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GATE ME 2019 Set 1
All 65 solved GATE ME 2019 Set 1 questions in exam order. Open a question, commit to an answer, and learn from the step-by-step solution. One question at a time.
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65
Paper marks
100
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General Aptitude (GA)
101
Q1MCQ1 markEasyJohn Thomas, an __________________ writer, passed away in 2018.Think it through. Then check your answer.Question
John Thomas, an __________________ writer, passed away in 2018.Correct answer
(C) eminent
Step-by-step solution
The word 'eminent' is used to describe a person who is famous and respected within a particular sphere, which fits the context of a writer. 'Imminent' means about to happen. 'Prominent' means important or famous, but 'eminent' is more specifically used for distinguished professionals. 'Dominant' means most influential or powerful.2
Q2MCQ1 markEasy________ I permitted him to leave, I wouldn't have had any problem with him being absent, ________ I?Think it through. Then check your answer.Question
________ I permitted him to leave, I wouldn't have had any problem with him being absent, ________ I?Correct answer
(C) Had, would
Step-by-step solution
The sentence is a third conditional structure. The first part should be 'Had I permitted' (equivalent to 'If I had permitted'). The second part is a question tag for 'I wouldn't have had', which is 'would I?'. Therefore, the correct pair is 'Had, would'.3
Q3MCQ1 markEasyA worker noticed that the hour hand on the factory clock had moved by 225 degrees during her stay at the factory. For how long did she stay in the factory?Think it through. Then check your answer.Question
A worker noticed that the hour hand on the factory clock had moved by 225 degrees during her stay at the factory. For how long did she stay in the factory?Correct answer
(D) 7.5 hours
Step-by-step solution
The hour hand of a clock completes one full rotation (360 degrees) in 12 hours.
Degrees per hour = per hour.
If the hour hand moved by , the time duration is hours.4
Q4MCQ1 markEasyThe sum and product of two integers are 26 and 165 respectively. The difference between these two integers is ______.Think it through. Then check your answer.Question
The sum and product of two integers are 26 and 165 respectively. The difference between these two integers is ______.Correct answer
(C) 4
Step-by-step solution
Let the two integers be and .
Given:
We know the identity:
Substituting the given values:
Taking the square root:
The difference between the two integers is 4.5
Q5MCQ1 markEasyThe minister avoided any mention of the issue of women's reservation in the private sector. He was accused of ______ the issue.Think it through. Then check your answer.Question
The minister avoided any mention of the issue of women's reservation in the private sector. He was accused of ______ the issue.Correct answer
(B) skirting
Step-by-step solution
The context of the sentence is that the minister avoided talking about a specific issue. To "skirt" an issue means to avoid dealing with it or talking about it directly. Therefore, "skirting" is the most appropriate word.6
Q6MCQ2 marksMediumUnder a certain legal system, prisoners are allowed to make one statement. If their statement turns out to be true then they are hanged. If the statement turns out to be false…Think it through. Then check your answer.Question
Under a certain legal system, prisoners are allowed to make one statement. If their statement turns out to be true then they are hanged. If the statement turns out to be false then they are shot. One prisoner made a statement and the judge had no option but to set him free. Which one of the following could be that statement?Correct answer
(C) I will be shot
Step-by-step solution
This is a classic logical paradox. Let's analyze the statement "I will be shot":1.If the statement is true, according to the rules, the prisoner must be hanged. However, if he is hanged, the statement "I will be shot" becomes false. This is a contradiction.2.If the statement is false, according to the rules, the prisoner must be shot. However, if he is shot, the statement "I will be shot" becomes true. This is also a contradiction.Since neither rule can be applied without creating a logical contradiction, the judge has no choice but to set the prisoner free.7
Q7MCQ2 marksMediumA person divided an amount of Rs. 100,000 into two parts and invested in two different schemes. In one he got 10% profit and in the other he got 12%. If the profit percentages are…Think it through. Then check your answer.Question
A person divided an amount of Rs. 100,000 into two parts and invested in two different schemes. In one he got 10% profit and in the other he got 12%. If the profit percentages are interchanged with these investments he would have got Rs. 120 less. Find the ratio between his investments in the two schemes.Correct answer
(D) 47: 53
Step-by-step solution
Let the investments in the two schemes be and respectively.
Total investment: --- (1)
Profit in the first case:
Profit in the second case (interchanged):
Given that :
--- (2)
Adding equations (1) and (2):
Substituting in (1):
The ratio between the investments is .8
Q8MCQ2 marksEasyCongo was named by Europeans. Congo’s dictator Mobuto later changed the name of the country and the river to Zaire with the objective of Africanising names of persons and spaces.…Think it through. Then check your answer.Question
Congo was named by Europeans. Congo’s dictator Mobuto later changed the name of the country and the river to Zaire with the objective of Africanising names of persons and spaces. However, the name Zaire was a Portuguese alteration of Nzadi o Nzere, a local African term meaning ‘River that swallows Rivers’. Zaire was the Portuguese name for the Congo river in the 16th and 17th centuries.
Which one of the following statements can be inferred from the paragraph above?Correct answer
(A) Mobuto was not entirely successful in Africanising the name of his country
Step-by-step solution
Mobuto's objective was to Africanise names. He chose the name 'Zaire'. However, the passage states that 'Zaire' was a Portuguese alteration of a local term and was used by the Portuguese in the 16th and 17th centuries. This implies that by choosing a name with significant European (Portuguese) influence, Mobuto did not fully achieve his goal of pure Africanisation. Thus, statement (A) is a valid inference.9
Q9MCQ2 marksMediumA firm hires employees at five different skill levels P, Q, R, S, T. The shares of employment at these skill levels of total employment in 2010 is given in the pie chart as shown.…Think it through. Then check your answer.Question
A firm hires employees at five different skill levels P, Q, R, S, T. The shares of employment at these skill levels of total employment in 2010 is given in the pie chart as shown. There were a total of 600 employees in 2010 and the total employment increased by 15% from 2010 to 2016. The total employment at skill levels P, Q and R remained unchanged during this period. If the employment at skill level S increased by 40% from 2010 to 2016, how many employees were there at skill level T in 2016?
Correct answer
(C) 60
Step-by-step solution
Total employees in 2010 = 600.
From the pie chart, the number of employees at each level in 2010:
P:
Q:
R:
S:
T: Total employment in 2016 = .
In 2016:
P, Q, and R remain unchanged: .
Employment at level S increased by 40%: .
Total employment in 2016 is the sum of all levels:
.10
Q10MCQ2 marksMediumand had four children , , and . Of them, only and were married. They had children and respectively. If is a legitimate child of , which…Think it through. Then check your answer.Question
and had four children , , and . Of them, only and were married. They had children and respectively. If is a legitimate child of , which one of the following statements is necessarily FALSE?Correct answer
(D) W is the wife of P
Step-by-step solution
From the problem statement:1. and are the parents of four children: and .2.Only and are married. The mention of children and 'respectively' indicates that is the parent of and is the parent of in separate marital units.3. is a legitimate child of . Since is also the child of , and must be the parents of . For to be a legitimate child, must be the spouse of .Evaluating the statements:- (A) is the grandmother of : This is possible if is the mother of . It is not necessarily false.
- (B) is the father of : This is possible if is male. It is not necessarily false.
- (C) is the wife of : This is possible if is male and is female. It is not necessarily false.
- (D) is the wife of : Since is the spouse of , and is the sibling of , cannot be the wife of (assuming monogamy and that siblings are not married to each other). Therefore, this statement is necessarily FALSE.
Mechanical Engineering (Set 1)
5511
Q11MCQ1 markEasyConsider the matrix The number of distinct eigenvalues of isThink it through. Then check your answer.Question
Consider the matrixThe number of distinct eigenvalues of isCorrect answer
(B) 1
Step-by-step solution
The matrix is an upper triangular matrix. The eigenvalues of an upper triangular matrix are its diagonal elements. Here, the diagonal elements are 1, 1, and 1. Thus, the only eigenvalue is 1. The number of distinct eigenvalues is 1.12
Q12MCQ1 markMediumA parabola with is shown in the figure. The volume of the solid of rotation obtained by rotating the shaded area by around the -axis is…Think it through. Then check your answer.Question
A parabola with is shown in the figure. The volume of the solid of rotation obtained by rotating the shaded area by around the -axis is
Correct answer
(B) (π)/(2)
Step-by-step solution
The volume of the solid of rotation obtained by rotating a curve about the -axis from to is given by:Given the parabola , we have . The limits for are .13
Q13MCQ1 markEasyFor the equation , if , then the value of isThink it through. Then check your answer.Question
For the equation , if , then the value of isCorrect answer
(C) (3)/(7) e^(-7/3)
Step-by-step solution
The given differential equation is:This is a first-order separable differential equation:Integrating both sides:Using the initial condition :So, the solution is:To find :14
Q14MCQ1 markMediumThe lengths of a large stock of titanium rods follow a normal distribution with a mean () of and a standard deviation () of . What is the…Think it through. Then check your answer.Question
The lengths of a large stock of titanium rods follow a normal distribution with a mean () of and a standard deviation () of . What is the percentage of rods whose lengths lie between and ?Correct answer
(A) 81.85\%
Step-by-step solution
Given:
Mean () =
Standard deviation () = We need to find the percentage of rods with lengths between and , which is .First, convert the values to the standard normal variable using the formula:For :For :The required probability is :Using standard normal distribution tables:
Substituting these values:To find the percentage:Thus, the correct option is (A).15
Q15MCQ1 markMediumA flat-faced follower is driven using a circular eccentric cam rotating at a constant angular velocity . At time , the vertical position of the follower is…Think it through. Then check your answer.Question
A flat-faced follower is driven using a circular eccentric cam rotating at a constant angular velocity . At time , the vertical position of the follower is , and the system is in the configuration shown below.The vertical position of the follower face, is given by
Correct answer
(C) e(1 - cos ω t)
Step-by-step solution
For a circular eccentric cam with eccentricity and radius , the distance from the center of rotation to the flat-faced follower is given by if the follower is at its lowest position at . Given that the angular velocity is constant, the angle of rotation is . At , the follower is at its lowest position as shown by the dashed circle in the diagram. The distance from the center of rotation to the follower face is:At any time , the cam has rotated by . The vertical distance from the center of rotation to the follower face is:The vertical displacement is the change in position from the initial state at :Thus, the correct option is (C).16
Q16MCQ1 markEasyThe natural frequencies corresponding to the spring-mass systems I and II are and , respectively. The ratio is [figure]Think it through. Then check your answer.Question
The natural frequencies corresponding to the spring-mass systems I and II are and , respectively. The ratio is
Correct answer
(B) (1)/(2)
Step-by-step solution
For SYSTEM I, the two springs are connected in series. The equivalent stiffness is calculated as:The natural frequency is:For SYSTEM II, the two springs are connected in parallel. The equivalent stiffness is:The natural frequency is:The ratio of the natural frequencies is:Therefore, the correct option is (B).17
Q17MCQ1 markMediumA spur gear with full depth teeth is transmitting at . The pitch circle diameter of the gear is . The magnitude of the…Think it through. Then check your answer.Question
A spur gear with full depth teeth is transmitting at . The pitch circle diameter of the gear is . The magnitude of the force applied on the gear in the radial direction isCorrect answer
(B) 0.73 kN
Step-by-step solution
Given:
Power
Angular velocity
Pitch circle diameter Radius
Pressure angle Step 1: Calculate the torque ()Step 2: Calculate the tangential force ()Step 3: Calculate the radial force ()Hence, the correct option is (B).18
Q18MCQ1 markEasyDuring a non-flow thermodynamic process (1-2) executed by a perfect gas, the heat interaction is equal to the work interaction () when the process isThink it through. Then check your answer.Question
During a non-flow thermodynamic process (1-2) executed by a perfect gas, the heat interaction is equal to the work interaction () when the process isCorrect answer
(C) Isothermal
Step-by-step solution
From the First Law of Thermodynamics for a non-flow process:Given that , it implies that the change in internal energy .For a perfect gas, internal energy is a function of temperature only (). Therefore, implies that the temperature remains constant throughout the process ().A process occurring at constant temperature is called an isothermal process.Hence, the correct option is (C).19
Q19MCQ1 markMediumFor a hydrodynamically and thermally fully developed laminar flow through a circular pipe of constant cross-section, the Nusselt number at constant wall heat flux () and…Think it through. Then check your answer.Question
For a hydrodynamically and thermally fully developed laminar flow through a circular pipe of constant cross-section, the Nusselt number at constant wall heat flux () and that at constant wall temperature () are related asCorrect answer
(A) Nu_q Nu_T
Step-by-step solution
For a hydrodynamically and thermally fully developed laminar flow in a circular pipe, the Nusselt numbers are standard constant values:1.Constant wall heat flux ():2.Constant wall temperature ():Comparing the two values, we have , which means .Hence, the correct option is (A).20
Q20MCQ1 markEasyAs per common design practice, the three types of hydraulic turbines, in descending order of flow rate, areThink it through. Then check your answer.Question
As per common design practice, the three types of hydraulic turbines, in descending order of flow rate, areCorrect answer
(A) Kaplan, Francis, Pelton
Step-by-step solution
Hydraulic turbines are classified based on their specific speed and flow rate requirements. Kaplan turbines have the highest specific speed and are designed for high flow rates at low heads. Francis turbines are medium specific speed turbines for medium flow rates and heads. Pelton wheels are low specific speed turbines designed for low flow rates at high heads. Therefore, the descending order of flow rate is Kaplan, Francis, Pelton.21
Q21MCQ1 markEasyA slender rod of length , diameter () and thermal conductivity is joined with another rod of identical dimensions, but of thermal conductivity , to form…Think it through. Then check your answer.Question
A slender rod of length , diameter () and thermal conductivity is joined with another rod of identical dimensions, but of thermal conductivity , to form a composite cylindrical rod of length . The heat transfer in radial direction and contact resistance are negligible. The effective thermal conductivity of the composite rod isCorrect answer
(D) (2 k₁ k₂)/(k₁ + k₂)
Step-by-step solution
The two rods are connected in series. The total thermal resistance is the sum of the individual thermal resistances and .
For a cylindrical rod, thermal resistance is given by , where is length, is thermal conductivity, and is cross-sectional area.
Dividing by :22
Q22MCQ1 markMediumConsider an ideal vapor compression refrigeration cycle. If the throttling process is replaced by an isentropic expansion process, keeping all the other processes unchanged, which…Think it through. Then check your answer.Question
Consider an ideal vapor compression refrigeration cycle. If the throttling process is replaced by an isentropic expansion process, keeping all the other processes unchanged, which one of the following statements is true for the modified cycle?Correct answer
(A) Coefficient of performance is higher than that of the original cycle.
Step-by-step solution
In a standard vapor compression refrigeration cycle (VCRS), the expansion process is a throttling process, which is isenthalpic (). If this is replaced by an isentropic expansion process (), the enthalpy at the end of expansion () will be lower than . This results in two improvements:1.The refrigerating effect () increases because .2.The expander produces work output (), which can be used to reduce the net work input required for the cycle ().Since , an increase in and a decrease in both contribute to a higher Coefficient of Performance (COP).23
Q23MCQ1 markEasyIn a casting process, a vertical channel through which molten metal flows downward from pouring basin to runner for reaching the mold cavity is calledThink it through. Then check your answer.Question
In a casting process, a vertical channel through which molten metal flows downward from pouring basin to runner for reaching the mold cavity is calledCorrect answer
(B) sprue
Step-by-step solution
In the gating system of a sand casting process, the molten metal is poured into a pouring basin. From there, it flows through a vertical channel called the sprue. The sprue leads to horizontal channels called runners, which then distribute the metal to the mold cavity through gates.- Blister is a casting defect.
- Riser is a reservoir of molten metal used to compensate for shrinkage during solidification.
- Pin hole is a type of gas porosity defect.
24
Q24MCQ1 markEasyWhich one of the following welding methods provides the highest heat flux ()?Think it through. Then check your answer.Question
Which one of the following welding methods provides the highest heat flux ()?Correct answer
(D) Laser beam welding
Step-by-step solution
Heat flux (power density) refers to the amount of energy delivered per unit area.- Oxy-acetylene welding has the lowest heat flux ().
- TIG welding has a moderate heat flux ().
- Plasma arc welding has a higher heat flux ().
- Laser beam welding (and Electron beam welding) provides the highest heat flux () because the energy is concentrated into an extremely small spot size.
25
Q25MCQ1 markMediumThe length, width and thickness of a steel sample are , and , respectively. Its thickness needs to be uniformly reduced by…Think it through. Then check your answer.Question
The length, width and thickness of a steel sample are , and , respectively. Its thickness needs to be uniformly reduced by in a single pass by using horizontal slab milling. The milling cutter (diameter: , width: ) has teeth and rotates at . The feed per tooth is . The feed direction is along the length of the sample. If the over-travel distance is the same as the approach distance, the approach distance and time taken to complete the required machining task areCorrect answer
(D) 14 mm, 21.4 s
Step-by-step solution
Given:
Length of workpiece () =
Depth of cut () =
Cutter diameter () =
Number of teeth () =
Rotational speed () =
Feed per tooth () =1.Approach distance ():For slab milling, .2.Total length of travel ():Over-travel () = Approach distance () = .
.3.Table feed rate ():.4.Machining time ():.
Converting to seconds: .Thus, the approach distance is and the time taken is .26
Q26MCQ1 markMediumThe position vector of point is rotated anti-clockwise in X-Y plane by an angle such that point occupies position , as shown in…Think it through. Then check your answer.Question
The position vector of point is rotated anti-clockwise in X-Y plane by an angle such that point occupies position , as shown in the figure. The coordinates of are
Correct answer
(C) (12.32, 18.66)
Step-by-step solution
The rotation of a point by an angle anti-clockwise about the origin is given by the rotation matrix:Given and :Thus, the coordinates of are . Correct option is (C).27
Q27MCQ1 markEasyThe table presents the demand of a product. By simple three-months moving average method, the demand-forecast of the product for the month of September is | Month | Demand | |…Think it through. Then check your answer.Question
The table presents the demand of a product. By simple three-months moving average method, the demand-forecast of the product for the month of September isMonth Demand January 450 February 440 March 460 April 510 May 520 June 495 July 475 August 560 Correct answer
(B) 510
Step-by-step solution
The simple three-months moving average forecast for September is the average of the demands for the three preceding months: June, July, and August.Correct option is (B).28
Q28NAT1 markEasyEvaluation of using a 2-equal-segment trapezoidal rule gives a value of ________.Think it through. Then check your answer.Question
Evaluation of using a 2-equal-segment trapezoidal rule gives a value of ________.Correct answer
63 to 63
Step-by-step solution
For the integral using equal segments, the step size is .
Here, , so .
The points are .
The function values are:
Using the trapezoidal rule:29
Q29NAT1 markEasyA block of mass 10 kg rests on a horizontal floor. The acceleration due to gravity is . The coefficient of static friction between the floor and the block is…Think it through. Then check your answer.Question
A block of mass 10 kg rests on a horizontal floor. The acceleration due to gravity is . The coefficient of static friction between the floor and the block is 0.2. A horizontal force of 10 N is applied on the block as shown in the figure. The magnitude of force of friction (in N) on the block is ______
Correct answer
10 to 10
Step-by-step solution
First, we calculate the normal force acting on the block:
Next, we determine the maximum possible static friction force :
The applied horizontal force is .
Since the applied force (10 N) is less than the maximum static friction force (19.62 N), the block will not move. It remains in static equilibrium.
In static equilibrium, the friction force must exactly balance the applied force to prevent motion:30
Q30NAT1 markMediumA cylindrical rod of diameter and length is fixed at one end. The other end is twisted by an angle of by applying a torque. If the maximum…Think it through. Then check your answer.Question
A cylindrical rod of diameter and length is fixed at one end. The other end is twisted by an angle of by applying a torque. If the maximum shear strain in the rod is , then is equal to ______ (round off to two decimal places).Correct answer
0.8 to 0.9
Step-by-step solution
1.The maximum shear strain () in a cylindrical rod of radius and length subjected to an angle of twist is given by:2.Given:- Diameter radius
- Length
- Angle of twist
4.The question states the maximum shear strain is .5.Rounding off to two decimal places, we get .31
Q31NAT1 markMediumA solid cube of side is kept at a room temperature of . The coefficient of linear thermal expansion of the cube material is…Think it through. Then check your answer.Question
A solid cube of side is kept at a room temperature of . The coefficient of linear thermal expansion of the cube material is and the bulk modulus is . If the cube is constrained all around and heated uniformly to , then the magnitude of volumetric (mean) stress (in MPa) induced due to heating is ______.Correct answer
59.5 to 60.5
Step-by-step solution
1.When a solid cube is constrained in all directions and heated uniformly, it experiences a state of hydrostatic stress.2.The volumetric strain that would occur if the cube were free to expand is:where is the coefficient of linear thermal expansion and is the change in temperature.3.Since the cube is fully constrained, the net volumetric strain is zero. This induces a compressive volumetric (mean) stress such that:where is the bulk modulus.4.Given:32
Q32NAT1 markMediumDuring a high cycle fatigue test, a metallic specimen is subjected to cyclic loading with a mean stress of MPa, and a minimum stress of MPa. The -ratio (minimum…Think it through. Then check your answer.Question
During a high cycle fatigue test, a metallic specimen is subjected to cyclic loading with a mean stress of MPa, and a minimum stress of MPa. The -ratio (minimum stress to maximum stress) for this cyclic loading is ______ (round off to one decimal place)Correct answer
-0.2
Step-by-step solution
Given:
Mean stress, MPa
Minimum stress, MPaWe know that mean stress is given by:The -ratio is defined as the ratio of minimum stress to maximum stress:33
Q33NAT1 markMediumWater flows through a pipe with a velocity given by m/s, where is the unit vector in the direction, (…Think it through. Then check your answer.Question
Water flows through a pipe with a velocity given by m/s, where is the unit vector in the direction, () is in seconds, and and are in meters. The magnitude of total acceleration at the point at s is ______ m/s.Correct answer
3 to 3
Step-by-step solution
The velocity vector is , where .
The components of velocity are , , and .The acceleration components are:
Calculating the partial derivatives for :
Substituting these into the expression for :
At the point and s:
The magnitude of total acceleration is:34
Q34NAT1 markEasyAir of mass , initially at and , is allowed to expand isothermally till it reaches a pressure of . Assuming air as an…Think it through. Then check your answer.Question
Air of mass , initially at and , is allowed to expand isothermally till it reaches a pressure of . Assuming air as an ideal gas with gas constant of , the change in entropy of air (in , round off to two decimal places) is _______Correct answer
0.64 to 0.68
Step-by-step solution
For an ideal gas, the change in specific entropy is given by the relation:For an isothermal process, the temperature remains constant (), which simplifies the equation to:Given:- Mass of air,
- Gas constant,
- Initial pressure,
- Final pressure,
35
Q35NAT1 markEasyConsider the stress-strain curve for an ideal elastic-plastic strain hardening metal as shown in the figure. The metal was loaded in uniaxial tension starting from O. Upon…Think it through. Then check your answer.Question
Consider the stress-strain curve for an ideal elastic-plastic strain hardening metal as shown in the figure. The metal was loaded in uniaxial tension starting from O. Upon loading, the stress-strain curve passes through initial yield point at P, and then strain hardens to point Q, where the loading was stopped. From point Q, the specimen was unloaded to point R, where the stress is zero. If the same specimen is reloaded in tension from point R, the value of stress at which the material yields again is _____ MPa.Correct answer
210 to 210
Step-by-step solution
For an ideal elastic-plastic strain hardening material, when it is loaded beyond the initial yield point to a point in the strain-hardening region, it undergoes plastic deformation. Upon unloading from , the material follows an elastic path parallel to the initial elastic region . When reloaded from point , it will follow the same elastic path back to point . The material will only begin to yield again when the stress reaches the maximum stress level it had previously experienced, which is the stress at point . From the provided stress-strain curve, the stress at point is MPa. Therefore, the new yield stress is MPa.36
Q36MCQ2 marksMediumThe set of equations has infinite solutions, ifThink it through. Then check your answer.Question
The set of equationshas infinite solutions, ifCorrect answer
(C) 4
Step-by-step solution
For a system of linear equations to have infinite solutions, the determinant of the coefficient matrix must be zero, and the rank of the augmented matrix must be equal to the rank of , which must be less than the number of variables (3).The coefficient matrix is .
Setting :
.Case 1:
Augmented matrix
Performing row operations:
Here, . Thus, infinite solutions exist for .Case 2:
Augmented matrix
Here, and . Thus, no solution exists for .37
Q37MCQ2 marksEasyA harmonic function is analytic if it satisfies the Laplace equation. If is a harmonic function, then its conjugate harmonic function isThink it through. Then check your answer.Question
A harmonic function is analytic if it satisfies the Laplace equation. If is a harmonic function, then its conjugate harmonic function isCorrect answer
(A) 4xy - 2x² + 2y² + constant
Step-by-step solution
Given . For to be the conjugate harmonic function, the Cauchy-Riemann equations must be satisfied:
1)
2) From (1):
So, Now, differentiate with respect to :
From (2):
So,
Substituting back into the expression for :
This matches option (A).38
Q38MCQ2 marksMediumThe variable takes a value between 0 and 10 with uniform probability distribution. The variable takes a value between 0 and 20 with uniform probability distribution. The…Think it through. Then check your answer.Question
The variable takes a value between 0 and 10 with uniform probability distribution. The variable takes a value between 0 and 20 with uniform probability distribution. The probability of the sum of variables being greater than 20 isCorrect answer
(B) 0.25
Step-by-step solution
The joint probability density function for independent uniform random variables and is for and . The total area of the sample space is . We want to find . The region within the rectangle is a triangle with vertices , , and . The area of this triangle is . Thus, the probability is .39
Q39MCQ2 marksMediumA car having weight is moving in the direction as shown in the figure. The center of gravity (CG) of the car is located at height from the ground, midway between the front…Think it through. Then check your answer.Question
A car having weight is moving in the direction as shown in the figure. The center of gravity (CG) of the car is located at height from the ground, midway between the front and rear wheels. The distance between the front and rear wheels is . The acceleration of the car is , and acceleration due to gravity is . The reactions on the front wheels () and rear wheels () are given by
Correct answer
(C) R_f = (W)/(2) - (W)/(g) ((h)/(l)) a; Rᵣ = (W)/(2) + (W)/(g) ((h)/(l)) a
Step-by-step solution
Using D'Alembert's principle, an inertial force acts at the CG in the direction opposite to the motion (to the left).1.Vertical equilibrium: .2.Taking moments about the rear wheel contact point: .Solving for : .
Then, .40
Q40MCQ2 marksMediumIn a four bar planar mechanism shown in the figure, , and . In the configuration shown, both and are perpendicular…Think it through. Then check your answer.Question
In a four bar planar mechanism shown in the figure, , and . In the configuration shown, both and are perpendicular to . The bar rotates with an angular velocity of . The magnitude of angular velocity (in rad/s) of bar at this instant is
Correct answer
(D) 25
Step-by-step solution
Using the property of instantaneous centers for a four-bar mechanism: .
Let be the origin . Then is , is , and is .
is at and is at .
is the intersection of the fixed link and the coupler link .
The line is .
The line passes through and . Its equation is .
Intersection occurs at .
Distance .
Distance .
Applying the formula: .41
Q41MCQ2 marksMediumThe rotor of a turbojet engine of an aircraft has a mass 180 kg and polar moment of inertia about the rotor axis. The rotor rotates at a constant…Think it through. Then check your answer.Question
The rotor of a turbojet engine of an aircraft has a mass 180 kg and polar moment of inertia about the rotor axis. The rotor rotates at a constant speed of 1100 rad/s in the clockwise direction when viewed from the front of the aircraft. The aircraft while flying at a speed of 800 km per hour takes a turn with a radius of 1.5 km to the left. The gyroscopic moment exerted by the rotor on the aircraft structure and the direction of motion of the nose when the aircraft turns, areCorrect answer
(B) 1629.6 N·m and the nose goes down
Step-by-step solution
1.Calculate Angular Velocity of Rotor ():. Since it is clockwise viewed from the front, the spin vector points towards the rear of the aircraft.2.Calculate Angular Velocity of Precession ():Velocity .
Radius .
.
For a left turn, the precession vector points upwards.3.Calculate Gyroscopic Moment ():.4.Determine Direction of Nose Motion:Using the right-hand rule:- Spin vector is backward ( direction).
- Precession vector is upward ( direction).
- Active gyroscopic couple (towards the left).
- Reactive gyroscopic couple (towards the right).
42
Q42MCQ2 marksHardThe wall of a constant diameter pipe of length 1 m is heated uniformly with flux by wrapping a heater coil around it. The flow at the inlet to the pipe is hydrodynamically…Think it through. Then check your answer.Question
The wall of a constant diameter pipe of length 1 m is heated uniformly with flux by wrapping a heater coil around it. The flow at the inlet to the pipe is hydrodynamically fully developed. The fluid is incompressible and the flow is assumed to be laminar and steady all through the pipe. The bulk temperature of the fluid is equal to at the inlet and at the exit. The wall temperatures are measured at three locations, P, Q and R, as shown in the figure. The flow thermally develops after some distance from the inlet. The following measurements are made:Point P Q R Wall Temp () 50 80 90 Among the locations P, Q and R, the flow is thermally developed at
Correct answer
(C) Q and R only
Step-by-step solution
1.Analyze Bulk Temperature ():For a constant wall heat flux , the bulk temperature of the fluid increases linearly along the length of the pipe.
.2.Calculate at points P, Q, and R:- At P (): .
- At Q (): .
- At R (): .
In the thermally developed region with constant heat flux, the heat transfer coefficient is constant. Since , the temperature difference must be constant.- At P: .
- At Q: .
- At R: .
The temperature difference is constant at points Q and R (), but different at P. Therefore, the flow is thermally developed at Q and R only.43
Q43MCQ2 marksMediumA gas is heated in a duct as it flows over a resistance heater. Consider a 101 kW electric heating system. The gas enters the heating section of the duct at 100 kPa and…Think it through. Then check your answer.Question
A gas is heated in a duct as it flows over a resistance heater. Consider a 101 kW electric heating system. The gas enters the heating section of the duct at 100 kPa and with a volume flow rate of . If heat is lost from the gas in the duct to the surroundings at a rate of 51 kW, the exit temperature of the gas is(Assume constant pressure, ideal gas, negligible change in kinetic and potential energies and constant specific heat; ; )Correct answer
(A) 32^
Step-by-step solution
1.Calculate Net Heat Addition ():.2.Calculate Mass Flow Rate ():Using the ideal gas law: .
.3.Apply Energy Balance Equation:.
.
.
.44
Q44MCQ2 marksMediumA plane-strain compression (forging) of a block is shown in the figure. The strain in the -direction is zero. The yield strength () in uniaxial tension/compression of the…Think it through. Then check your answer.Question
A plane-strain compression (forging) of a block is shown in the figure. The strain in the -direction is zero. The yield strength () in uniaxial tension/compression of the material of the block is and it follows the Tresca (maximum shear stress) criterion. Assume that the entire block has started yielding. At a point where (compressive) and , the stress component is
Correct answer
(A) 340 MPa (compressive)
Step-by-step solution
In plane strain forging, . For an isotropic material undergoing plastic deformation, the Poisson's ratio , which leads to the stress in the -direction being the average of the other two principal stresses: . This makes the intermediate principal stress. The Tresca criterion states that yielding occurs when the maximum shear stress reaches half the yield strength, or . Given (compressive). In a compression process like forging, the vertical stress is also compressive and typically larger in magnitude than the lateral stress . Thus, let and . Applying the Tresca criterion: . Therefore, (compressive).45
Q45MCQ2 marksHardIn orthogonal turning of a cylindrical tube of wall thickness , the axial and the tangential cutting forces were measured as and ,…Think it through. Then check your answer.Question
In orthogonal turning of a cylindrical tube of wall thickness , the axial and the tangential cutting forces were measured as and , respectively. The measured chip thickness after machining was found to be . The rake angle was and the axial feed was . The rotational speed of the spindle was . Assuming the material to be perfectly plastic and Merchant's first solution, the shear strength of the material is closest toCorrect answer
(A) 722 MPa
Step-by-step solution
1.Calculate feed per revolution (): . For orthogonal turning of a tube, uncut chip thickness .2.Calculate chip thickness ratio (): .3.Calculate shear angle (): .4.Use Merchant's first solution to find friction angle (): .5.Calculate shear force (): Given tangential force and axial (thrust) force . .6.Calculate shear area (): , where (wall thickness). .7.Calculate shear strength (): .46
Q46MCQ2 marksMediumA circular shaft having diameter is manufactured by turning process. A thick coating of TiN is deposited on the shaft.…Think it through. Then check your answer.Question
A circular shaft having diameter is manufactured by turning process. A thick coating of TiN is deposited on the shaft. Allowed variation in TiN film thickness is . The minimum hole diameter (in mm) to just provide clearance fit isCorrect answer
(B) 65.12
Step-by-step solution
1.Determine the maximum diameter of the uncoated shaft: .2.Determine the maximum thickness of the TiN coating: .3.The coating is applied to the entire circumference, so the diameter increases by twice the coating thickness. Maximum coated shaft diameter: .4.To ensure a clearance fit even in the worst-case scenario (largest shaft), the minimum hole diameter must be equal to the maximum coated shaft diameter. Therefore, minimum hole diameter .47
Q47MCQ2 marksEasyMatch the following sand mold casting defects with their respective causes. | | Defect | | Cause | |---|---|---|---| | P | Blow hole | 1 | Poor collapsibility | | Q | Misrun | 2 |…Think it through. Then check your answer.Question
Match the following sand mold casting defects with their respective causes.Defect Cause P Blow hole 1 Poor collapsibility Q Misrun 2 Mold erosion R Hot tearing 3 Poor permeability S Wash 4 Insufficient fluidity Correct answer
(D) P-3, Q-4, R-1, S-2
Step-by-step solution
The correct matching for sand mold casting defects and their causes is:- Blow hole (P) is caused by gas entrapment, which occurs when the mold has poor permeability (3).
- Misrun (Q) occurs when the molten metal solidifies before completely filling the mold cavity, typically due to insufficient fluidity (4).
- Hot tearing (R) refers to cracks formed during cooling when the mold resists the contraction of the casting, often due to poor collapsibility (1).
- Wash (S) is a defect where the mold surface is eroded by the flow of molten metal, caused by mold erosion (2).
48
Q48NAT2 marksMediumA truss is composed of members AB, BC, CD, AD and BD, as shown in the figure. A vertical load of 10 kN is applied at point D. The magnitude of force (in kN) in the member BC is…Think it through. Then check your answer.Question
A truss is composed of members AB, BC, CD, AD and BD, as shown in the figure. A vertical load of 10 kN is applied at point D. The magnitude of force (in kN) in the member BC is ______
Correct answer
4.98 to 5.02
Step-by-step solution
1.Analyze the overall equilibrium of the truss:Due to the symmetry of the truss and the loading, the vertical reactions at the supports and are equal:
2.Analyze joint B:Joint is a connection between members , , and . Since there is no vertical external load or reaction at joint , the vertical member must be a zero-force member to satisfy vertical equilibrium (). Thus, .
For horizontal equilibrium at joint : .3.Analyze joint C:The forces acting at joint are the reaction kN (upwards), the force in member (, horizontal), and the force in member (, at to the horizontal).
For vertical equilibrium at joint :
4.Calculate the force in member BC:For horizontal equilibrium at joint :
Therefore, the magnitude of the force in member is 5 kN.49
Q49NAT2 marksMediumConsider an elastic straight beam of length m, with square cross-section of side mm, and Young's modulus GPa. This straight beam was bent in such a…Think it through. Then check your answer.Question
Consider an elastic straight beam of length m, with square cross-section of side mm, and Young's modulus GPa. This straight beam was bent in such a way that the two ends meet, to form a circle of mean radius . Assuming that Euler-Bernoulli beam theory is applicable to this bending problem, the maximum tensile bending stress in the bent beam is ______ MPa.
Correct answer
99 to 101
Step-by-step solution
1.Determine the radius of curvature ():The beam of length is bent into a full circle. The circumference of this circle is equal to the length of the beam:
Given m:
2.Apply the bending stress formula:According to the Euler-Bernoulli bending equation:
where is the bending stress, is the distance from the neutral axis, is Young's modulus, and is the radius of curvature.3.Calculate the maximum tensile stress:The maximum tensile stress occurs at the fiber furthest from the neutral axis (). For a square cross-section of side mm:
Given GPa MPa:
Therefore, the maximum tensile bending stress is 100 MPa.50
Q50NAT2 marksMediumConsider a prismatic straight beam of length m, pinned at the two ends as shown in the figure. The beam has a square cross-section of side mm. The Young's…Think it through. Then check your answer.Question
Consider a prismatic straight beam of length m, pinned at the two ends as shown in the figure. The beam has a square cross-section of side mm. The Young's modulus GPa, and the coefficient of thermal expansion . The minimum temperature rise required to cause Euler buckling of the beam is _______ K.
Correct answer
1 to 1
Step-by-step solution
For a pinned-pinned beam, the Euler buckling load is given by:Given m, we have:The thermal force developed in the beam due to a temperature rise is:For buckling to occur, the thermal force must reach the critical buckling load:For a square cross-section of side , the area and the moment of inertia . Substituting these:Substituting the given values m and :51
Q51NAT2 marksHardIn a UTM experiment, a sample of length 100 mm, was loaded in tension until failure. The failure load was 40 kN. The displacement, measured using the cross-head motion, at…Think it through. Then check your answer.Question
In a UTM experiment, a sample of length 100 mm, was loaded in tension until failure. The failure load was 40 kN. The displacement, measured using the cross-head motion, at failure, was 15 mm. The compliance of the UTM is constant and is given by m/N. The strain at failure in the sample is ________ %.Correct answer
12 to 14
Step-by-step solution
Given:
Original length of sample, mm = 0.1 m
Failure load, kN = N
Total displacement (cross-head motion), mm = m
Compliance of UTM, m/NThe total displacement measured by the cross-head is the sum of the displacement of the sample and the displacement of the machine itself due to its compliance.
Displacement of the machine:
mmDisplacement of the sample:
mmStrain at failure in the sample:
In percentage:
The strain at failure in the sample is 13%.52
Q52NAT2 marksMediumAt a critical point in a component, the state of stress is given as MPa, MPa, MPa and all other stress…Think it through. Then check your answer.Question
At a critical point in a component, the state of stress is given as MPa, MPa, MPa and all other stress components are zero. The yield strength of the material is 468 MPa. The factor of safety on the basis of maximum shear stress theory is ________ (round off to one decimal place).Correct answer
1.7 to 1.9
Step-by-step solution
Given state of stress:
MPa
MPa
MPa
Yield strength, MPaStep 1: Calculate principal stresses and . MPa
MPa
Since it's a 2D state of stress and both are positive, .Step 2: Calculate maximum shear stress .Step 3: Apply Maximum Shear Stress Theory (Tresca Criterion).
According to Tresca theory, yielding occurs when .The factor of safety is 1.8.53
Q53NAT2 marksHardA uniform thin disk of mass and radius is kept on a surface as shown in the figure. A spring of stiffness is connected to the…Think it through. Then check your answer.Question
A uniform thin disk of mass and radius is kept on a surface as shown in the figure. A spring of stiffness is connected to the disk center and another spring of stiffness is connected at point just above point on the circumference of the disk. Initially, both the springs are unstretched. Assume pure rolling of the disk. For small disturbance from the equilibrium, the natural frequency of vibration of the system is ______ (round off to one decimal place).Correct answer
23 to 24
Step-by-step solution
1.Given Data:- Mass of disk,
- Radius of disk,
- Stiffness (at center )
- Stiffness (at point , distance from contact point)
For pure rolling, the instantaneous center of rotation (ICR) is the point of contact with the ground.
3.Equation of Motion:Let the disk rotate by a small angle .- Displacement of center :
- Displacement of point :
Differentiating with respect to time :
4.Natural Frequency:Rounding to one decimal place, we get .54
Q54NAT2 marksMediumA single block brake with a short shoe and torque capacity of is shown. The cylindrical brake drum rotates anticlockwise at and the…55
Q55NAT2 marksMediumTwo immiscible, incompressible, viscous fluids having same densities but different viscosities are contained between two infinite horizontal parallel plates, apart as…Think it through. Then check your answer.Question
Two immiscible, incompressible, viscous fluids having same densities but different viscosities are contained between two infinite horizontal parallel plates, apart as shown below. The bottom plate is fixed and the upper plate moves to the right with a constant velocity of . With the assumptions of Newtonian fluid, steady, and fully developed laminar flow with zero pressure gradient in all directions, the momentum equations simplify to If the dynamic viscosity of the lower fluid, , is twice that of the upper fluid, , then the velocity at the interface (round off to two decimal places) is ______ .Correct answer
0.98 to 1.02
Step-by-step solution
1.Velocity Profile:The equation implies a linear velocity profile in each fluid: .2.Boundary Conditions:- At (bottom plate):
- At (top plate):
- At (interface): (velocity continuity)
- At (interface): (shear stress continuity)
- Lower fluid ():
- Upper fluid ():
Given :
5.Final Answer:The interface velocity is .56
Q56NAT2 marksHardA cube of side 100 mm is placed at the bottom of an empty container on one of its faces. The density of the material of the cube is 800 kg/m. Liquid of density 1000 kg/m…Think it through. Then check your answer.Question
A cube of side 100 mm is placed at the bottom of an empty container on one of its faces. The density of the material of the cube is 800 kg/m. Liquid of density 1000 kg/m is now poured into the container. The minimum height to which the liquid needs to be poured into the container for the cube to just lift up is ______ mm.Correct answer
80 to 80
Step-by-step solution
Let mm be the side of the cube.
Density of the cube kg/m.
Density of the liquid kg/m.
For the cube to just lift up, the upward buoyancy force must equal the weight of the cube.
Assuming the liquid seeps under the cube, the upward force is due to the pressure at the bottom: .
The weight of the cube is .
Equating the two:
.
Since , the cube is partially submerged when it lifts, and the calculation is consistent.57
Q57NAT2 marksMediumThree slabs are joined together as shown in the figure. There is no thermal contact resistance at the interfaces. The center slab experiences a non-uniform internal heat…Think it through. Then check your answer.Question
Three slabs are joined together as shown in the figure. There is no thermal contact resistance at the interfaces. The center slab experiences a non-uniform internal heat generation with an average value equal to 10000 Wm, while the left and right slabs have no internal heat generation. All slabs have thickness equal to 1 m and thermal conductivity of each slab is equal to 5 Wm K. The two extreme faces are exposed to fluid with heat transfer coefficient 100 Wm K and bulk temperature 30 C as shown. The heat transfer in the slabs is assumed to be one dimensional and steady, and all properties are constant. If the left extreme face temperature is measured to be 100 C, the right extreme face temperature is ______ C.
Correct answer
60 to 60
Step-by-step solution
Total heat generated in the center slab per unit area is .
Under steady state, this heat must be dissipated through the left and right faces: .
The heat flux leaving the left face is .
Therefore, the heat flux leaving the right face is .
The heat flux leaving the right face is also given by .
.58
Q58NAT2 marksEasyIf one mole of gas occupies a rigid container with a capacity of 1000 litres and the temperature is raised from to , the change in…Think it through. Then check your answer.Question
If one mole of gas occupies a rigid container with a capacity of 1000 litres and the temperature is raised from to , the change in pressure of the contained gas (round off to two decimal places), assuming ideal gas behaviour, is ________ Pa. ()Correct answer
82.14 to 84.14
Step-by-step solution
Given:- Number of moles () = 1 mol
- Volume () = 1000 litres =
- Initial temperature () =
- Final temperature () =
- Universal gas constant () =
59
Q59NAT2 marksMediumA steam power cycle with regeneration as shown below on the diagram employs a single open feedwater heater for efficiency improvement. The fluids mix with each other in an…Think it through. Then check your answer.Question
A steam power cycle with regeneration as shown below on the diagram employs a single open feedwater heater for efficiency improvement. The fluids mix with each other in an open feedwater heater. The turbine is isentropic and the input (bleed) to the feedwater heater from the turbine is at state 2 as shown in the figure. Process 3-4 occurs in the condenser. The pump work is negligible. The input to the boiler is at state 5. The following information is available from the steam tables:State 1 2 3 4 5 6 Enthalpy (kJ/kg) 3350 2800 2300 175 700 1000 The mass flow rate of steam bled from the turbine as a percentage of the total mass flow rate at the inlet to the turbine at state 1 is _______.
Correct answer
19 to 21
Step-by-step solution
To find the percentage of steam bled from the turbine, we perform an energy balance on the open feedwater heater (OFWH).Let be the total mass flow rate at the turbine inlet (state 1).
Let be the mass flow rate of steam bled from the turbine at state 2.
Let be the fraction of steam bled.In the OFWH, the bled steam at state 2 mixes with the condensate from the condenser at state 4 to produce saturated liquid at state 5. Since pump work is negligible, the state after the condenser pump is assumed to be state 4.Energy balance for the OFWH:Dividing by :From the given table:
kJ/kg
kJ/kg
kJ/kgSubstituting the values:As a percentage:The mass flow rate of steam bled is of the total mass flow rate at the inlet.60
Q60NAT2 marksHardA gas turbine with air as the working fluid has an isentropic efficiency of 0.70 when operating at a pressure ratio of 3. Now, the pressure ratio of the turbine is increased to 5,…Think it through. Then check your answer.Question
A gas turbine with air as the working fluid has an isentropic efficiency of 0.70 when operating at a pressure ratio of 3. Now, the pressure ratio of the turbine is increased to 5, while maintaining the same inlet conditions. Assume air as a perfect gas with specific heat ratio . If the specific work output remains the same for both the cases, the isentropic efficiency of the turbine at the pressure ratio of 5 is ________ (round off to two decimal places)Correct answer
0.5 to 0.52
Step-by-step solution
The specific work output of a turbine is given by:Given that the specific work output remains the same for both cases:Rounding off to two decimal places, the isentropic efficiency is 0.51.61
Q61NAT2 marksEasyThe value of the following definite integral is ________ (round off to three decimal places)Think it through. Then check your answer.Question
The value of the following definite integral is ________ (round off to three decimal places)Correct answer
2.09 to 2.104
Step-by-step solution
Using integration by parts:
Let and . Then and .Evaluating the definite integral from 1 to :Since and :Using :Rounding off to three decimal places, the value is 2.097.62
Q62NAT2 marksMediumIn ASA system, the side cutting and end cutting edge angles of a sharp turning tool are and , respectively. The feed during cylindrical turning is …Think it through. Then check your answer.Question
In ASA system, the side cutting and end cutting edge angles of a sharp turning tool are and , respectively. The feed during cylindrical turning is mm/rev. The center line average surface roughness (in m, round off to one decimal place) of the generated surface is ______.Correct answer
3.5 to 3.9
Step-by-step solution
The center line average (CLA) surface roughness, , for a turning operation is given by the formula:where:
is the feed rate = mm/rev
is the side cutting edge angle (SCEA) =
is the end cutting edge angle (ECEA) = Substitute the given values:We know .
And Convert to m:Rounding off to one decimal place, m.The final answer is .63
Q63NAT2 marksMediumTaylor's tool life equation is given by , where is in m/min and is in min. In a turning operation, two tools X and Y are used. For tool X, and …Think it through. Then check your answer.Question
Taylor's tool life equation is given by , where is in m/min and is in min. In a turning operation, two tools X and Y are used. For tool X, and and for tool Y, and . Both the tools will have the same tool life for the cutting speed (in m/min, round off to one decimal place) of ______.Correct answer
38 to 42
Step-by-step solution
Taylor's tool life equation is .For tool X:
For tool Y:
We are given that both tools will have the same tool life () for the same cutting speed (). So, .From the equation for tool X:
From the equation for tool Y:
We can write as . So, substitute from the first modified equation into the second:
m/minThe cutting speed for which both tools have the same tool life is m/min.The final answer is .64
Q64NAT2 marksMediumFive jobs (J1, J2, J3, J4 and J5) need to be processed in a factory. Each job can be assigned to any of the five different machines (M1, M2, M3, M4 and M5). The time durations…Think it through. Then check your answer.Question
Five jobs (J1, J2, J3, J4 and J5) need to be processed in a factory. Each job can be assigned to any of the five different machines (M1, M2, M3, M4 and M5). The time durations taken (in minutes) by the machines for each of the jobs, are given in the table. However, each job is assigned to a specific machine in such a way that the total processing time is minimum. The total processing time is ________ minutes.M1 M2 M3 M4 M5 J1 40 30 50 50 58 J2 26 38 60 26 38 J3 40 34 28 24 30 J4 28 40 40 32 48 J5 28 32 38 22 44 Correct answer
146 to 146
Step-by-step solution
This is an assignment problem that can be solved using the Hungarian Method to minimize total time.Step 1: Row Reduction (subtract minimum of each row from all elements in that row)- J1: min 30 [10, 0, 20, 20, 28]
- J2: min 26 [0, 12, 34, 0, 12]
- J3: min 24 [16, 10, 4, 0, 6]
- J4: min 28 [0, 12, 12, 4, 20]
- J5: min 22 [6, 10, 16, 0, 22]
- M1: min 0, M2: min 0, M3: min 4, M4: min 0, M5: min 6
Step 3: Optimal AssignmentM1 M2 M3 M4 M5 J1 10 0 16 20 22 J2 0 12 30 0 6 J3 16 10 0 0 0 J4 0 12 8 4 14 J5 6 10 12 0 16
By drawing minimum lines to cover zeros and iterating (or by inspection for small matrices), we find the optimal assignment:- J1 M2: 30
- J2 M5: 38
- J3 M3: 28
- J4 M1: 28
- J5 M4: 22
65
Q65NAT2 marksMediumA project consists of six activities. The immediate predecessor of each activity and the estimated duration is also provided in the table below: | Activity | Immediate predecessor…Think it through. Then check your answer.Question
A project consists of six activities. The immediate predecessor of each activity and the estimated duration is also provided in the table below:If all activities other than S take the estimated amount of time, the maximum duration (in weeks) of the activity S without delaying the completion of the project is ________Activity Immediate predecessor Estimated duration (weeks) P - 5 Q - 1 R Q 2 S P, R 4 T P 6 U S, T 3 Correct answer
6 to 6
Step-by-step solution
To find the maximum duration of activity S without delaying the project, we first determine the original project completion time.1.Calculate Earliest Finish (EF) for each activity:- weeks (starts at 0)
- week (starts at 0)
- weeks
- weeks
- weeks
- weeks
2.Determine the constraint on activity S:Activity S lies on two paths that must not exceed the project duration of 14 weeks:- Path :
- Path :