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GATE CE 2016 Set 2
All 65 solved GATE CE 2016 Set 2 questions in exam order. Open a question, commit to an answer, and learn from the step-by-step solution. One question at a time.
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65
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General Aptitude (GA)
101
Q1MCQ1 markEasyIf I were you, I __________ that laptop. It’s much too expensive.Think it through. Then check your answer.Question
If I were you, I __________ that laptop. It’s much too expensive.Correct answer
(C) wouldn’t buy
Step-by-step solution
This sentence uses the second conditional, which is used to talk about hypothetical or imaginary situations in the present or future. The structure is: If + past simple, would + base verb. Given the context that the laptop is 'much too expensive', the speaker is expressing a hypothetical negative action. Therefore, 'wouldn’t buy' is the grammatically correct and logically appropriate choice.2
Q2MCQ1 markEasyHe turned a deaf ear to my request. What does the underlined phrasal verb mean?Think it through. Then check your answer.Question
He turned a deaf ear to my request.
What does the underlined phrasal verb mean?Correct answer
(A) ignored
Step-by-step solution
The idiom 'to turn a deaf ear' means to refuse to listen to something, or to deliberately ignore a request, suggestion, or complaint. Thus, 'ignored' is the correct meaning.3
Q3MCQ1 markEasyChoose the most appropriate set of words from the options given below to complete the following sentence. _______ _______ is a will, _______ is a way.Think it through. Then check your answer.Question
Choose the most appropriate set of words from the options given below to complete the following sentence.
_______ _______ is a will, _______ is a way.Correct answer
(C) Where, there, there
Step-by-step solution
The sentence is a well-known English proverb: 'Where there is a will, there is a way.'- 'Where' is used to introduce the condition.
- 'There' is used as an introductory subject in both clauses.
- 'Their' is a possessive pronoun and is incorrect in this context.
4
Q4MCQ1 markEasyis equivalent to ________.Think it through. Then check your answer.Question
is equivalent to ________.Correct answer
(A) 2 \% of xy
Step-by-step solution
.
.
Sum .5
Q5MCQ1 markEasyThe sum of the digits of a two digit number is 12. If the new number formed by reversing the digits is greater than the original number by 54, find the original number.Think it through. Then check your answer.Question
The sum of the digits of a two digit number is 12. If the new number formed by reversing the digits is greater than the original number by 54, find the original number.Correct answer
(A) 39
Step-by-step solution
Let the two-digit number be .
Sum of digits: .
Reversing the digits gives .
Given: .
Solving the two equations:
.
Substituting in .
The original number is .6
Q6MCQ2 marksMediumTwo finance companies, P and Q, declared fixed annual rates of interest on the amounts invested with them. The rates of interest offered by these companies may differ from year to…Think it through. Then check your answer.Question
Two finance companies, P and Q, declared fixed annual rates of interest on the amounts invested with them. The rates of interest offered by these companies may differ from year to year. Year-wise annual rates of interest offered by these companies are shown by the line graph provided below.If the amounts invested in the companies, P and Q, in 2006 are in the ratio 8:9, then the amounts received after one year as interests from companies P and Q would be in the ratio:
Correct answer
(D) 4:3
Step-by-step solution
From the line graph, for the year 2006:- Interest rate for company P
- Interest rate for company Q
Interest from company P
Interest from company Q Ratio of interests .7
Q7MCQ2 marksEasyToday, we consider Ashoka as a great ruler because of the copious evidence he left behind in the form of stone carved edicts. Historians tend to correlate greatness of a king at…Think it through. Then check your answer.Question
Today, we consider Ashoka as a great ruler because of the copious evidence he left behind in the form of stone carved edicts. Historians tend to correlate greatness of a king at his time with the availability of evidence today.
Which of the following can be logically inferred from the above sentences?Correct answer
(D) A king's greatness, as we know him today, is interpreted by historians.
Step-by-step solution
The passage states that Ashoka is considered a great ruler "because of the copious evidence he left behind in the form of stone carved edicts" and that "Historians tend to correlate greatness of a king at his time with the availability of evidence today." This directly implies that the current perception of a king's greatness is shaped by how historians interpret the available evidence.Option (A) is too strong; the passage does not say emperors are completely forgotten if they don't leave evidence, only that their greatness might not be recognized. Option (B) attributes an intention to Ashoka that is not stated or implied. Option (C) is a general statement about statues, which is not the main inference from the given sentences about Ashoka and historians.Therefore, option (D) is the most logical inference.8
Q8MCQ2 marksMediumFact 1: Humans are mammals. Fact 2: Some humans are engineers. Fact 3: Engineers build houses. If the above statements are facts, which of the following can be logically inferred?…Think it through. Then check your answer.Question
Fact 1: Humans are mammals.
Fact 2: Some humans are engineers.
Fact 3: Engineers build houses.If the above statements are facts, which of the following can be logically inferred?I. All mammals build houses.
II. Engineers are mammals.
III. Some humans are not engineers.Correct answer
(B) III only.
Step-by-step solution
Let be the set of humans, be the set of mammals, be the set of engineers, and be the set of those who build houses.From the given facts:1.Fact 1: (All humans are mammals).2.Fact 2: (Some humans are engineers).3.Fact 3: (All engineers build houses).Evaluating the inferences:- Inference I: 'All mammals build houses' (). This is not necessarily true because we only know that engineers build houses, and not all mammals are engineers.
- Inference II: 'Engineers are mammals' (). While we know that the intersection of humans and engineers () is a subset of mammals (), we do not have information about engineers who are not humans. Therefore, we cannot logically infer that all engineers are mammals.
- Inference III: 'Some humans are not engineers' (). In the context of syllogistic reasoning in competitive exams like GATE, the statement 'Some humans are engineers' is typically interpreted to imply that there is also a group of humans who are not engineers. Given the options and the official answer key, this is the only valid inference.
9
Q9MCQ2 marksMediumA square pyramid has a base perimeter , and the slant height is half of the perimeter. What is the lateral surface area of the pyramid?Think it through. Then check your answer.Question
A square pyramid has a base perimeter , and the slant height is half of the perimeter. What is the lateral surface area of the pyramid?Correct answer
(D) 0.25 x²
Step-by-step solution
Let the side length of the square base be .
The base perimeter . So, .The slant height is given as half of the perimeter, so .The lateral surface area of a pyramid is given by the formula: .Substituting the given values:
Thus, the lateral surface area of the pyramid is .10
Q10MCQ2 marksMediumAnanth takes 6 hours and Bharath takes 4 hours to read a book. Both started reading copies of the book at the same time. After how many hours is the number of pages **to be read**…Think it through. Then check your answer.Question
Ananth takes 6 hours and Bharath takes 4 hours to read a book. Both started reading copies of the book at the same time. After how many hours is the number of pages to be read by Ananth, twice that to be read by Bharath? Assume Ananth and Bharath read all the pages with constant pace.Correct answer
(C) 3
Step-by-step solution
Let be the total number of pages in the book. Ananth's reading rate is pages per hour.
Bharath's reading rate is pages per hour.Let be the time in hours after which the condition is met.
The number of pages remaining to be read by Ananth after hours is:
The number of pages remaining to be read by Bharath after hours is:
According to the problem, :
Dividing both sides by :
Rearranging the terms to solve for :
hours.Thus, after 3 hours, the number of pages to be read by Ananth is twice that of Bharath.
Civil Engineering Set-2
5511
Q11NAT1 markEasyThe spot speeds (expressed in km/hr) observed at a road section are 66, 62, 45, 79, 32, 51, 56, 60, 53, and 49. The median speed (expressed in km/hr) is _________ (Note: answer…Think it through. Then check your answer.Question
The spot speeds (expressed in km/hr) observed at a road section are 66, 62, 45, 79, 32, 51, 56, 60, 53, and 49. The median speed (expressed in km/hr) is _________
(Note: answer with one decimal accuracy)Correct answer
54.49 to 54.51
Step-by-step solution
1.Arrange the spot speeds in ascending order: 32, 45, 49, 51, 53, 56, 60, 62, 66, 79.2.The number of observations , which is even.3.The median is the average of the and terms.4.The term is 53 and the term is 56.5.Median = km/hr.12
Q12MCQ1 markEasyThe optimum value of the function isThink it through. Then check your answer.Question
The optimum value of the function isCorrect answer
(D) -2 (minimum)
Step-by-step solution
1.Given .2.Find the first derivative: .3.Set to find critical points: .4.Find the second derivative: .5.Since , the function has a minimum at .6.The minimum value is .7.Thus, the optimum value is -2 (minimum).13
Q13MCQ1 markMediumThe Fourier series of the function, in the interval is…Think it through. Then check your answer.Question
The Fourier series of the function,in the interval isThe convergence of the above Fourier series at givesCorrect answer
(C) Σₙ₌₁^(∞) (1)/((2n-1)²) = (π²)/(8)
Step-by-step solution
1.According to Dirichlet's theorem, at a point of discontinuity , the Fourier series converges to .2.At , and .3.The series converges to .4.Substituting into the given Fourier series:
5.Rearranging the terms:
.14
Q14MCQ1 markMediumand are two random independent events. It is known that and . Which one of the following is the value of ?Think it through. Then check your answer.Question
and are two random independent events. It is known that and . Which one of the following is the value of ?Correct answer
(A) 0.7
Step-by-step solution
Given and are independent events, and are also independent.
Since they are independent, .
Thus, .
Now,
.15
Q15MCQ1 markEasyWhat is the value of ?Think it through. Then check your answer.Question
What is the value of ?Correct answer
(D) Limit does not exist
Step-by-step solution
To check the existence of the limit, we evaluate it along different paths approaching .
Let's take the path :
The value of the limit depends on the slope of the path. Since the limit is not unique, it does not exist.16
Q16MCQ1 markMediumThe kinematic indeterminacy of the plane truss shown in the figure isThink it through. Then check your answer.Question
The kinematic indeterminacy of the plane truss shown in the figure isCorrect answer
(A) 11
Step-by-step solution
The kinematic indeterminacy () for a plane truss is given by:
where is the number of joints and is the number of support reactions.
From the figure, the joints are:- 3 joints on the bottom chord (including the two supports).
- 3 joints on the middle horizontal chord.
- 1 joint at the top apex.
The supports are a hinge (2 reactions) and a roller (1 reaction), so .
.17
Q17MCQ1 markEasyAs per IS 456-2000 for the design of reinforced concrete beam, the maximum allowable shear stress depends on theThink it through. Then check your answer.Question
As per IS 456-2000 for the design of reinforced concrete beam, the maximum allowable shear stress depends on theCorrect answer
(B) grade of concrete only
Step-by-step solution
According to IS 456:2000, Clause 40.2.3 and Table 20, the maximum shear stress in beams depends only on the grade of concrete. It is independent of the percentage of reinforcement and the grade of steel.18
Q18MCQ1 markMediumAn assembly made of a rigid arm A-B-C hinged at end A and supported by an elastic rope C-D at end C is shown in the figure. The members may be assumed to be weightless and the…Think it through. Then check your answer.Question
An assembly made of a rigid arm A-B-C hinged at end A and supported by an elastic rope C-D at end C is shown in the figure. The members may be assumed to be weightless and the lengths of the respective members are as shown in the figure.Under the action of a concentrated load at C as shown, the magnitude of tension developed in the rope is
Correct answer
(B) P√(2)
Step-by-step solution
Taking moments about hinge A:Clockwise moment due to load at C:
Counter-clockwise moment due to tension in rope CD:
The rope CD makes an angle of with the horizontal (since horizontal and vertical projections are both ).
The tension acts at point C.
Horizontal component
Vertical component
Moment of about A: (CCW)
Moment of about A: (CCW)
Total CCW moment
Equating moments:19
Q19MCQ1 markEasyAs per Indian standards for bricks, minimum acceptable compressive strength of any class of burnt clay bricks in dry state isThink it through. Then check your answer.Question
As per Indian standards for bricks, minimum acceptable compressive strength of any class of burnt clay bricks in dry state isCorrect answer
(D) 3.5 MPa
Step-by-step solution
According to IS 1077:1992, the minimum compressive strength for any class of common burnt clay bricks is 3.5 MPa (Class 3.5).20
Q20MCQ1 markMediumA construction project consists of twelve activities. The estimated duration (in days) required to complete each of the activities along with the corresponding network diagram is…Think it through. Then check your answer.Question
A construction project consists of twelve activities. The estimated duration (in days) required to complete each of the activities along with the corresponding network diagram is shown below.Activity Duration (days) Activity Duration (days) A Inauguration 1 G Flooring 25 B Foundation work 7 H Electrification 7 C Structural construction-1 30 I Plumbing 7 D Structural construction-2 30 J Wood work 7 E Brick masonry work 25 K Coloring 3 F Plastering 7 L Handing over function 1 Total floats (in days) for the activities 5-7 and 11-12 for the project are, respectively,
Correct answer
(C) 0 and 0
Step-by-step solution
To find the total float, we first identify the critical path(s) of the network. The duration of various paths from node 1 to node 12 are:1.Path 1-2-3-4-6-8-10-11-12: days.2.Path 1-2-3-5-7-9-10-11-12: days.3.Path 1-2-3-4-5-7-9-10-11-12 (via dummy 4-5): days.Since the maximum duration is 81 days, all these paths are critical paths. Activity 5-7 (G) lies on Path 2 and Path 3, which are critical. Activity 11-12 (L) lies on all critical paths. The total float for any activity on a critical path is 0. Therefore, the total floats for activities 5-7 and 11-12 are 0 and 0, respectively.21
Q21MCQ1 markEasyA strip footing is resting on the surface of a purely clayey soil deposit. If the width of the footing is doubled, the ultimate bearing capacity of the soilThink it through. Then check your answer.Question
A strip footing is resting on the surface of a purely clayey soil deposit. If the width of the footing is doubled, the ultimate bearing capacity of the soilCorrect answer
(D) remains the same
Step-by-step solution
According to Terzaghi's bearing capacity theory for a strip footing:For purely clayey soil, the angle of internal friction , which gives the bearing capacity factors , , and .
For a footing resting on the surface, the surcharge (since ).
Substituting these values into the equation:The ultimate bearing capacity is independent of the width of the footing. Therefore, if the width is doubled, the ultimate bearing capacity remains the same.22
Q22MCQ1 markEasyThe relationship between the specific gravity of sand () and the hydraulic gradient () to initiate quick condition in the sand layer having porosity of 30% isThink it through. Then check your answer.Question
The relationship between the specific gravity of sand () and the hydraulic gradient () to initiate quick condition in the sand layer having porosity of 30% isCorrect answer
(C) G = 1.43i + 1
Step-by-step solution
The critical hydraulic gradient required to initiate quick condition is given by the formula:where is the specific gravity and is the void ratio.
The relationship between void ratio () and porosity () is:Given porosity , we have:Substituting into the formula for :Rearranging to solve for :Thus, the correct relationship is .23
Q23MCQ1 markMediumThe results of a consolidation test on an undisturbed soil, sampled at a depth of m below the ground level are as follows: | Parameter | Value | | :--- | :--- | | Saturated…Think it through. Then check your answer.Question
The results of a consolidation test on an undisturbed soil, sampled at a depth of m below the ground level are as follows:The water table was encountered at the ground level. Assuming the unit weight of water as kN/m, the over-consolidation ratio of the soil isParameter Value Saturated unit weight kN/m Pre-consolidation pressure kPa Correct answer
(B) 1.50
Step-by-step solution
1.Calculate the effective overburden pressure () at a depth of m.Since the water table is at the ground level, the soil is fully saturated.
.2.Calculate the Over-Consolidation Ratio (OCR).OCR =
OCR = .Therefore, the correct option is (B).24
Q24MCQ1 markMediumProfile of a weir on permeable foundation is shown in figure I and an elementary profile of 'upstream pile only case' according to Khosla's theory is shown in figure II. The…Think it through. Then check your answer.Question
Profile of a weir on permeable foundation is shown in figure I and an elementary profile of 'upstream pile only case' according to Khosla's theory is shown in figure II. The uplift pressure heads at key points Q, R and S are m, m and m, respectively (refer figure II).What is the uplift pressure head at point P downstream of the weir (junction of floor and pile as shown in the figure I)?
Correct answer
(B) 1.25 m
Step-by-step solution
According to Khosla's theory, for an elementary profile with an upstream pile (Figure II), the uplift pressure heads are given as m, m, and m for a total head m.In Figure I, point P is the junction of the floor and the pile at the downstream end. The total floor length is m, which matches the length in Figure II. The pile depth at P is m, which also matches the pile depth in Figure II.By the principle of symmetry in Khosla's theory, the uplift pressure at the downstream junction () is related to the uplift pressure at the upstream junction () as follows:
.Thus, the correct option is (B).25
Q25NAT1 markMediumWater table of an aquifer drops by cm over an area of km. The porosity and specific retention of the aquifer material are and , respectively. The…Think it through. Then check your answer.Question
Water table of an aquifer drops by cm over an area of km. The porosity and specific retention of the aquifer material are and , respectively. The amount of water (expressed in km) drained out from the area is _________Correct answer
0.19 to 0.21
Step-by-step solution
Specific yield () is defined as the ratio of the volume of water that a saturated rock or soil will yield by gravity to the total volume of the rock or soil. It is calculated as:where is the porosity and is the specific retention.Given:
Porosity,
Specific retention,
Specific yield, The volume of water drained () is given by:where:
(Area)
(Drop in water table)Substituting the values:Thus, the amount of water drained out from the area is .26
Q26MCQ1 markEasyGroup I contains the types of fluids while Group II contains the shear stress - rate of shear relationship of different types of fluids, as shown in the figure. | Group I | Group…Think it through. Then check your answer.Question
Group I contains the types of fluids while Group II contains the shear stress - rate of shear relationship of different types of fluids, as shown in the figure.Group I Group II P. Newtonian fluid 1. Curve 1 Q. Pseudo plastic fluid 2. Curve 2 R. Plastic fluid 3. Curve 3 S. Dilatant fluid 4. Curve 4 5. Curve 5 
Correct answer
(C) P-2, Q-4, R-5, S-3
Step-by-step solution
Newtonian fluid (P) has a linear relationship between shear stress and rate of shear passing through the origin, which is Curve 2. Pseudo plastic fluid (Q) is shear-thinning, meaning its viscosity decreases with increasing shear rate, represented by Curve 4. Dilatant fluid (S) is shear-thickening, represented by Curve 3. Plastic fluid (R), specifically Bingham plastic, requires a certain yield stress before it starts to flow, represented by Curve 5. Thus, the correct match is P-2, Q-4, R-5, S-3.27
Q27MCQ1 markEasyThe atmospheric layer closest to the earth surface isThink it through. Then check your answer.Question
The atmospheric layer closest to the earth surface isCorrect answer
(D) the troposphere
Step-by-step solution
The layers of the atmosphere starting from the Earth's surface are the troposphere, stratosphere, mesosphere, thermosphere, and exosphere. Therefore, the troposphere is the closest layer.28
Q28NAT1 markMediumA water supply board is responsible for treating of water. A settling column analysis indicates that an overflow rate of will…Think it through. Then check your answer.Question
A water supply board is responsible for treating of water. A settling column analysis indicates that an overflow rate of will produce satisfactory removal for a depth of . It is decided to have two circular settling tanks in parallel. The required diameter (expressed in ) of the settling tanks is __________Correct answer
6.8 to 7
Step-by-step solution
Given:
Total flow rate,
Number of circular settling tanks in parallel,
Overflow rate (surface loading rate),
Depth of settling column, (This is a distractor as the overflow rate depends on the surface area, not the depth)Step 1: Calculate the flow rate per tank ():
Since the tanks are in parallel, the total flow is divided equally:Step 2: Calculate the required surface area () for each tank:
Using the overflow rate formula :Step 3: Calculate the diameter () of the circular tank:
The surface area of a circular tank is given by :The required diameter of the settling tanks is approximately , which falls within the acceptable range of to .29
Q29NAT1 markMediumThe hardness of a ground water sample was found to be 420 mg/L as CaCO. A softener containing ion exchange resins was installed to reduce the total hardness to 75 mg/L as…Think it through. Then check your answer.Question
The hardness of a ground water sample was found to be 420 mg/L as CaCO. A softener containing ion exchange resins was installed to reduce the total hardness to 75 mg/L as CaCO before supplying to 4 households. Each household gets treated water at a rate of 540 L/day. If the efficiency of the softener is 100%, the bypass flow rate (expressed in L/day) is _________Correct answer
380 to 390
Step-by-step solution
Total water demand for 4 households is calculated as:
Given:- Initial hardness () = 420 mg/L as CaCO
- Desired final hardness () = 75 mg/L as CaCO
- Softener efficiency = 100%, so hardness of softened water () = 0 mg/L
Applying the mass balance for hardness:
The bypass flow rate is approximately 385.71 L/day, which falls within the specified range of 380 to 390.30
Q30MCQ1 markEasyThe sound pressure (expressed in ) of the faintest sound that a normal healthy individual can hear isThink it through. Then check your answer.Question
The sound pressure (expressed in ) of the faintest sound that a normal healthy individual can hear isCorrect answer
(C) 20
Step-by-step solution
The threshold of hearing for a normal healthy individual is defined as a sound pressure of (or ) at a frequency of .31
Q31MCQ1 markMediumIn the context of the IRC 58-2011 guidelines for rigid pavement design, consider the following pair of statements. I: Radius of relative stiffness is directly related to modulus…Think it through. Then check your answer.Question
In the context of the IRC 58-2011 guidelines for rigid pavement design, consider the following pair of statements.I: Radius of relative stiffness is directly related to modulus of elasticity of concrete and inversely related to Poisson's ratio
II: Radius of relative stiffness is directly related to thickness of slab and modulus of subgrade reaction.Which one of the following combinations is correct?Correct answer
(B) I: False; II: False
Step-by-step solution
The radius of relative stiffness () is given by the formula:
where:
= Modulus of elasticity of concrete
= Thickness of the slab
= Modulus of subgrade reaction
= Poisson's ratioAnalysis of Statement I:- , so it is directly related to the modulus of elasticity.
- . As Poisson's ratio () increases, the term decreases, which causes to increase. Thus, is directly related to Poisson's ratio, not inversely. Therefore, Statement I is False.
- , so it is directly related to the thickness of the slab.
- , meaning it is inversely related to the modulus of subgrade reaction. The statement claims it is directly related, which is incorrect. Therefore, Statement II is False.
32
Q32MCQ1 markMediumIf the total number of commercial vehicles per day ranges from 3000 to 6000, the minimum percentage of commercial traffic to be surveyed for axle load isThink it through. Then check your answer.Question
If the total number of commercial vehicles per day ranges from 3000 to 6000, the minimum percentage of commercial traffic to be surveyed for axle load isCorrect answer
(A) 15
Step-by-step solution
According to IRC:37-2012 (Guidelines for the Design of Flexible Pavements), the minimum sample size for axle load surveys depends on the commercial vehicles per day (CVPD). For a traffic volume ranging from 3000 to 6000 CVPD, the recommended minimum sample size is 15%.33
Q33MCQ1 markEasyOptimal flight planning for a photogrammetric survey should be carried out consideringThink it through. Then check your answer.Question
Optimal flight planning for a photogrammetric survey should be carried out consideringCorrect answer
(D) both side-lap as well as end-lap
Step-by-step solution
In photogrammetry, to ensure complete coverage of the area and to enable stereoscopic viewing (3D perception) of the terrain, photographs must overlap in both directions.1.End-lap (Longitudinal overlap): Overlap between successive photos along the flight line, typically around 60%.2.Side-lap (Lateral overlap): Overlap between adjacent flight strips, typically around 30%.Therefore, both are essential for optimal flight planning.34
Q34MCQ1 markEasyThe reduced bearing of a m long line is N E. The departure of the line isThink it through. Then check your answer.Question
The reduced bearing of a m long line is N E. The departure of the line isCorrect answer
(D) 5.00 m
Step-by-step solution
Given:
Length of the line () = m
Reduced Bearing () = N EIn surveying, the departure () of a line is its projection on the East-West axis, calculated as:Since the bearing is in the North-East quadrant, the departure is positive (East).35
Q35MCQ1 markEasyA circular curve of radius connects two straights with a deflection angle of . The tangent length isThink it through. Then check your answer.Question
A circular curve of radius connects two straights with a deflection angle of . The tangent length isCorrect answer
(A) 0.577 R
Step-by-step solution
The tangent length of a simple circular curve is given by the formula:where is the radius and is the deflection angle.Given , we have:Thus, the correct option is (A).36
Q36MCQ2 marksMediumConsider the following linear system. This system is consistent if , and satisfy the equationThink it through. Then check your answer.Question
Consider the following linear system.
This system is consistent if , and satisfy the equationCorrect answer
(B) 3a + b - c = 0
Step-by-step solution
The system of equations is:
1)
2)
3) Observe the relationship between the left-hand sides of the equations. If we multiply the first equation by 3 and add it to the second equation:This result is exactly the left-hand side of the third equation. For the system to be consistent, the right-hand side constants must follow the same linear combination:Thus, the correct option is (B).37
Q37MCQ2 marksMediumIf and are two probability density functions,…Think it through. Then check your answer.Question
If and are two probability density functions,Which one of the following statements is true?Correct answer
(B) Mean of f(x) and g(x) are same; Variance of f(x) and g(x) are different
Step-by-step solution
1.Mean Analysis: Both and are symmetric about over the interval . For any probability density function symmetric about a point , the mean is . Therefore, and . The means are the same.2.Normalization: For and to be valid PDFs, the area under the curve must be 1.and . This implies for them to be normalized PDFs.3.Variance Analysis: Variance . Since the means are 0, .For (assuming ):For (assuming ):Since , the variances are different.Thus, the correct option is (B).38
Q38MCQ2 marksMediumThe angle of intersection of the curves and at point isThink it through. Then check your answer.Question
The angle of intersection of the curves and at point isCorrect answer
(D) 90^o
Step-by-step solution
To find the angle of intersection of two curves at a point, we find the slopes of the tangents to the curves at that point.Curve 1: . Differentiating with respect to : . At , the slope .Curve 2: . Differentiating with respect to : . Thus, . At , the slope .Since one tangent is horizontal () and the other is vertical (), the angle of intersection is .39
Q39NAT2 marksEasyThe area between the parabola and the straight line is _________.Think it through. Then check your answer.Question
The area between the parabola and the straight line is _________.Correct answer
85 to 85.5
Step-by-step solution
To find the area between the parabola and the straight line :1.Find the points of intersection:Equating the two expressions for :
2.Set up the area integral:The area is the integral of the upper function () minus the lower function () from to .
3.Evaluate the integral:Since the integrand is an even function, we can simplify the calculation:
The area is approximately .40
Q40MCQ2 marksEasyThe quadratic approximation of at the point isThink it through. Then check your answer.Question
The quadratic approximation of at the point isCorrect answer
(B) -3x² - 5
Step-by-step solution
The quadratic approximation of a function at is given by the first three terms of its Taylor series:Given and :
Substituting these values into the formula:
Rearranging, we get .41
Q41MCQ2 marksEasyAn elastic isotropic body is in a hydrostatic state of stress as shown in the figure. For no change in the volume to occur, what should be its Poisson's ratio? [figure]Think it through. Then check your answer.Question
An elastic isotropic body is in a hydrostatic state of stress as shown in the figure. For no change in the volume to occur, what should be its Poisson's ratio?
Correct answer
(C) 0.50
Step-by-step solution
For an elastic isotropic body, the volumetric strain is given by:In a hydrostatic state of stress, . Thus,For no change in volume to occur, . This implies:Therefore, the Poisson's ratio must be 0.50.42
Q42MCQ2 marksMediumFor the stress state (in MPa) shown in the figure, the major principal stress is 10 MPa. [figure] The shear stress isThink it through. Then check your answer.Question
For the stress state (in MPa) shown in the figure, the major principal stress is 10 MPa.The shear stress is
Correct answer
(B) 5.0 MPa
Step-by-step solution
Given the stress state:
MPa (tensile)
MPa (tensile)
The major principal stress is calculated as:Substituting the given values:43
Q43MCQ2 marksMediumThe portal frame shown in the figure is subjected to a uniformly distributed vertical load (per unit length). [figure] The bending moment in the beam at the joint ‘Q’ isThink it through. Then check your answer.Question
The portal frame shown in the figure is subjected to a uniformly distributed vertical load (per unit length).The bending moment in the beam at the joint ‘Q’ is
Correct answer
(A) zero
Step-by-step solution
In the given portal frame, support P is a hinge and support S is a roller.1.Since there are no horizontal loads acting on the frame, the horizontal reaction at the hinge support P () must be zero ().2.The bending moment at any point in the column PQ is given by , where is the distance from P. Since , the bending moment throughout the column PQ is zero.3.At joint Q, by equilibrium of the joint, the moment in the beam QR must equal the moment in the column PQ. Since the moment in the column at Q is zero, the bending moment in the beam at joint Q is also zero.44
Q44MCQ2 marksHardConsider the structural system shown in the figure under the action of weight . All the joints are hinged. The properties of the members in terms of length (), area ()…Think it through. Then check your answer.Question
Consider the structural system shown in the figure under the action of weight . All the joints are hinged. The properties of the members in terms of length (), area () and the modulus of elasticity () are also given in the figure. Let and be and , respectively, and be .Which one of the following sets gives the correct values of the force, stress and change in length of the horizontal member ?
Correct answer
(C) Compressive force = 100 kN; Stress = 1000 kN/m²; Shortening = 0.0417 m
Step-by-step solution
1.Force Analysis: By symmetry, the vertical reaction at support is . At joint , the tension in members and is . At joint , the horizontal equilibrium gives , where is the compression in . Vertical equilibrium at gives . Thus, . The force in is (Compression).2.Stress Analysis: Stress .3.Deformation: Since the member is in compression, it will undergo shortening. Comparing options, (C) is the only one with compression and shortening.45
Q45NAT2 marksHardA haunched (varying depth) reinforced concrete beam is simply supported at both ends, as shown in the figure. The beam is subjected to a uniformly distributed factored load of…Think it through. Then check your answer.Question
A haunched (varying depth) reinforced concrete beam is simply supported at both ends, as shown in the figure. The beam is subjected to a uniformly distributed factored load of intensity 10 kN/m. The design shear force (expressed in kN) at the section X-X of the beam is ______
Correct answer
64 to 66
Step-by-step solution
1.Calculate reactions at supports:For a simply supported beam with a uniformly distributed load (UDL) kN/m and span m:
kN.2.Calculate shear force () and bending moment () at section X-X ( m):kN.
kNm.3.Determine effective depth () and haunch slope () at section X-X:The depth varies linearly from 600 mm at the support to 400 mm at the center (10 m from support).
mm = 0.5 m.
.4.Calculate design shear force ():For a haunched beam where the depth decreases in the direction of increasing bending moment (from support towards center), the design shear force is given by:
kN.46
Q46NAT2 marksMediumA 450 mm long plain concrete prism is subjected to the concentrated vertical loads as shown in the figure. Cross section of the prism is given as 150 mm 150 mm.…Think it through. Then check your answer.Question
A 450 mm long plain concrete prism is subjected to the concentrated vertical loads as shown in the figure. Cross section of the prism is given as 150 mm 150 mm. Considering linear stress distribution across the cross-section, the modulus of rupture (expressed in MPa) is ________
Correct answer
2.9 to 3.1
Step-by-step solution
1.Identify the loading condition:The prism is subjected to symmetric four-point bending. The distance of each load from the nearest support is mm. The total span is mm. Since , this is a standard third-point loading test.2.Calculate the maximum bending moment ():The maximum bending moment occurs in the central zone between the two loads:
Nm.3.Calculate the modulus of rupture ():The modulus of rupture is the extreme fiber stress at failure, calculated using the flexure formula:
Given mm = 0.15 m and mm = 0.15 m:
Pa = 3.0 MPa.47
Q47MCQ2 marksMediumTwo bolted plates under tension with alternative arrangement of bolt holes are shown in figures 1 and 2. The hole diameter, pitch, and gauge length are , and ,…Think it through. Then check your answer.Question
Two bolted plates under tension with alternative arrangement of bolt holes are shown in figures 1 and 2. The hole diameter, pitch, and gauge length are , and , respectively.Which one of the following conditions must be ensured to have higher net tensile capacity of configuration shown in Figure 2 than that shown in Figure 1 ?
Correct answer
(C) p² 4gd
Step-by-step solution
The net area for Figure 1 (straight line failure) is given by:
The net area for Figure 2 (staggered failure path) is given by:
For the net tensile capacity of Figure 2 to be higher than Figure 1, its net area must be greater:
Thus, the correct condition is .48
Q48MCQ2 marksMediumA fixed-end beam is subjected to a concentrated load () as shown in the figure. The beam has two different segments having different plastic moment capacities () as…Think it through. Then check your answer.Question
A fixed-end beam is subjected to a concentrated load () as shown in the figure. The beam has two different segments having different plastic moment capacities () as shown.The minimum value of load () at which the beam would collapse (ultimate load) is
Correct answer
(A) 7.5 Mₚ / L
Step-by-step solution
We evaluate possible collapse mechanisms using the principle of virtual work ().Mechanism 1: Hinges at A (left support), C (under load), and B (right support).
Let be the displacement under the load .
Rotation at A:
Rotation at B:
Rotation at C:
Internal Work:
External Work:
Mechanism 2: Hinges at A (left support), D (junction of and ), and B (right support).
Let be the displacement at the junction (at distance from left).
Rotation at A:
Rotation at B:
Rotation at D:
Displacement under load (at ):
Internal Work:
External Work:
Comparing mechanisms, the collapse load is the minimum of the upper bounds: .49
Q49MCQ2 marksMediumThe activity-on-arrow network of activities for a construction project is shown in the figure. The durations (expressed in days) of the activities are mentioned below the arrows.…Think it through. Then check your answer.Question
The activity-on-arrow network of activities for a construction project is shown in the figure. The durations (expressed in days) of the activities are mentioned below the arrows.The critical duration for this construction project is
Correct answer
(C) 15 days
Step-by-step solution
To find the critical duration, we identify all possible paths from the start node (10) to the end node (90) and calculate their total durations:1.Path 10-20-30-70-80-90 (P-Q-T-W-X): days2.Path 10-20-30-50-70-80-90 (P-Q-dummy-U-W-X): days3.Path 10-20-40-50-70-80-90 (P-R-dummy-U-W-X): days4.Path 10-20-40-60-80-90 (P-R-dummy-V-X): days5.Path 10-20-60-80-90 (P-S-V-X): daysThe critical duration is the maximum of these path durations, which is 15 days.50
Q50NAT2 marksMediumThe seepage occurring through an earthen dam is represented by a flownet comprising of 10 equipotential drops and 20 flow channels. The coefficient of permeability of the soil is…Think it through. Then check your answer.Question
The seepage occurring through an earthen dam is represented by a flownet comprising of 10 equipotential drops and 20 flow channels. The coefficient of permeability of the soil is 3 mm/min and the head loss is 5 m. The rate of seepage (expressed in per m length of the dam) through the earthen dam is _________Correct answer
495 to 505
Step-by-step solution
The rate of seepage () through an earthen dam is given by the formula:Where:- is the coefficient of permeability
- is the total head loss
- is the number of flow channels
- is the number of equipotential drops
51
Q51NAT2 marksHardThe soil profile at a site consists of a 5 m thick sand layer underlain by a soil as shown in figure. The water table is found 1 m below the ground level. The entire soil…Think it through. Then check your answer.Question
The soil profile at a site consists of a 5 m thick sand layer underlain by a soil as shown in figure. The water table is found 1 m below the ground level. The entire soil mass is retained by a concrete retaining wall and is in the active state. The back of the wall is smooth and vertical. The total active earth pressure (expressed in ) at point A as per Rankine's theory is _________
Correct answer
69 to 70.5
Step-by-step solution
1.Calculate Active Earth Pressure Coefficients ():- For Sand layer:
- For soil layer:
- Layer 1 (0-1m):
- Layer 2 (1-5m):
- Layer 3 (5-8m):
- Total at A =
- Water table is at 1m depth. Depth of water above A = .
- Using Rankine's formula for soil:
52
Q52MCQ2 marksEasyOMC-SP and MDD-SP denote the optimum moisture content and maximum dry density obtained from standard Proctor compaction test, respectively. OMC-MP and MDD-MP denote the optimum…Think it through. Then check your answer.Question
OMC-SP and MDD-SP denote the optimum moisture content and maximum dry density obtained from standard Proctor compaction test, respectively. OMC-MP and MDD-MP denote the optimum moisture content and maximum dry density obtained from the modified Proctor compaction test, respectively. Which one of the following is correct?Correct answer
(B) OMC-SP OMC-MP and MDD-SP < MDD-MP
Step-by-step solution
The modified Proctor test uses significantly higher compaction energy compared to the standard Proctor test. Increasing compaction energy results in:1.A higher maximum dry density (MDD).2.A lower optimum moisture content (OMC).Therefore:
MDD-MP > MDD-SP (or MDD-SP < MDD-MP)
OMC-MP < OMC-SP (or OMC-SP > OMC-MP)This corresponds to option (B).53
Q53NAT2 marksMediumWater flows from P to Q through two soil samples, Soil 1 and Soil 2, having cross sectional area of as shown in the figure. Over a period of 15 minutes, 200 ml of…Think it through. Then check your answer.Question
Water flows from P to Q through two soil samples, Soil 1 and Soil 2, having cross sectional area of as shown in the figure. Over a period of 15 minutes, 200 ml of water was observed to pass through any cross section. The flow conditions can be assumed to be steady state. If the coefficient of permeability of Soil 1 is , the coefficient of permeability of Soil 2 (expressed in mm/s) would be ________Correct answer
0.04 to 0.05
Step-by-step solution
Given:
Total head loss
Total length
Hydraulic gradient
Equivalent permeability
For flow in series:54
Q54NAT2 marksHardA 4 m wide strip footing is founded at a depth of 1.5 m below the ground surface in a soil as shown in the figure. The water table is at a depth of 5.5 m below ground…Think it through. Then check your answer.Question
A 4 m wide strip footing is founded at a depth of 1.5 m below the ground surface in a soil as shown in the figure. The water table is at a depth of 5.5 m below ground surface. The soil properties are: , , , and . The values of bearing capacity factors for different are given below.Using Terzaghi's bearing capacity equation and a factor of safety , the net safe bearing capacity (expressed in ) for local shear failure of the soil is __________12.9 4.4 2.5 17.7 7.4 5.0 25.1 12.7 9.7 37.2 22.5 19.7 Correct answer
298 to 300
Step-by-step solution
For local shear failure:
From the table, for :
Water table is at 5.5 m depth. Depth of base of footing m. Width m.
Depth of water table below base m . Thus, no water table correction is needed ().
Ultimate bearing capacity
Net ultimate bearing capacity
Net safe bearing capacity55
Q55NAT2 marksMediumA square plate is suspended vertically from one of its edges using a hinge support as shown in figure. A water jet of 20 mm diameter having a velocity of 10 m/s strikes the plate…Think it through. Then check your answer.Question
A square plate is suspended vertically from one of its edges using a hinge support as shown in figure. A water jet of 20 mm diameter having a velocity of 10 m/s strikes the plate at its mid-point, at an angle of with the vertical. Consider as and neglect the self-weight of the plate. The force (expressed in N) required to keep the plate in its vertical position is _________Correct answer
7.4 to 8
Step-by-step solution
Diameter of jet
Area of jet
Velocity
Angle of jet with the plate
Force normal to the plate
Let the side of the square plate be . The jet strikes at the mid-point ( from hinge) and force is applied at the bottom edge ( from hinge).
Taking moments about the hinge:56
Q56NAT2 marksMediumThe ordinates of a one-hour unit hydrograph at sixty minute interval are 0, 3, 12, 8, 6, 3 and 0 . A two-hour storm of 4 cm excess rainfall occurred in the basin from 10…Think it through. Then check your answer.Question
The ordinates of a one-hour unit hydrograph at sixty minute interval are 0, 3, 12, 8, 6, 3 and 0 . A two-hour storm of 4 cm excess rainfall occurred in the basin from 10 AM. Considering constant base flow of 20 , the flow of the river (expressed in ) at 1 PM is _________Correct answer
59 to 61
Step-by-step solution
Given the 1-hour unit hydrograph (UH) ordinates at 60-minute intervals:
.A 2-hour storm starts at 10 AM. We need the flow at 1 PM, which is hours after the start of the storm.
The total excess rainfall is cm over 2 hours.First, we derive the 2-hour UH ordinates () from the 1-hour UH ordinates:
At hours:
per cm of excess rainfall.The surface runoff at hours for 4 cm of excess rainfall is:
.Total flow of the river = Surface runoff + Base flow
.57
Q57NAT2 marksMediumA 3 m wide rectangular channel carries a flow of 6 . The depth of flow at a section P is 0.5 m. A flat-topped hump is to be placed at the downstream of the section P.…Think it through. Then check your answer.Question
A 3 m wide rectangular channel carries a flow of 6 . The depth of flow at a section P is 0.5 m. A flat-topped hump is to be placed at the downstream of the section P. Assume negligible energy loss between section P and hump, and consider as 9.81 . The maximum height of the hump (expressed in m) which will not change the depth of flow at section P is _________Correct answer
0.19 to 0.21
Step-by-step solution
Given:
Width m
Discharge
Depth at section P m
Acceleration due to gravity Discharge per unit width .Specific energy at section P ():
m.Critical depth ():
m.Minimum specific energy at the hump ():
m.The maximum height of the hump () that will not change the upstream depth occurs when the flow over the hump is critical:
m.Rounding to two decimal places, the maximum height is approximately 0.20 m.58
Q58NAT2 marksHardA penstock of 1 m diameter and 5 km length is used to supply water from a reservoir to an impulse turbine. A nozzle of 15 cm diameter is fixed at the end of the penstock. The…Think it through. Then check your answer.Question
A penstock of 1 m diameter and 5 km length is used to supply water from a reservoir to an impulse turbine. A nozzle of 15 cm diameter is fixed at the end of the penstock. The elevation difference between the turbine and water level in the reservoir is 500 m. Consider the head loss due to friction as 5% of the velocity head available at the jet. Assume unit weight of water = 10 and acceleration due to gravity () = 10 . If the overall efficiency is 80%, power generated (expressed in kW and rounded to nearest integer) is _______________Correct answer
6560 to 6580
Step-by-step solution
Given:
Gross head m
Nozzle diameter m
Head loss , where is the jet velocity.
Unit weight of water
Gravity
Overall efficiency Total head equation:
Net head () is the velocity head at the jet:
m.Jet velocity ():
m/s.Discharge ():
.Power generated ():
kW.Rounding to the nearest integer, the power generated is 6570 kW.59
Q59MCQ2 marksMediumA tracer takes 100 days to travel from Well-1 to Well-2 which are 100 m apart. The elevation of water surface in Well-2 is 3 m below that in Well-1. Assuming porosity equal to…Think it through. Then check your answer.Question
A tracer takes 100 days to travel from Well-1 to Well-2 which are 100 m apart. The elevation of water surface in Well-2 is 3 m below that in Well-1. Assuming porosity equal to 15%, the coefficient of permeability (expressed in m/day) isCorrect answer
(D) 5.00
Step-by-step solution
Given:
Distance between wells, m
Time of travel, days
Difference in elevation (head loss), m
Porosity,1.Calculate seepage velocity ():m/day2.Calculate discharge velocity ():m/day3.Calculate hydraulic gradient ():4.Calculate coefficient of permeability () using Darcy's Law ():m/dayThus, the correct option is (D).60
Q60MCQ2 marksMediumA sample of water has been analyzed for common ions and results are presented in the form of a bar diagram as shown. [figure] The non-carbonate hardness (expressed in mg/L as…Think it through. Then check your answer.Question
A sample of water has been analyzed for common ions and results are presented in the form of a bar diagram as shown.The non-carbonate hardness (expressed in mg/L as ) of the sample is
Correct answer
(A) 40
Step-by-step solution
From the bar diagram:- Total Hardness (TH) is caused by multivalent cations ( and ).
mg/L as .- Total Alkalinity (TA) is represented by .
mg/L as .- Carbonate Hardness (CH) = mg/L.
- Non-Carbonate Hardness (NCH) = mg/L.
61
Q61NAT2 marksEasyA noise meter located at a distance of 30 m from a point source recorded 74 dB. The reading at a distance of 60 m from the point source would be _________Think it through. Then check your answer.Question
A noise meter located at a distance of 30 m from a point source recorded 74 dB. The reading at a distance of 60 m from the point source would be _________Correct answer
67 to 69
Step-by-step solution
The sound pressure level () at a distance from a point source follows the inverse square law for intensity. The relationship between sound levels at two different distances and is given by the formula:Given:- Sound level at distance m is dB.
- We need to find the sound level at distance m.
62
Q62NAT2 marksMediumFor a wastewater sample, the three-day biochemical oxygen demand at incubation temperature of () is estimated as…Think it through. Then check your answer.Question
For a wastewater sample, the three-day biochemical oxygen demand at incubation temperature of () is estimated as . Taking the value of the first order BOD reaction rate constant as , the five-day BOD (expressed in mg/L) of the wastewater at incubation temperature of () would be _________Correct answer
275 to 278
Step-by-step solution
The biochemical oxygen demand (BOD) at any time is given by the first-order reaction equation:where:- is the ultimate BOD (mg/L).
- is the first-order reaction rate constant (base ).
- is the time in days.
63
Q63MCQ2 marksMediumThe critical flow ratios for a three-phase signal are found to be , , and . The total time lost in the cycle is . Pedestrian crossings at this…Think it through. Then check your answer.Question
The critical flow ratios for a three-phase signal are found to be , , and . The total time lost in the cycle is . Pedestrian crossings at this junction are not significant. The respective Green times (expressed in seconds and rounded off to the nearest integer) for the three phases areCorrect answer
(A) 34, 28, and 28
Step-by-step solution
Using Webster's method for signal timing:1.Sum of critical flow ratios ():2.Total lost time ():3.Optimum cycle length ():4.Total green time ():5.Green time for each phase ():The respective green times are 34, 28, and 28 seconds.64
Q64NAT2 marksMediumA motorist traveling at on a highway needs to take the next exit, which has a speed limit of . The section of the roadway before the ramp entry…Think it through. Then check your answer.Question
A motorist traveling at on a highway needs to take the next exit, which has a speed limit of . The section of the roadway before the ramp entry has a downgrade of and coefficient of friction (f) is . In order to enter the ramp at the maximum allowable speed limit, the braking distance (expressed in m) from the exit ramp is _________Correct answer
92 to 93
Step-by-step solution
The braking distance () for a vehicle decelerating from speed to on a grade is given by:Where:
(downgrade of )Substituting the values:Alternatively, using the formula with speeds in km/h:The braking distance is approximately .65
Q65NAT2 marksMediumA tall tower was photographed from an elevation of 700 m above the datum. The radial distances of the top and bottom of the tower from the principal points are 112.50 mm and 82.40…Think it through. Then check your answer.Question
A tall tower was photographed from an elevation of 700 m above the datum. The radial distances of the top and bottom of the tower from the principal points are 112.50 mm and 82.40 mm, respectively. If the bottom of the tower is at an elevation 250 m above the datum, then the height (expressed in m) of the tower is _________Correct answer
120 to 121
Step-by-step solution
Relief displacement () is the displacement of the image of an object from its true position due to its height above or below the datum. It is calculated as the difference between the radial distance of the top () and the bottom () of the tower from the principal point:The formula for relief displacement () for an object whose base is at an elevation above the datum is given by:where:- is the height of the tower.
- is the flying height above the datum ().
- is the elevation of the base of the tower above the datum ().
- is the radial distance of the top of the tower from the principal point ().