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GATE CE 2024 Set 2
All 65 solved GATE CE 2024 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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General Aptitude (GA)
101
Q1MCQ1 markEasyIf ‘’ denotes increasing order of intensity, then the meaning of the words [drizzle rain downpour] is analogous to [ ______ …Think it through. Then check your answer.Question
If ‘’ denotes increasing order of intensity, then the meaning of the words [drizzle rain downpour] is analogous to [ ______ quarrel feud].Which one of the given options is appropriate to fill the blank?Correct answer
(A) bicker
Step-by-step solution
The relationship given is one of increasing intensity.1.Drizzle is light precipitation, rain is moderate, and downpour is heavy precipitation.2.Similarly, for the second set: bicker is a petty argument, quarrel is a more serious disagreement, and feud is a long-standing, intense conflict.Therefore, 'bicker' correctly fits the increasing order of intensity.2
Q2MCQ1 markEasyStatements: 1. All heroes are winners. 2. All winners are lucky people. Inferences: I. All lucky people are heroes. II. Some lucky people are heroes. III. Some winners are heroes.…Think it through. Then check your answer.Question
Statements:1.All heroes are winners.2.All winners are lucky people.Inferences:
I. All lucky people are heroes.
II. Some lucky people are heroes.
III. Some winners are heroes.Which of the above inferences can be logically deduced from statements 1 and 2?Correct answer
(B) Only II and III
Step-by-step solution
Let be the set of heroes, be the set of winners, and be the set of lucky people.
From Statement 1: (All heroes are winners).
From Statement 2: (All winners are lucky people).
Combining these, we get .Evaluating Inferences:
I. All lucky people are heroes (): Not necessarily true. is the superset.
II. Some lucky people are heroes (): Since , if there is at least one hero, then some lucky people are definitely heroes. This is a valid logical deduction in standard syllogism.
III. Some winners are heroes (): Since , if there is at least one hero, then some winners are definitely heroes. This is also a valid logical deduction.Thus, only II and III follow.3
Q3MCQ1 markMediumA student was supposed to multiply a positive real number with another positive real number . Instead, the student divided by . If the percentage error in…Think it through. Then check your answer.Question
A student was supposed to multiply a positive real number with another positive real number . Instead, the student divided by . If the percentage error in the student’s answer is 80%, the value of isCorrect answer
(D) √(5)
Step-by-step solution
Let the correct answer be and the student's answer be .
The percentage error is given by:Case 1:
Case 2:
Comparing with the given options, is the correct value.4
Q4MCQ1 markEasyIf the sum of the first 20 consecutive positive odd numbers is divided by , the result isThink it through. Then check your answer.Question
If the sum of the first 20 consecutive positive odd numbers is divided by , the result isCorrect answer
(A) 1
Step-by-step solution
The sum of the first consecutive positive odd numbers is given by the formula .
For , the sum is .
The question asks for the result when this sum is divided by :
Result .
Therefore, the correct option is (A).5
Q5MCQ1 markMediumThe ratio of the number of girls to boys in class VIII is the same as the ratio of the number of boys to girls in class IX. The total number of students (boys and girls) in…Think it through. Then check your answer.Question
The ratio of the number of girls to boys in class VIII is the same as the ratio of the number of boys to girls in class IX. The total number of students (boys and girls) in classes VIII and IX is 450 and 360, respectively. If the number of girls in classes VIII and IX is the same, then the number of girls in each class isCorrect answer
(B) 200
Step-by-step solution
Let and be the number of girls and boys in class VIII, and and be the number of girls and boys in class IX.
Given:1.2.3.4. (let the common number of girls be )Substituting these into the ratio equation:
The number of girls in each class is 200. Correct option is (B).6
Q6MCQ2 marksMediumIn the given text, the blanks are numbered (i)−(iv). Select the best match for all the blanks. Yoko Roi stands (i) as an author for standing (ii) as an honorary fellow, after she…Think it through. Then check your answer.Question
In the given text, the blanks are numbered (i)−(iv). Select the best match for all the blanks.Yoko Roi stands
(i)
as an author for standing
(ii)
as an honorary
fellow, after she stood
(iii)
her writings that stand
(iv)
the freedom of
speech.Correct answer
(D) (i) out (ii) down (iii) by (iv) for
Step-by-step solution
The sentence requires appropriate phrasal verbs:
(i) stands out: to be much better than other similar things or people (prominent).
(ii) standing down: to leave an important job or position so that someone else can take it.
(iii) stood by: to remain loyal to something (her writings).
(iv) stand for: to support or represent a particular idea or set of values (freedom of speech).Putting it together: "Yoko Roi stands out as an author for standing down as an honorary fellow, after she stood by her writings that stand for the freedom of speech."
This matches option (D).7
Q7MCQ2 marksMediumSeven identical cylindrical chalk-sticks are fitted tightly in a cylindrical container. The figure below shows the arrangement of the chalk-sticks inside the cylinder. [figure]…Think it through. Then check your answer.Question
Seven identical cylindrical chalk-sticks are fitted tightly in a cylindrical container. The figure below shows the arrangement of the chalk-sticks inside the cylinder.The length of the container is equal to the length of the chalk-sticks. The ratio of the occupied space to the empty space of the container is
Correct answer
(B) 7/2
Step-by-step solution
Let the radius of each chalk-stick be .1.The arrangement shows a central chalk-stick surrounded by six others. The distance from the center of the central stick to the center of any outer stick is .2.The radius of the outer cylindrical container must be to fit them tightly.3.Let the length of the sticks and container be .4.Volume of the 7 chalk-sticks (occupied space) = .5.Total volume of the container = .6.Empty space = Total volume Occupied space = .7.Ratio of occupied space to empty space = .8
Q8MCQ2 marksEasyThe plot below shows the relationship between the mortality risk of cardiovascular disease and the number of steps a person walks per day. Based on the data, which one of the…Think it through. Then check your answer.Question
The plot below shows the relationship between the mortality risk of cardiovascular disease and the number of steps a person walks per day. Based on the data, which one of the following options is true?
Correct answer
(C) For any 5000 increment in steps/day the largest risk reduction occurs on going from 0 to 5000.
Step-by-step solution
The graph represents a convex decreasing function. The 'risk reduction' for a specific interval of steps is the change in the y-value (Mortality Risk).1.From 0 to 5000 steps, the risk drops significantly from 1.0 to approximately 0.4 (a reduction of 0.6).2.In subsequent 5000-step intervals (5000-10000, 10000-15000, etc.), the curve flattens, meaning the vertical drop (risk reduction) becomes smaller and smaller.3.Therefore, the largest risk reduction for any 5000-step increment occurs in the first interval, from 0 to 5000.9
Q9MCQ2 marksMediumFive cubes of identical size and another smaller cube are assembled as shown in Figure A. If viewed from direction X, the planar image of the assembly appears as Figure B.…Think it through. Then check your answer.Question
Five cubes of identical size and another smaller cube are assembled as shown in Figure A. If viewed from direction X, the planar image of the assembly appears as Figure B.📷 Figure: Figure A showing assembly of cubes and Figure B showing view from XIf viewed from direction Y, the planar image of the assembly (Figure A) will appear asCorrect answer
(A) [figure]
Step-by-step solution
To find the view from direction Y:1.Identify the columns visible from that side.2.The left column consists of a stack of 2 large cubes.3.The right column consists of 1 large cube at the base with the small cube placed on top of it.4.Projecting this into a 2D plane, we see a rectangle of height 2 units on the left and a rectangle of height 1 unit with a smaller square on top on the right. This matches the diagram in option (A).10
Q10MCQ2 marksMediumVisualize a cube that is held with one of the four body diagonals aligned to the vertical axis. Rotate the cube about this axis such that its view remains unchanged. The magnitude…Think it through. Then check your answer.Question
Visualize a cube that is held with one of the four body diagonals aligned to the vertical axis. Rotate the cube about this axis such that its view remains unchanged. The magnitude of the minimum angle of rotation isCorrect answer
(A) 120°
Step-by-step solution
A cube has 3-fold rotational symmetry about its body diagonals. This means that if you rotate the cube about a body diagonal, it will look exactly the same after every rotation (). Therefore, the minimum angle of rotation for the view to remain unchanged is .
Civil Engineering Set 2 (CE2)
5511
Q11MCQ1 markMediumA partial differential equation is defined for the two-dimensional field , inside a…Think it through. Then check your answer.Question
A partial differential equationis defined for the two-dimensional field , inside a planar square domain of size 2 m × 2 m. Three boundary edges of the square domain are maintained at value , whereas the fourth boundary edge is maintained at .The value of at the center of the domain isCorrect answer
(B) 62.5
Step-by-step solution
The given equation is Laplace's equation. For a square domain with constant values on each edge, the value at the center of the domain is the arithmetic mean of the values on the four boundary edges due to the mean value property of harmonic functions.Given and :12
Q12MCQ1 markEasyThe statements P and Q are related to matrices A and B, which are conformable for both addition and multiplication. P:…Think it through. Then check your answer.Question
The statements P and Q are related to matrices A and B, which are conformable for both addition and multiplication.P:
Q: Which one of the following options is CORRECT?Correct answer
(A) P is TRUE and Q is FALSE
Step-by-step solution
Statement P: is a fundamental property of the transpose of a matrix. It is always TRUE.
Statement Q: is FALSE. The correct property for the transpose of a product is (the reversal law).13
Q13MCQ1 markMediumThe second derivative of a function is computed using the fourth-order Central Divided Difference method with a step length . The CORRECT expression for the second…Think it through. Then check your answer.Question
The second derivative of a function is computed using the fourth-order Central Divided Difference method with a step length . The CORRECT expression for the second derivative isCorrect answer
(A) (1)/(12h²) [-fᵢ₊₂ + 16 fᵢ₊₁ - 30 fᵢ + 16 fᵢ₋₁ - fᵢ₋₂]
Step-by-step solution
The fourth-order central difference approximation for the second derivative is derived using Taylor series expansions. The standard formula is:In subscript notation, this is:This matches option (A).14
Q14MCQ1 markMediumThe function hasThink it through. Then check your answer.Question
The function hasCorrect answer
(B) Minima point
Step-by-step solution
Given for .1.Find the first derivative: .2.Set to find critical points: .3.Check which critical points lie in the interval . Only is within the range.4.Find the second derivative: .5.Evaluate the second derivative at the critical point : .6.Since , the function has a local minimum at .Thus, the function has a minima point in the given interval.15
Q15MCQ1 markMediumConsider two Ordinary Differential Equations (ODEs): P: Q: Which one of the following options is…Think it through. Then check your answer.Question
Consider two Ordinary Differential Equations (ODEs):P: Q: Which one of the following options is CORRECT?Correct answer
(B) P is a homogeneous ODE and Q is not an exact ODE.
Step-by-step solution
Analysis of ODE P:
Since , P is a homogeneous ODE.Analysis of ODE Q:
This is in the form , where and .
Check for exactness: and .
Since , the ODE is not exact.Conclusion: P is homogeneous and Q is not exact. Correct option is (B).16
Q16MCQ1 markMediumA long, horizontal, rigid, uniform beam has negligible mass. The beam is subjected to a concentrated vertically downward force at from…Think it through. Then check your answer.Question
A long, horizontal, rigid, uniform beam has negligible mass. The beam is subjected to a concentrated vertically downward force at from , as shown in the figure. The beam is resting on vertical linear springs at the ends and . For the spring at the end , the spring constant .(Figure NOT to scale)If the beam DOES NOT rotate under the application of the force and displaces only vertically, the value of the spring constant (in ) for the spring at the end is
Correct answer
(C) 50
Step-by-step solution
For the beam to displace only vertically without rotation, the vertical displacement at both ends must be equal ().
Let and be the reaction forces from the springs at and respectively.
and .
Taking moments about the point of application of the load:
Substituting the spring force expressions:
Given :
.17
Q17MCQ1 markEasyConsider the statements and . : In a Pure project organization, the project manager maintains complete authority and has maximum control over the project. : A Matrix…Think it through. Then check your answer.Question
Consider the statements and .: In a Pure project organization, the project manager maintains complete authority and has maximum control over the project.: A Matrix organization structure facilitates quick response to changes, conflicts, and project needs.Which one of the following options is CORRECT?Correct answer
(A) Both P and Q are TRUE
Step-by-step solution
Statement is true: In a pure project organization, the project is a separate unit from the parent organization, and the project manager has full authority over the project resources and personnel.
Statement is true: A matrix organization combines functional and project structures, allowing for better resource sharing and flexibility, which facilitates quicker responses to project-specific needs and changes.18
Q18MCQ1 markMediumFor a thin-walled section shown in the figure, points P, Q , and R are located on the major bending axis of the section. Point Q is located on the web whereas point S is…Think it through. Then check your answer.Question
For a thin-walled section shown in the figure, points P, Q , and R are located on the major bending axis of the section. Point Q is located on the web whereas point S is located at the intersection of the web and the top flange of the section.(Figure NOT to scale)Qualitatively, the shear center of the section lies at
Correct answer
(C) R
Step-by-step solution
The shear center is the point through which the resultant of the internal shear forces passes. For a section with one axis of symmetry, the shear center must lie on that axis. In this case, the horizontal axis is the axis of symmetry, so the shear center lies on it.Consider a vertical shear force acting downwards on the section. This force induces shear flow in the flanges, given by .1.Top Flange (): The shear flow is directed from the tips towards the web. Since the left segment () is longer than the right segment (), the net horizontal force in the top flange is directed to the left.2.Bottom Flange (): The shear flow is directed from the web towards the tips. Consequently, the net horizontal force in the bottom flange is directed to the right.3.Internal Couple: These two equal and opposite horizontal forces in the flanges form a counter-clockwise couple.4.Equilibrium: To maintain equilibrium, the external downward force must be applied at a position that creates an equal and opposite (clockwise) moment about the web. A downward force applied to the right of the web will produce a clockwise moment.Therefore, the shear center lies to the right of the web, which corresponds to point R.19
Q19MCQ1 markEasyConsider the following data for a project of 300 days duration. Budgeted Cost of Work Scheduled (BCWS) = Rs. 200 Budgeted Cost of Work Performed (BCWP) = Rs. 150 Actual Cost of…Think it through. Then check your answer.Question
Consider the following data for a project of 300 days duration.Budgeted Cost of Work Scheduled (BCWS) = Rs. 200
Budgeted Cost of Work Performed (BCWP) = Rs. 150
Actual Cost of Work Performed (ACWP) = Rs. 190The ‘schedule variance’ for the project isCorrect answer
(A) (−)Rs. 50
Step-by-step solution
Schedule Variance (SV) is defined as the difference between the Budgeted Cost of Work Performed (BCWP) and the Budgeted Cost of Work Scheduled (BCWS).Since the variance is negative, it indicates that the project is behind schedule. The value is expressed in monetary terms (Rs.). Therefore, the schedule variance is (−)Rs. 50.20
Q20MCQ1 markMediumA simply supported, uniformly loaded, two-way slab panel is torsionally unrestrained. The effective span lengths along the short span (x) and long span (y) directions of the panel…Think it through. Then check your answer.Question
A simply supported, uniformly loaded, two-way slab panel is torsionally unrestrained. The effective span lengths along the short span (x) and long span (y) directions of the panel are and , respectively. The design moments for the reinforcements along the x and y directions are and , respectively. By using Rankine-Grashoff method, the ratio is proportional toCorrect answer
(D) (l_y/lₓ)²
Step-by-step solution
According to the Rankine-Grashoff theory for two-way slabs, the load shared in the and directions ( and ) are inversely proportional to the fourth power of their respective spans to ensure equal deflection at the center:The design moments for a simply supported slab are given by:Taking the ratio:Thus, the ratio is proportional to .21
Q21MCQ1 markEasyThe structural design method that DOES NOT take into account the safety factors on the design loads isThink it through. Then check your answer.Question
The structural design method that DOES NOT take into account the safety factors on the design loads isCorrect answer
(A) working stress method.
Step-by-step solution
The Working Stress Method (WSM) is based on elastic theory where the structure is designed to perform under service loads. It applies a Factor of Safety (FoS) to the material strengths (stresses) to keep them within the elastic limit, but it does not apply any safety factors (load factors) to the design loads themselves.In contrast:- Load Factor Method and Ultimate Load Method apply load factors to the service loads to find the ultimate load.
- Limit State Method (LSM) applies partial safety factors to both loads and material strengths.
22
Q22MCQ1 markMediumThe contact pressure distribution shown in the figure belongs to a [figure]Think it through. Then check your answer.Question
The contact pressure distribution shown in the figure belongs to a
Correct answer
(B) rigid footing resting on a cohesive soil.
Step-by-step solution
The contact pressure distribution depends on the rigidity of the footing and the type of soil it rests upon.1.Rigid Footing on Cohesive Soil (Clay): A rigid footing undergoes uniform settlement. In cohesive soils, the soil at the edges is less confined and tends to yield more. To maintain uniform settlement, the contact pressure must be higher at the edges and lower at the center. This matches the distribution shown in the figure.2.Rigid Footing on Cohesionless Soil (Sand): The contact pressure is zero at the edges (due to lack of confinement) and maximum at the center.3.Flexible Footing: For a flexible footing, the contact pressure is always uniform (equal to the applied load intensity), but the settlement is non-uniform (maximum at the center for clay, maximum at the edges for sand).Therefore, the figure represents a rigid footing resting on a cohesive soil.23
Q23MCQ1 markEasyWhich one of the following saturated fine-grained soils can attain a negative Skempton’s pore pressure coefficient ()?Think it through. Then check your answer.Question
Which one of the following saturated fine-grained soils can attain a negative Skempton’s pore pressure coefficient ()?Correct answer
(D) Over-consolidated clays
Step-by-step solution
Skempton's pore pressure coefficient is related to the volume change tendency of soil during shear. Over-consolidated clays (with a high OCR) tend to dilate (increase in volume) when subjected to shear stress. In undrained conditions, this tendency to dilate results in a decrease in pore water pressure (negative pore pressure), which leads to a negative value for the coefficient .24
Q24MCQ1 markEasyThe following figure shows a plot between shear stress and velocity gradient for materials/fluids . [figure] Which one of the following options is…Think it through. Then check your answer.Question
The following figure shows a plot between shear stress and velocity gradient for materials/fluids .Which one of the following options is CORRECT?
Correct answer
(B) P ightarrow Real solid; Q ightarrow Ideal Bingham plastic; S ightarrow Newtonian fluid; T ightarrow Ideal Fluid
Step-by-step solution
Based on the rheological plot of shear stress () vs velocity gradient ():1.P lies on the shear stress axis (), meaning it can sustain shear stress without flowing. This represents a Real solid.2.Q has a non-zero intercept (yield stress) and a linear relationship, representing an Ideal Bingham plastic.3.S is a straight line passing through the origin, representing a Newtonian fluid.4.T lies on the velocity gradient axis (), meaning it offers no resistance to flow. This represents an Ideal Fluid.5.R has a yield stress and a non-linear relationship, representing a Non-Newtonian fluid.Option (B) correctly identifies these relationships.25
Q25MCQ1 markMediumWhat is the CORRECT match between the air pollutants and treatment techniques given in the table? | Air pollutants | Treatment techniques | | :--- | :--- | | P - NO | i -…Think it through. Then check your answer.Question
What is the CORRECT match between the air pollutants and treatment techniques given in the table?Air pollutants Treatment techniques P - NO i - Flaring Q - SO ii - Cyclonic separator R - CO iii - Lime scrubbing S - Particles iv - NH injection Correct answer
(D) P-iv, Q-iii, R-i, S-ii
Step-by-step solution
The correct matches for air pollutant treatment techniques are:1.NO (Nitrogen Dioxide): Removed via Selective Catalytic Reduction (SCR) or Selective Non-Catalytic Reduction (SNCR) where NH injection (iv) is used to reduce NOx to N.2.SO (Sulfur Dioxide): Removed using Flue Gas Desulfurization (FGD) systems, most commonly through Lime scrubbing (iii).3.CO (Carbon Monoxide): Combustible gases like CO are typically treated by Flaring (i) to oxidize them into CO.4.Particles: Particulate matter is separated from gas streams using mechanical collectors like a Cyclonic separator (ii).Therefore, the match is P-iv, Q-iii, R-i, S-ii, which corresponds to option (D).26
Q26MCQ1 markEasyWhich one of the following products is NOT obtained in anaerobic decomposition of glucose?Think it through. Then check your answer.Question
Which one of the following products is NOT obtained in anaerobic decomposition of glucose?Correct answer
(C) H₂S
Step-by-step solution
Anaerobic decomposition of glucose () involves metabolic pathways such as fermentation or methanogenesis in the absence of oxygen.1.Methanogenesis: The overall reaction for the anaerobic digestion of glucose is often represented as:This produces methane () and carbon dioxide ().2.Fermentation: Other anaerobic pathways like alcoholic fermentation produce ethanol and , while lactic acid fermentation produces lactic acid.3.Water (): Water is a common byproduct in various biochemical reactions, including anaerobic ones.4.Hydrogen Sulfide (): is produced during the anaerobic decomposition of organic matter that contains sulfur (such as proteins containing sulfur-bearing amino acids like cysteine) or through the reduction of sulfates (). Since pure glucose () consists only of carbon, hydrogen, and oxygen, it cannot yield upon decomposition.Therefore, is the product NOT obtained from the anaerobic decomposition of glucose.27
Q27MCQ1 markMediumThe longitudinal sections of a runway have gradients as shown in the table. | End to end for sections of runway (m) | Gradient (%) | | :--- | :--- | | 0 to 200 | +1.0 | | 200 to…Think it through. Then check your answer.Question
The longitudinal sections of a runway have gradients as shown in the table.Consider the reduced level (RL) at the starting point of the runway as 100 m. The effective gradient of the runway isEnd to end for sections of runway (m) Gradient (%) 0 to 200 +1.0 200 to 600 -1.0 600 to 1200 +0.8 1200 to 1600 +0.2 1600 to 2000 -0.5 Correct answer
(C) 0.28%
Step-by-step solution
The effective gradient is defined as the ratio of the maximum difference in elevation (RL) to the total length of the runway.1.Calculate RL at each change point:- m
- m
- m
- m
- m
- m
- Maximum RL = 103.6 m
- Minimum RL = 98.0 m
- Maximum difference = m
- Total Length = 2000 m
- Effective Gradient =
28
Q28MCQ1 markEasyIn general, the outer edge is raised above the inner edge in horizontal curves forThink it through. Then check your answer.Question
In general, the outer edge is raised above the inner edge in horizontal curves forCorrect answer
(B) Highways and Railways only
Step-by-step solution
Super-elevation (or cant) is the inward transverse slope provided to the pavement or track to counteract the effect of centrifugal force in horizontal curves.1.Highways: Super-elevation is a standard design requirement to ensure vehicle stability and passenger comfort at design speeds.2.Railways: Super-elevation is provided to distribute the load equally on both rails and prevent derailment or excessive flange wear.3.Taxiways: Aircraft move at very low speeds on taxiways. Providing super-elevation could cause issues for slow-moving or stationary aircraft, such as fuel imbalance or tipping. Therefore, taxiways are generally not super-elevated.Thus, the outer edge is raised above the inner edge for Highways and Railways only. The correct option is (B).29
Q29MCQ1 markMediumVarious stresses in jointed plain concrete pavement with slab size of are denoted as follows: Wheel load stress at interior = Wheel…Think it through. Then check your answer.Question
Various stresses in jointed plain concrete pavement with slab size of are denoted as follows:Wheel load stress at interior =
Wheel load stress at edge =
Wheel load stress at corner =
Warping stress at interior =
Warping stress at edge =
Warping stress at corner =
Frictional stress between slab and supporting layer = The critical stress combination in the concrete slab during a summer midnight isCorrect answer
(A) S_(wl)^c + Sₜ^c
Step-by-step solution
In a concrete pavement slab:1.Summer Midnight: The top surface is cooler than the bottom surface. This causes the slab to warp upwards at the corners (curling). This creates tensile stress at the top of the corner.2.Wheel Load at Corner: A wheel load applied at the corner also causes tensile stress at the top of the slab.3.Critical Combination: Since both warping and wheel load create tensile stress at the same location (top of corner), they are additive. Frictional stress is typically considered for interior/edge regions and is negligible at corners.Therefore, the critical combination is .30
Q30MCQ1 markEasyFor a reconnaissance survey, it is necessary to obtain vertical aerial photographs of a terrain at an average scale of using a camera. If the permissible flying height…Think it through. Then check your answer.Question
For a reconnaissance survey, it is necessary to obtain vertical aerial photographs of a terrain at an average scale of using a camera. If the permissible flying height is assumed as above a datum and the average terrain elevation is above the datum, the required focal length (in mm) of the camera isCorrect answer
(B) 150
Step-by-step solution
The scale () of a vertical aerial photograph is given by the formula:Where:
= focal length of the camera
= flying height above datum =
= average terrain elevation =
= Substituting the values:Converting to mm:Thus, the required focal length is .31
Q31MCQ1 markEasyWhat is the CORRECT match between the survey instruments/parts of instruments shown in the table and the operations carried out with them? | Instruments/Parts of instruments |…Think it through. Then check your answer.Question
What is the CORRECT match between the survey instruments/parts of instruments shown in the table and the operations carried out with them?Instruments/Parts of instruments Operations P - Bubble tube i - Tacheometry Q - Plumb bob ii - Minor movements R - Tangent screw iii - Centering S - Stadia cross-wire iv - Levelling Correct answer
(B) P-iv, Q-iii, R-ii, S-i
Step-by-step solution
To find the correct match, we evaluate the function of each instrument/part:1.Bubble tube (P): A spirit level or bubble tube is used to establish a horizontal line of sight. This process is known as levelling (iv).2.Plumb bob (Q): A plumb bob is used to define a vertical line passing through a point. In surveying, it is primarily used for centering (iii) the instrument exactly over a station mark on the ground.3.Tangent screw (R): Tangent screws are used for making minor movements (ii) or fine adjustments in the horizontal or vertical circles after the respective clamps have been tightened.4.Stadia cross-wire (S): Stadia hairs or cross-wires are used in tacheometry (i) to measure horizontal distances and vertical elevations by reading the intercept on a graduated staff.Matching these pairs gives: P-iv, Q-iii, R-ii, S-i, which corresponds to option (B).32
Q32MCQ1 markEasyTo finalize the direction of a survey, four surveyors set up a theodolite at a station P and performed all the temporary adjustments. From the station P, each of the surveyors…Think it through. Then check your answer.Question
To finalize the direction of a survey, four surveyors set up a theodolite at a station P and performed all the temporary adjustments. From the station P, each of the surveyors observed the bearing to a tower located at station Q with the same instrument without shifting it. The bearings observed by the surveyors are , , and . Assuming that each measurement is taken with equal precision, the most probable value of the bearing isCorrect answer
(B) 30^o 30' 20''
Step-by-step solution
For measurements taken with equal precision, the most probable value (MPV) is the arithmetic mean of the observed values.Observed bearings:1.2.3.4.Sum of bearings =
Sum =
Since and :
Sum = Arithmetic Mean =
MPV = .33
Q33NAT1 markHardThe steel angle section shown in the figure has elastic section modulus of about the horizontal axis, which passes through the centroid of the…Think it through. Then check your answer.Question
The steel angle section shown in the figure has elastic section modulus of about the horizontal axis, which passes through the centroid of the section.The shape factor of the section is ________ (rounded off to 2 decimal places).
Correct answer
1.75 to 1.85
Step-by-step solution
1.Identify the dimensions of the angle section:- Total height () =
- Total width () =
- Thickness of both legs () =
3.Locate the Plastic Neutral Axis (PNA):The PNA divides the total area into two equal halves ().- Area of the horizontal leg = .
- Since this equals , the PNA lies exactly at the junction of the two legs, which is from the bottom edge.
is the sum of the first moments of area about the PNA.- Area above PNA () = . Distance of its centroid from PNA () = .
- Area below PNA () = . Distance of its centroid from PNA () = .
5.Calculate the Shape Factor ():Given elastic section modulus .
Rounding off to 2 decimal places, the shape factor is 1.79.34
Q34NAT1 markMediumA reinforced concrete pile of length and diameter is embedded in a saturated pure clay with unit cohesion of . If the adhesion factor…Think it through. Then check your answer.Question
A reinforced concrete pile of length and diameter is embedded in a saturated pure clay with unit cohesion of . If the adhesion factor is , the net ultimate uplift pullout capacity (in kN) of the pile is _________________ (rounded off to the nearest integer).Correct answer
545 to 555
Step-by-step solution
The net ultimate uplift capacity () of a pile in saturated clay is provided by the skin friction resistance along the pile shaft.The formula for net ultimate uplift capacity is:Where:- is the adhesion factor =
- is the unit cohesion =
- is the surface area of the pile shaft =
- is the diameter of the pile =
- is the embedded length of the pile =
35
Q35NAT1 markMediumA wide rectangular channel is carrying a discharge of at a bed slope of in . Assuming the energy correction factor as and…Think it through. Then check your answer.Question
A wide rectangular channel is carrying a discharge of at a bed slope of in . Assuming the energy correction factor as and acceleration due to gravity as , the critical depth of flow (in meters) is _____________ (rounded off to decimal places).Correct answer
2.88 to 2.94
Step-by-step solution
For critical flow conditions in an open channel, the following relationship holds:For a rectangular channel:- Top width () =
- Area () =
- is the critical depth
- Discharge () =
- Width () =
- Energy correction factor () =
- Acceleration due to gravity () =
36
Q36MCQ2 marksMediumIn a sample of heart patients, each patient has chance of having a heart attack without medicine X. It is clinically known that medicine X reduces the probability of…Think it through. Then check your answer.Question
In a sample of heart patients, each patient has chance of having a heart attack without medicine X. It is clinically known that medicine X reduces the probability of having a heart attack by . Medicine X is taken by of these patients. The probability that a randomly selected patient, out of the patients, takes medicine X and has a heart attack isCorrect answer
(C) 20%
Step-by-step solution
Let be the event that a patient takes medicine X, and be the event that a patient has a heart attack.Given:
Total patients
Patients taking medicine X,
Probability of heart attack without medicine,
Medicine X reduces the probability of heart attack by . This means the new probability is of the original probability:
We need to find the probability that a patient takes medicine X AND has a heart attack, which is :Thus, the correct option is (C).37
Q37MCQ2 marksMediumA linearly elastic beam of length with flexural rigidity has negligible mass. A massless spring with a spring constant and a rigid block of mass are attached to…Think it through. Then check your answer.Question
A linearly elastic beam of length with flexural rigidity has negligible mass. A massless spring with a spring constant and a rigid block of mass are attached to the beam as shown in the figure.The natural frequency of this system is
Correct answer
(A) √((kl³ + 6EI)/(ml³))
Step-by-step solution
The system consists of a simply supported beam and a spring acting in parallel to resist the vertical displacement of mass .1.The stiffness of a simply supported beam of length at its center is given by:.2.Since the spring and the beam are in parallel, the equivalent stiffness is:.3.The natural frequency is:.
Thus, option (A) is correct.38
Q38MCQ2 marksMediumA critical activity in a project is estimated to take 15 days to complete at a cost of Rs. 30,000. The activity can be expedited to complete in 12 days by spending a total amount…Think it through. Then check your answer.Question
A critical activity in a project is estimated to take 15 days to complete at a cost of Rs. 30,000. The activity can be expedited to complete in 12 days by spending a total amount of Rs. 54,000. Consider the statements P and Q.P: It is economically advisable to complete the activity early by crashing, if the indirect cost of the project is Rs. 8,500 per day.Q: It is economically advisable to complete the activity early by crashing, if the indirect cost of the project is Rs. 10,000 per day.Which one of the following options is CORRECT?Correct answer
(A) Both P and Q are TRUE
Step-by-step solution
1.Calculate the cost slope of the activity:Cost Slope = per day.2.Crashing an activity is economically advisable if the indirect cost per day saved is greater than the cost slope of the activity.3.For statement P: Indirect cost = Rs. 8,500/day. Since , crashing is advisable. P is TRUE.4.For statement Q: Indirect cost = Rs. 10,000/day. Since , crashing is advisable. Q is TRUE.Therefore, both P and Q are TRUE.39
Q39MCQ2 marksMediumA homogeneous, prismatic, linearly elastic steel bar fixed at both the ends has a slenderness ratio () of 105, where is the bar length and is the radius of gyration.…Think it through. Then check your answer.Question
A homogeneous, prismatic, linearly elastic steel bar fixed at both the ends has a slenderness ratio () of 105, where is the bar length and is the radius of gyration. The coefficient of thermal expansion of steel is . Consider the effective length of the steel bar as and neglect the self-weight of the bar.The differential increase in temperature (rounded off to the nearest integer) at which the bar buckles isCorrect answer
(A) 298 ^
Step-by-step solution
1.The Euler buckling load for a column is .2.The thermal force developed in a fixed-end bar due to temperature increase is .3.At the point of buckling, :
Since , where is the radius of gyration:4.Given and , the effective slenderness ratio is:.5.Substitute the values:
.
Rounding to the nearest integer, we get .40
Q40MCQ2 marksMediumConsider the statements P and Q related to the analysis/design of retaining walls. P: When a rough retaining wall moves toward the backfill, the wall friction…Think it through. Then check your answer.Question
Consider the statements P and Q related to the analysis/design of retaining walls.P: When a rough retaining wall moves toward the backfill, the wall friction force/resistance mobilizes in upward direction along the wall.Q: Most of the earth pressure theories calculate the earth pressure due to surcharge by neglecting the actual distribution of stresses due to surcharge.Which one of the following options is CORRECT?Correct answer
(A) Both P and Q are TRUE
Step-by-step solution
Statement P is TRUE: In the passive state (wall moving toward the backfill), the soil wedge tends to move upward relative to the wall. Consequently, the wall friction force on the wall acts in the upward direction.
Statement Q is TRUE: Classical earth pressure theories like Rankine's and Coulomb's typically assume a uniform increase in lateral pressure due to surcharge, effectively neglecting the complex stress distribution (like Boussinesq's) that occurs in reality.41
Q41MCQ2 marksMediumA round-bottom triangular lined canal is to be laid at a slope of in , to carry a discharge of . The side slopes of the canal cross-section are…Think it through. Then check your answer.Question
A round-bottom triangular lined canal is to be laid at a slope of in , to carry a discharge of . The side slopes of the canal cross-section are to be kept at . If Manning’s roughness coefficient is , the flow depth (in meters) will be in the range ofCorrect answer
(A) 2.39 to 2.42
Step-by-step solution
For a round-bottomed triangular section with side slope and radius :
Area and Wetted Perimeter , where .
.
Hydraulic radius .
Using Manning's equation:
.
This falls in the range 2.39 to 2.42.42
Q42MCQ2 marksHardA hypothetical multimedia filter, consisting of anthracite particles (specific gravity: ), silica sand (specific gravity: ), and ilmenite sand (specific gravity:…Think it through. Then check your answer.Question
A hypothetical multimedia filter, consisting of anthracite particles (specific gravity: ), silica sand (specific gravity: ), and ilmenite sand (specific gravity: ), is to be designed for treating water/wastewater. After backwashing, the particles should settle forming three layers: coarse anthracite particles at the top of the bed, silica sand in the middle, and small ilmenite sand particles at the bottom of the bed.Assume
(i) Slow discrete settling (Stoke’s law is applicable)
(ii) All particles are spherical
(iii) Diameter of silica sand particles is The CORRECT option fulfilling the diameter requirements for this filter media isCorrect answer
(A) diameter of anthracite particles is slightly less than 0.35 mm and diameter of ilmenite particles is slightly greater than 0.141 mm.
Step-by-step solution
According to Stoke's Law, settling velocity . For the layers to form as specified (anthracite top, silica middle, ilmenite bottom), the settling velocities must follow: .1.For anthracite to be above silica:
.2.For ilmenite to be below silica:
.
Thus, and . Option (A) matches these conditions.43
Q43MCQ2 marksMediumThe consolidated data of a spot speed study for a certain stretch of a highway is given in the table. | Speed range (kmph) | Number of observations | | :--- | :--- | | 0 - 10 | 7…Think it through. Then check your answer.Question
The consolidated data of a spot speed study for a certain stretch of a highway is given in the table.The “upper speed limit” (in kmph) for the traffic sign isSpeed range (kmph) Number of observations 0 - 10 7 10 - 20 31 20 - 30 76 30 - 40 129 40 - 50 104 50 - 60 78 60 - 70 29 70 - 80 24 80 - 90 13 90 - 100 9 Correct answer
(B) 55
Step-by-step solution
The "upper speed limit" for traffic signs is typically taken as the 85th percentile speed ().1.Calculate the total number of observations ():2.Determine the rank of the 85th percentile:Rank3.Calculate cumulative frequencies:- Up to 10: 7
- Up to 20: 38
- Up to 30: 114
- Up to 40: 243
- Up to 50: 347
- Up to 60: 425
The cumulative frequency reaches exactly 425 at the upper boundary of the 50-60 kmph range. Thus, the 85th percentile speed is 60 kmph. Note: While the calculation yields 60 kmph, based on the provided answer key, the correct option is (B) 55.44
Q44MSQ2 marksMediumThree vectors , , and are given as …Think it through. Then check your answer.Question
Three vectors , , and are given as Which of the following is/are CORRECT?Correct answer
(A) p × (q × r) + q × (r × p) + r × (p × q) = 0; (B) p × (q × r) = (p · r) q - (p · q) r
Step-by-step solution
Let's evaluate each identity:(A) Jacobi's Identity: For any three vectors, . This is a fundamental property of the cross product. Thus, (A) is correct.(B) Vector Triple Product Expansion: The standard formula for the vector triple product is . This matches the expression in (B). Thus, (B) is correct.(C) Associativity: The vector triple product is generally not associative, i.e., . Thus, (C) is incorrect.(D) Scalar Triple Product: is the scalar triple product . By cyclic property, . However, . Thus, the equality holds only if the scalar triple product is zero. While the given vectors are coplanar (), based on the provided answer key, only (A) and (B) are considered correct.45
Q45MSQ2 marksMediumConsider the statements P, Q , and R. P: Compacted fine-grained soils with flocculated structure have isotropic permeability. Q: Phreatic surface/line is the line along which the…Think it through. Then check your answer.Question
Consider the statements P, Q , and R.P: Compacted fine-grained soils with flocculated structure have isotropic permeability.
Q: Phreatic surface/line is the line along which the pore water pressure is always maximum.
R: The piping phenomenon occurring below the dam foundation is typically known as blowout piping.Which of the following option(s) is/are CORRECT?Correct answer
(C) P is TRUE and R is FALSE; (D) Both Q and R are FALSE
Step-by-step solution
Let's analyze the statements:Statement P: Compacted fine-grained soils with a flocculated structure (typically compacted on the dry side of optimum) have a random orientation of particles, which results in more isotropic permeability compared to dispersed structures. Thus, P is TRUE.Statement Q: The phreatic surface is the locus of points where the pore water pressure is atmospheric (zero gauge pressure). It is not the line of maximum pressure. Thus, Q is FALSE.Statement R: Piping is the progressive internal erosion of soil. Blowout (or boiling) refers to the heave of soil at the downstream toe due to high exit gradients. While related, piping below a dam foundation is not typically called "blowout piping". Thus, R is FALSE.Evaluating the options:
(A) Both P and R are TRUE: False (R is false).
(B) P is FALSE and Q is TRUE: False (P is true, Q is false).
(C) P is TRUE and R is FALSE: TRUE.
(D) Both Q and R are FALSE: TRUE.Therefore, the correct options are (C) and (D).46
Q46MSQ2 marksMediumIn the context of pavement material characterization, the CORRECT statement(s) is/areThink it through. Then check your answer.Question
In the context of pavement material characterization, the CORRECT statement(s) is/areCorrect answer
(A) The load penetration curve of CBR test may need origin correction due to the non-vertical penetrating plunger of the loading machine.; (C) Grading of normal (unmodified) bitumen binders is done based on viscosity test results.; (D) In compacted bituminous mix, Voids in the Mineral Aggregate (VMA) is equal to the sum of total volume of air voids (Vᵥ) and total volume of bitumen (V_b).
Step-by-step solution
(A) Correct. Origin correction is required if the initial part of the CBR curve is concave upwards, which can be caused by surface irregularities or a non-vertical plunger.
(B) Incorrect. The Los Angeles abrasion test determines hardness (resistance to wear), while the aggregate impact test determines toughness (resistance to impact). The statement swaps these.
(C) Correct. Per IS 73:2013, paving grade bitumen is classified into four grades (VG-10, VG-20, VG-30, VG-40) based on absolute viscosity at .
(D) Correct. VMA is the volume of intergranular void space between the aggregate particles of a compacted paving mixture that includes the air voids and the effective bitumen content ().47
Q47NAT2 marksEasyThe expression for computing the effective interest rate () using continuous compounding for a nominal interest rate of 5% is…Think it through. Then check your answer.Question
The expression for computing the effective interest rate () using continuous compounding for a nominal interest rate of 5% isThe effective interest rate (in percentage) is ____________ (rounded off to 2 decimal places).Correct answer
5.11 to 5.15
Step-by-step solution
The effective interest rate () for continuous compounding is derived from the limit definition of the exponential function:where is the nominal interest rate.Given the nominal interest rate , we substitute this into the formula:Using the value of :To express the effective interest rate as a percentage:Rounding off to two decimal places, we get 5.13%. The official range provided is 5.11 to 5.15.48
Q48NAT2 marksEasyConsider two matrices and . The…Think it through. Then check your answer.Question
Consider two matrices and .
The determinant of the matrix is __________(in integer).Correct answer
10 to 10
Step-by-step solution
First, we compute the product matrix :Now, we find the determinant of :49
Q49NAT2 marksMediumFor the 6 m long horizontal cantilever beam PQR shown in the figure, Q is the mid-point. Segment PQ of the beam has flexural rigidity whereas…Think it through. Then check your answer.Question
For the 6 m long horizontal cantilever beam PQR shown in the figure, Q is the mid-point. Segment PQ of the beam has flexural rigidity whereas the segment QR has infinite flexural rigidity. Segment QR is subjected to uniformly distributed, vertically downward load of 5 kN/m.(Figure NOT to scale)The magnitude of the vertical displacement (in mm) at point Q is ________ (rounded off to 3 decimal places).
Correct answer
1.176 to 1.186
Step-by-step solution
The segment QR is rigid (), so it does not bend. The load on QR acts as a concentrated force and a moment at point Q.1.Total vertical force at Q due to UDL on QR: .2.Moment at Q due to UDL on QR: .The vertical displacement at Q () is the deflection of the cantilever segment PQ (length ) under the action of point load and moment at its free end Q:Substituting the values:Converting to mm:Rounding off to 3 decimal places, the magnitude is .50
Q50NAT2 marksMediumThe horizontal beam PQRS shown in the figure has a fixed support at point P, an internal hinge at point Q, and a pin support at point R. A concentrated vertically downward load…Think it through. Then check your answer.Question
The horizontal beam PQRS shown in the figure has a fixed support at point P, an internal hinge at point Q, and a pin support at point R. A concentrated vertically downward load (V) of 10 kN can act at any point over the entire length of the beam.The maximum magnitude of the moment reaction (in kN. m) that can act at the support P due to V is ____________ (in integer).
Correct answer
150 to 150
Step-by-step solution
To find the maximum moment reaction at support P (), we consider the influence of the load kN at different positions.1.Load on segment PQ (0 ≤ x ≤ 15m):The beam acts as a cantilever fixed at P and hinged at Q. The maximum moment at P occurs when the load is at the furthest point from P, which is the hinge Q ( m).
kN.m.2.Load on segment QRS (15m < x ≤ 30m):The load on segment QRS creates a reaction at the hinge Q (), which is then transferred to segment PQ.
For segment QRS, taking moments about R:
for (overhang RS).
Max occurs when is at S ( m):
kN (downward).
The moment at P due to this reaction is kN.m.
Comparing the two cases, the maximum magnitude of the moment reaction at P is 150 kN.m.51
Q51NAT2 marksHardA concrete column section of size as shown in the figure is subjected to both axial compression and bending along the major axis. The depth of…Think it through. Then check your answer.Question
A concrete column section of size as shown in the figure is subjected to both axial compression and bending along the major axis. The depth of the neutral axis () is times the depth of the column, as shown.(Figure NOT to scale)The maximum compressive strain () at highly compressive extreme fiber in concrete, where there is no tension in the section, is ______________ (rounded off to 2 decimal places).
Correct answer
3.2 to 3.4
Step-by-step solution
Given:- Column width
- Column depth
- Depth of neutral axis
52
Q52NAT2 marksMediumThe table shows the activities and their durations and dependencies in a project. | Activity | Duration (Days) | Depends on | |----------|-----------------|------------| | A | 8 |…Think it through. Then check your answer.Question
The table shows the activities and their durations and dependencies in a project.The total duration (in days) of the project is___________ (in integer).Activity Duration (Days) Depends on A 8 - B 4 A C 4 B D 4 C, L F 4 A G 4 F H 6 G, L K 10 A L 6 F, K Correct answer
30 to 30
Step-by-step solution
We calculate the Earliest Finish (EF) for each activity based on dependencies:- A: EF = 8
- B: EF = EF(A) + 4 = 8 + 4 = 12
- C: EF = EF(B) + 4 = 12 + 4 = 16
- F: EF = EF(A) + 4 = 8 + 4 = 12
- G: EF = EF(F) + 4 = 12 + 4 = 16
- K: EF = EF(A) + 10 = 8 + 10 = 18
- L: EF = max(EF(F), EF(K)) + 6 = max(12, 18) + 6 = 18 + 6 = 24
- D: EF = max(EF(C), EF(L)) + 4 = max(16, 24) + 4 = 24 + 4 = 28
- H: EF = max(EF(G), EF(L)) + 6 = max(16, 24) + 6 = 24 + 6 = 30
Duration = max(EF(D), EF(H)) = max(28, 30) = 30 days.53
Q53NAT2 marksHardA homogeneous earth dam has a maximum water head difference of between the upstream and downstream sides. A flownet was drawn with the number of potential drops as…Think it through. Then check your answer.Question
A homogeneous earth dam has a maximum water head difference of between the upstream and downstream sides. A flownet was drawn with the number of potential drops as and the average length of the element as . Specific gravity of the soil is . For a factor of safety of against piping failure, void ratio of the soil is ______________ (rounded off to decimal places).Correct answer
0.63 to 0.67
Step-by-step solution
Given:
Maximum water head difference,
Number of potential drops,
Average length of the exit element,
Specific gravity of soil,
Factor of safety against piping, Step 1: Calculate the head drop per potential drop ():Step 2: Calculate the exit gradient ():Step 3: Determine the critical hydraulic gradient () using the factor of safety:Step 4: Calculate the void ratio () using the formula for critical hydraulic gradient:The void ratio of the soil is .54
Q54NAT2 marksMediumThe in-situ percentage of voids of a sand deposit is . The maximum and minimum densities of sand determined from the laboratory tests are and…Think it through. Then check your answer.Question
The in-situ percentage of voids of a sand deposit is . The maximum and minimum densities of sand determined from the laboratory tests are and , respectively. Assume the specific gravity of sand as . The relative density index of the in-situ sand is ______________ (rounded off to decimal places).Correct answer
0.12 to 0.14
Step-by-step solution
Given:
In-situ porosity (percentage of voids),
Maximum dry density,
Minimum dry density,
Specific gravity of sand,
Density of water, Step 1: Calculate the in-situ void ratio ():Step 2: Calculate the minimum void ratio () corresponding to maximum density:Step 3: Calculate the maximum void ratio () corresponding to minimum density:Step 4: Calculate the relative density index ():Rounding off to two decimal places, the relative density index is .55
Q55NAT2 marksMediumA drained triaxial test was conducted on a saturated sand specimen using a stress-path triaxial testing system. The specimen failed when the axial stress reached a value of…Think it through. Then check your answer.Question
A drained triaxial test was conducted on a saturated sand specimen using a stress-path triaxial testing system. The specimen failed when the axial stress reached a value of from an initial confining pressure of . The angle of shearing plane (in degrees) with respect to horizontal is ________________ (rounded off to the nearest integer).Correct answer
30 to 30
Step-by-step solution
Given:
Initial state: .
Failure state: Axial stress , Radial stress .
Since axial stress decreased, this is a triaxial extension test. In this case, the radial stress is the major principal stress () and the axial stress is the minor principal stress ().Step 1: Calculate the angle of internal friction ().
For sand ():
.Step 2: Determine the angle of the shearing plane with respect to horizontal.
The failure plane makes an angle with the major principal plane.
In this extension test, the major principal stress () is radial (horizontal), so the major principal plane is vertical.
The failure plane makes with the vertical plane.
Therefore, the angle with respect to the horizontal plane is .56
Q56NAT2 marksMediumA storm with a recorded precipitation of , as shown in the table, produced a direct run-off of . | Time from start (hours) | 1 | 2 | 3 | 4 | 5 | 6 |…Think it through. Then check your answer.Question
A storm with a recorded precipitation of , as shown in the table, produced a direct run-off of .The -index of this storm is ____________ (rounded off to 2 decimal places).Time from start (hours) 1 2 3 4 5 6 7 8 Recorded cumulative precipitation (cm) 0.5 1.5 3.1 5.5 7.3 8.9 10.2 11.0 Correct answer
0.64 to 0.65
Step-by-step solution
1.Calculate total precipitation () and total run-off ():, .2.Calculate total infiltration ():.3.Calculate rainfall intensities () for each hour:5.Since , exclude the first hour. The effective rainfall duration .6.Recalculate using only periods where :.7.Check remaining intensities: all are . Thus, .57
Q57NAT2 marksMediumA 500 m long water distribution pipeline P with diameter 1.0 m, is used to convey of flow. A new pipeline Q, with the same length and flow rate, is to…Think it through. Then check your answer.Question
A 500 m long water distribution pipeline P with diameter 1.0 m, is used to convey of flow. A new pipeline Q, with the same length and flow rate, is to replace P. The friction factors for P and Q are 0.04 and 0.01, respectively. The diameter of the pipeline Q (in meters) is ______________ (rounded off to 2 decimal places).Correct answer
0.7 to 0.8
Step-by-step solution
To maintain the same flow rate and replace the pipeline, we assume the head loss remains the same. Using the Darcy-Weisbach equation in terms of discharge:Since and are identical for both pipelines P and Q, and :Given , , and :Rounding to two decimal places, the diameter of pipeline Q is .58
Q58NAT2 marksMediumA tank of 6 m height is provided with a 100 mm diameter orifice at the center of its base. The orifice is plugged and the tank is filled up to 5 m…Think it through. Then check your answer.Question
A tank of 6 m height is provided with a 100 mm diameter orifice at the center of its base. The orifice is plugged and the tank is filled up to 5 m height. Consider the average value of discharge coefficient as 0.6 and acceleration due to gravity () as . After unplugging the orifice, the time (in seconds) taken for the water level to drop from 5 m to 3.5 m under free discharge condition is ____________ (rounded off to 2 decimal places).Correct answer
102 to 106
Step-by-step solution
The time required for the water level in a tank to drop from height to through an orifice is given by:Where:59
Q59NAT2 marksHardA rectangular channel is 4.0 m wide and carries a discharge of 2.0 m/s with a depth of 0.4 m. The channel transitions to a maximum width contraction at a downstream location,…Think it through. Then check your answer.Question
A rectangular channel is 4.0 m wide and carries a discharge of 2.0 m/s with a depth of 0.4 m. The channel transitions to a maximum width contraction at a downstream location, without influencing the upstream flow conditions. The width (in meters) at the maximum contraction is ________________ (rounded off to 2 decimal places).Correct answer
3.3 to 3.7
Step-by-step solution
1.Calculate the specific energy at the upstream section (Section 1):m, m/s, m
m/s
m2.For maximum width contraction without affecting upstream conditions, the flow at the contracted section (Section 2) must be critical:m3.For a rectangular channel, critical depth is related to specific energy by:m4.The critical discharge per unit width is:m/s5.The width at the maximum contraction is:mRounding to two decimal places, we get 3.53 m.60
Q60NAT2 marksMediumA circular settling tank is to be designed for primary treatment of sewage at a flow rate of 10 million liters/day. Assume a detention period of 2.0 hours and surface loading rate…Think it through. Then check your answer.Question
A circular settling tank is to be designed for primary treatment of sewage at a flow rate of 10 million liters/day. Assume a detention period of 2.0 hours and surface loading rate of 40000 liters/m/day. The height (in meters) of the water column in the tank is _______________ (rounded off to 2 decimal places).Correct answer
3.25 to 3.4
Step-by-step solution
1.Convert flow rate to m/day:liters/day = 10,000 m/day2.Calculate the volume of the tank using detention time ():hours = day
m3.Calculate the surface area () using the Surface Loading Rate (SLR):liters/m/day = 40 m/m/day
m4.Calculate the height () of the water column:mRounding to two decimal places, the height is 3.33 m.61
Q61NAT2 marksMediumAn organic waste is represented as C O H N S. (Atomic weights: S-32, H-1, C-12, O-16, N-14). Assume complete conversion of S to SO while burning.…Think it through. Then check your answer.Question
An organic waste is represented as C O H N S.
(Atomic weights: S-32, H-1, C-12, O-16, N-14).
Assume complete conversion of S to SO while burning.
SO generated (in grams) per kg of this waste is ___________
(rounded off to 1 decimal place).Correct answer
9.9 to 10.2
Step-by-step solution
1.Calculate the molecular weight of the organic waste (C O H N S):
g/mol2.Determine the mass of Sulfur (S) in 1 mole of waste:Mass of S = 32 g3.According to the reaction , 1 mole of S (32 g) produces 1 mole of SO (32 + 2 16 = 64 g).4.Calculate the mass of SO generated per kg (1000 g) of waste:Mass of SO = g
Mass of SO = gRounding to one decimal place, we get 10.1 g.62
Q62NAT2 marksMediumA horizontal curve of radius (with transition curves on either side) in a Broad Gauge railway track is designed and constructed for an equilibrium speed of…Think it through. Then check your answer.Question
A horizontal curve of radius (with transition curves on either side) in a Broad Gauge railway track is designed and constructed for an equilibrium speed of . However, a few years after construction, the Railway Authorities decided to run express trains on this track. The maximum allowable cant deficiency is .The maximum restricted speed (in ) of the express trains running on this track is _______________ (rounded off to the nearest integer).Correct answer
113 to 116
Step-by-step solution
1.Equilibrium Cant ():For a Broad Gauge (), the equilibrium cant is given by:
Given and :
2.Maximum Permissible Cant ():The maximum cant for the express train is the sum of the equilibrium cant and the maximum allowable cant deficiency ():
Given :
3.Maximum Restricted Speed ():Using the cant formula for :
Rounding to the nearest integer, we get .63
Q63NAT2 marksHardA vertical summit curve on a freight corridor is formed at the intersection of two gradients, and . Assume the following: Only large-sized trucks are allowed on…Think it through. Then check your answer.Question
A vertical summit curve on a freight corridor is formed at the intersection of two gradients, and .Assume the following:
Only large-sized trucks are allowed on this corridor
Design speed
Eye height of truck drivers above the road surface
Height of object above the road surface for which trucks need to stop
Total reaction time of the truck drivers
Coefficient of longitudinal friction of the road
Stopping sight distance gets compensated on the gradientThe design length of the summit curve (in meters) to accommodate the stopping sight distance is __________ (rounded off to decimal places).Correct answer
117 to 120
Step-by-step solution
1.Deviation Angle ():,
2.Stopping Sight Distance ():Given , , :
3.Length of Summit Curve ():Assume . The formula for length is:
Where and :
Since , our assumption is correct.64
Q64NAT2 marksMediumA child walks on a level surface from point to point at a bearing of , from point to point at a bearing of and then directly returns to the…Think it through. Then check your answer.Question
A child walks on a level surface from point to point at a bearing of , from point to point at a bearing of and then directly returns to the starting point at a bearing of . The straight-line paths and are each. Assuming that all bearings are measured from the magnetic north in degrees, the straight-line path length (in meters) is _________________ (rounded off to the nearest integer).Correct answer
6 to 8
Step-by-step solution
1.Geometry of the Path:- Path : Length , Bearing .
- Path : Length , Bearing .
- Path : Bearing (Return to ).
- The bearing of is .
- The bearing of is .
- Angle .
4.Verification of Bearing :Using Sine Rule:
Bearing of .
Bearing of . This matches the problem statement.Rounding to the nearest integer gives .65
Q65NAT2 marksMediumDifferential levelling is carried out from point P (BM: +200.000 m) to point R. The readings taken are given in the table. | Points | Staff readings (m) | | Remarks | | :--- |…Think it through. Then check your answer.Question
Differential levelling is carried out from point P (BM: +200.000 m) to point R. The readings taken are given in the table.Reduced Level (in meters) of the point R is _____ (rounded off to 3 decimal places).Points Staff readings (m) Remarks Back Sight Fore Sight P (−)2.050 BM: +200.000 m Q 1.050 0.950 Q is a change point R (−)1.655 Correct answer
199.704 to 199.706
Step-by-step solution
Given:- Reduced Level (RL) of point P = m
- Back Sight (BS) at P = m
- Fore Sight (FS) at Q = m
- Back Sight (BS) at Q = m
- Fore Sight (FS) at R = m