation test: Expulsion of water from clayey soil takes time under the applied load condition.

Pycnometer test is used for the determination of specific gravity of the soil.

Negative skin friction due to settlement of soil nearby pile foundation acts in downward direction.

Gate Mock Test Civil Engineering (CE)- 5 - Question 44

Find the deflection midway between the supports for the overhanging beam shown in the figure below.

Detailed Solution for Gate Mock Test Civil Engineering (CE)- 5 - Question 44
Draw free body diagram.

Gate Mock Test Civil Engineering (CE)- 5 - Question 45

The value of the integral ex + y dydx is

Detailed Solution for Gate Mock Test Civil Engineering (CE)- 5 - Question 45

= 1/2(e2 - 1)2

*Answer can only contain numeric values
Gate Mock Test Civil Engineering (CE)- 5 - Question 46

The number of tracks required per km length of the track is 1500. The sleeper density for B.G. track is ____________. (Answer up to the nearest integer)

Detailed Solution for Gate Mock Test Civil Engineering (CE)- 5 - Question 46
Let sleeper density be n + 5

Here, n is the length of one rail

Number of tracks required is

15n = n + 5

0.5n = 5

n = 10

So, sleeper density is n + 5 = 10 + 5 = 15

*Answer can only contain numeric values
Gate Mock Test Civil Engineering (CE)- 5 - Question 47

A wide channel is 1 m deep and has a velocity of flow V as 2.13 m/s. If a disturbance is caused, an elementary wave can travel upstream with a velocity (in m/s) of

(Answer up to two decimal places)

Detailed Solution for Gate Mock Test Civil Engineering (CE)- 5 - Question 47

Here, wide channel, depth y = 1 m, v = 2.13 m/s.

c = celerity = relative velocity of the wave w.r.t velocity of flow = vw - v

∴ vw = 3.13 + 2.13 = 5.26 m/s

An elementary Wave can travel upstream with a velocity of 5.26 m/s

*Answer can only contain numeric values
Gate Mock Test Civil Engineering (CE)- 5 - Question 48

The sag correction in a tape of length 20 m and weight 15 kg/m suspended at its ends is ________ m. Take a pull equal to 45 kg. (Answer up to two decimal places)

Detailed Solution for Gate Mock Test Civil Engineering (CE)- 5 - Question 48
Given: l = 20 m, W = 15 kg/m and P = 45 kg

Sag correction is

*Answer can only contain numeric values
Gate Mock Test Civil Engineering (CE)- 5 - Question 49

A beam PQRS is 18 m long and is simply supported points Q and R at 10 m apart. Overhangs PQ and RS are 3 m and 5 m, respectively. A train of two point loads of 150 kN and 100 kN, 5 m apart, crosses this beam from left to right with 100 kN load leading.

The maximum sagging moment (in kNm) under the 150 kN load anywhere is (Answer up to the nearest integer)

Detailed Solution for Gate Mock Test Civil Engineering (CE)- 5 - Question 49

Max B.M = 150 x 2.4 + 100 x 0.4

=360 + 40

= 400 kNm

*Answer can only contain numeric values
Gate Mock Test Civil Engineering (CE)- 5 - Question 50

A cantilever beam of 1.5 m carries a uniformly distributed load of 24 kN/m over its full length and a force of 36 kN acts in upward direction at its free end. The magnitude of net deflection of the free end is X/El m. The value of X is __________. (Answer up to two decimal places)

Detailed Solution for Gate Mock Test Civil Engineering (CE)- 5 - Question 50
Given: w = 24 kN/m, L = 1.5 m and W = 36 kN = wL

Net deflection of the free end is

*Answer can only contain numeric values
Gate Mock Test Civil Engineering (CE)- 5 - Question 51

The plan area of a reservoir is 1 km2. The water level in the reservoir is observed to decline by 20 cm in a certain period. During this period, the reservoir receives a surface inflow of 10 hectare-meters, and 20 hectare-meters are abstracted from the reservoir for irrigation and power. The pan evaporation and rainfall recorded during the same period at a near by meteorological station are 12 cm and 3 cm respectively. The calibrated pan factor is 0.7. The seepage from the reservoir during this period in hectare-meters is

(Answer up to one decimal place)

Detailed Solution for Gate Mock Test Civil Engineering (CE)- 5 - Question 51

Area = 1 km2 = 1 x 106 m2, declined by 20 cm. For a certain period,

Water budget equation

So, actual evaporation = 0.12 x 0.7 x 106 m3.

Inflow - Outflow = Change in storage

⇒ Seepage in hectare-m

= 20 + 10 + 0.03 x 102 - 0.12 x 0.7 x 102 - 20

= 4.6 hectare-m

*Answer can only contain numeric values
Gate Mock Test Civil Engineering (CE)- 5 - Question 52

For a vertical cut 5 m deep in soil, find the maximum depth(in m) of excavation left unsupported when ∅’ = 17.2o, C' = 1.91 t/m2 and γ = 1.74 t/m2. (Answer up to two decimal places

Detailed Solution for Gate Mock Test Civil Engineering (CE)- 5 - Question 52

Given: ∅’ = 17.2o, C' = 1.91 t/m2 = 19.1 kN/m2

and γ = 1.74 t/m2 = 17.4 kN/m2

= 45o + 8.6o

= 53.6o

Maximum depth of excavation left unsupported is

H = 2Z0

= 2(2.98) = 5.96

*Answer can only contain numeric values
Gate Mock Test Civil Engineering (CE)- 5 - Question 53

If 50 g of CO2 and 25 g of CH4 are produced from the decomposition of municipal solid waste (MSW) with a formula weight of 120 g, then what is the average per capita greenhouse gas production (in g/day) in a city of 1 million people with a MSW production rate of 500 ton/day? (Answer up to the nearest integer)

Detailed Solution for Gate Mock Test Civil Engineering (CE)- 5 - Question 53

CO2 and CH4 are the green house gases.

Production of MSW per capita

120g MSW produce (50 + 25) = 75 g green house gas

500 g MSW will produce

*Answer can only contain numeric values
Gate Mock Test Civil Engineering (CE)- 5 - Question 54

Moment of inertia of quarter circle of radius 10 cm about the X–axis is ________________ cm4. (Answer up to the nearest integer)

Detailed Solution for Gate Mock Test Civil Engineering (CE)- 5 - Question 54

Ixx = 1/2(0.11 R4) = 0.055 R4

= 0.055(10)4 = 550 cm4

*Answer can only contain numeric values
Gate Mock Test Civil Engineering (CE)- 5 - Question 55

The following data pertains to the number of commercial vehicles per day for the design of a flexible pavement for a national highway as per IRC: 37-1984.

Assuming a traffic growth factor of 7.5% per annum for both the types of vehicles, the cumulative number of standard axle load repetitions (in million) for a design life of ten years is (Answer up to one decimal place)

Detailed Solution for Gate Mock Test Civil Engineering (CE)- 5 - Question 55

= 57.8 million

*Answer can only contain numeric values
Gate Mock Test Civil Engineering (CE)- 5 - Question 56

A couple of 25 kN/m is acting at one end of a simply supported beam. The maximum slope occuring on the beam is _______________ × 10-5 radian. Take E = 250 GPa and I = 10,00,000 mm4. (Answer up to one decimal place)

Detailed Solution for Gate Mock Test Civil Engineering (CE)- 5 - Question 56
Consider the diagram,

M = 25000 N/m, E = 250 x 109 Pa, I = 0.001 m4

Maximum slope is

= 3.3 × 10-5

*Answer can only contain numeric values
Gate Mock Test Civil Engineering (CE)- 5 - Question 57

The culturable command area for a distributary channel is 20,000 hectares. Wheat grown in the entire area and the intensity of irrigation is 50%. The kor period for wheat is 30 days and the kor water depth is 120 mm. The outlet discharge (in m3/sec) for the distributary should be

(Answer up to two decimal places)

Detailed Solution for Gate Mock Test Civil Engineering (CE)- 5 - Question 57

*Answer can only contain numeric values
Gate Mock Test Civil Engineering (CE)- 5 - Question 58

A solid cone is rotating at an angular velocity of 60 rad/s. An oil of dynamic viscosity 0.45 Pa.s and thickness 25 mm fills the gap between the cone and the housing. The required torque to be applied is _____________ Nm. Take radius equal to 0.5 m and vortex angle equal to 136° for the solid cone. (Answer up to one decimal place)

Detailed Solution for Gate Mock Test Civil Engineering (CE)- 5 - Question 58

Given: R = 0.5 m, 2θ = 136o, μ = 0.45 Pa.s, t = 25 mm and ω = 60 rad/s

Consider an elementary ring of bearing surface of radius r at a distance h from the apex and let r + dr is the radius at a distance of h + dh.

Bearing area is

A = 2πrdr

Shear stress is

Tangential resistance on the ring

Torque due to the force dF is

Total required torque is

= 114.3557

≈ 114.4 Nm

*Answer can only contain numeric values
Gate Mock Test Civil Engineering (CE)- 5 - Question 59

The design speed on a road is 60 kmph. Assuming the driver reaction time of 2.5 seconds and the coefficient of friction of pavement surface as 0.35, the required stopping distance (in m) for two-way traffic on a single lane road is (Answer up to one decimal place)

Detailed Solution for Gate Mock Test Civil Engineering (CE)- 5 - Question 59

= 82.1 m

But for two - way single lane road,

Stopping sight distance = 2(Stopping sight distance) = 2 (82.1) 164.2 m

So, the required stopping distance for two-way traffic on a single lane road is 164.2 m.

*Answer can only contain numeric values
Gate Mock Test Civil Engineering (CE)- 5 - Question 60

For an I-beam, flange size is 300 x 30 mm and web size is 800 x 16 mm. If the beam is subjected to a bending moment of 65 x 105 kg-cm and a shear force of 60,000 kg, the magnitude of shear stress at a point 25 cm above the neutral axis is ____________ kg/cm2. (Answer up to two decimal places)

Detailed Solution for Gate Mock Test Civil Engineering (CE)- 5 - Question 60

Given: F = 60000 kg, M = 65 x 105 kg-cm and Y = 25 cm

Moment of interia of I-beam is

Magnitude of shear stress at a point 25 cm above the neutral axis is

= 60.43 kg/cm2

*Answer can only contain numeric values
Gate Mock Test Civil Engineering (CE)- 5 - Question 61

A reinforced concrete beam, size 200 mm wide and 300 mm deep overall is simply supported over a span of 3 m. It is subjected to two point loads P of equal magnitude placed at middle third points. The two loads are gradually increased, simultaneously. Beam is reinforced with 2 HYSD bars of 16 mm diameter placed at an effective cover of 40 mm bottom face and nominal shear reinforcement. The characteristics compressive strength and the bending tensile strength of the concrete are 20.0 N/mm2 and 2.2 N/mm2, respectively.

The theoretical failure load (in kN) of the beam for attainment of limit state of collapse in flexure is (Answer up to one decimal place)

Detailed Solution for Gate Mock Test Civil Engineering (CE)- 5 - Question 61

Ast: Area of tensile steel reinforcement

= 2 × 201 = 402 mm2

xu: Depth of neutral axis

xu,lim = 0.48d = 0.48 × 260 = 124.8 mm

xu < />u,lim, the section in URS

Mu = 0.87fy Ast (d - 0.42xu)

= 0.87 × 415 × 402(260 - 0.42 × 100.8)

= 31.6 kNm

*Answer can only contain numeric values
Gate Mock Test Civil Engineering (CE)- 5 - Question 62

A beam is shown in the figure below. When the shear force is - 1.65 kN in the beam, the value of the bending moment at that point is _________ kN/m. (Answer up to three decimal places)

Detailed Solution for Gate Mock Test Civil Engineering (CE)- 5 - Question 62
Consider the free body diagram of the given beam.

Draw the SF diagram.

Draw the BM diagram.

From the diagrams, required BM is 2.175 kN-m.

*Answer can only contain numeric values
Gate Mock Test Civil Engineering (CE)- 5 - Question 63

An average rainfall of 16 cm occurs over a catchment during a period of 12 hours with uniform intensity. The unit hydrograph (unit depth = 1 cm, duration = 6 hours) of the catchment rises linearly from 0 to 30 cumecs in six hours and then falls linearly from 30 to 0 cumecs in the next 12 hours.Φ index of the catchment is known to be 0.5 cm/hr. Base flow in the river is known to be 5 cumecs.

Area of the catchment in hectares is (Answer up to the nearest integer)

Detailed Solution for Gate Mock Test Civil Engineering (CE)- 5 - Question 63

Area of unit hydrograph provides the volume of water due to 1 cm of ER

A x 0.01 = 1/2 x 30 x 18 x 60 x 60

A = 9720 x 104 m2

= 9720 hectare

*Answer can only contain numeric values
Gate Mock Test Civil Engineering (CE)- 5 - Question 64

At a point in a loaded member, a state of plane stress exists and the strains are εx = 270 x 10-6, εy = -90 x 10-6 and εxy = 360 x 10-6. If E = 200 GPa, μ = 0.25 and G = 80 GPa, then the value of normal stress (major) (in MPa) is (Answer up to one decimal place)

Detailed Solution for Gate Mock Test Civil Engineering (CE)- 5 - Question 64

Larger will be the major normal stress.

*Answer can only contain numeric values
Gate Mock Test Civil Engineering (CE)- 5 - Question 65

A benchmark has been established at the soffit of an ornamental arch at the known elevation of 100.0 m above the sea level. The back sight used to establish height of instrument is an inverted staff reading of 2.105 m. A forward sight reading with a normally held staff of 1.105 m is taken on a recently constructed plinth. The elevation of the plinth (in m) is (Answer up to two decimal places)

Detailed Solution for Gate Mock Test Civil Engineering (CE)- 5 - Question 65
RL of Plinth = 100.000 - B.S - F.S

= 100.000 - 2.105 - 1.105 = 96.79 m

## GATE Civil Engineering (CE) 2023 Mock Test Series

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## GATE Civil Engineering (CE) 2023 Mock Test Series

27 docs|296 tests