Page 1 2011 AEROSPACE ENGINEERING – AE AE: AEROSPACE ENGINEERING ONLINE Examination Duration: Three Hours Maximum Marks: 100 Read the following instructions carefully. 1. Questions must be answered using computers provided by the GATE at the examination centers. Each computer shall run specialized examination software that permits a maximum of one answer to be selected for questions of multiple choice type. 2. Your answers shall be updated and saved on the server periodically and at the end of the examination. The examination will automatically stop once the duration of the examination is over. 3. There are a total of 65 questions carrying 100 marks. All questions are of objective type. 4. Questions Q.1 – Q.25 carry 1-mark each, and questions Q.26 – Q.55 carry 2-marks each. 5. Questions Q.26 - Q.30 are of numerical answer type. For each of these questions, the correct answer is a number. All other questions are of multiple choice type. Each of these questions carries four choices for the answer labeled A, B, C and D. Only one of the four choices is the correct answer. 6. Questions Q.48 – Q.51 (2 pairs) are common data questions and question pairs (Q.52, Q.53) and (Q.54, Q.55) are linked answer questions. The answer to the second question of the linked answer questions depends on the answer to the first question of the pair. If the first question in the linked pair is wrongly answered or is unattempted, then the answer to the second question in the pair will not be evaluated. 7. Questions Q.56 – Q.65 belong to General Aptitude (GA). Questions Q.56 – Q.60 carry 1-mark each, and questions Q.61 – Q.65 carry 2-marks each. 8. Unattempted questions will result in zero mark. There is no negative marking for questions of numerical answer type, i.e., for Q.26 – Q.30. For questions of multiple choice type, wrong answers will result in NEGATIVE marks. For Q.1 – Q.25 and Q.56 – Q.60, ? mark will be deducted for each wrong answer. For Q.31 – Q.51 and Q.61 – Q.65, ? mark will be deducted for each wrong answer. The question pairs (Q.52, Q.53), and (Q.54, Q.55) are questions with linked answers. There will be negative marks only for wrong answer to the first question of the linked answer question pair, i.e. for Q.52 and Q.54, ? mark will be deducted for each wrong answer. There is no negative marking for Q.53 and Q.55. 9. Calculator is allowed whereas charts, graph sheets or tables are NOT allowed in the examination hall. 10. Rough work can be done in the specified area only. 11. Candidates may use the back side of this page to record their answers for their own convenience. 12. To login, type your Registration Number and password as per instructions provided in the envelope. 13. In order to answer a question, you may select the question using the left side selection panel on the screen and choose the correct answer by clicking on the radio button next to the answer. The answered questions shall be indicated by a solid black ball on the selection panel. In order to change the answer, you may just click on another option. If you wish to leave a previously answered question unanswered, you may click on DESELECT ANSWER button. 14. You may also select questions using NEXT and PREVIOUS buttons. 15. You may also mark questions for reviewing later using MARK button. All marked questions are indicated by a rectangle in the selection panel. Questions which are answered but are marked for the review are indicated by a solid black rectangle and questions which are not answered but are marked for the review are indicated by an outlined rectangle in the selection panel. 16. You must sign this sheet and leave it with the invigilators at the end of the examination. DECLARATION I hereby declare that I have read and followed all the instructions given in this sheet. Paper Code: AE Registration No:__________________Name: ___________________________ Signature AE Page 2 2011 AEROSPACE ENGINEERING – AE AE: AEROSPACE ENGINEERING ONLINE Examination Duration: Three Hours Maximum Marks: 100 Read the following instructions carefully. 1. Questions must be answered using computers provided by the GATE at the examination centers. Each computer shall run specialized examination software that permits a maximum of one answer to be selected for questions of multiple choice type. 2. Your answers shall be updated and saved on the server periodically and at the end of the examination. The examination will automatically stop once the duration of the examination is over. 3. There are a total of 65 questions carrying 100 marks. All questions are of objective type. 4. Questions Q.1 – Q.25 carry 1-mark each, and questions Q.26 – Q.55 carry 2-marks each. 5. Questions Q.26 - Q.30 are of numerical answer type. For each of these questions, the correct answer is a number. All other questions are of multiple choice type. Each of these questions carries four choices for the answer labeled A, B, C and D. Only one of the four choices is the correct answer. 6. Questions Q.48 – Q.51 (2 pairs) are common data questions and question pairs (Q.52, Q.53) and (Q.54, Q.55) are linked answer questions. The answer to the second question of the linked answer questions depends on the answer to the first question of the pair. If the first question in the linked pair is wrongly answered or is unattempted, then the answer to the second question in the pair will not be evaluated. 7. Questions Q.56 – Q.65 belong to General Aptitude (GA). Questions Q.56 – Q.60 carry 1-mark each, and questions Q.61 – Q.65 carry 2-marks each. 8. Unattempted questions will result in zero mark. There is no negative marking for questions of numerical answer type, i.e., for Q.26 – Q.30. For questions of multiple choice type, wrong answers will result in NEGATIVE marks. For Q.1 – Q.25 and Q.56 – Q.60, ? mark will be deducted for each wrong answer. For Q.31 – Q.51 and Q.61 – Q.65, ? mark will be deducted for each wrong answer. The question pairs (Q.52, Q.53), and (Q.54, Q.55) are questions with linked answers. There will be negative marks only for wrong answer to the first question of the linked answer question pair, i.e. for Q.52 and Q.54, ? mark will be deducted for each wrong answer. There is no negative marking for Q.53 and Q.55. 9. Calculator is allowed whereas charts, graph sheets or tables are NOT allowed in the examination hall. 10. Rough work can be done in the specified area only. 11. Candidates may use the back side of this page to record their answers for their own convenience. 12. To login, type your Registration Number and password as per instructions provided in the envelope. 13. In order to answer a question, you may select the question using the left side selection panel on the screen and choose the correct answer by clicking on the radio button next to the answer. The answered questions shall be indicated by a solid black ball on the selection panel. In order to change the answer, you may just click on another option. If you wish to leave a previously answered question unanswered, you may click on DESELECT ANSWER button. 14. You may also select questions using NEXT and PREVIOUS buttons. 15. You may also mark questions for reviewing later using MARK button. All marked questions are indicated by a rectangle in the selection panel. Questions which are answered but are marked for the review are indicated by a solid black rectangle and questions which are not answered but are marked for the review are indicated by an outlined rectangle in the selection panel. 16. You must sign this sheet and leave it with the invigilators at the end of the examination. DECLARATION I hereby declare that I have read and followed all the instructions given in this sheet. Paper Code: AE Registration No:__________________Name: ___________________________ Signature AE 2011 AEROSPACE ENGINEERING – AE Q. 1 – Q. 25 carry one mark each. Consider z y x , , to be right-handed Cartesian coordinates. A vector function is defined in this coordinate system as , where and k j i v 2 3 3 yz xy x ? ? ? j i, k are the unit vectors along y x, and z axes, respectively. The curl of is given by v Q.1 (A) k i y z 3 2 ? (B) k j y z 3 2 ? (C) j i y z 3 2 ? (D) k i y z 3 2 ? ? Which of the following functions is periodic? Q.2 (A) 2 ) ( x x f ? (B) x x f log ) ( ? (C) x e x f ? ) ( (D) . ) ( const x f ? The function has its minimum value at 14 6 4 2 ) , , ( 3 2 1 2 3 2 2 2 1 3 2 1 ? ? ? ? ? ? ? x x x x x x x x x f Q.3 (A) (1, 2, 3) (B) (0, 0, 0) (C) (3, 2, 1) (D) (1, 1, 3) Consider the function . The vector pointing in the direction of maximum increase of the function at the point (1, -1) is 2 1 2 2 2 1 2 1 2 ) , ( x x e x x x x f ? ? ? ? ? Q.4 (A) ? ? ? ? ? ? ? ? ? 5 2 (B) ? ? ? ? ? ? ? ? ? 5 1 (C) ? ? ? ? ? ? ? ? ? ? 73 . 6 73 . 0 (D) ? ? ? ? ? ? ? ? ? 4 2 Two simultaneous equations given by x y ? ? ? and ? ? ? x y have (A) a unique solution (B) infinitely many solutions Q.5 (C) no solution (D) a finite number of multiple solutions In three-dimensional linear elastic solids, the number of non-trivial stress-strain relations, strain- displacement equations and equations of equilibrium are, respectively, Q.6 (A) 3, 3 and 3 (B) 6, 3 and 3 (C) 6, 6 and 3 (D) 6, 3 and 6 An Euler-Bernoulli beam in bending is assumed to satisfy (A) both plane stress as well as plane strain conditions (B) plane strain condition but not plane stress condition (C) plane stress condition but not plane strain condition Q.7 (D) neither plane strain condition nor plane stress condition A statically indeterminate frame structure has (A) same number of joint degrees of freedom as the number of equilibrium equations (B) number of joint degrees of freedom greater than the number of equilibrium equations (C) number of joint degrees of freedom less than the number of equilibrium equations Q.8 (D) unknown number of joint degrees of freedom, which cannot be solved using laws of mechanics Consider a single degree of freedom spring-mass-damper system with mass, damping and stiffness of , and , respectively. The logarithmic decrement of this system can be calculated using m c k Q.9 (A) 2 4 2 c mk c ? ? (B) 2 4 c mk c ? ? (C) 2 2 c mk c ? ? (D) 2 4 2 c mk c ? ? AE Page 3 2011 AEROSPACE ENGINEERING – AE AE: AEROSPACE ENGINEERING ONLINE Examination Duration: Three Hours Maximum Marks: 100 Read the following instructions carefully. 1. Questions must be answered using computers provided by the GATE at the examination centers. Each computer shall run specialized examination software that permits a maximum of one answer to be selected for questions of multiple choice type. 2. Your answers shall be updated and saved on the server periodically and at the end of the examination. The examination will automatically stop once the duration of the examination is over. 3. There are a total of 65 questions carrying 100 marks. All questions are of objective type. 4. Questions Q.1 – Q.25 carry 1-mark each, and questions Q.26 – Q.55 carry 2-marks each. 5. Questions Q.26 - Q.30 are of numerical answer type. For each of these questions, the correct answer is a number. All other questions are of multiple choice type. Each of these questions carries four choices for the answer labeled A, B, C and D. Only one of the four choices is the correct answer. 6. Questions Q.48 – Q.51 (2 pairs) are common data questions and question pairs (Q.52, Q.53) and (Q.54, Q.55) are linked answer questions. The answer to the second question of the linked answer questions depends on the answer to the first question of the pair. If the first question in the linked pair is wrongly answered or is unattempted, then the answer to the second question in the pair will not be evaluated. 7. Questions Q.56 – Q.65 belong to General Aptitude (GA). Questions Q.56 – Q.60 carry 1-mark each, and questions Q.61 – Q.65 carry 2-marks each. 8. Unattempted questions will result in zero mark. There is no negative marking for questions of numerical answer type, i.e., for Q.26 – Q.30. For questions of multiple choice type, wrong answers will result in NEGATIVE marks. For Q.1 – Q.25 and Q.56 – Q.60, ? mark will be deducted for each wrong answer. For Q.31 – Q.51 and Q.61 – Q.65, ? mark will be deducted for each wrong answer. The question pairs (Q.52, Q.53), and (Q.54, Q.55) are questions with linked answers. There will be negative marks only for wrong answer to the first question of the linked answer question pair, i.e. for Q.52 and Q.54, ? mark will be deducted for each wrong answer. There is no negative marking for Q.53 and Q.55. 9. Calculator is allowed whereas charts, graph sheets or tables are NOT allowed in the examination hall. 10. Rough work can be done in the specified area only. 11. Candidates may use the back side of this page to record their answers for their own convenience. 12. To login, type your Registration Number and password as per instructions provided in the envelope. 13. In order to answer a question, you may select the question using the left side selection panel on the screen and choose the correct answer by clicking on the radio button next to the answer. The answered questions shall be indicated by a solid black ball on the selection panel. In order to change the answer, you may just click on another option. If you wish to leave a previously answered question unanswered, you may click on DESELECT ANSWER button. 14. You may also select questions using NEXT and PREVIOUS buttons. 15. You may also mark questions for reviewing later using MARK button. All marked questions are indicated by a rectangle in the selection panel. Questions which are answered but are marked for the review are indicated by a solid black rectangle and questions which are not answered but are marked for the review are indicated by an outlined rectangle in the selection panel. 16. You must sign this sheet and leave it with the invigilators at the end of the examination. DECLARATION I hereby declare that I have read and followed all the instructions given in this sheet. Paper Code: AE Registration No:__________________Name: ___________________________ Signature AE 2011 AEROSPACE ENGINEERING – AE Q. 1 – Q. 25 carry one mark each. Consider z y x , , to be right-handed Cartesian coordinates. A vector function is defined in this coordinate system as , where and k j i v 2 3 3 yz xy x ? ? ? j i, k are the unit vectors along y x, and z axes, respectively. The curl of is given by v Q.1 (A) k i y z 3 2 ? (B) k j y z 3 2 ? (C) j i y z 3 2 ? (D) k i y z 3 2 ? ? Which of the following functions is periodic? Q.2 (A) 2 ) ( x x f ? (B) x x f log ) ( ? (C) x e x f ? ) ( (D) . ) ( const x f ? The function has its minimum value at 14 6 4 2 ) , , ( 3 2 1 2 3 2 2 2 1 3 2 1 ? ? ? ? ? ? ? x x x x x x x x x f Q.3 (A) (1, 2, 3) (B) (0, 0, 0) (C) (3, 2, 1) (D) (1, 1, 3) Consider the function . The vector pointing in the direction of maximum increase of the function at the point (1, -1) is 2 1 2 2 2 1 2 1 2 ) , ( x x e x x x x f ? ? ? ? ? Q.4 (A) ? ? ? ? ? ? ? ? ? 5 2 (B) ? ? ? ? ? ? ? ? ? 5 1 (C) ? ? ? ? ? ? ? ? ? ? 73 . 6 73 . 0 (D) ? ? ? ? ? ? ? ? ? 4 2 Two simultaneous equations given by x y ? ? ? and ? ? ? x y have (A) a unique solution (B) infinitely many solutions Q.5 (C) no solution (D) a finite number of multiple solutions In three-dimensional linear elastic solids, the number of non-trivial stress-strain relations, strain- displacement equations and equations of equilibrium are, respectively, Q.6 (A) 3, 3 and 3 (B) 6, 3 and 3 (C) 6, 6 and 3 (D) 6, 3 and 6 An Euler-Bernoulli beam in bending is assumed to satisfy (A) both plane stress as well as plane strain conditions (B) plane strain condition but not plane stress condition (C) plane stress condition but not plane strain condition Q.7 (D) neither plane strain condition nor plane stress condition A statically indeterminate frame structure has (A) same number of joint degrees of freedom as the number of equilibrium equations (B) number of joint degrees of freedom greater than the number of equilibrium equations (C) number of joint degrees of freedom less than the number of equilibrium equations Q.8 (D) unknown number of joint degrees of freedom, which cannot be solved using laws of mechanics Consider a single degree of freedom spring-mass-damper system with mass, damping and stiffness of , and , respectively. The logarithmic decrement of this system can be calculated using m c k Q.9 (A) 2 4 2 c mk c ? ? (B) 2 4 c mk c ? ? (C) 2 2 c mk c ? ? (D) 2 4 2 c mk c ? ? AE 2011 AEROSPACE ENGINEERING – AE Consider a single degree of freedom spring-mass system of spring stiffness and mass which has a natural frequency of 10 rad/s. Consider another single degree of freedom spring-mass system of spring stiffness and mass which has a natural frequency of 20 rad/s. The spring stiffness is equal to 1 k m 2 k m 2 k Q.10 (A) 1 k (B) 1 2k (C) 4 1 k (D) 1 4k Consider a simply supported two-dimensional beam If the beam is converted into a fixed-fixed beam as then the degree of static indeterminacy will Q.11 (A) increase by 3 (B) increase by 2 (C) decrease by 1 (D) decrease by 3 An impulsive launch of a rocket minimizes the loss of burn-out velocity due to (A) aerodynamic drag force only (B) gravitational force only (C) both aerodynamic drag and gravitational forces Q.12 (D) reaction jet control force Multi-staging in rockets improves the burn-out performance by increasing mainly stage-wise (A) payload mass ratios (B) structural mass efficiencies Q.13 (C) propellant masses (D) control system masses In an un-powered glide of an aircraft having weight W, lift L and drag D, the equilibrium glide angle is defined as Q.14 (A) ? ? ? ? ? ? ? D L 1 tan (B) ? ? ? ? ? ? ? L D 1 tan (C) ? ? ? ? ? ? ? W L 1 tan (D) ? ? ? ? ? ? ? L W 1 tan Lift on an aircraft climbing vertically up is (A) equal to its weight (B) zero Q.15 (C) equal to the drag (D) equal to the thrust If an aircraft is performing a positive yawing manoeuvre, the side slip angle Q.16 (A) is always zero (B) is never zero (C) is always negative (D) could be any value For an airplane to be statically stable, its centre of gravity must always be (A) ahead of wing aerodynamic centre (B) aft of the wing aerodynamic centre Q.17 (C) ahead of neutral point (D) aft of neutral point It is seen that the drag polar of a certain aerofoil is symmetric about the C d axis. This drag polar could refer to Q.18 (A) NACA 0012 (B) NACA 4415 (C) NACA 23012 (D) None of the above AE Page 4 2011 AEROSPACE ENGINEERING – AE AE: AEROSPACE ENGINEERING ONLINE Examination Duration: Three Hours Maximum Marks: 100 Read the following instructions carefully. 1. Questions must be answered using computers provided by the GATE at the examination centers. Each computer shall run specialized examination software that permits a maximum of one answer to be selected for questions of multiple choice type. 2. Your answers shall be updated and saved on the server periodically and at the end of the examination. The examination will automatically stop once the duration of the examination is over. 3. There are a total of 65 questions carrying 100 marks. All questions are of objective type. 4. Questions Q.1 – Q.25 carry 1-mark each, and questions Q.26 – Q.55 carry 2-marks each. 5. Questions Q.26 - Q.30 are of numerical answer type. For each of these questions, the correct answer is a number. All other questions are of multiple choice type. Each of these questions carries four choices for the answer labeled A, B, C and D. Only one of the four choices is the correct answer. 6. Questions Q.48 – Q.51 (2 pairs) are common data questions and question pairs (Q.52, Q.53) and (Q.54, Q.55) are linked answer questions. The answer to the second question of the linked answer questions depends on the answer to the first question of the pair. If the first question in the linked pair is wrongly answered or is unattempted, then the answer to the second question in the pair will not be evaluated. 7. Questions Q.56 – Q.65 belong to General Aptitude (GA). Questions Q.56 – Q.60 carry 1-mark each, and questions Q.61 – Q.65 carry 2-marks each. 8. Unattempted questions will result in zero mark. There is no negative marking for questions of numerical answer type, i.e., for Q.26 – Q.30. For questions of multiple choice type, wrong answers will result in NEGATIVE marks. For Q.1 – Q.25 and Q.56 – Q.60, ? mark will be deducted for each wrong answer. For Q.31 – Q.51 and Q.61 – Q.65, ? mark will be deducted for each wrong answer. The question pairs (Q.52, Q.53), and (Q.54, Q.55) are questions with linked answers. There will be negative marks only for wrong answer to the first question of the linked answer question pair, i.e. for Q.52 and Q.54, ? mark will be deducted for each wrong answer. There is no negative marking for Q.53 and Q.55. 9. Calculator is allowed whereas charts, graph sheets or tables are NOT allowed in the examination hall. 10. Rough work can be done in the specified area only. 11. Candidates may use the back side of this page to record their answers for their own convenience. 12. To login, type your Registration Number and password as per instructions provided in the envelope. 13. In order to answer a question, you may select the question using the left side selection panel on the screen and choose the correct answer by clicking on the radio button next to the answer. The answered questions shall be indicated by a solid black ball on the selection panel. In order to change the answer, you may just click on another option. If you wish to leave a previously answered question unanswered, you may click on DESELECT ANSWER button. 14. You may also select questions using NEXT and PREVIOUS buttons. 15. You may also mark questions for reviewing later using MARK button. All marked questions are indicated by a rectangle in the selection panel. Questions which are answered but are marked for the review are indicated by a solid black rectangle and questions which are not answered but are marked for the review are indicated by an outlined rectangle in the selection panel. 16. You must sign this sheet and leave it with the invigilators at the end of the examination. DECLARATION I hereby declare that I have read and followed all the instructions given in this sheet. Paper Code: AE Registration No:__________________Name: ___________________________ Signature AE 2011 AEROSPACE ENGINEERING – AE Q. 1 – Q. 25 carry one mark each. Consider z y x , , to be right-handed Cartesian coordinates. A vector function is defined in this coordinate system as , where and k j i v 2 3 3 yz xy x ? ? ? j i, k are the unit vectors along y x, and z axes, respectively. The curl of is given by v Q.1 (A) k i y z 3 2 ? (B) k j y z 3 2 ? (C) j i y z 3 2 ? (D) k i y z 3 2 ? ? Which of the following functions is periodic? Q.2 (A) 2 ) ( x x f ? (B) x x f log ) ( ? (C) x e x f ? ) ( (D) . ) ( const x f ? The function has its minimum value at 14 6 4 2 ) , , ( 3 2 1 2 3 2 2 2 1 3 2 1 ? ? ? ? ? ? ? x x x x x x x x x f Q.3 (A) (1, 2, 3) (B) (0, 0, 0) (C) (3, 2, 1) (D) (1, 1, 3) Consider the function . The vector pointing in the direction of maximum increase of the function at the point (1, -1) is 2 1 2 2 2 1 2 1 2 ) , ( x x e x x x x f ? ? ? ? ? Q.4 (A) ? ? ? ? ? ? ? ? ? 5 2 (B) ? ? ? ? ? ? ? ? ? 5 1 (C) ? ? ? ? ? ? ? ? ? ? 73 . 6 73 . 0 (D) ? ? ? ? ? ? ? ? ? 4 2 Two simultaneous equations given by x y ? ? ? and ? ? ? x y have (A) a unique solution (B) infinitely many solutions Q.5 (C) no solution (D) a finite number of multiple solutions In three-dimensional linear elastic solids, the number of non-trivial stress-strain relations, strain- displacement equations and equations of equilibrium are, respectively, Q.6 (A) 3, 3 and 3 (B) 6, 3 and 3 (C) 6, 6 and 3 (D) 6, 3 and 6 An Euler-Bernoulli beam in bending is assumed to satisfy (A) both plane stress as well as plane strain conditions (B) plane strain condition but not plane stress condition (C) plane stress condition but not plane strain condition Q.7 (D) neither plane strain condition nor plane stress condition A statically indeterminate frame structure has (A) same number of joint degrees of freedom as the number of equilibrium equations (B) number of joint degrees of freedom greater than the number of equilibrium equations (C) number of joint degrees of freedom less than the number of equilibrium equations Q.8 (D) unknown number of joint degrees of freedom, which cannot be solved using laws of mechanics Consider a single degree of freedom spring-mass-damper system with mass, damping and stiffness of , and , respectively. The logarithmic decrement of this system can be calculated using m c k Q.9 (A) 2 4 2 c mk c ? ? (B) 2 4 c mk c ? ? (C) 2 2 c mk c ? ? (D) 2 4 2 c mk c ? ? AE 2011 AEROSPACE ENGINEERING – AE Consider a single degree of freedom spring-mass system of spring stiffness and mass which has a natural frequency of 10 rad/s. Consider another single degree of freedom spring-mass system of spring stiffness and mass which has a natural frequency of 20 rad/s. The spring stiffness is equal to 1 k m 2 k m 2 k Q.10 (A) 1 k (B) 1 2k (C) 4 1 k (D) 1 4k Consider a simply supported two-dimensional beam If the beam is converted into a fixed-fixed beam as then the degree of static indeterminacy will Q.11 (A) increase by 3 (B) increase by 2 (C) decrease by 1 (D) decrease by 3 An impulsive launch of a rocket minimizes the loss of burn-out velocity due to (A) aerodynamic drag force only (B) gravitational force only (C) both aerodynamic drag and gravitational forces Q.12 (D) reaction jet control force Multi-staging in rockets improves the burn-out performance by increasing mainly stage-wise (A) payload mass ratios (B) structural mass efficiencies Q.13 (C) propellant masses (D) control system masses In an un-powered glide of an aircraft having weight W, lift L and drag D, the equilibrium glide angle is defined as Q.14 (A) ? ? ? ? ? ? ? D L 1 tan (B) ? ? ? ? ? ? ? L D 1 tan (C) ? ? ? ? ? ? ? W L 1 tan (D) ? ? ? ? ? ? ? L W 1 tan Lift on an aircraft climbing vertically up is (A) equal to its weight (B) zero Q.15 (C) equal to the drag (D) equal to the thrust If an aircraft is performing a positive yawing manoeuvre, the side slip angle Q.16 (A) is always zero (B) is never zero (C) is always negative (D) could be any value For an airplane to be statically stable, its centre of gravity must always be (A) ahead of wing aerodynamic centre (B) aft of the wing aerodynamic centre Q.17 (C) ahead of neutral point (D) aft of neutral point It is seen that the drag polar of a certain aerofoil is symmetric about the C d axis. This drag polar could refer to Q.18 (A) NACA 0012 (B) NACA 4415 (C) NACA 23012 (D) None of the above AE 2011 AEROSPACE ENGINEERING – AE AE The aerodynamic centre of a supersonic aerofoil, with chord c, is located at Q.19 (A) the leading edge (B) 0.25c (C) 0.5c (D) 0.75c Winglets are used on wings to minimize Q.20 (A) skin friction drag (B) profile drag (C) wave drag (D) induced drag Consider a potential flow with free stream velocity V 8 , over a spinning circular cylinder of radius R and circulation ?. The stream function, ?, where ? = 0 on the cylinder surface, in cylindrical coordinates (r, ?) is given by (A) R r r R r V ln 2 1 cos 2 2 ? ? ? ? ? ? ? ? ? ? ? ? ? ? (B) R r r R r V ln 2 1 cos 2 2 ? ? ? ? ? ? ? ? ? ? ? ? ? ? Q.21 (C) R r r R r V ln 2 1 sin 2 2 ? ? ? ? ? ? ? ? ? ? ? ? ? ? (D) R r r R r V ln 2 1 sin 2 2 ? ? ? ? ? ? ? ? ? ? ? ? ? ? A main objective of by-pass in a turbo-fan engine is to increase (A) mass flow rate through engine inlet (B) turbine inlet temperature Q.22 (C) mass flow rate through exhaust nozzle (D) compressor pressure ratio The pressure ratio in any one stage of a jet engine compressor is limited by (A) entry stagnation temperature in that stage (B) entry Mach number in that stage (C) pressure gradient induced separation in that stage Q.23 (D) mass flow rate in that stage Thermodynamic cycle on which the jet engine operates can be Q.24 (A) open Rankine cycle only (B) either open or closed Rankine cycle (C) open Brayton cycle only (D) either open or closed Brayton cycle Propulsion efficiency of a jet engine is (A) directly proportional to both the thrust power and the air mass flow rate (B) inversely proportional to both the thrust power and the air mass flow rate (C) directly proportional to the thrust power and inversely proportional to the air mass flow rate Q.25 (D) inversely proportional to the thrust power and directly proportional to the air mass flow rate Q. 26 to Q. 55 carry two marks each. Questions Q.26 to Q. 30 are numerica l answer type. The answer to each of these questio ns is either a positive whole number, or a positive real number with maximum of 2 decimal places. Consider a cantilever beam having length L=1 m, square cross-section (width = depth = 0.01 m) and Young’s modulus 50 GPa. The beam is subjected to a transverse load P = 1 N at the mid-span (L/2) at the center of the cross-section. Under the small deformation theory, the transverse deflection of the beam (in mm) at its free-end is Q.26 P L L/2 Page 5 2011 AEROSPACE ENGINEERING – AE AE: AEROSPACE ENGINEERING ONLINE Examination Duration: Three Hours Maximum Marks: 100 Read the following instructions carefully. 1. Questions must be answered using computers provided by the GATE at the examination centers. Each computer shall run specialized examination software that permits a maximum of one answer to be selected for questions of multiple choice type. 2. Your answers shall be updated and saved on the server periodically and at the end of the examination. The examination will automatically stop once the duration of the examination is over. 3. There are a total of 65 questions carrying 100 marks. All questions are of objective type. 4. Questions Q.1 – Q.25 carry 1-mark each, and questions Q.26 – Q.55 carry 2-marks each. 5. Questions Q.26 - Q.30 are of numerical answer type. For each of these questions, the correct answer is a number. All other questions are of multiple choice type. Each of these questions carries four choices for the answer labeled A, B, C and D. Only one of the four choices is the correct answer. 6. Questions Q.48 – Q.51 (2 pairs) are common data questions and question pairs (Q.52, Q.53) and (Q.54, Q.55) are linked answer questions. The answer to the second question of the linked answer questions depends on the answer to the first question of the pair. If the first question in the linked pair is wrongly answered or is unattempted, then the answer to the second question in the pair will not be evaluated. 7. Questions Q.56 – Q.65 belong to General Aptitude (GA). Questions Q.56 – Q.60 carry 1-mark each, and questions Q.61 – Q.65 carry 2-marks each. 8. Unattempted questions will result in zero mark. There is no negative marking for questions of numerical answer type, i.e., for Q.26 – Q.30. For questions of multiple choice type, wrong answers will result in NEGATIVE marks. For Q.1 – Q.25 and Q.56 – Q.60, ? mark will be deducted for each wrong answer. For Q.31 – Q.51 and Q.61 – Q.65, ? mark will be deducted for each wrong answer. The question pairs (Q.52, Q.53), and (Q.54, Q.55) are questions with linked answers. There will be negative marks only for wrong answer to the first question of the linked answer question pair, i.e. for Q.52 and Q.54, ? mark will be deducted for each wrong answer. There is no negative marking for Q.53 and Q.55. 9. Calculator is allowed whereas charts, graph sheets or tables are NOT allowed in the examination hall. 10. Rough work can be done in the specified area only. 11. Candidates may use the back side of this page to record their answers for their own convenience. 12. To login, type your Registration Number and password as per instructions provided in the envelope. 13. In order to answer a question, you may select the question using the left side selection panel on the screen and choose the correct answer by clicking on the radio button next to the answer. The answered questions shall be indicated by a solid black ball on the selection panel. In order to change the answer, you may just click on another option. If you wish to leave a previously answered question unanswered, you may click on DESELECT ANSWER button. 14. You may also select questions using NEXT and PREVIOUS buttons. 15. You may also mark questions for reviewing later using MARK button. All marked questions are indicated by a rectangle in the selection panel. Questions which are answered but are marked for the review are indicated by a solid black rectangle and questions which are not answered but are marked for the review are indicated by an outlined rectangle in the selection panel. 16. You must sign this sheet and leave it with the invigilators at the end of the examination. DECLARATION I hereby declare that I have read and followed all the instructions given in this sheet. Paper Code: AE Registration No:__________________Name: ___________________________ Signature AE 2011 AEROSPACE ENGINEERING – AE Q. 1 – Q. 25 carry one mark each. Consider z y x , , to be right-handed Cartesian coordinates. A vector function is defined in this coordinate system as , where and k j i v 2 3 3 yz xy x ? ? ? j i, k are the unit vectors along y x, and z axes, respectively. The curl of is given by v Q.1 (A) k i y z 3 2 ? (B) k j y z 3 2 ? (C) j i y z 3 2 ? (D) k i y z 3 2 ? ? Which of the following functions is periodic? Q.2 (A) 2 ) ( x x f ? (B) x x f log ) ( ? (C) x e x f ? ) ( (D) . ) ( const x f ? The function has its minimum value at 14 6 4 2 ) , , ( 3 2 1 2 3 2 2 2 1 3 2 1 ? ? ? ? ? ? ? x x x x x x x x x f Q.3 (A) (1, 2, 3) (B) (0, 0, 0) (C) (3, 2, 1) (D) (1, 1, 3) Consider the function . The vector pointing in the direction of maximum increase of the function at the point (1, -1) is 2 1 2 2 2 1 2 1 2 ) , ( x x e x x x x f ? ? ? ? ? Q.4 (A) ? ? ? ? ? ? ? ? ? 5 2 (B) ? ? ? ? ? ? ? ? ? 5 1 (C) ? ? ? ? ? ? ? ? ? ? 73 . 6 73 . 0 (D) ? ? ? ? ? ? ? ? ? 4 2 Two simultaneous equations given by x y ? ? ? and ? ? ? x y have (A) a unique solution (B) infinitely many solutions Q.5 (C) no solution (D) a finite number of multiple solutions In three-dimensional linear elastic solids, the number of non-trivial stress-strain relations, strain- displacement equations and equations of equilibrium are, respectively, Q.6 (A) 3, 3 and 3 (B) 6, 3 and 3 (C) 6, 6 and 3 (D) 6, 3 and 6 An Euler-Bernoulli beam in bending is assumed to satisfy (A) both plane stress as well as plane strain conditions (B) plane strain condition but not plane stress condition (C) plane stress condition but not plane strain condition Q.7 (D) neither plane strain condition nor plane stress condition A statically indeterminate frame structure has (A) same number of joint degrees of freedom as the number of equilibrium equations (B) number of joint degrees of freedom greater than the number of equilibrium equations (C) number of joint degrees of freedom less than the number of equilibrium equations Q.8 (D) unknown number of joint degrees of freedom, which cannot be solved using laws of mechanics Consider a single degree of freedom spring-mass-damper system with mass, damping and stiffness of , and , respectively. The logarithmic decrement of this system can be calculated using m c k Q.9 (A) 2 4 2 c mk c ? ? (B) 2 4 c mk c ? ? (C) 2 2 c mk c ? ? (D) 2 4 2 c mk c ? ? AE 2011 AEROSPACE ENGINEERING – AE Consider a single degree of freedom spring-mass system of spring stiffness and mass which has a natural frequency of 10 rad/s. Consider another single degree of freedom spring-mass system of spring stiffness and mass which has a natural frequency of 20 rad/s. The spring stiffness is equal to 1 k m 2 k m 2 k Q.10 (A) 1 k (B) 1 2k (C) 4 1 k (D) 1 4k Consider a simply supported two-dimensional beam If the beam is converted into a fixed-fixed beam as then the degree of static indeterminacy will Q.11 (A) increase by 3 (B) increase by 2 (C) decrease by 1 (D) decrease by 3 An impulsive launch of a rocket minimizes the loss of burn-out velocity due to (A) aerodynamic drag force only (B) gravitational force only (C) both aerodynamic drag and gravitational forces Q.12 (D) reaction jet control force Multi-staging in rockets improves the burn-out performance by increasing mainly stage-wise (A) payload mass ratios (B) structural mass efficiencies Q.13 (C) propellant masses (D) control system masses In an un-powered glide of an aircraft having weight W, lift L and drag D, the equilibrium glide angle is defined as Q.14 (A) ? ? ? ? ? ? ? D L 1 tan (B) ? ? ? ? ? ? ? L D 1 tan (C) ? ? ? ? ? ? ? W L 1 tan (D) ? ? ? ? ? ? ? L W 1 tan Lift on an aircraft climbing vertically up is (A) equal to its weight (B) zero Q.15 (C) equal to the drag (D) equal to the thrust If an aircraft is performing a positive yawing manoeuvre, the side slip angle Q.16 (A) is always zero (B) is never zero (C) is always negative (D) could be any value For an airplane to be statically stable, its centre of gravity must always be (A) ahead of wing aerodynamic centre (B) aft of the wing aerodynamic centre Q.17 (C) ahead of neutral point (D) aft of neutral point It is seen that the drag polar of a certain aerofoil is symmetric about the C d axis. This drag polar could refer to Q.18 (A) NACA 0012 (B) NACA 4415 (C) NACA 23012 (D) None of the above AE 2011 AEROSPACE ENGINEERING – AE AE The aerodynamic centre of a supersonic aerofoil, with chord c, is located at Q.19 (A) the leading edge (B) 0.25c (C) 0.5c (D) 0.75c Winglets are used on wings to minimize Q.20 (A) skin friction drag (B) profile drag (C) wave drag (D) induced drag Consider a potential flow with free stream velocity V 8 , over a spinning circular cylinder of radius R and circulation ?. The stream function, ?, where ? = 0 on the cylinder surface, in cylindrical coordinates (r, ?) is given by (A) R r r R r V ln 2 1 cos 2 2 ? ? ? ? ? ? ? ? ? ? ? ? ? ? (B) R r r R r V ln 2 1 cos 2 2 ? ? ? ? ? ? ? ? ? ? ? ? ? ? Q.21 (C) R r r R r V ln 2 1 sin 2 2 ? ? ? ? ? ? ? ? ? ? ? ? ? ? (D) R r r R r V ln 2 1 sin 2 2 ? ? ? ? ? ? ? ? ? ? ? ? ? ? A main objective of by-pass in a turbo-fan engine is to increase (A) mass flow rate through engine inlet (B) turbine inlet temperature Q.22 (C) mass flow rate through exhaust nozzle (D) compressor pressure ratio The pressure ratio in any one stage of a jet engine compressor is limited by (A) entry stagnation temperature in that stage (B) entry Mach number in that stage (C) pressure gradient induced separation in that stage Q.23 (D) mass flow rate in that stage Thermodynamic cycle on which the jet engine operates can be Q.24 (A) open Rankine cycle only (B) either open or closed Rankine cycle (C) open Brayton cycle only (D) either open or closed Brayton cycle Propulsion efficiency of a jet engine is (A) directly proportional to both the thrust power and the air mass flow rate (B) inversely proportional to both the thrust power and the air mass flow rate (C) directly proportional to the thrust power and inversely proportional to the air mass flow rate Q.25 (D) inversely proportional to the thrust power and directly proportional to the air mass flow rate Q. 26 to Q. 55 carry two marks each. Questions Q.26 to Q. 30 are numerica l answer type. The answer to each of these questio ns is either a positive whole number, or a positive real number with maximum of 2 decimal places. Consider a cantilever beam having length L=1 m, square cross-section (width = depth = 0.01 m) and Young’s modulus 50 GPa. The beam is subjected to a transverse load P = 1 N at the mid-span (L/2) at the center of the cross-section. Under the small deformation theory, the transverse deflection of the beam (in mm) at its free-end is Q.26 P L L/2 2011 AEROSPACE ENGINEERING – AE AE Consider a beam in bending with a solid circular cross-section of 1 mm 2 , which is subjected to a transverse shear force of 1 N. The shear stress at the center of the cross-section (in N/mm 2 ) is Q.27 A simply supported slender column of square cross section (width=depth=d) has to be designed such that it buckles at the same instant as it yields. Length of the column is given to be 1.57 ?m and it is made of a material whose Young’s modulus is 200 GPa and yield stress is 240 MPa. The width, d, of the column (in cm) should be Q.28 A turbojet powered aircraft is flying at Mach number 0.8 at an altitude of 10 km. The inlet and exit areas of the engine are 0.7 m 2 and 0.4 m 2 respectively. The exhaust gases have velocity of 500 m/s and pressure of 60 kPa. The free stream pressure, density and speed of sound are 26.5 kPa, 0.413 kg/m 3 and 299.5 m/s respectively. The thrust of the engine (in kN) is Q.29 A low speed wind tunnel has a contraction ratio of 14:1 and the cross-sectional area of the test section is 1 m 2 . The static pressure difference between the settling chamber and the test section is 40 cm of water column. Assume , and . The speed of air in the test section (in m/s) is 2 m/s 81 . 9 ? g 3 kg/m 2 . 1 ? air ? 3 kg/m 1000 ? water ? Q.30 Questions Q.31 to Q.55 are multiple choice type. Consider the function . The Newton-Raphson iteration formula to find the root of the function starting from an initial guess at iteration k is ) sin( ) ( x x x f ? ? ) 0 ( x (A) ) ( ) ( ) ( ) 1 ( cos 1 cos sin k k k k k x x x x x ? ? ? ? (B) ) ( ) ( ) ( ) 1 ( cos 1 cos sin k k k k k x x x x x ? ? ? ? Q.31 (C) ) ( ) ( ) ( ) 1 ( cos 1 cos sin k k k k k x x x x x ? ? ? ? (D) ) ( ) ( ) ( ) 1 ( cos 1 cos sin k k k k k x x x x x ? ? ? ? Consider the matrix where a and b are real numbers. The two eigenvalues of this matrix ? ? ? ? ? ? 2 2 b a 1 ? and 2 ? are real and distinct ?? 2 1 ? ? ? when Q.32 (A) 0 and 0 ab ? ? ? (B) 0 and 0 ab ? (C) 0 and 0 ab ? ? (D) 0 and 0 ab ?? The solution of 32 t dy y et dt ? with initial condition 1 ) 0 ( ? y is given by (A) 2 1 (3) 9 t et ? (B) 2 9 52( 2 2) t et t ? ?? Q.33 (C) 2 4 (2) t e t ? (D) 2 1 52 ( 2 2) t et t ? ??Read More

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