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GATE ME 2015 Set 3
All 65 solved GATE ME 2015 Set 3 questions in exam order. Open a question, commit to an answer, and learn from the step-by-step solution. One question at a time.
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65
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General Aptitude (GA)
101
Q1MCQ1 markEasyChoose the appropriate word/phrase, out of the four options given below, to complete the following sentence: Apparent lifelessness ______________ dormant life.Think it through. Then check your answer.Question
Choose the appropriate word/phrase, out of the four options given below, to complete the following sentence:Apparent lifelessness ______________ dormant life.Correct answer
(A) harbours
Step-by-step solution
The sentence aims to convey that what appears to be lifeless actually contains or conceals life that is in a dormant state. We need to choose the verb that best fits this meaning.Let's analyze the options:- (A) harbours: To 'harbour' something means to keep it in one's mind or to give a home or shelter to it. In this context, it means that the apparent lifelessness conceals or holds the dormant life within. This fits the sentence perfectly.
- (B) leads to: This implies a causal relationship. Apparent lifelessness does not cause dormant life.
- (C) supports: While the lifeless exterior might physically support the dormant life, 'harbours' is a more nuanced and appropriate word that implies concealment and sheltering, which is the essence of the sentence.
- (D) affects: This means to have an effect on. The state of being apparently lifeless doesn't 'affect' the dormant life in the way the sentence implies; rather, it describes the condition in which the dormant life exists.
2
Q2MCQ1 markEasyFill in the blank with the correct idiom/phrase. That boy from the town was a _______________ in the sleepy village.Think it through. Then check your answer.Question
Fill in the blank with the correct idiom/phrase.That boy from the town was a _______________ in the sleepy village.Correct answer
(C) fish out of water
Step-by-step solution
The idiom 'a fish out of water' describes a person who feels awkward or uncomfortable because they are in an unfamiliar situation. A boy from a bustling town would likely feel out of place and different in a quiet, 'sleepy village'. Therefore, 'fish out of water' is the most appropriate idiom to complete the sentence.- (A) dog out of herd: This is not a standard English idiom.
- (B) sheep from the heap: This is not a standard English idiom.
- (C) fish out of water: This is the correct idiom for someone in an unfamiliar and uncomfortable environment.
- (D) bird from the flock: While 'birds of a feather flock together' is an idiom, 'bird from the flock' does not convey the meaning of being out of place.
3
Q3MCQ1 markMediumChoose the statement where underlined word is used correctly.Think it through. Then check your answer.Question
Choose the statement where underlined word is used correctly.Correct answer
(B) When the thief keeps <u eluding</u the police, he is being elusive.
Step-by-step solution
The question tests the correct usage of the words 'elude', 'elusive', 'allude', and 'allusive'.- Elude: To escape from or avoid a danger, enemy, or pursuer, typically in a skillful or cunning way.
- Elusive: Difficult to find, catch, or achieve.
- Allude: To suggest or call attention to something indirectly; to refer to.
- Allusive: Containing suggestions or indirect references.
- (A) When the teacher eludes to different authors, he is being elusive.
- (B) When the thief keeps eluding the police, he is being elusive.
- (C) Matters that are difficult to understand, identify or remember are allusive.
- (D) Mirages can be allusive, but a better way to express them is illusory.
4
Q4MCQ1 markEasyTanya is older than Eric. Cliff is older than Tanya. Eric is older than Cliff. If the first two statements are true, then the third statement is:Think it through. Then check your answer.Question
Tanya is older than Eric.
Cliff is older than Tanya.
Eric is older than Cliff.If the first two statements are true, then the third statement is:Correct answer
(B) False
Step-by-step solution
Let be Tanya's age, be Eric's age, and be Cliff's age.1.Tanya is older than Eric:2.Cliff is older than Tanya:Combining these two statements, we get: .The third statement says 'Eric is older than Cliff' (), which directly contradicts the combined result . Therefore, the third statement is False.5
Q5MCQ1 markEasyFive teams have to compete in a league, with every team playing every other team exactly once, before going to the next round. How many matches will have to be held to complete…Think it through. Then check your answer.Question
Five teams have to compete in a league, with every team playing every other team exactly once, before going to the next round. How many matches will have to be held to complete the league round of matches?Correct answer
(B) 10
Step-by-step solution
In a league where every team plays every other team exactly once, the number of matches is determined by the combination formula , where is the number of teams.
Given :
Number of matches .6
Q6MCQ2 marksEasySelect the appropriate option in place of underlined part of the sentence. Increased productivity necessary reflects greater efforts made by the employees.Think it through. Then check your answer.Question
Select the appropriate option in place of underlined part of the sentence.Increased productivity necessary reflects greater efforts made by the employees.Correct answer
(C) Increase in productivity necessarily
Step-by-step solution
The sentence requires a subject and an adverb to modify the verb 'reflects'.- 'Increase in productivity' acts as the noun phrase subject.
- 'necessarily' is the adverb required to modify the verb 'reflects'.
Option (B) creates a run-on structure that is grammatically incorrect.
Option (C) correctly provides the subject and the modifying adverb.7
Q7MCQ2 marksEasyGiven below are two statements followed by two conclusions. Assuming these statements to be true, decide which one logically follows. Statements: I. No manager is a leader. II.…Think it through. Then check your answer.Question
Given below are two statements followed by two conclusions. Assuming these statements to be true, decide which one logically follows.Statements:
I. No manager is a leader.
II. All leaders are executives.Conclusions:
I. No manager is an executive.
II. No executive is a manager.Correct answer
(C) Neither conclusion I nor II follows.
Step-by-step solution
Let be the set of managers, be the set of leaders, and be the set of executives.
From Statement I: (No manager is a leader).
From Statement II: (All leaders are executives).Now evaluate the conclusions:
Conclusion I: "No manager is an executive" (). This is not necessarily true. While no manager is a leader, a manager could still be an executive who is not a leader. The given statements do not rule this out.
Conclusion II: "No executive is a manager" (). This is logically equivalent to Conclusion I and is also not necessarily true for the same reason.Since neither conclusion must be true based on the given statements, the correct option is (C).8
Q8NAT2 marksMediumIn the given figure angle is a right angle, , and . If area of triangle is , then the area of triangle in…Think it through. Then check your answer.Question
In the given figure angle is a right angle, , and . If area of triangle is , then the area of triangle in is _______.
Correct answer
280 to 280
Step-by-step solution
In the right-angled triangle , . Points and lie on the legs and respectively.Given:
Area() =
From the given ratios:1.2.The area of triangle is:
Area() =
Area() =
Area() = Substituting :
Area() = .9
Q9MCQ2 marksHardRight triangle is to be constructed in the - plane so that the right angle is at and line is parallel to the -axis. The and coordinates of…Think it through. Then check your answer.Question
Right triangle is to be constructed in the - plane so that the right angle is at and line is parallel to the -axis. The and coordinates of are to be integers that satisfy the inequalities: and . How many different triangles could be constructed with these properties?Correct answer
(C) 9,900
Step-by-step solution
To construct the triangle with the given properties:1.Identify the range of coordinates:- For : . The number of integer values is .
- For : . The number of integer values is .
- Total available integer points in the region = .
Vertex can be any of the 110 available points. Let .3.Choose vertex :Line must be parallel to the -axis, so . Vertex must have an -coordinate from the 10 available values.
Number of choices for = .4.Choose vertex :Since the right angle is at , must be perpendicular to . Since is horizontal, must be vertical. Thus, . Vertex must have a -coordinate from the 11 available values.
Number of choices for = .5.Calculate total triangles:Total triangles = (Choices for ) (Choices for ) (Choices for )
Total = .10
Q10MCQ2 marksMediumA coin is tossed thrice. Let be the event that head occurs in each of the first two tosses. Let be the event that a tail occurs on the third toss. Let be the event…Think it through. Then check your answer.Question
A coin is tossed thrice. Let be the event that head occurs in each of the first two tosses. Let be the event that a tail occurs on the third toss. Let be the event that two tails occur in three tosses. Based on the above information, which one of the following statements is TRUE?Correct answer
(B) Y and Z are dependent
Step-by-step solution
The sample space for three coin tosses is , so .1.Event : Head in first two tosses , .2.Event : Tail on third toss , .3.Event : Two tails in three tosses , .Check independence:- For and : , . Since , and are independent. (Statement A is false).
- For and : , . Since , and are dependent. (Statement B is true, Statement C is false).
- For and : , . Since , and are dependent. (Statement D is false).
Mechanical Engineering
5511
Q11MCQ1 markEasyFor the given fluctuating fatigue load, the values of stress amplitude and stress ratio are respectively [figure]Think it through. Then check your answer.Question
For the given fluctuating fatigue load, the values of stress amplitude and stress ratio are respectively
Correct answer
(C) 100 MPa and 0.20
Step-by-step solution
From the given stress-time graph:
Maximum stress,
Minimum stress,1.Stress amplitude ():2.Stress ratio ():Thus, the values are and .12
Q12MCQ1 markEasyFor the same material and the mass, which of the following configurations of flywheel will have maximum mass moment of inertia about the axis of rotation passing through the…Think it through. Then check your answer.Question
For the same material and the mass, which of the following configurations of flywheel will have maximum mass moment of inertia about the axis of rotation passing through the center of gravity.Correct answer
(B) Rimmed wheel [figure]
Step-by-step solution
Mass moment of inertia () is defined as . For a given mass, the moment of inertia is maximized when the mass is distributed as far as possible from the axis of rotation.- In a rimmed wheel, almost all the mass is concentrated at the outer radius (the rim), resulting in the largest possible radius of gyration ().
- In solid cylinders, spheres, and cubes, the mass is distributed throughout the volume, including regions very close to the axis of rotation, which reduces the overall moment of inertia compared to a rimmed wheel of the same mass.
13
Q13MCQ1 markEasyA gear train is made up of five spur gears as shown in the figure. Gear 2 is driver and gear 6 is driven member. and represent number of teeth on gears…Think it through. Then check your answer.Question
A gear train is made up of five spur gears as shown in the figure. Gear 2 is driver and gear 6 is driven member. and represent number of teeth on gears 2, 3, 4, 5, and 6 respectively. The gear(s) which act(s) as idler(s) is/are
Correct answer
(C) Only 5
Step-by-step solution
An idler gear is an intermediate gear in a gear train that meshes with both a preceding and a succeeding gear in a simple mesh sequence. It changes the direction of rotation but does not affect the overall gear ratio. In the given compound gear train:1.Gear 2 (driver) meshes with Gear 3.2.Gear 3 and Gear 4 are on the same shaft (compound gear).3.Gear 4 meshes with Gear 5.4.Gear 5 meshes with Gear 6 (driven).Gear 5 is the only gear that meshes with both a preceding gear (Gear 4) and a succeeding gear (Gear 6), thus acting as an idler. Gear 3 is not an idler because it is part of a compound gear and does not mesh with Gear 4. Therefore, only gear 5 acts as an idler.14
Q14MCQ1 markEasyIn the figure, link 2 rotates with constant angular velocity . A slider link 3 moves outwards with a constant relative velocity , where Q is a point on slider 3…Think it through. Then check your answer.Question
In the figure, link 2 rotates with constant angular velocity . A slider link 3 moves outwards with a constant relative velocity , where Q is a point on slider 3 and P is a point on link 2. The magnitude and direction of Coriolis component of acceleration is given by
Correct answer
(A) 2 ω₂ V_(Q/P); direction of V_(Q/P) rotated by 90^ in the direction of ω₂
Step-by-step solution
The Coriolis component of acceleration () for a point moving along a rotating path is given by the formula , where is the angular velocity of the path and is the relative velocity of the point along that path. In this case, the magnitude is . The direction of the Coriolis acceleration is determined by rotating the relative velocity vector () by in the direction of the angular velocity (). Thus, option (A) is correct.15
Q15MCQ1 markEasyThe strain hardening exponent of stainless steel SS 304 with distinct yield and UTS values undergoing plastic deformation isThink it through. Then check your answer.Question
The strain hardening exponent of stainless steel SS 304 with distinct yield and UTS values undergoing plastic deformation isCorrect answer
(C) 0 < n < 1
Step-by-step solution
The plastic deformation of many metals is described by the Hollomon equation , where is the strain hardening exponent. For materials that exhibit strain hardening (like SS 304), is a positive value typically between 0.1 and 0.5. A value of corresponds to a perfectly plastic material, and corresponds to a perfectly elastic material. Since the material undergoes plastic deformation with distinct yield and UTS points, the exponent must be in the range .16
Q16MCQ1 markEasyIn a machining operation, if the generatrix and directrix both are straight lines, the surface obtained isThink it through. Then check your answer.Question
In a machining operation, if the generatrix and directrix both are straight lines, the surface obtained isCorrect answer
(C) plane
Step-by-step solution
A surface is generated by the relative motion between a line (generatrix) and a path (directrix). When both the generatrix and the directrix are straight lines, the resulting surface is a plane. For example, in a shaping or planing operation, the tool's straight cutting edge (generatrix) moves along a straight path (directrix) to produce a flat plane surface.17
Q17MCQ1 markEasyIn full mould (cavity-less) casting process, the pattern is made ofThink it through. Then check your answer.Question
In full mould (cavity-less) casting process, the pattern is made ofCorrect answer
(A) expanded polystyrene
Step-by-step solution
Full mould casting, also known as lost foam casting or cavity-less casting, uses a pattern made of expanded polystyrene (EPS). The pattern is placed in a flask and surrounded by unbonded sand. When molten metal is poured, the heat causes the polystyrene pattern to vaporize and escape through the sand, leaving the metal to fill the resulting cavity.18
Q18MCQ1 markEasyIn the notation for summarizing the characteristics of queueing situation, the letters '' and '' stand respectively forThink it through. Then check your answer.Question
In the notation for summarizing the characteristics of queueing situation, the letters '' and '' stand respectively forCorrect answer
(A) service time distribution and queue discipline
Step-by-step solution
In Kendall's notation for queueing systems, :- : Arrival distribution (inter-arrival time distribution)
- : Service time distribution
- : Number of parallel servers
- : Queue discipline (e.g., FIFO, LIFO, SIRO)
- : Maximum number allowed in the system (system capacity)
- : Size of the calling source (population size)
19
Q19MCQ1 markEasyCouette flow is characterized byThink it through. Then check your answer.Question
Couette flow is characterized byCorrect answer
(D) steady, incompressible, laminar flow between one fixed plate and the other moving with a constant velocity
Step-by-step solution
Couette flow is defined as the flow of a viscous fluid in the space between two surfaces, one of which is moving tangentially relative to the other. In its simplest form, it is the steady, incompressible, laminar flow between two infinite parallel plates, where one plate is stationary and the other moves at a constant velocity.- Option (A) describes Poiseuille flow in a pipe.
- Option (C) describes Plane Poiseuille flow (between two fixed plates).
20
Q20MCQ1 markEasyThe thermodynamic cycle shown in figure (- diagram) indicates [figure]Think it through. Then check your answer.Question
The thermodynamic cycle shown in figure (- diagram) indicates
Correct answer
(B) reversed Brayton cycle
Step-by-step solution
The given - diagram consists of two constant pressure processes () and two isentropic processes (vertical lines). This is the characteristic of a Brayton cycle. Since the cycle is traced in the counter-clockwise direction (1-2-3-4-1), it represents a refrigeration cycle, specifically the reversed Brayton cycle (also known as the Bell-Coleman cycle).21
Q21MCQ1 markEasyThe ratio of momentum diffusivity () to thermal diffusivity (), is calledThink it through. Then check your answer.Question
The ratio of momentum diffusivity () to thermal diffusivity (), is calledCorrect answer
(A) Prandtl number
Step-by-step solution
The Prandtl number () is a dimensionless number defined as the ratio of momentum diffusivity (kinematic viscosity, ) to thermal diffusivity ():It provides a measure of the relative thickness of the velocity and thermal boundary layers.22
Q22MCQ1 markEasySaturated vapor is condensed to saturated liquid in a condenser. The heat capacity ratio is . The effectiveness () of the condenser isThink it through. Then check your answer.Question
Saturated vapor is condensed to saturated liquid in a condenser. The heat capacity ratio is . The effectiveness () of the condenser isCorrect answer
(D) 1-exp(-NTU)
Step-by-step solution
In a condenser, one fluid undergoes a phase change (vapor to liquid) at a constant temperature. This means its heat capacity is effectively infinite. Therefore, this fluid has the maximum heat capacity, .The heat capacity ratio is defined as .Substituting , we get:
.The effectiveness of a heat exchanger where one fluid's temperature is constant (i.e., for boiling or condensation, where ) is given by the formula:This relationship is independent of the flow arrangement (parallel, counter, cross-flow, etc.) when .Let's check the options:
(A) is the effectiveness for a parallel flow heat exchanger. For , it simplifies to .
(B) is the effectiveness for a counter flow heat exchanger. For , it simplifies to .
(C) is the effectiveness for a counter flow heat exchanger when .
(D) is the general formula for the case where .Since the question asks for the effectiveness of the condenser, which is a special case where , the correct expression is given in option (D).23
Q23NAT1 markMediumUsing a unit step size, the value of integral by trapezoidal rule is ________Think it through. Then check your answer.Question
Using a unit step size, the value of integral by trapezoidal rule is ________Correct answer
0.68 to 0.7
Step-by-step solution
The trapezoidal rule for an integral with step size is given by . For the given integral with unit step size ():1.Identify the limits and step size: . This gives two points: and .2.Identify the function: .3.Calculate function values at the points:
.The calculated value is approximately 0.69, which falls within the specified range of 0.68 to 0.70.24
Q24MCQ1 markEasyIf , , and , the value of isThink it through. Then check your answer.Question
If , , and , the value of isCorrect answer
(C) 1/3
Step-by-step solution
The conditional probability is defined as the probability of event occurring given that event has already occurred. The formula is:Given values:25
Q25NAT1 markEasyThe lowest eigenvalue of the matrix isThink it through. Then check your answer.Question
The lowest eigenvalue of the matrix isCorrect answer
2 to 2
Step-by-step solution
To find the eigenvalues of the matrix , we solve the characteristic equation :Factoring the quadratic equation:The eigenvalues are and . The lowest eigenvalue is 2.26
Q26NAT1 markEasyThe value of isThink it through. Then check your answer.Question
The value of isCorrect answer
-0.35 to -0.3
Step-by-step solution
The limit is in the indeterminate form. Applying L'Hôpital's rule:Substituting :27
Q27NAT1 markMediumA cylindrical tank with closed ends is filled with compressed air at a pressure of 500 kPa. The inner radius of the tank is 2 m, and it has wall thickness of 10 mm. The magnitude…Think it through. Then check your answer.Question
A cylindrical tank with closed ends is filled with compressed air at a pressure of 500 kPa. The inner radius of the tank is 2 m, and it has wall thickness of 10 mm. The magnitude of maximum in-plane shear stress (in MPa) isCorrect answer
25 to 25
Step-by-step solution
Given:
Internal pressure,
Inner radius,
Wall thickness, For a thin cylindrical pressure vessel:
Hoop stress,
Longitudinal stress, The maximum in-plane shear stress is given by:28
Q28MCQ1 markEasyA weight of is supported by two metallic ropes as shown in the figure. The values of tensions and are respectively [figure]Think it through. Then check your answer.Question
A weight of is supported by two metallic ropes as shown in the figure. The values of tensions and are respectively
Correct answer
(A) 433 N and 250 N
Step-by-step solution
From the figure, the angles between the forces at the junction are:1.Angle between and is .2.Angle between and the vertical weight () is (since makes with the horizontal ceiling, its angle with the vertical is ).3.Angle between and the vertical weight is .Using Lami's Theorem:Calculating :Calculating :Thus, and .29
Q29MCQ1 markMediumWhich of the following statements are TRUE for damped vibrations? P. For a system having critical damping, the value of damping ratio is unity and system does not undergo a…Think it through. Then check your answer.Question
Which of the following statements are TRUE for damped vibrations?
P. For a system having critical damping, the value of damping ratio is unity and system does not undergo a vibratory motion.
Q. Logarithmic decrement method is used to determine the amount of damping in a physical system.
R. In case of damping due to dry friction between moving surfaces resisting force of constant magnitude acts opposite to the relative motion.
S. For the case of viscous damping, drag force is directly proportional to the square of relative velocity.Correct answer
(C) P, Q and R only
Step-by-step solution
Analysis of statements:
P. True: For critical damping, the damping ratio . The system returns to equilibrium in the shortest time without oscillation.
Q. True: Logarithmic decrement is a standard method to find the damping ratio in underdamped systems.
R. True: Coulomb damping (dry friction) is characterized by a constant magnitude force that always opposes the direction of motion.
S. False: In linear viscous damping, the damping force is directly proportional to the velocity (), not the square of the velocity.Therefore, P, Q, and R are true.30
Q30MCQ1 markEasyA drill is positioned at point P and it has to proceed to point Q. The coordinates of point Q in the incremental system of defining position of a point in CNC part program will be…Think it through. Then check your answer.Question
A drill is positioned at point P and it has to proceed to point Q. The coordinates of point Q in the incremental system of defining position of a point in CNC part program will be
Correct answer
(D) (4, 7)
Step-by-step solution
In an incremental coordinate system (G91 in CNC), the coordinates of a target point are defined relative to the current position.Current position (P): , .
Target position (Q): , .Incremental coordinates from P to Q:So, the incremental coordinates are .31
Q31MCQ1 markEasyThe ratio of momentum diffusivity () to thermal diffusivity (), is calledThink it through. Then check your answer.Question
The ratio of momentum diffusivity () to thermal diffusivity (), is calledCorrect answer
(A) Prandtl number
Step-by-step solution
The Prandtl number () is a dimensionless number defined as the ratio of momentum diffusivity (kinematic viscosity) to thermal diffusivity. It is expressed as:where is the kinematic viscosity and is the thermal diffusivity.32
Q32MCQ1 markEasySaturated vapor is condensed to saturated liquid in a condenser. The heat capacity ratio is . The effectiveness () of the condenser isThink it through. Then check your answer.Question
Saturated vapor is condensed to saturated liquid in a condenser. The heat capacity ratio is . The effectiveness () of the condenser isCorrect answer
(D) 1 - exp(-NTU)
Step-by-step solution
In a condenser, one of the fluids (the condensing vapor) undergoes a phase change at constant temperature. During a phase change, the effective specific heat is infinite, meaning . Consequently, the heat capacity ratio . For any heat exchanger (parallel or counter-flow) where , the effectiveness formula simplifies to:Thus, option (D) is the correct expression.33
Q33NAT1 markEasyUsing a unit step size, the value of integral by trapezoidal rule is ________Think it through. Then check your answer.Question
Using a unit step size, the value of integral by trapezoidal rule is ________Correct answer
0.68 to 0.7
Step-by-step solution
To evaluate the integral using the trapezoidal rule with a unit step size ():1.Identify the function and interval:on the interval .2.Determine the points:With , the points are and .3.Calculate function values:
4.Apply the Trapezoidal Rule:The calculated value is approximately 0.693, which falls within the range 0.68 to 0.70.34
Q34MCQ1 markEasyA rigid container of volume contains of water at (, ).…Think it through. Then check your answer.Question
A rigid container of volume contains of water at (, ). The state of water isCorrect answer
(C) a mixture of saturated liquid and saturated vapor
Step-by-step solution
The specific volume of the water in the container is . At , the given saturated liquid specific volume is and the saturated vapor specific volume is . Since (), the water exists as a mixture of saturated liquid and saturated vapor.35
Q35MCQ1 markEasyLet be an arbitrary smooth real valued scalar function and be an arbitrary smooth vector valued function in a three-dimensional space. Which one of the following…Think it through. Then check your answer.Question
Let be an arbitrary smooth real valued scalar function and be an arbitrary smooth vector valued function in a three-dimensional space. Which one of the following is an identity?Correct answer
(C) Div Curl V = 0
Step-by-step solution
The divergence of the curl of any smooth vector field is always zero, i.e., . This is a fundamental vector identity.36
Q36MCQ2 marksMediumAn air-standard Diesel cycle consists of the following processes: 1-2: Air is compressed isentropically. 2-3: Heat is added at constant pressure. 3-4: Air expands isentropically…Think it through. Then check your answer.Question
An air-standard Diesel cycle consists of the following processes:
1-2: Air is compressed isentropically.
2-3: Heat is added at constant pressure.
3-4: Air expands isentropically to the original volume.
4-1: Heat is rejected at constant volume.
If and denote the specific heat ratio and temperature, respectively, the efficiency of the cycle isCorrect answer
(B) 1 - (T₄ - T₁)/(γ(T₃ - T₂))
Step-by-step solution
The efficiency of a thermodynamic cycle is given by . For an air-standard Diesel cycle:1.Heat addition () occurs at constant pressure (process 2-3): .2.Heat rejection () occurs at constant volume (process 4-1): .Substituting these into the efficiency formula:
.37
Q37NAT2 marksMediumA cylindrical tank with closed ends is filled with compressed air at a pressure of . The inner radius of the tank is , and it has wall thickness of…Think it through. Then check your answer.Question
A cylindrical tank with closed ends is filled with compressed air at a pressure of . The inner radius of the tank is , and it has wall thickness of . The magnitude of maximum in-plane shear stress (in MPa) is ________Correct answer
25 to 25
Step-by-step solution
Given:
Pressure
Inner radius
Wall thickness For a thin cylindrical pressure vessel:
Hoop stress
Longitudinal stress The maximum in-plane shear stress is given by:38
Q38MCQ2 marksEasyA weight of is supported by two metallic ropes as shown in the figure. The values of tensions and are respectively [figure]Think it through. Then check your answer.Question
A weight of is supported by two metallic ropes as shown in the figure. The values of tensions and are respectively
Correct answer
(A) 433 N and 250 N
Step-by-step solution
From the geometry of the figure:
Angle of with horizontal
Angle between and
Therefore, angle of with horizontal Resolving forces horizontally:
Resolving forces vertically:
Now, So, and .39
Q39MCQ2 marksMediumWhich of the following statements are TRUE for damped vibrations? P. For a system having critical damping, the value of damping ratio is unity and system does not undergo…40
Q40NAT2 marksEasyFor ball bearings, the fatigue life measured in number of revolutions and the radial load are related by , where is a constant. It withstands a radial…Think it through. Then check your answer.Question
For ball bearings, the fatigue life measured in number of revolutions and the radial load are related by , where is a constant. It withstands a radial load of for a life of million revolutions. The load (in kN) for a life of one million revolutions is ________Correct answer
15 to 17
Step-by-step solution
Given the relationship for ball bearings: , where is a constant.
Let and revolutions.
We need to find for revolutions.
Since is constant:
.
The range provided is 15 to 17.41
Q41NAT2 marksMediumIn a rolling operation using rolls of diameter , if a thick plate cannot be reduced to less than in one pass, the coefficient of…Think it through. Then check your answer.Question
In a rolling operation using rolls of diameter , if a thick plate cannot be reduced to less than in one pass, the coefficient of friction between the roll and the plate is ________Correct answer
0.1 to 0.15
Step-by-step solution
In rolling, the maximum possible reduction (draft) is given by:Where:
Substituting the values:
The range provided is 0.10 to 0.15.42
Q42NAT2 marksMediumRatio of solidification time of a cylindrical casting (height = radius) to that of a cubic casting of side two times the height of cylindrical casting is ________Think it through. Then check your answer.Question
Ratio of solidification time of a cylindrical casting (height = radius) to that of a cubic casting of side two times the height of cylindrical casting is ________Correct answer
0.5 to 0.6
Step-by-step solution
According to Chvorinov's rule, solidification time .
Let the radius of the cylinder be . Then height .
For the cylinder:
For the cube:
Side
Ratio of solidification times:
The range provided is 0.5 to 0.6.43
Q43NAT2 marksMediumThe annual requirement of rivets at a ship manufacturing company is . The rivets are supplied in units of costing Rs. each. If it costs Rs.…Think it through. Then check your answer.Question
The annual requirement of rivets at a ship manufacturing company is . The rivets are supplied in units of costing Rs. each. If it costs Rs. to place an order and the annual cost of carrying one unit is of its purchase cost, the cycle length of the order (in days) will be ________Correct answer
76 to 78
Step-by-step solution
Given:
Annual demand () =
Unit cost () = Rs.
Ordering cost () = Rs.
Carrying cost () = of unit cost = First, calculate the Economic Order Quantity ():Next, find the number of orders per year ():Finally, calculate the cycle length in days:The value lies within the range to .44
Q44MCQ2 marksMediumOrthogonal turning of a mild steel tube with a tool of rake angle is carried out at a feed of . If the thickness of the chip produced is…Think it through. Then check your answer.Question
Orthogonal turning of a mild steel tube with a tool of rake angle is carried out at a feed of . If the thickness of the chip produced is , the values of shear angle and shear strain will be respectivelyCorrect answer
(A) 28²⁰' and 2.19
Step-by-step solution
Given:
Rake angle () =
Uncut chip thickness () = feed =
Chip thickness () =1.Calculate chip thickness ratio ():2.Calculate shear angle ():3.Calculate shear strain ():Thus, the values are and . Correct option is (A).45
Q45MCQ2 marksMediumIn a CNC milling operation, the tool has to machine the circular arc from point to at sequence number of the CNC part program. If the center of the arc…Think it through. Then check your answer.Question
In a CNC milling operation, the tool has to machine the circular arc from point to at sequence number of the CNC part program. If the center of the arc is at and the machine has incremental mode of defining position coordinates, the correct tool path command isCorrect answer
(B) N 05 G91 G03 X-10 Y-10 R10
Step-by-step solution
To determine the correct CNC command:1.Sequence Number: The sequence number is , so the command starts withN 05.2.Coordinate Mode: The machine uses incremental mode, which is specified byG91.3.Interpolation Direction:- Start point:
- End point:
- Center:
- The vector from the center to the start point is .
- The vector from the center to the end point is .
- Moving from to along a circular path is a counter-clockwise (CCW) motion.
- CCW circular interpolation is specified by
G03.
- Incremental
- Incremental
N 05 G91 G03 X-10 Y-10 R10. Correct option is (B).46
Q46NAT2 marksMediumA Prandtl tube (Pitot-static tube with ) is used to measure the velocity of water. The differential manometer reading is of liquid column with a relative…Think it through. Then check your answer.Question
A Prandtl tube (Pitot-static tube with ) is used to measure the velocity of water. The differential manometer reading is of liquid column with a relative density of . Assuming , the velocity of water (in m/s) is ________Correct answer
1.3 to 1.34
Step-by-step solution
The velocity of water using a Prandtl tube is given by the formula:
where is the pressure head difference in terms of the flowing fluid (water).The head difference is calculated from the manometer reading as:
Given:- Manometer reading
- Relative density of manometer liquid
Calculating velocity :
The answer lies within the range 1.30 to 1.34.47
Q47NAT2 marksMediumRefrigerant vapor enters into the compressor of a standard vapor compression cycle at () and leaves the compressor at …Think it through. Then check your answer.Question
Refrigerant vapor enters into the compressor of a standard vapor compression cycle at () and leaves the compressor at (). It leaves the condenser at (). The COP of the cycle is ________Correct answer
5.5 to 5.5
Step-by-step solution
For a standard vapor compression cycle (VCC), the Coefficient of Performance (COP) is defined as:
Given enthalpies:- Compressor inlet ():
- Compressor outlet ():
- Condenser outlet ():
Calculating COP:48
Q48NAT2 marksEasySteam enters a turbine at , (, ) and exits the turbine as saturated liquid at …Think it through. Then check your answer.Question
Steam enters a turbine at , (, ) and exits the turbine as saturated liquid at (, ). Heat loss to the surrounding is of steam flowing through the turbine. Neglecting changes in kinetic energy and potential energy, the work output of the turbine (in kJ/kg of steam) is ________Correct answer
2717 to 2717
Step-by-step solution
Applying the Steady Flow Energy Equation (SFEE) for the turbine per unit mass of steam:
Given that changes in kinetic energy (KE) and potential energy (PE) are neglected:
Where:- (Inlet enthalpy)
- (Exit enthalpy)
- (Heat loss is negative as it leaves the system)
- is the work output per unit mass
49
Q49NAT2 marksMediumAir in a room is at and 60% relative humidity (). The pressure in the room is 0.1 MPa. The saturation pressure of water at is 5.63 kPa.…Think it through. Then check your answer.Question
Air in a room is at and 60% relative humidity (). The pressure in the room is 0.1 MPa. The saturation pressure of water at is 5.63 kPa. The humidity ratio of the air (in gram/kg of dry air) isCorrect answer
21.7 to 21.9
Step-by-step solution
Given:
Temperature
Relative humidity
Total pressure MPa = 100 kPa
Saturation pressure kPaPartial pressure of water vapor kPa.Humidity ratio is given by:
kg/kg dry air.Converting to g/kg dry air:
g/kg dry air.50
Q50MCQ2 marksMediumA solid sphere 1 of radius '' is placed inside a hollow, closed hemispherical surface 2 of radius ''. The shape factor is [figure]Think it through. Then check your answer.Question
A solid sphere 1 of radius '' is placed inside a hollow, closed hemispherical surface 2 of radius ''. The shape factor is
Correct answer
(A) 1/12
Step-by-step solution
Surface 1 is a sphere of radius . Area .
Surface 2 is a closed hemisphere of radius . Area .
.By reciprocity theorem: .
Since surface 1 is completely enclosed by surface 2, all radiation leaving 1 must strike 2, so .
.51
Q51NAT2 marksMediumThe value of , (where is the boundary of the region bounded by , and ) isThink it through. Then check your answer.Question
The value of , (where is the boundary of the region bounded by , and ) isCorrect answer
1.6 to 1.7
Step-by-step solution
Using Green's Theorem: .
Here, and .
.The region is a triangle bounded by .
.52
Q52MCQ2 marksEasyFor a given matrix , where , the inverse of matrix isThink it through. Then check your answer.Question
For a given matrix , where , the inverse of matrix isCorrect answer
(A) (1)/(24) bmatrix 4 - 3i & i \ -i & 4 + 3i bmatrix
Step-by-step solution
To find the inverse of matrix :1.Calculate the determinant:.2.Calculate the adjugate matrix (swap diagonal elements and change signs of off-diagonal elements):.3.The inverse is .This matches option A.53
Q53NAT2 marksMediumNewton-Raphson method is used to find the roots of the equation, . If the initial guess is , then the value of after iteration is…Think it through. Then check your answer.Question
Newton-Raphson method is used to find the roots of the equation, . If the initial guess is , then the value of after iteration is ________Correct answer
0.29 to 0.31
Step-by-step solution
Given . Its derivative is .
Using the Newton-Raphson formula :1.First iteration ():.2.Second iteration ():.
The value after the 2nd iteration is approximately 0.304.54
Q54MCQ2 marksEasyLaplace transform of the function is given by . Laplace transform of the function shown below is given by…Think it through. Then check your answer.Question
Laplace transform of the function is given by . Laplace transform of the function shown below is given by
Correct answer
(C) 2 - 2e^(-s)s
Step-by-step solution
From the given graph, the function is defined as:
for
otherwise.
The Laplace transform is calculated as:
.
This matches option C.55
Q55MCQ2 marksMediumIn a CNC milling operation, the tool has to machine the circular arc from point to at sequence number 5 of the CNC part program. If the center of the arc is…Think it through. Then check your answer.Question
In a CNC milling operation, the tool has to machine the circular arc from point to at sequence number 5 of the CNC part program. If the center of the arc is at and the machine has incremental mode of defining position coordinates, the correct tool path command isCorrect answer
(B) N 05 G91 G03 X-10 Y-10 R10
Step-by-step solution
To machine a circular arc from to with center at :1.Mode: The question specifies incremental mode, which is G91.2.Incremental Coordinates:
3.Direction:Start point:
End point:
Center:
The vector from center to start is .
The vector from center to end is .
Moving from to on a circle is a counter-clockwise (CCW) motion.
The command for CCW circular interpolation is G03.4.Command: Combining these, we get N 05 G91 G03 X-10 Y-10 R10.Thus, option (B) is correct.56
Q56NAT2 marksMediumA Prandtl tube (Pitot-static tube with ) is used to measure the velocity of water. The differential manometer reading is of liquid column with a relative…Think it through. Then check your answer.Question
A Prandtl tube (Pitot-static tube with ) is used to measure the velocity of water. The differential manometer reading is of liquid column with a relative density of . Assuming , the velocity of water (in m/s) is ___________Correct answer
1.3 to 1.34
Step-by-step solution
The velocity of water measured by a Prandtl tube is given by:
where is the head in terms of the flowing fluid (water).
The manometer reading of a liquid with relative density .
The relative density of water is .
Given and :
The range is 1.30 to 1.34.57
Q57NAT2 marksEasyRefrigerant vapor enters into the compressor of a standard vapor compression cycle at () and leaves the compressor at …Think it through. Then check your answer.Question
Refrigerant vapor enters into the compressor of a standard vapor compression cycle at () and leaves the compressor at (). It leaves the condenser at (). The COP of the cycle is ___________Correct answer
5.5 to 5.5
Step-by-step solution
Given enthalpies for the standard vapor compression cycle:
Compressor inlet (state 1):
Compressor outlet (state 2):
Condenser outlet (state 3):
In a standard cycle, the expansion process is isenthalpic, so .
The Coefficient of Performance (COP) is:58
Q58NAT2 marksEasySteam enters a turbine at , (, ) and exits the turbine as saturated liquid at …Think it through. Then check your answer.Question
Steam enters a turbine at , (, ) and exits the turbine as saturated liquid at (, ). Heat loss to the surrounding is of steam flowing through the turbine. Neglecting changes in kinetic energy and potential energy, the work output of the turbine (in kJ/kg of steam) is ________.Correct answer
2717 to 2717
Step-by-step solution
Using the Steady Flow Energy Equation (SFEE) for a turbine:Where:
(inlet enthalpy)
(outlet enthalpy)
(heat loss is negative)
is the work output per unit mass.Rearranging for :The work output of the turbine is .59
Q59NAT2 marksMediumAir in a room is at and relative humidity (). The pressure in the room is . The saturation pressure of water at is…Think it through. Then check your answer.Question
Air in a room is at and relative humidity (). The pressure in the room is . The saturation pressure of water at is . The humidity ratio of the air (in gram/kg of dry air) is ________.Correct answer
21.7 to 21.9
Step-by-step solution
Given:
Temperature
Relative humidity
Total pressure
Saturation pressure Step 1: Calculate partial pressure of water vapor ():Step 2: Calculate humidity ratio ():Step 3: Convert to g/kg of dry air:The humidity ratio is approximately .60
Q60MCQ2 marksMediumA solid sphere 1 of radius '' is placed inside a hollow, closed hemispherical surface 2 of radius ''. The shape factor is [figure]Think it through. Then check your answer.Question
A solid sphere 1 of radius '' is placed inside a hollow, closed hemispherical surface 2 of radius ''. The shape factor is
Correct answer
(A) 1/12
Step-by-step solution
Let surface 1 be the solid sphere and surface 2 be the closed hemispherical enclosure.Step 1: Determine . Since the sphere is completely enclosed by surface 2, all radiation leaving surface 1 must strike surface 2.Step 2: Use the reciprocity relation:Where:
Step 3: Solve for :Thus, the shape factor is .61
Q61MCQ2 marksMediumFor the linear programming problem: Maximize Subject to The above problem hasThink it through. Then check your answer.Question
For the linear programming problem:
Maximize
Subject to
The above problem hasCorrect answer
(A) unbounded solution
Step-by-step solution
The constraints for the linear programming problem are:
1)
2)
3) In the first quadrant (), as increases towards infinity, we can always find a value for (for example, ) that satisfies both constraints. For , the constraints become and , both of which are satisfied for all .
The objective function is . As and , . Since the objective function can increase without bound within the feasible region, the problem has an unbounded solution.62
Q62MCQ2 marksMediumWhich of the following statements are TRUE, when the cavitation parameter ? (i) the local pressure is reduced to vapor pressure (ii) cavitation starts (iii) boiling of…Think it through. Then check your answer.Question
Which of the following statements are TRUE, when the cavitation parameter ?
(i) the local pressure is reduced to vapor pressure
(ii) cavitation starts
(iii) boiling of liquid starts
(iv) cavitation stopsCorrect answer
(D) (i), (ii) and (iii)
Step-by-step solution
The cavitation parameter is defined as:where is the local pressure and is the vapor pressure of the liquid at the given temperature.
When , it implies , or .- Statement (i): The local pressure is reduced to vapor pressure. This is TRUE.
- Statement (ii): Cavitation starts when the local pressure drops to the vapor pressure. This is TRUE.
- Statement (iii): Boiling of the liquid starts at the vapor pressure for a given temperature. This is TRUE.
- Statement (iv): Cavitation starts, not stops, at this condition. This is FALSE.
63
Q63NAT2 marksMediumOne side of a wall is maintained at and the other at . The rate of heat transfer through the wall is and the surrounding temperature…Think it through. Then check your answer.Question
One side of a wall is maintained at and the other at . The rate of heat transfer through the wall is and the surrounding temperature is . Assuming no generation of heat within the wall, the irreversibility (in ) due to heat transfer through the wall is ________.Correct answer
247 to 249
Step-by-step solution
Irreversibility () is calculated using the Gouy-Stodola theorem:where is the surrounding temperature and is the entropy generation rate.
Given:
(Source temperature)
(Sink temperature)
(Heat transfer rate)
For steady-state heat transfer through a wall with no internal heat generation, the entropy generation rate is:Now, calculate the irreversibility:The value falls within the range 247 to 249.64
Q64MCQ2 marksMediumA brick wall () of thickness separates the warm air in a room from the cold ambient air. On a particular winter day, the outside air…Think it through. Then check your answer.Question
A brick wall () of thickness separates the warm air in a room from the cold ambient air. On a particular winter day, the outside air temperature is and the room needs to be maintained at . The heat transfer coefficient associated with outside air is . Neglecting the convective resistance of the air inside the room, the heat loss, in , isCorrect answer
(C) 128
Step-by-step solution
Given:
Thermal conductivity of brick wall,
Thickness of wall,
Inside room temperature,
Outside ambient temperature,
Outside convective heat transfer coefficient,
Inside convective resistance is neglected ().The total thermal resistance per unit area is:The heat loss per unit area () is given by:Thus, the correct option is (C).65
Q65NAT2 marksMediumA mixture of ideal gases has the following composition by mass: | | | | |-------|-------|--------| | | | | If the universal gas constant is…Think it through. Then check your answer.Question
A mixture of ideal gases has the following composition by mass:If the universal gas constant is , the characteristic gas constant of the mixture (in J/kg-K) is ________Correct answer
274 to 276
Step-by-step solution
Given mass fractions ():
Molecular weights ():
The equivalent molecular weight of the mixture () is calculated as:The characteristic gas constant of the mixture () is:The value lies within the range 274 to 276.