The PYQ practice room
GATE CE 2021 Set 2
All 65 solved GATE CE 2021 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.
Go beyond PYQs with Success TrackerAI-powered personalised practice and doubt support. Unlimited practice on eligible plans; AI usage limits apply.Questions
65
Paper marks
100
Question formats
3
MCQ · NAT · MSQ
Revision mode
Self-paced
No timer. Focus on understanding.
Difficulty mixEasy 30Medium 29Hard 6
Explore the questions
General Aptitude (GA)
101
Q1MCQ1 markEasy(i) Arun and Aparna are here. (ii) Arun and Aparna is here. (iii) Arun's families is here. (iv) Arun's family is here. Which of the above sentences are grammatically CORRECT?Think it through. Then check your answer.Question
(i) Arun and Aparna are here.
(ii) Arun and Aparna is here.
(iii) Arun's families is here.
(iv) Arun's family is here.Which of the above sentences are grammatically CORRECT?Correct answer
(B) (i) and (iv)
Step-by-step solution
Sentence (i) is correct because a compound subject joined by 'and' takes a plural verb ('are'). Sentence (iv) is correct because 'family' is a collective noun that takes a singular verb ('is') when referring to the unit as a whole. Sentence (ii) is incorrect because it uses a singular verb for a plural subject. Sentence (iii) is incorrect because 'families' is plural and requires the plural verb 'are'.2
Q2MCQ1 markEasy[figure] The mirror image of the above text about the x-axis isThink it through. Then check your answer.Question
📷 Figure: The word PHYLAXIS shown in the first quadrant of a Cartesian coordinate systemThe mirror image of the above text about the x-axis isCorrect answer
(B) [figure]
Step-by-step solution
A mirror image about the x-axis results in a vertical flip of the original text. Flipping 'PHYLAXIS' vertically, the letters P, Y, L, A, and S change their orientation vertically, while H, X, and I remain visually similar if they are symmetric. Option (B) correctly represents this vertical transformation.3
Q3MCQ1 markEasyTwo identical cube shaped dice each with faces numbered 1 to 6 are rolled simultaneously. The probability that an even number is rolled out on each dice is:Think it through. Then check your answer.Question
Two identical cube shaped dice each with faces numbered 1 to 6 are rolled simultaneously. The probability that an even number is rolled out on each dice is:Correct answer
(D) (1)/(4)
Step-by-step solution
The probability of rolling an even number (2, 4, or 6) on a single six-sided die is . Since the two dice are rolled simultaneously and are independent, the probability that both dice show an even number is the product of their individual probabilities: .4
Q4MCQ1 markEasyand are two operators on numbers and such that , and Then,…Think it through. Then check your answer.Question
and are two operators on numbers and such that
, and
Then,Correct answer
(D) -40
Step-by-step solution
Given operators:1.2.We need to evaluate: Step 1: Evaluate inner parentheses:
Step 2: Substitute these values back into the expression:
Step 3: Evaluate the next level of operations:
Step 4: Final operation:
Therefore, the correct option is (D).5
Q5MCQ1 markEasyFour persons P, Q, R and S are to be seated in a row. R should not be seated at the second position from the left end of the row. The number of distinct seating arrangements…Think it through. Then check your answer.Question
Four persons P, Q, R and S are to be seated in a row. R should not be seated at the second position from the left end of the row. The number of distinct seating arrangements possible is:Correct answer
(C) 18
Step-by-step solution
Total number of persons = 4 (P, Q, R, S).
Total number of ways to arrange 4 persons in a row = .Now, let's find the number of arrangements where R is seated at the second position from the left end:- Position 1: Can be filled by any of the remaining 3 persons (P, Q, S).
- Position 2: Fixed for R (1 way).
- Position 3: Can be filled by any of the remaining 2 persons.
- Position 4: Can be filled by the last remaining person.
= .Therefore, the correct option is (C).6
Q6MCQ2 marksMediumOn a planar field, you travelled 3 units East from a point O. Next you travelled 4 units South to arrive at point P. Then you travelled from P in the North-East direction such…Think it through. Then check your answer.Question
On a planar field, you travelled 3 units East from a point O. Next you travelled 4 units South to arrive at point P. Then you travelled from P in the North-East direction such that you arrive at a point that is 6 units East of point O. Next, you travelled in the North-West direction, so that you arrive at point Q that is 8 units North of point P.The distance of point Q to point O, in the same units, should be ________Correct answer
(C) 5
Step-by-step solution
Let the starting point O be at the origin .1.Travel 3 units East: New position is .2.Travel 4 units South to arrive at P: .3.Travel from P in North-East direction (slope = 1) to a point R that is 6 units East of O ():Equation of path from P: .
At , . So, .4.Travel from R in North-West direction (slope = -1) to arrive at point Q that is 8 units North of P:Point P is . 8 units North of P is the line .
Equation of path from R: .
At , . So, .
Note: The phrasing 'point Q that is 8 units North of point P' can also be interpreted as Q having the same x-coordinate as P, i.e., . Let's check if (3, 4) is North-West of R(6, -1). From R to Q, (West) and (North). This is indeed a North-West direction. If , then distance .Distance .Therefore, the correct option is (C).7
Q7MCQ2 marksEasyThe author said, “Musicians rehearse before their concerts. Actors rehearse their roles before the opening of a new play. On the other hand, I find it strange that many public…Think it through. Then check your answer.Question
The author said, “Musicians rehearse before their concerts. Actors rehearse their roles before the opening of a new play. On the other hand, I find it strange that many public speakers think they can just walk on to the stage and start speaking. In my opinion, it is no less important for public speakers to rehearse their talks.”Based on the above passage, which one of the following is TRUE?Correct answer
(A) The author is of the opinion that rehearsing is important for musicians, actors and public speakers.
Step-by-step solution
The author states that it is "no less important" for public speakers to rehearse their talks compared to musicians and actors. This implies that rehearsal is equally important for all three groups mentioned. Therefore, option (A) is the correct inference.8
Q8MCQ2 marksEasy1.Some football players play cricket. 2. All cricket players play hockey. Among the options given below, the statement that logically follows from the two statements 1 and…Think it through. Then check your answer.Question
1.Some football players play cricket.2.All cricket players play hockey.Among the options given below, the statement that logically follows from the two statements 1 and 2 above, is:Correct answer
(B) Some football players play hockey.
Step-by-step solution
This is a syllogism problem.
Statement 1: Some Football players (F) are Cricket players (C).
Statement 2: All Cricket players (C) are Hockey players (H).
From Statement 1, there exists at least one player who is both F and C. Since all C are H (Statement 2), that player must also be H. Thus, there exists at least one player who is both F and H. This logically leads to the conclusion: "Some football players play hockey."9
Q9MCQ2 marksMediumIn the figure shown above, PQRS is a square. The shaded portion is formed by the intersection of sectors of circles with radius equal to the side of the square and centers at S…Think it through. Then check your answer.Question
In the figure shown above, PQRS is a square. The shaded portion is formed by the intersection of sectors of circles with radius equal to the side of the square and centers at S and Q.The probability that any point picked randomly within the square falls in the shaded area is __________
Correct answer
(C) (π)/(2) - 1
Step-by-step solution
Let the side of the square PQRS be .
Total area of the square = .
The shaded region is the intersection of two quarter-circles (quadrants) of radius , one centered at S and the other at Q.
Area of one quadrant = .
Area of the shaded region = (Area of quadrant centered at S) + (Area of quadrant centered at Q) - (Area of square PQRS)
Area of shaded region = .
The probability that a randomly picked point falls in the shaded area is the ratio of the shaded area to the total area:
.10
Q10MCQ2 marksMediumIn an equilateral triangle , side is divided into four equal parts, side is divided into six equal parts and side is divided into eight equal parts. The length…Think it through. Then check your answer.Question
In an equilateral triangle , side is divided into four equal parts, side is divided into six equal parts and side is divided into eight equal parts. The length of each subdivided part in cm is an integer.The minimum area of the triangle possible, in , isCorrect answer
(D) 144√(3)
Step-by-step solution
Let the side length of the equilateral triangle be .
According to the problem, the side is divided into 4 equal parts, into 6 equal parts, and into 8 equal parts.
The length of each subdivided part is an integer, which implies:
, , and , where are integers.This means must be a common multiple of 4, 6, and 8. To find the minimum area, we need the smallest possible value for , which is the Least Common Multiple (LCM) of 4, 6, and 8.
.Thus, the minimum side length is 24 cm.
The area of an equilateral triangle with side is given by:Substituting :Therefore, the minimum area of the triangle is , which corresponds to option (D).
Civil Engineering (CE, Set-2)
5511
Q11MCQ1 markEasyThe value of isThink it through. Then check your answer.Question
The value of isCorrect answer
(A) 0
Step-by-step solution
To find the limit , we observe that as , both the numerator and denominator approach infinity, resulting in an indeterminate form.Applying L'Hôpital's Rule:This is still an form. Applying L'Hôpital's Rule a second time:Therefore, the value of the limit is 0. The correct option is (A).12
Q12MCQ1 markMediumThe rank of the matrix isThink it through. Then check your answer.Question
The rank of the matrix isCorrect answer
(C) 3
Step-by-step solution
Let . We can find the rank by reducing the matrix to row-echelon form using elementary row operations:1.:2.Swap and :3.:4.Swap and :The number of non-zero rows in the row-echelon form is 3. Thus, the rank of the matrix is 3. The correct option is (C).13
Q13MCQ1 markEasyThe unit normal vector to the surface at the point isThink it through. Then check your answer.Question
The unit normal vector to the surface at the point isCorrect answer
(B) 1√(3), 1√(3), 1√(3)
Step-by-step solution
Let the surface be defined by . The normal vector to the surface at any point is given by the gradient :At the point :The magnitude of the normal vector is:The unit normal vector is:In component form, this is . The correct option is (B).14
Q14MCQ1 markEasyIf is a square matrix then orthogonality property mandatesThink it through. Then check your answer.Question
If is a square matrix then orthogonality property mandatesCorrect answer
(A) AA^T = I
Step-by-step solution
A square matrix is defined as orthogonal if its transpose is equal to its inverse, i.e., . Multiplying both sides by from the left gives , where is the identity matrix.15
Q15MCQ1 markEasyIn general, the CORRECT sequence of surveying operations isThink it through. Then check your answer.Question
In general, the CORRECT sequence of surveying operations isCorrect answer
(C) Reconnaissance arrow Field observations arrow Data analysis arrow Map making
Step-by-step solution
The standard sequence of operations in a surveying project is:1.Reconnaissance: A preliminary inspection of the area to be surveyed to understand the terrain and plan the survey.2.Field observations: The actual measurement of distances, angles, and elevations in the field.3.Data analysis: Processing and calculating the observed data in the office.4.Map making: Plotting the final results to create a map or plan.16
Q16MCQ1 markEasyStrain hardening of structural steel meansThink it through. Then check your answer.Question
Strain hardening of structural steel meansCorrect answer
(A) experiencing higher stress than yield stress with increased deformation
Step-by-step solution
Strain hardening (or work hardening) is the process by which a metal becomes stronger and harder through plastic deformation. In the stress-strain curve for structural steel, this occurs after the plastic plateau. In this region, the material requires an increase in stress to produce further strain, meaning it experiences stress levels higher than the initial yield stress as deformation increases.17
Q17MCQ1 markMediumA single story building model is shown in the figure. The rigid bar of mass '' is supported by three massless elastic columns whose ends are fixed against rotation. For each of…Think it through. Then check your answer.Question
A single story building model is shown in the figure. The rigid bar of mass '' is supported by three massless elastic columns whose ends are fixed against rotation. For each of the columns, the applied lateral force () and corresponding lateral deflection () are also shown in the figure. The lateral deflection () of the bar is given by , where is the effective length of the column, is the Young's modulus of elasticity and is the area moment of inertia of the column cross-section with respect to its neutral axis.📷 Figure: Building model and lateral deflection profileFor the lateral deflection profile of the columns as shown in the figure, the natural frequency of the system for horizontal oscillation isCorrect answer
(A) 6 √((EI)/(mL³)) rad/s
Step-by-step solution
The stiffness of a single column fixed at both ends is given by . Since there are three identical columns supporting the rigid bar in parallel, the total lateral stiffness of the system is . The natural frequency of the system is calculated as .18
Q18MCQ1 markEasySeasoning of timber for use in construction is done essentially toThink it through. Then check your answer.Question
Seasoning of timber for use in construction is done essentially toCorrect answer
(A) increase strength and durability
Step-by-step solution
Seasoning is the process of reducing the moisture content of timber under controlled conditions. This process increases the strength, durability, and dimensional stability of the timber, making it suitable for construction purposes.19
Q19MCQ1 markEasyIn case of bids in Two-Envelop System, the correct option isThink it through. Then check your answer.Question
In case of bids in Two-Envelop System, the correct option isCorrect answer
(A) Technical bid is opened first
Step-by-step solution
In a Two-Envelope bidding system, bidders submit their technical and financial proposals in separate sealed envelopes. The technical bids are opened and evaluated first to determine the eligibility and competence of the bidders. The financial bids are only opened for those bidders who successfully pass the technical evaluation stage.20
Q20MCQ1 markEasyThe most appropriate triaxial test to assess the long-term stability of an excavated clay slope isThink it through. Then check your answer.Question
The most appropriate triaxial test to assess the long-term stability of an excavated clay slope isCorrect answer
(A) consolidated drained test
Step-by-step solution
Long-term stability of an excavated clay slope is governed by effective stress parameters. In the long term, excess pore water pressures generated during excavation have reached equilibrium (dissipated). The Consolidated Drained (CD) test is the most appropriate as it simulates this condition by allowing full consolidation and drainage during the shearing process, providing the effective stress parameters ( and ) needed for long-term analysis.21
Q21MCQ1 markEasyAs per the Unified Soil Classification System (USCS), the type of soil represented by '**MH**' isThink it through. Then check your answer.Question
As per the Unified Soil Classification System (USCS), the type of soil represented by '**MH**' isCorrect answer
(A) Inorganic silts of high plasticity with liquid limit more than 50%
Step-by-step solution
In the Unified Soil Classification System (USCS), soil symbols consist of two letters:1.The first letter indicates the primary soil type: M stands for Silt (from the Swedish word Mo).2.The second letter indicates the plasticity or grading: H stands for High plasticity (Liquid Limit > 50%).Therefore, MH represents inorganic silts of high plasticity with a liquid limit greater than 50%.22
Q22MCQ1 markMediumThe ratio of the momentum correction factor to the energy correction factor for a laminar flow in a pipe isThink it through. Then check your answer.Question
The ratio of the momentum correction factor to the energy correction factor for a laminar flow in a pipe isCorrect answer
(B) (2)/(3)
Step-by-step solution
For fully developed laminar flow in a circular pipe:- The energy correction factor () is given by:
- The momentum correction factor () is given by:
23
Q23MCQ1 markEasyRelationship between traffic speed and density is described using a negatively sloped straight line. If is the free-flow speed then the speed at which the maximum flow…Think it through. Then check your answer.Question
Relationship between traffic speed and density is described using a negatively sloped straight line. If is the free-flow speed then the speed at which the maximum flow occurs isCorrect answer
(C) (v_f)/(2)
Step-by-step solution
The relationship between traffic speed () and density () is given as a negatively sloped straight line, which corresponds to the Greenshields model:where is the free-flow speed and is the jam density.
Traffic flow () is defined as:To find the maximum flow, we differentiate with respect to and set it to zero:Substituting back into the speed-density equation to find the speed at maximum flow ():Thus, the speed at which maximum flow occurs is .24
Q24MCQ1 markEasyDetermine the correctness or otherwise of the following Assertion [a] and the Reason [r]. Assertion [a]: One of the best ways to reduce the amount of solid wastes is to reduce…Think it through. Then check your answer.Question
Determine the correctness or otherwise of the following Assertion [a] and the Reason [r].Assertion [a]: One of the best ways to reduce the amount of solid wastes is to reduce the consumption of raw materials.Reason [r]: Solid wastes are seldom generated when raw materials are converted to goods for consumption.Correct answer
(D) [a] is true but [r] is false
Step-by-step solution
Assertion [a] is true. Source reduction, which includes reducing the consumption of raw materials, is considered the most effective strategy in the waste management hierarchy to minimize solid waste generation.Reason [r] is false. The conversion of raw materials into finished goods (manufacturing and processing) is a major source of industrial solid waste. It is incorrect to say that waste is 'seldom' generated during this process.Therefore, [a] is true but [r] is false.25
Q25MCQ1 markEasyThe hardness of a water sample is measured directly by titration with solution of ethylenediamine tetraacetic acid (EDTA) using eriochrome black T (EBT) as an…Think it through. Then check your answer.Question
The hardness of a water sample is measured directly by titration with solution of ethylenediamine tetraacetic acid (EDTA) using eriochrome black T (EBT) as an indicator. The EBT reacts and forms complexes with divalent metallic cations present in the water. During titration, the EDTA replaces the EBT in the complex. When the replacement of EBT is complete at the end point of the titration, the colour of the solution changes fromCorrect answer
(D) wine red to blue
Step-by-step solution
In the EDTA titration method for determining water hardness:1.The indicator Eriochrome Black T (EBT) is added to the water sample buffered at pH 10.2.EBT forms a complex with divalent metal ions (like and ), which has a characteristic wine red color.3.As EDTA is added during titration, it displaces the EBT from the metal-indicator complex because EDTA forms a more stable complex with the metal ions.4.At the end point, when all metal ions are sequestered by EDTA, the free EBT indicator is released into the solution. The free form of EBT at pH 10 is blue.Thus, the color change at the end point is from wine red to blue.26
Q26MCQ1 markEasyThe softening point of bitumen has the same unit as that ofThink it through. Then check your answer.Question
The softening point of bitumen has the same unit as that ofCorrect answer
(B) temperature
Step-by-step solution
The softening point of bitumen is defined as the temperature at which the substance attains a particular degree of softening under specified conditions of test. It is measured in degrees Celsius (), which is the unit of temperature.27
Q27MSQ1 markMediumWhich of the following statement(s) is/are correct?Think it through. Then check your answer.Question
Which of the following statement(s) is/are correct?Correct answer
(A) Increased levels of carbon monoxide in the indoor environment result in the formation of carboxyhemoglobin and the long term exposure becomes a cause of cardiovascular diseases.; (B) Volatile organic compounds act as one of the precursors to the formation of photochemical smog in the presence of sunlight.; (C) Long term exposure to the increased level of photochemical smog becomes a cause of chest constriction and irritation of the mucous membrane.
Step-by-step solution
Statement (A) is correct: Carbon monoxide (CO) binds with hemoglobin to form carboxyhemoglobin, which reduces the oxygen-carrying capacity of blood. Chronic exposure is linked to cardiovascular issues.
Statement (B) is correct: Photochemical smog is formed by the reaction of volatile organic compounds (VOCs) and nitrogen oxides () in the presence of sunlight.
Statement (C) is correct: Photochemical smog contains ozone and other oxidants that are respiratory irritants, causing chest constriction and irritation of mucous membranes.
Statement (D) is incorrect: Photochemical smog formation requires sunlight and , which are typically not present in sufficient concentrations indoors for VOCs to form smog. Furthermore, smog is primarily a respiratory irritant rather than a direct cause of cardiovascular disease compared to CO.28
Q28NAT1 markEasyThe value (round off to one decimal place) of is ________Think it through. Then check your answer.Question
The value (round off to one decimal place) of is ________Correct answer
0 to 0
Step-by-step solution
Let .
To check if the function is even or odd, we find :
.
Since , the function is an odd function.
The integral of an odd function over a symmetric interval is always zero:Rounding off to one decimal place, the value is 0.0.29
Q29NAT1 markMediumA solid circular torsional member OPQ is subjected to torsional moments as shown in the figure (not to scale). The yield shear strength of the constituent material is 160 MPa.…Think it through. Then check your answer.Question
A solid circular torsional member OPQ is subjected to torsional moments as shown in the figure (not to scale). The yield shear strength of the constituent material is 160 MPa.The absolute maximum shear stress in the member (in MPa, round off to one decimal place) is ___________
Correct answer
14 to 16
Step-by-step solution
The torsional member consists of two segments: OP and PQ.1.Torque in each segment:- Segment PQ:
- Segment OP:
3.Shear stress in segment PQ:30
Q30NAT1 markEasyA propped cantilever beam XY, with an internal hinge at the middle, is carrying a uniformly distributed load of 10 kN/m, as shown in the figure. [figure] The vertical reaction at…Think it through. Then check your answer.Question
A propped cantilever beam XY, with an internal hinge at the middle, is carrying a uniformly distributed load of 10 kN/m, as shown in the figure.The vertical reaction at support X (in kN, in integer) is ___________
Correct answer
30 to 30
Step-by-step solution
The beam has an internal hinge at O. We can split the beam into two parts: OY and XO.1.Analyze part OY:- It is a simply supported beam with a hinge at O and a roller at Y.
- Length , UDL .
- Taking moments about O: .
- Vertical equilibrium: (upwards on OY).
- It is a cantilever fixed at X with a point load acting downwards at O and a UDL.
- (downwards on XO).
- Vertical equilibrium: .
31
Q31NAT1 markEasyThe internal () and external () diameters of a Shelby sampler are 48 mm and 52 mm, respectively. The area ratio () of the sampler (in %, *round off to two decimal…Think it through. Then check your answer.Question
The internal () and external () diameters of a Shelby sampler are 48 mm and 52 mm, respectively. The area ratio () of the sampler (in %, round off to two decimal places) is ___________Correct answer
17.25 to 17.45
Step-by-step solution
The area ratio () of a soil sampler is given by the formula:Given:- Internal diameter,
- External diameter,
32
Q32NAT1 markEasyA -hour unit hydrograph (of cm excess rainfall) of a catchment is of a triangular shape with a base width of hour and a peak discharge of m/s. The area of…Think it through. Then check your answer.Question
A -hour unit hydrograph (of cm excess rainfall) of a catchment is of a triangular shape with a base width of hour and a peak discharge of m/s. The area of the catchment (in km, round off to the nearest integer) is ___________Correct answer
595 to 598
Step-by-step solution
Given:
Base width of triangular unit hydrograph, hours
Peak discharge, m/s
Excess rainfall, cm mThe volume of runoff is equal to the area under the unit hydrograph:
Also,
Converting to km:
Rounding off to the nearest integer, the area is km.33
Q33NAT1 markEasyA lake has a maximum depth of m. If the mean atmospheric pressure in the lake region is kPa and the unit weight of the lake water is N/m, the absolute…Think it through. Then check your answer.Question
A lake has a maximum depth of m. If the mean atmospheric pressure in the lake region is kPa and the unit weight of the lake water is N/m, the absolute pressure (in kPa, round off to two decimal places) at the maximum depth of the lake is ___________Correct answer
677.5 to 679.5
Step-by-step solution
Given:
Maximum depth, m
Atmospheric pressure, kPa
Unit weight of water, N/mAbsolute pressure at depth is given by:
Calculating gauge pressure in kPa:
Absolute pressure:
Rounding off to two decimal places, the absolute pressure is kPa.34
Q34NAT1 markEasyIn a three-phase signal system design for a four-leg intersection, the critical flow ratios for each phase are , , and . The total loss time in each of the…Think it through. Then check your answer.Question
In a three-phase signal system design for a four-leg intersection, the critical flow ratios for each phase are , , and . The total loss time in each of the phases is s. As per Webster’s formula, the optimal cycle length (in s, round off to the nearest integer) is ___________Correct answer
48 to 52
Step-by-step solution
Given:
Number of phases,
Critical flow ratios: , ,
Sum of critical flow ratios,
Loss time per phase, s
Total loss time, sAccording to Webster's formula for optimal cycle length ():
sThe optimal cycle length is s.35
Q35NAT1 markEasyA horizontal angle is measured by four different surveyors multiple times and the values reported are given below. | Surveyor | Angle | Number of observations |…Think it through. Then check your answer.Question
A horizontal angle is measured by four different surveyors multiple times and the values reported are given below.The most probable value of the angle (in degree, round off to two decimal places) is ________.Surveyor Angle Number of observations 1 4 2 3 3 8 4 4 Correct answer
36 to 36
Step-by-step solution
The most probable value of an observed quantity is its weighted mean.
Given observations:
Weighted Mean36
Q36MCQ2 marksEasyIf is a constant, the general solution of will be in the form ofThink it through. Then check your answer.Question
If is a constant, the general solution of will be in the form ofCorrect answer
(A) y = x ln(kx)
Step-by-step solution
The given equation is a linear differential equation of the form , where and .
Integrating Factor () .
The general solution is given by:
Let , where is a constant.37
Q37MCQ2 marksMediumThe smallest eigenvalue and the corresponding eigenvector of the matrix , respectively, areThink it through. Then check your answer.Question
The smallest eigenvalue and the corresponding eigenvector of the matrix , respectively, areCorrect answer
(A) 1.55 and Bmatrix 2.00 \ 0.45 Bmatrix
Step-by-step solution
Let . The characteristic equation is .
The smallest eigenvalue is .
To find the eigenvector for :
From the first row: .
Checking option A: . This matches.38
Q38MCQ2 marksMediumA prismatic steel beam is shown in the figure. [figure] The plastic moment, calculated for the collapse mechanism using static method and kinematic method isThink it through. Then check your answer.Question
A prismatic steel beam is shown in the figure.The plastic moment, calculated for the collapse mechanism using static method and kinematic method is
Correct answer
(C) M_(p,static) = (2PL)/(9) = M_(p,kinematic)
Step-by-step solution
According to the uniqueness theorem of plastic analysis, for the true collapse mechanism, the plastic moment calculated by the static method (lower bound theorem) and the kinematic method (upper bound theorem) must be equal ().For the given beam with a hinge at A and a roller at C, a plastic hinge forms under the load at B at collapse. Using the principle of virtual work:
External Work =
Internal Work =
From geometry, .
Internal Work =
Equating work: .
Thus, .39
Q39MCQ2 marksHardA frame EFG is shown in the figure. All members are prismatic and have equal flexural rigidity. The member FG carries a uniformly distributed load per unit length. Axial…Think it through. Then check your answer.Question
A frame EFG is shown in the figure. All members are prismatic and have equal flexural rigidity. The member FG carries a uniformly distributed load per unit length. Axial deformation of any member is neglected.Considering the joint F being rigid, the support reaction at G is
Correct answer
(C) 0.482 wL
Step-by-step solution
Using the slope-deflection method and considering sway (since G is a roller and the frame is unsymmetrical):1.Stiffnesses: , (since G is a roller).2.Sway condition: Horizontal reaction at E must be zero () because and there are no horizontal loads. This implies .3.Slope-deflection equations with sway :
.4.Joint equilibrium at F:5.Moment at F in FG:6.Vertical reaction at G: for member FG:.40
Q40MCQ2 marksMediumA clay layer of thickness has a preconsolidation pressure and an initial void ratio . The initial effective overburden stress at the mid-height of the layer is…Think it through. Then check your answer.Question
A clay layer of thickness has a preconsolidation pressure and an initial void ratio . The initial effective overburden stress at the mid-height of the layer is . At the same location, the increment in effective stress due to applied external load is . The compression and swelling indices of the clay are and , respectively. If , then the correct expression to estimate the consolidation settlement () of the clay layer isCorrect answer
(B) s_c = (H)/(1+e₀) [ Cₛ log (p_c)/(p₀) + C_c log (p₀ + Δ p)/(p_c) ]
Step-by-step solution
When the initial effective stress is less than the preconsolidation pressure , the soil is overconsolidated. If the final stress exceeds , the settlement calculation must be split into two parts:1.Recompression range (from to ): The settlement is calculated using the swelling index .2.Virgin compression range (from to ): The settlement is calculated using the compression index .
Total settlement . This matches option B.41
Q41MCQ2 marksMediumA rectangular open channel of width is carrying a discharge of . Consider the acceleration due to gravity as and assume…Think it through. Then check your answer.Question
A rectangular open channel of width is carrying a discharge of . Consider the acceleration due to gravity as and assume water as incompressible and inviscid. The depth of flow in the channel at which the specific energy of the flowing water is minimum for the given discharge will then beCorrect answer
(B) 1.04 m
Step-by-step solution
For minimum specific energy in an open channel, the flow must be at critical depth ().
The critical depth for a rectangular channel is given by the formula:
where is the discharge per unit width (), is the total discharge, is the channel width, and is the acceleration due to gravity.Given:
First, calculate the discharge per unit width :
Now, calculate the critical depth :
Rounding to two decimal places, .Therefore, the depth of flow at which the specific energy is minimum is .The final answer is42
Q42MCQ2 marksMediumRead the statements given below. (i) Value of the wind profile exponent for the 'very unstable' atmosphere is smaller than the wind profile exponent for the 'neutral' atmosphere.…Think it through. Then check your answer.Question
Read the statements given below.
(i) Value of the wind profile exponent for the 'very unstable' atmosphere is smaller than the wind profile exponent for the 'neutral' atmosphere.
(ii) Downwind concentration of air pollutants due to an elevated point source will be inversely proportional to the wind speed.
(iii) Value of the wind profile exponent for the 'neutral' atmosphere is smaller than the wind profile exponent for the 'very unstable' atmosphere.
(iv) Downwind concentration of air pollutants due to an elevated point source will be directly proportional to the wind speed.
Select the correct option.Correct answer
(D) (iii) is False and (iv) is False
Step-by-step solution
Let's analyze each statement:(i) Value of the wind profile exponent for the 'very unstable' atmosphere is smaller than the wind profile exponent for the 'neutral' atmosphere.- The wind profile exponent (p) in the power law is related to atmospheric stability. For unstable conditions, there is more vertical mixing, leading to a more uniform wind profile with height, hence a smaller exponent. For neutral conditions, the exponent is higher than for unstable conditions. Therefore, this statement is True.
- According to the Gaussian plume model, the concentration of pollutants () is inversely proportional to the wind speed (). A higher wind speed means the plume is stretched more horizontally, leading to lower concentrations. So, . Therefore, this statement is True.
- This is the inverse of statement (i). As explained above, the wind profile exponent for neutral atmosphere is larger than for very unstable atmosphere. Therefore, this statement is False.
- This is the inverse of statement (ii). As explained above, the concentration is inversely proportional to the wind speed. Therefore, this statement is False.
- (A) (i) is False and (iii) is True: Incorrect, (i) is True and (iii) is False.
- (B) (i) is True and (iv) is True: Incorrect, (iv) is False.
- (C) (ii) is False and (iii) is False: Incorrect, (ii) is True.
- (D) (iii) is False and (iv) is False: Correct, both (iii) and (iv) are False.
43
Q43MCQ2 marksHardA water filtration unit is made of uniform-size sand particles of diameter with a shape factor of and specific gravity of . The depth of the filter…Think it through. Then check your answer.Question
A water filtration unit is made of uniform-size sand particles of diameter with a shape factor of and specific gravity of . The depth of the filter bed is and the porosity is . The filter bed is to be expanded to a porosity of by hydraulic backwash. If the terminal settling velocity of sand particles during backwash is , the required backwash velocity isCorrect answer
(B) 6.35 × 10⁻³ m/s
Step-by-step solution
To determine the required backwash velocity for filter bed expansion, we can use the modified Kozeny-Carman equation or the relationship for hindered settling. A common approach for bed expansion is to use the following relationship derived from the Richardson-Zaki equation or similar empirical models:where:
= backwash velocity (or superficial velocity during fluidization)
= terminal settling velocity of the particles
= expanded bed porosity
= an exponent, often taken as for laminar flow or can be calculated based on particle Reynolds number.However, a simpler and more direct approach for calculating the backwash velocity () when the bed is fluidized to a certain porosity () is to use the concept that at incipient fluidization, the drag force equals the submerged weight of the particles. For an expanded bed, the backwash velocity is essentially the superficial velocity that maintains the expanded porosity.The relationship between the backwash velocity () and the terminal settling velocity () for an expanded bed with porosity is given by:
For granular media like sand, the exponent is often approximated as for a wide range of Reynolds numbers relevant to filtration. However, a more accurate value for can be determined from the Richardson-Zaki equation, which relates the hindered settling velocity to the terminal settling velocity and porosity. For typical sand particles in water, is often in the range of to .Let's use the common approximation for this type of problem, or check if a simpler relationship is expected.Another common formula for backwash velocity is based on the concept that the head loss through the expanded bed equals the submerged weight of the bed per unit area. At fluidization, the head loss is constant and equal to the submerged weight of the particles. The backwash velocity is then related to the terminal settling velocity and the expanded porosity.The relationship for backwash velocity () for an expanded bed is often given as:
where is an exponent that depends on the flow regime. For typical filter backwash, is often taken as to .Given:
Terminal settling velocity,
Expanded bed porosity, Using the formula :
Rounding to three significant figures, .Let's check the options:
(A)
(B)
(C)
(D) The calculated value matches option (B).Note: The initial porosity, particle diameter, shape factor, specific gravity, and initial bed depth are not directly used in this calculation if the terminal settling velocity and expanded porosity are given. These parameters would be used to calculate if it were not provided, or to determine the exponent more precisely if a more complex model (like Richardson-Zaki) was required and the flow regime (Reynolds number) was to be calculated.The final answer is \boxed{\text{6.35 \times 10^{-3} m/s}}44
Q44MCQ2 marksMediumFor a given traverse, latitudes and departures are calculated and it is found that sum of latitudes is equal to m and the sum of departures is equal to m. The length…Think it through. Then check your answer.Question
For a given traverse, latitudes and departures are calculated and it is found that sum of latitudes is equal to m and the sum of departures is equal to m. The length and bearing of the closing error, respectively, areCorrect answer
(A) 3.50 m and 53⁷' 48'' NW
Step-by-step solution
1.The length of the closing error () is given by the square root of the sum of the squares of the sum of latitudes () and the sum of departures ():2.The reduced bearing angle () is calculated as:3.Converting to degrees, minutes, and seconds:4.Since the sum of latitudes is positive (North) and the sum of departures is negative (West), the bearing lies in the North-West (NW) quadrant.Thus, the length is m and the bearing is NW.45
Q45MCQ2 marksEasyFrom laboratory investigations, the liquid limit, plastic limit, natural moisture content and flow index of a soil specimen are obtained as , , and ,…Think it through. Then check your answer.Question
From laboratory investigations, the liquid limit, plastic limit, natural moisture content and flow index of a soil specimen are obtained as , , and , respectively. The corresponding toughness index and liquidity index of the soil specimen, respectively, areCorrect answer
(C) 1.22 and 0.15
Step-by-step solution
Given data:
Liquid Limit () =
Plastic Limit () =
Natural moisture content () =
Flow Index () =1.Calculate Plasticity Index ():2.Calculate Toughness Index ():3.Calculate Liquidity Index ():Therefore, the toughness index is and the liquidity index is .46
Q46NAT2 marksMediumA function is defined in Cartesian coordinate system as . The value of the directional derivative of the function (in integer) at the point along the…Think it through. Then check your answer.Question
A function is defined in Cartesian coordinate system as . The value of the directional derivative of the function (in integer) at the point along the direction of the straight line segment from point to point is ____________.Correct answer
1 to 1
Step-by-step solution
1.Find the gradient of :2.Evaluate the gradient at the point :3.Find the direction vector from to :4.Find the unit vector in the direction of :5.Calculate the directional derivative :The directional derivative is 1.47
Q47NAT2 marksMediumAn elevated cylindrical water storage tank is shown in the figure. The tank has inner diameter of . It is supported on a solid steel circular column of diameter…Think it through. Then check your answer.Question
An elevated cylindrical water storage tank is shown in the figure. The tank has inner diameter of . It is supported on a solid steel circular column of diameter and total height () of . Take, water density = and acceleration due to gravity = .If elastic modulus () of steel is , ignoring self-weight of the tank, for the supporting steel column to remain unbuckled, the maximum depth () of the water permissible (in m, round off to one decimal place) is _______________.
Correct answer
2.5 to 2.9
Step-by-step solution
1.The supporting column is modeled as a cantilever (fixed at the base and free at the top with the tank load). The critical buckling load is given by Euler's formula:where for a cantilever.2.Calculate the moment of inertia for the circular column:3.Calculate :4.The load on the column is the weight of the water :5.Equating to for the buckling limit:Rounding to one decimal place, .48
Q48NAT2 marksMediumA prismatic fixed-fixed beam, modelled with a total lumped-mass of as a single degree of freedom (SDOF) system is shown in the figure. [figure] If the flexural…Think it through. Then check your answer.Question
A prismatic fixed-fixed beam, modelled with a total lumped-mass of as a single degree of freedom (SDOF) system is shown in the figure.If the flexural stiffness of the beam is , its natural frequency of vibration (in Hz, in integer) in the flexural mode will be _______________.
Correct answer
10 to 10
Step-by-step solution
The natural frequency of a single degree of freedom (SDOF) system is given by:Given:
Flexural stiffness
Lumped mass
Substituting the values:The natural frequency is .49
Q49NAT2 marksHardA perfectly flexible and inextensible cable is shown in the figure (not to scale). The external loads at and are acting vertically. [figure] The magnitude of tension in…Think it through. Then check your answer.Question
A perfectly flexible and inextensible cable is shown in the figure (not to scale). The external loads at and are acting vertically.The magnitude of tension in the cable segment (in kN, round off to two decimal places) is _______________.
Correct answer
8.1 to 8.4
Step-by-step solution
1.Let be the constant horizontal component of tension. Let and be vertical reactions at supports and .2.Taking moments about ( at , at , at , at ):3.Vertical equilibrium:4.Moment at from left:5.Substitute into vertical equilibrium:6.Substitute into moment equation:7.Vertical shear in segment :8.Tension in :Rounding to two decimal places, .50
Q50NAT2 marksEasyA fire hose nozzle directs a steady stream of water of velocity at an angle of above the horizontal. The stream rises initially but then eventually…Think it through. Then check your answer.Question
A fire hose nozzle directs a steady stream of water of velocity at an angle of above the horizontal. The stream rises initially but then eventually falls to the ground. Assume water as incompressible and inviscid. Consider the density of air and the air friction as negligible, and assume the acceleration due to gravity as . The maximum height (in m, round off to two decimal places) reached by the stream above the hose nozzle will then be ________Correct answer
63.5 to 63.9
Step-by-step solution
The maximum height reached by a projectile is given by the formula:Given:- Initial velocity
- Angle of projection
- Acceleration due to gravity
51
Q51NAT2 marksMediumA rectangular cross-section of a reinforced concrete beam is shown in the figure. The diameter of each reinforcing bar is . The values of modulus of elasticity of…Think it through. Then check your answer.Question
A rectangular cross-section of a reinforced concrete beam is shown in the figure. The diameter of each reinforcing bar is . The values of modulus of elasticity of concrete and steel are and , respectively.The distance of the centroidal axis from the centerline of the reinforcement () for the uncracked section (in mm, round off to one decimal place) is ________
Correct answer
129 to 130
Step-by-step solution
1.Modular Ratio ():2.Section Properties:- Width
- Total depth
- Effective depth (distance from top to reinforcement centerline)
- Area of steel
For an uncracked section, the equivalent concrete area is:
4.Centroidal Axis from Top ():Taking moments about the top edge:
5.Distance :is the distance from the centroidal axis to the reinforcement centerline:
Rounding off to one decimal place, .52
Q52NAT2 marksMediumThe activity details for a small project are given in the Table. | Activity | Duration (days) | Depends on | | :--- | :--- | :--- | | A | 6 | - | | B | 10 | A | | C | 14 | A | | D…Think it through. Then check your answer.Question
The activity details for a small project are given in the Table.The total time (in days, in integer) for project completion is ________Activity Duration (days) Depends on A 6 - B 10 A C 14 A D 8 B E 12 C F 8 C G 16 D, E H 8 F, G K 2 B L 5 G, K Correct answer
56 to 56
Step-by-step solution
To find the project completion time, we perform a forward pass to find the Earliest Finish (EF) time for each activity:- EF(A) = 6
- EF(B) = EF(A) + 10 = 16
- EF(C) = EF(A) + 14 = 20
- EF(D) = EF(B) + 8 = 24
- EF(E) = EF(C) + 12 = 32
- EF(F) = EF(C) + 8 = 28
- EF(G) = max(EF(D), EF(E)) + 16 = max(24, 32) + 16 = 48
- EF(H) = max(EF(F), EF(G)) + 8 = max(28, 48) + 8 = 56
- EF(K) = EF(B) + 2 = 18
- EF(L) = max(EF(G), EF(K)) + 5 = max(48, 18) + 5 = 53
Project Duration = max(EF(H), EF(L)) = max(56, 53) = 56 days.53
Q53NAT2 marksMediumAn equipment has been purchased at an initial cost of ₹160000 and has an estimated salvage value of ₹10000. The equipment has an estimated life of 5 years. The difference between…Think it through. Then check your answer.Question
An equipment has been purchased at an initial cost of ₹160000 and has an estimated salvage value of ₹10000. The equipment has an estimated life of 5 years. The difference between the book values (in ₹, in integer) obtained at the end of year using straight line method and sum of years digit method of depreciation is ___________Correct answer
20000 to 20000
Step-by-step solution
1.Straight Line Method (SLM):- Annual Depreciation =
- Accumulated Depreciation at end of 4 years =
- Book Value at end of 4 years () =
- Sum of years =
- Depreciation in year 1 =
- Depreciation in year 2 =
- Depreciation in year 3 =
- Depreciation in year 4 =
- Accumulated Depreciation at end of 4 years =
- Book Value at end of 4 years () =
- Difference =
54
Q54NAT2 marksHardA rectangular footing of size is embedded in a clay layer and a vertical load is placed with an eccentricity of as shown in the…Think it through. Then check your answer.Question
A rectangular footing of size is embedded in a clay layer and a vertical load is placed with an eccentricity of as shown in the figure (not to scale). Take Bearing capacity factors: , , and ; Shape factors: , and ; Depth factors: , and ; and Inclination factors: and and .Using Meyerhoff’s method, the load (in kN, round off to two decimal places) that can be applied on the footing with a factor of safety of 2.5 is ___________
Correct answer
439 to 442
Step-by-step solution
1.Effective Dimensions:- Effective Area
- For clay ():
- Overburden pressure
55
Q55NAT2 marksMediumThe soil profile at a road construction site is as shown in figure (not to scale). A large embankment is to be constructed at the site. The ground water table (GWT) is located at…Think it through. Then check your answer.Question
The soil profile at a road construction site is as shown in figure (not to scale). A large embankment is to be constructed at the site. The ground water table (GWT) is located at the surface of the clay layer, and the capillary rise in the sandy soil is negligible. The effective stress at the middle of the clay layer after the application of the embankment loading is . Take unit weight of water, .The primary consolidation settlement (in m, round off to two decimal places) of the clay layer resulting from this loading will be ___________
Correct answer
0.32 to 0.34
Step-by-step solution
1.Initial Void Ratio ():- Assuming saturation below GWT:
- Mid-depth is at from surface.
- Given
56
Q56NAT2 marksMediumNumerically integrate, from lower limit to upper limit . Use Trapezoidal rule with five equal subdivisions. The value (in units, round off to…Think it through. Then check your answer.Question
Numerically integrate, from lower limit to upper limit . Use Trapezoidal rule with five equal subdivisions. The value (in units, round off to two decimal places) obtained is ________.Correct answer
0.38 to 0.42
Step-by-step solution
Given:
Lower limit , Upper limit
Number of subdivisions
Step size The values of and are:
Using the Trapezoidal rule:
The value obtained is 0.40.57
Q57NAT2 marksMediumThe void ratio of a clay soil sample M decreased from 0.575 to 0.510 when the applied pressure is increased from 120 kPa to 180 kPa. For the same increment in pressure, the void…Think it through. Then check your answer.Question
The void ratio of a clay soil sample M decreased from 0.575 to 0.510 when the applied pressure is increased from 120 kPa to 180 kPa. For the same increment in pressure, the void ratio of another clay soil sample N decreases from 0.600 to 0.550. If the ratio of hydraulic conductivity of sample M to sample N is 0.125, then the ratio of coefficient of consolidation of sample M to sample N (round off to three decimal places) is ________.Correct answer
0.09 to 0.105
Step-by-step solution
The coefficient of consolidation is given by , where .For sample M:
kPa
For sample N:
kPa
Given .The ratio of coefficient of consolidation is:
Rounding off to three decimal places, the ratio is 0.095.58
Q58NAT2 marksMediumThe hyetograph in the figure corresponds to a rainfall event of 3 cm. [figure] If the rainfall event has produced a direct runoff of 1.6 cm, the -index of the event (in…Think it through. Then check your answer.Question
The hyetograph in the figure corresponds to a rainfall event of 3 cm.If the rainfall event has produced a direct runoff of 1.6 cm, the -index of the event (in mm/hour, round off to one decimal place) would be ________.
Correct answer
4.2 to 4.2
Step-by-step solution
Total rainfall cm = 30 mm.
Direct runoff cm = 16 mm.
Time interval hour.From the hyetograph, the rainfall intensities () in mm/hr for each 0.5 hr interval are:
Total rainfall check: mm. Correct.The -index is defined such that for all .Assume is between 4 and 4.5 mm/hr. Then are greater than .
mm/hr.Since is between 4 and 4.5, our assumption is correct.
-index = 4.2 mm/hour.59
Q59NAT2 marksMediumA venturimeter as shown in the figure (not to scale) is connected to measure the flow of water in a vertical pipe of 20 cm diameter. [figure] Assume . When…Think it through. Then check your answer.Question
A venturimeter as shown in the figure (not to scale) is connected to measure the flow of water in a vertical pipe of 20 cm diameter.
Assume . When the deflection in the mercury manometer is 15 cm, the flow rate (in lps, round off to two decimal places) considering no loss in the venturimeter is ___________Correct answer
49 to 50
Step-by-step solution
Given:
Diameter of pipe,
Area of pipe,
Diameter of throat,
Area of throat,
Manometer deflection,
Specific gravity of mercury,
Specific gravity of water,
Differential head,
Flow rate,60
Q60NAT2 marksMediumA reservoir with a live storage of 300 million cubic metre irrigates 40000 hectares (1 hectare = m) of a crop with two fillings of the reservoir. If the base period of…Think it through. Then check your answer.Question
A reservoir with a live storage of 300 million cubic metre irrigates 40000 hectares (1 hectare = m) of a crop with two fillings of the reservoir. If the base period of the crop is 120 days, the duty for this crop (in hectares per cumec, round off to integer) will then be ________________.Correct answer
689 to 693
Step-by-step solution
1.Calculate the total volume of water available:The reservoir has a live storage of 300 million m and is filled twice.
Total volume = m.2.Calculate the Delta ():Delta is the total depth of water required by the crop over the base period.
Area irrigated = 40,000 hectares = m m.
3.Calculate the Duty ():The relationship between Duty ( in hectares/cumec), Base period ( in days), and Delta ( in metres) is:
Given days and m:
4.Final Answer:Rounding off to the nearest integer, the duty is 691.61
Q61NAT2 marksHardAn activated sludge process (ASP) is designed for secondary treatment of of municipal wastewater. After primary clarifier, the ultimate BOD of the…Think it through. Then check your answer.Question
An activated sludge process (ASP) is designed for secondary treatment of of municipal wastewater. After primary clarifier, the ultimate BOD of the influent, which enters into ASP reactor is . Treated effluent after secondary clarifier is required to have an ultimate BOD of . Mix liquor volatile suspended solids (MLVSS) concentration in the reactor and the underflow is maintained as and , respectively. The hydraulic retention time and mean cell residence time are and , respectively. A representative flow diagram of the ASP is shown below.The underflow volume (in , round off to one decimal place) of sludge wastage is __________.
Correct answer
37 to 38
Step-by-step solution
Given:
Influent flow rate,
MLVSS in reactor,
MLVSS in underflow,
Hydraulic retention time,
Mean cell residence time, Step 1: Calculate the volume of the reactor ()Step 2: Calculate the sludge wastage rate ()
The formula for mean cell residence time () is:Assuming effluent suspended solids () are negligible as they are not provided in the problem:Substituting the given values:The underflow volume of sludge wastage is .62
Q62NAT2 marksMediumA grit chamber of rectangular cross-section is to be designed to remove particles with diameter of and specific gravity of . The terminal settling velocity…Think it through. Then check your answer.Question
A grit chamber of rectangular cross-section is to be designed to remove particles with diameter of and specific gravity of . The terminal settling velocity of the particles is estimated as . The chamber is having a width of and has to carry a peak wastewater flow of giving the depth of flow as . If a flow-through velocity of has to be maintained using a proportional weir at the outlet end of the chamber, the minimum length of the chamber (in , in integer) to remove particles completely is ____________Correct answer
9 to 9
Step-by-step solution
Given data:
Settling velocity,
Flow-through velocity,
Depth of flow, For complete removal of particles, the detention time must be equal to the settling time:The minimum length of the chamber is .63
Q63NAT2 marksMediumIn an aggregate mix, the proportions of coarse aggregate, fine aggregate and mineral filler are , and , respectively. The values of bulk specific gravity of the…Think it through. Then check your answer.Question
In an aggregate mix, the proportions of coarse aggregate, fine aggregate and mineral filler are , and , respectively. The values of bulk specific gravity of the coarse aggregate, fine aggregate and mineral filler are , and , respectively. The bulk specific gravity of the aggregate mix (round off to two decimal places) is ____________Correct answer
2.58 to 2.61
Step-by-step solution
The bulk specific gravity of the aggregate mix () is calculated using the weighted harmonic mean formula:Where:
are the percentages by weight ()
are the specific gravities ()Rounding off to two decimal places, we get .64
Q64NAT2 marksMediumThe stopping sight distance (SSD) for a level highway is for the design speed of . The acceleration due to gravity and deceleration rate are…Think it through. Then check your answer.Question
The stopping sight distance (SSD) for a level highway is for the design speed of . The acceleration due to gravity and deceleration rate are and , respectively. The perception/reaction time (in , round off to two decimal places) used in the SSD calculation is ____________Correct answer
1.9 to 2.1
Step-by-step solution
The formula for Stopping Sight Distance (SSD) is:Where:
= design speed in
= perception/reaction time in
= deceleration rate
Substituting the values:Rounding off to two decimal places, we get .65
Q65NAT2 marksHardFor a curve on a high speed Broad Gauge (BG) rail section, the maximum sanctioned speed is and the equilibrium speed is . Consider…Think it through. Then check your answer.Question
For a curve on a high speed Broad Gauge (BG) rail section, the maximum sanctioned speed is and the equilibrium speed is . Consider dynamic gauge of BG rail as . The degree of curve is defined as the angle subtended at its center by a arc. The cant deficiency for the curve (in mm, round off to integer) is ___________Correct answer
55 to 59
Step-by-step solution
Given:
Degree of curve,
Maximum sanctioned speed,
Equilibrium speed,
Dynamic gauge,
Length of chord, Step 1: Calculate the radius of the curve ().
(for a arc, )
Step 2: Calculate the actual cant () provided for the equilibrium speed.
Step 3: Calculate the theoretical cant () required for the maximum sanctioned speed.
Step 4: Calculate the cant deficiency ().
Rounding off to the nearest integer, the cant deficiency is .