Aeronautical Engineering (AE) 2012 GATE Paper without solution GATE Notes | EduRev

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GATE : Aeronautical Engineering (AE) 2012 GATE Paper without solution GATE Notes | EduRev

 Page 1


 
GATE 2012 Online Examination  
AE : AEROSPACE ENGINEERING 
Duration: Three Hours                          Maximum Marks: 100 
Read the following instructions carefully. 
 
1. The computer allotted to you at the examination center runs a specialized software that permits only 
one answer to be selected for multiple choice questions using a mouse. Your answers shall be updated 
and saved on a server periodically and at the end of the examination.  
 
2. To login, enter your Registration Number and password provided in the envelope. Go through the 
symbols used in the test and understand the meaning before you start the examination. You can view 
all questions by clicking on the View All Questions button in the screen after the start of the 
examination. 
 
3. To answer a question, select the question using the selection panel on the screen and choose the 
correct answer by clicking on the radio button next to the answer. To change the answer, just click on 
another option. If you wish to leave a previously answered question unanswered, click on the button 
next to the selected option. 
 
 
4. The examination will automatically stop at the end of 3 hours. 
 
5. There are a total of 65 questions carrying 100 marks. Except questions Q.26 – Q.30, all the other 
questions are of multiple choice type with only one correct answer. Questions Q.26 - Q.30 require a 
numerical answer, and a number should be entered using the virtual keyboard on the monitor.   
 
6. Questions Q.1 – Q.25 carry 1 mark each. Questions Q.26 – Q.55 carry 2 marks each. The 2 marks 
questions include two pairs of common data questions and two pairs of 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) section and carry a total of 15 marks. 
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 and wrong answers will result in NEGATIVE marks. 
There is no negative marking for questions of numerical answer type, i.e., for Q.26 – Q.30.  For all 1 
mark questions, ? mark will be deducted for each wrong answer. For all 2 marks questions, ? mark 
will be deducted for each wrong answer.  However, in the case of the linked answer question pair, 
there will be negative marks only for wrong answer to the first question and no negative marks for 
wrong answer to the second question.  
 
9. Calculator is allowed. Charts, graph sheets or tables are NOT allowed in the examination hall. Do the 
rough work in the Scribble Pad provided. 
 
10. 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. 
Registration Number 
AE 
      
 
 
Name  
Signature  
 
Verified that the above entries are correct. 
                                    Invigilator’s signature: 
 
Page 2


 
GATE 2012 Online Examination  
AE : AEROSPACE ENGINEERING 
Duration: Three Hours                          Maximum Marks: 100 
Read the following instructions carefully. 
 
1. The computer allotted to you at the examination center runs a specialized software that permits only 
one answer to be selected for multiple choice questions using a mouse. Your answers shall be updated 
and saved on a server periodically and at the end of the examination.  
 
2. To login, enter your Registration Number and password provided in the envelope. Go through the 
symbols used in the test and understand the meaning before you start the examination. You can view 
all questions by clicking on the View All Questions button in the screen after the start of the 
examination. 
 
3. To answer a question, select the question using the selection panel on the screen and choose the 
correct answer by clicking on the radio button next to the answer. To change the answer, just click on 
another option. If you wish to leave a previously answered question unanswered, click on the button 
next to the selected option. 
 
 
4. The examination will automatically stop at the end of 3 hours. 
 
5. There are a total of 65 questions carrying 100 marks. Except questions Q.26 – Q.30, all the other 
questions are of multiple choice type with only one correct answer. Questions Q.26 - Q.30 require a 
numerical answer, and a number should be entered using the virtual keyboard on the monitor.   
 
6. Questions Q.1 – Q.25 carry 1 mark each. Questions Q.26 – Q.55 carry 2 marks each. The 2 marks 
questions include two pairs of common data questions and two pairs of 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) section and carry a total of 15 marks. 
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 and wrong answers will result in NEGATIVE marks. 
There is no negative marking for questions of numerical answer type, i.e., for Q.26 – Q.30.  For all 1 
mark questions, ? mark will be deducted for each wrong answer. For all 2 marks questions, ? mark 
will be deducted for each wrong answer.  However, in the case of the linked answer question pair, 
there will be negative marks only for wrong answer to the first question and no negative marks for 
wrong answer to the second question.  
 
9. Calculator is allowed. Charts, graph sheets or tables are NOT allowed in the examination hall. Do the 
rough work in the Scribble Pad provided. 
 
10. 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. 
Registration Number 
AE 
      
 
 
Name  
Signature  
 
Verified that the above entries are correct. 
                                    Invigilator’s signature: 
 
2012                                                                                                                                                                            AEROSPACE ENGINEERING  –  AE  
AE 2/12
 
Q. 1 – Q. 25 carry one mark each. 
Q.1 The constraint A
2
 = A on any square matrix A is satisfied for 
(A) the identity matrix only. (B) the null matrix only. 
(C) both the identity matrix and the null matrix. (D) no square matrix A. 
 
Q.2 
The general solution of the differential equation 
2
2
20
dy dy
y
dt dt
+ -= is 
(A) 
2 tt
Ae Be
-
+ (B) 
2tt
Ae Be
--
+ (C) 
2tt
Ae Be
-
+ (D) 
2 tt
Ae Be + 
 
Q.3 An aircraft in trimmed condition has zero pitching moment at 
(A) its aerodynamic centre. (B) its centre of gravity. 
(C) 25% of its mean aerodynamic chord. (D) 50% of its wing root chord. 
 
Q.4 In an aircraft, constant roll rate can be produced using ailerons by applying 
(A) a step input. (B) a ramp input. 
(C) a sinusoidal input. (D) an impulse input. 
 
Q.5 For a symmetric airfoil, the lift coefficient for zero degree angle of attack is 
(A) – 1.0 (B) 0.0 (C) 0.5  (D) 1.0  
 
Q.6 The critical Mach number of an airfoil is attained when 
(A) the freestream Mach number is sonic. 
(B) the freestream Mach number is supersonic. 
(C) the Mach number somewhere on the airfoil is unity. 
(D) the Mach number everywhere on the airfoil is supersonic. 
 
Q.7 The shadowgraph flow visualization technique depends on 
(A) the variation of the value of density in the flow. 
(B) the first derivative of density with respect to spatial coordinate. 
(C) the second derivative of density with respect to spatial coordinate. 
(D) the third derivative of density with respect to spatial coordinate. 
 
Q.8 The Hohmann ellipse used as earth-Mars transfer orbit has 
(A) apogee at earth and perigee at Mars. (B) both apogee and perigee at earth. 
(C) apogee at Mars and perigee at earth. (D) both apogee and perigee at Mars. 
 
Q.9 The governing equation for the static transverse deflection of a beam under an uniformly distributed 
load, according to Euler-Bernoulli (engineering) beam theory, is a 
(A) 2
nd
 order linear homogenous partial differential equation. 
(B) 4
th
 order linear non-homogenous ordinary differential equation. 
(C) 2
nd
 order linear non-homogenous ordinary differential equation. 
(D) 4
th
 order nonlinear homogenous ordinary differential equation. 
 
Q.10 The Poisson’s ratio, ? of most aircraft grade metallic alloys has values in the range: 
(A) -1 ? ==0  (B) 0 ? == 0.2  (C)  0.2 ? = = 0.4 (D)  0.4 ? == 0.5 
 
Page 3


 
GATE 2012 Online Examination  
AE : AEROSPACE ENGINEERING 
Duration: Three Hours                          Maximum Marks: 100 
Read the following instructions carefully. 
 
1. The computer allotted to you at the examination center runs a specialized software that permits only 
one answer to be selected for multiple choice questions using a mouse. Your answers shall be updated 
and saved on a server periodically and at the end of the examination.  
 
2. To login, enter your Registration Number and password provided in the envelope. Go through the 
symbols used in the test and understand the meaning before you start the examination. You can view 
all questions by clicking on the View All Questions button in the screen after the start of the 
examination. 
 
3. To answer a question, select the question using the selection panel on the screen and choose the 
correct answer by clicking on the radio button next to the answer. To change the answer, just click on 
another option. If you wish to leave a previously answered question unanswered, click on the button 
next to the selected option. 
 
 
4. The examination will automatically stop at the end of 3 hours. 
 
5. There are a total of 65 questions carrying 100 marks. Except questions Q.26 – Q.30, all the other 
questions are of multiple choice type with only one correct answer. Questions Q.26 - Q.30 require a 
numerical answer, and a number should be entered using the virtual keyboard on the monitor.   
 
6. Questions Q.1 – Q.25 carry 1 mark each. Questions Q.26 – Q.55 carry 2 marks each. The 2 marks 
questions include two pairs of common data questions and two pairs of 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) section and carry a total of 15 marks. 
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 and wrong answers will result in NEGATIVE marks. 
There is no negative marking for questions of numerical answer type, i.e., for Q.26 – Q.30.  For all 1 
mark questions, ? mark will be deducted for each wrong answer. For all 2 marks questions, ? mark 
will be deducted for each wrong answer.  However, in the case of the linked answer question pair, 
there will be negative marks only for wrong answer to the first question and no negative marks for 
wrong answer to the second question.  
 
9. Calculator is allowed. Charts, graph sheets or tables are NOT allowed in the examination hall. Do the 
rough work in the Scribble Pad provided. 
 
10. 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. 
Registration Number 
AE 
      
 
 
Name  
Signature  
 
Verified that the above entries are correct. 
                                    Invigilator’s signature: 
 
2012                                                                                                                                                                            AEROSPACE ENGINEERING  –  AE  
AE 2/12
 
Q. 1 – Q. 25 carry one mark each. 
Q.1 The constraint A
2
 = A on any square matrix A is satisfied for 
(A) the identity matrix only. (B) the null matrix only. 
(C) both the identity matrix and the null matrix. (D) no square matrix A. 
 
Q.2 
The general solution of the differential equation 
2
2
20
dy dy
y
dt dt
+ -= is 
(A) 
2 tt
Ae Be
-
+ (B) 
2tt
Ae Be
--
+ (C) 
2tt
Ae Be
-
+ (D) 
2 tt
Ae Be + 
 
Q.3 An aircraft in trimmed condition has zero pitching moment at 
(A) its aerodynamic centre. (B) its centre of gravity. 
(C) 25% of its mean aerodynamic chord. (D) 50% of its wing root chord. 
 
Q.4 In an aircraft, constant roll rate can be produced using ailerons by applying 
(A) a step input. (B) a ramp input. 
(C) a sinusoidal input. (D) an impulse input. 
 
Q.5 For a symmetric airfoil, the lift coefficient for zero degree angle of attack is 
(A) – 1.0 (B) 0.0 (C) 0.5  (D) 1.0  
 
Q.6 The critical Mach number of an airfoil is attained when 
(A) the freestream Mach number is sonic. 
(B) the freestream Mach number is supersonic. 
(C) the Mach number somewhere on the airfoil is unity. 
(D) the Mach number everywhere on the airfoil is supersonic. 
 
Q.7 The shadowgraph flow visualization technique depends on 
(A) the variation of the value of density in the flow. 
(B) the first derivative of density with respect to spatial coordinate. 
(C) the second derivative of density with respect to spatial coordinate. 
(D) the third derivative of density with respect to spatial coordinate. 
 
Q.8 The Hohmann ellipse used as earth-Mars transfer orbit has 
(A) apogee at earth and perigee at Mars. (B) both apogee and perigee at earth. 
(C) apogee at Mars and perigee at earth. (D) both apogee and perigee at Mars. 
 
Q.9 The governing equation for the static transverse deflection of a beam under an uniformly distributed 
load, according to Euler-Bernoulli (engineering) beam theory, is a 
(A) 2
nd
 order linear homogenous partial differential equation. 
(B) 4
th
 order linear non-homogenous ordinary differential equation. 
(C) 2
nd
 order linear non-homogenous ordinary differential equation. 
(D) 4
th
 order nonlinear homogenous ordinary differential equation. 
 
Q.10 The Poisson’s ratio, ? of most aircraft grade metallic alloys has values in the range: 
(A) -1 ? ==0  (B) 0 ? == 0.2  (C)  0.2 ? = = 0.4 (D)  0.4 ? == 0.5 
 
2012                                                                                                                                                                            AEROSPACE ENGINEERING  –  AE  
AE 3/12
 
Q.11 The value of k for which the system of equations 21;2 83 xy kz x ky z + += + + = has no 
solution is 
(A) 0 (B) 2 (C)  4 (D)  8 
 
Q.12 
If () ut is a unit step function, the solution of the differential equation 
2
2
()
dx
mkxut
dt
+= in 
Laplace domain is 
(A) 
2
1
() sms k +
 (B) 
2
1
ms k +
 (C)  
2
s
ms k +
 (D)  
22
1
() sms k +
 
 
Q.13 
The general solution of the differential equation 20
dy
y
dx
- = is 
(A) 0 yx C -+ = 
(B) 0 yx C -+ = (C) 0 yxC - += (D)  0 yx C -+ = 
 
Q.14 During the ground roll manoeuvre of an aircraft, the force(s) acting on it parallel to the direction of 
motion  
(A) is thrust alone. (B) is drag alone. 
(C) are both thrust and drag. (D) are thrust, drag and a part of both weight and lift. 
 
Q.15 An aircraft in a steady climb suddenly experiences a 10% drop in thrust. After a new equilibrium is 
reached at the same speed, the new rate of climb is 
(A) lower by exactly 10%. (B) lower by more than 10%. 
(C) lower by less than 10%. (D) an unpredictable quantity. 
 
Q.16 In an aircraft, the dive manoeuvre can be initiated by 
(A) reducing the engine thrust alone. (B) reducing the angle of attack alone. 
(C) generating a nose down pitch rate. (D) increasing the engine thrust alone. 
 
Q.17 In an aircraft, elevator control effectiveness determines 
(A) turn radius. 
(B) rate of climb. 
(C) forward-most location of the centre of gravity. 
(D) aft-most location of the centre of gravity. 
 
Q.18 The Mach angle for a flow at Mach 2.0 is 
(A) 30
o
 (B) 45
o
 (C) 60
o
  (D) 90
o
  
 
Q.19 For a wing of aspect ratio AR, having an elliptical lift distribution, the induced drag coefficient is 
(where C
L
 is the lift coefficient) 
(A) 
L
C
AR p
 
(B) 
2
L
C
AR p
 
(C) 
2
L
C
AR p
 
(D) 
2
2
L
C
AR p
 
 
Q.20 Bernoulli’s equation is valid under steady state 
(A) only along a streamline in inviscid flow, and between any two points in potential flow. 
(B) between any two points in both inviscid flow and potential flow. 
(C) between any two points in inviscid flow, and only along a streamline in potential flow. 
(D) only along a streamline in both inviscid flow and potential flow. 
Page 4


 
GATE 2012 Online Examination  
AE : AEROSPACE ENGINEERING 
Duration: Three Hours                          Maximum Marks: 100 
Read the following instructions carefully. 
 
1. The computer allotted to you at the examination center runs a specialized software that permits only 
one answer to be selected for multiple choice questions using a mouse. Your answers shall be updated 
and saved on a server periodically and at the end of the examination.  
 
2. To login, enter your Registration Number and password provided in the envelope. Go through the 
symbols used in the test and understand the meaning before you start the examination. You can view 
all questions by clicking on the View All Questions button in the screen after the start of the 
examination. 
 
3. To answer a question, select the question using the selection panel on the screen and choose the 
correct answer by clicking on the radio button next to the answer. To change the answer, just click on 
another option. If you wish to leave a previously answered question unanswered, click on the button 
next to the selected option. 
 
 
4. The examination will automatically stop at the end of 3 hours. 
 
5. There are a total of 65 questions carrying 100 marks. Except questions Q.26 – Q.30, all the other 
questions are of multiple choice type with only one correct answer. Questions Q.26 - Q.30 require a 
numerical answer, and a number should be entered using the virtual keyboard on the monitor.   
 
6. Questions Q.1 – Q.25 carry 1 mark each. Questions Q.26 – Q.55 carry 2 marks each. The 2 marks 
questions include two pairs of common data questions and two pairs of 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) section and carry a total of 15 marks. 
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 and wrong answers will result in NEGATIVE marks. 
There is no negative marking for questions of numerical answer type, i.e., for Q.26 – Q.30.  For all 1 
mark questions, ? mark will be deducted for each wrong answer. For all 2 marks questions, ? mark 
will be deducted for each wrong answer.  However, in the case of the linked answer question pair, 
there will be negative marks only for wrong answer to the first question and no negative marks for 
wrong answer to the second question.  
 
9. Calculator is allowed. Charts, graph sheets or tables are NOT allowed in the examination hall. Do the 
rough work in the Scribble Pad provided. 
 
10. 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. 
Registration Number 
AE 
      
 
 
Name  
Signature  
 
Verified that the above entries are correct. 
                                    Invigilator’s signature: 
 
2012                                                                                                                                                                            AEROSPACE ENGINEERING  –  AE  
AE 2/12
 
Q. 1 – Q. 25 carry one mark each. 
Q.1 The constraint A
2
 = A on any square matrix A is satisfied for 
(A) the identity matrix only. (B) the null matrix only. 
(C) both the identity matrix and the null matrix. (D) no square matrix A. 
 
Q.2 
The general solution of the differential equation 
2
2
20
dy dy
y
dt dt
+ -= is 
(A) 
2 tt
Ae Be
-
+ (B) 
2tt
Ae Be
--
+ (C) 
2tt
Ae Be
-
+ (D) 
2 tt
Ae Be + 
 
Q.3 An aircraft in trimmed condition has zero pitching moment at 
(A) its aerodynamic centre. (B) its centre of gravity. 
(C) 25% of its mean aerodynamic chord. (D) 50% of its wing root chord. 
 
Q.4 In an aircraft, constant roll rate can be produced using ailerons by applying 
(A) a step input. (B) a ramp input. 
(C) a sinusoidal input. (D) an impulse input. 
 
Q.5 For a symmetric airfoil, the lift coefficient for zero degree angle of attack is 
(A) – 1.0 (B) 0.0 (C) 0.5  (D) 1.0  
 
Q.6 The critical Mach number of an airfoil is attained when 
(A) the freestream Mach number is sonic. 
(B) the freestream Mach number is supersonic. 
(C) the Mach number somewhere on the airfoil is unity. 
(D) the Mach number everywhere on the airfoil is supersonic. 
 
Q.7 The shadowgraph flow visualization technique depends on 
(A) the variation of the value of density in the flow. 
(B) the first derivative of density with respect to spatial coordinate. 
(C) the second derivative of density with respect to spatial coordinate. 
(D) the third derivative of density with respect to spatial coordinate. 
 
Q.8 The Hohmann ellipse used as earth-Mars transfer orbit has 
(A) apogee at earth and perigee at Mars. (B) both apogee and perigee at earth. 
(C) apogee at Mars and perigee at earth. (D) both apogee and perigee at Mars. 
 
Q.9 The governing equation for the static transverse deflection of a beam under an uniformly distributed 
load, according to Euler-Bernoulli (engineering) beam theory, is a 
(A) 2
nd
 order linear homogenous partial differential equation. 
(B) 4
th
 order linear non-homogenous ordinary differential equation. 
(C) 2
nd
 order linear non-homogenous ordinary differential equation. 
(D) 4
th
 order nonlinear homogenous ordinary differential equation. 
 
Q.10 The Poisson’s ratio, ? of most aircraft grade metallic alloys has values in the range: 
(A) -1 ? ==0  (B) 0 ? == 0.2  (C)  0.2 ? = = 0.4 (D)  0.4 ? == 0.5 
 
2012                                                                                                                                                                            AEROSPACE ENGINEERING  –  AE  
AE 3/12
 
Q.11 The value of k for which the system of equations 21;2 83 xy kz x ky z + += + + = has no 
solution is 
(A) 0 (B) 2 (C)  4 (D)  8 
 
Q.12 
If () ut is a unit step function, the solution of the differential equation 
2
2
()
dx
mkxut
dt
+= in 
Laplace domain is 
(A) 
2
1
() sms k +
 (B) 
2
1
ms k +
 (C)  
2
s
ms k +
 (D)  
22
1
() sms k +
 
 
Q.13 
The general solution of the differential equation 20
dy
y
dx
- = is 
(A) 0 yx C -+ = 
(B) 0 yx C -+ = (C) 0 yxC - += (D)  0 yx C -+ = 
 
Q.14 During the ground roll manoeuvre of an aircraft, the force(s) acting on it parallel to the direction of 
motion  
(A) is thrust alone. (B) is drag alone. 
(C) are both thrust and drag. (D) are thrust, drag and a part of both weight and lift. 
 
Q.15 An aircraft in a steady climb suddenly experiences a 10% drop in thrust. After a new equilibrium is 
reached at the same speed, the new rate of climb is 
(A) lower by exactly 10%. (B) lower by more than 10%. 
(C) lower by less than 10%. (D) an unpredictable quantity. 
 
Q.16 In an aircraft, the dive manoeuvre can be initiated by 
(A) reducing the engine thrust alone. (B) reducing the angle of attack alone. 
(C) generating a nose down pitch rate. (D) increasing the engine thrust alone. 
 
Q.17 In an aircraft, elevator control effectiveness determines 
(A) turn radius. 
(B) rate of climb. 
(C) forward-most location of the centre of gravity. 
(D) aft-most location of the centre of gravity. 
 
Q.18 The Mach angle for a flow at Mach 2.0 is 
(A) 30
o
 (B) 45
o
 (C) 60
o
  (D) 90
o
  
 
Q.19 For a wing of aspect ratio AR, having an elliptical lift distribution, the induced drag coefficient is 
(where C
L
 is the lift coefficient) 
(A) 
L
C
AR p
 
(B) 
2
L
C
AR p
 
(C) 
2
L
C
AR p
 
(D) 
2
2
L
C
AR p
 
 
Q.20 Bernoulli’s equation is valid under steady state 
(A) only along a streamline in inviscid flow, and between any two points in potential flow. 
(B) between any two points in both inviscid flow and potential flow. 
(C) between any two points in inviscid flow, and only along a streamline in potential flow. 
(D) only along a streamline in both inviscid flow and potential flow. 
2012                                                                                                                                                                            AEROSPACE ENGINEERING  –  AE  
AE 4/12
 
Q.21 The ratio of flight speed to the exhaust velocity for maximum propulsion efficiency is 
(A) 0.0 (B) 0.5 (C) 1.0 (D) 2.0 
 
Q.22 The ideal static pressure coefficient of a diffuser with an area ratio of 2.0 is 
(A) 0.25 (B) 0.50 (C) 0.75 (D) 1.0 
 
Q.23 A rocket is to be launched from the bottom of a very deep crater on Mars for earth return.  The 
specific impulse of the rocket, measured in seconds, is to be normalized by the acceleration due to 
gravity at 
(A) the bottom of the crater on Mars. (B) Mars standard “sea level”. 
(C) earth’s standard sea level. (D) the same depth of the crater on earth. 
 
Q.24 In a semi-monocoque construction of an aircraft wing, the skin and spar webs are the primary 
carriers of 
(A) shear stresses due to an aerodynamic moment component alone. 
(B) normal (bending) stresses due to aerodynamic forces. 
(C) shear stresses due to aerodynamic forces alone. 
(D) shear stresses due to aerodynamic forces and a moment component. 
 
Q.25 The logarithmic decrement measured for a viscously damped single degree of freedom system is 
0.125. The value of the damping factor in % is closest to 
(A) 0.5 (B) 1.0 (C) 1.5 (D) 2.0 
 
Q. 26 to Q. 55 carry two marks each. 
Questions Q.26 to Q.30 are numerical answer type. The answer to each of these questions is 
either a positive whole number, or a positive real number with maximum of 2 decimal places. 
 
Q.26 
The integration 
1
3
0
x dx
?
 computed using trapezoidal rule with 4 n = intervals is ____. 
 
Q.27 An aircraft has a steady rate of climb of 300 m/s at sea level and 150 m/s at 2500 m altitude. The 
time taken (in sec) for this aircraft to climb from 500 m altitude to 3000 m altitude is ____. 
 
Q.28 An airfoil generates a lift of 80 N when operating in a freestream flow of 60 m/s. If the ambient 
pressure and temperature are 100 kPa and 290 K respectively (specific gas constant is 287 J/kg-K), 
the circulation on the airfoil in m
2
/s is ____. 
 
Q.29 A rocket motor has combustion chamber temperature of 2600 K and the products have molecular 
weight of 25 g/mol and ratio of specific heats 1.2.  The universal gas constant is 8314 J/kg-mole-K.  
The value of theoretical c* (in m/s) is ____.  
 
Q.30 
The mode shapes of an un-damped two degrees of freedom system are {} 10.5
T
 and 
{} 10.675
T
- . The corresponding natural frequencies are 0.45 Hz and 1.2471 Hz. The maximum 
amplitude (in mm) of vibration of the first degree of freedom due to an initial displacement of 
{} 21
T
(in mm) and zero initial velocities is ____. 
Page 5


 
GATE 2012 Online Examination  
AE : AEROSPACE ENGINEERING 
Duration: Three Hours                          Maximum Marks: 100 
Read the following instructions carefully. 
 
1. The computer allotted to you at the examination center runs a specialized software that permits only 
one answer to be selected for multiple choice questions using a mouse. Your answers shall be updated 
and saved on a server periodically and at the end of the examination.  
 
2. To login, enter your Registration Number and password provided in the envelope. Go through the 
symbols used in the test and understand the meaning before you start the examination. You can view 
all questions by clicking on the View All Questions button in the screen after the start of the 
examination. 
 
3. To answer a question, select the question using the selection panel on the screen and choose the 
correct answer by clicking on the radio button next to the answer. To change the answer, just click on 
another option. If you wish to leave a previously answered question unanswered, click on the button 
next to the selected option. 
 
 
4. The examination will automatically stop at the end of 3 hours. 
 
5. There are a total of 65 questions carrying 100 marks. Except questions Q.26 – Q.30, all the other 
questions are of multiple choice type with only one correct answer. Questions Q.26 - Q.30 require a 
numerical answer, and a number should be entered using the virtual keyboard on the monitor.   
 
6. Questions Q.1 – Q.25 carry 1 mark each. Questions Q.26 – Q.55 carry 2 marks each. The 2 marks 
questions include two pairs of common data questions and two pairs of 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) section and carry a total of 15 marks. 
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 and wrong answers will result in NEGATIVE marks. 
There is no negative marking for questions of numerical answer type, i.e., for Q.26 – Q.30.  For all 1 
mark questions, ? mark will be deducted for each wrong answer. For all 2 marks questions, ? mark 
will be deducted for each wrong answer.  However, in the case of the linked answer question pair, 
there will be negative marks only for wrong answer to the first question and no negative marks for 
wrong answer to the second question.  
 
9. Calculator is allowed. Charts, graph sheets or tables are NOT allowed in the examination hall. Do the 
rough work in the Scribble Pad provided. 
 
10. 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. 
Registration Number 
AE 
      
 
 
Name  
Signature  
 
Verified that the above entries are correct. 
                                    Invigilator’s signature: 
 
2012                                                                                                                                                                            AEROSPACE ENGINEERING  –  AE  
AE 2/12
 
Q. 1 – Q. 25 carry one mark each. 
Q.1 The constraint A
2
 = A on any square matrix A is satisfied for 
(A) the identity matrix only. (B) the null matrix only. 
(C) both the identity matrix and the null matrix. (D) no square matrix A. 
 
Q.2 
The general solution of the differential equation 
2
2
20
dy dy
y
dt dt
+ -= is 
(A) 
2 tt
Ae Be
-
+ (B) 
2tt
Ae Be
--
+ (C) 
2tt
Ae Be
-
+ (D) 
2 tt
Ae Be + 
 
Q.3 An aircraft in trimmed condition has zero pitching moment at 
(A) its aerodynamic centre. (B) its centre of gravity. 
(C) 25% of its mean aerodynamic chord. (D) 50% of its wing root chord. 
 
Q.4 In an aircraft, constant roll rate can be produced using ailerons by applying 
(A) a step input. (B) a ramp input. 
(C) a sinusoidal input. (D) an impulse input. 
 
Q.5 For a symmetric airfoil, the lift coefficient for zero degree angle of attack is 
(A) – 1.0 (B) 0.0 (C) 0.5  (D) 1.0  
 
Q.6 The critical Mach number of an airfoil is attained when 
(A) the freestream Mach number is sonic. 
(B) the freestream Mach number is supersonic. 
(C) the Mach number somewhere on the airfoil is unity. 
(D) the Mach number everywhere on the airfoil is supersonic. 
 
Q.7 The shadowgraph flow visualization technique depends on 
(A) the variation of the value of density in the flow. 
(B) the first derivative of density with respect to spatial coordinate. 
(C) the second derivative of density with respect to spatial coordinate. 
(D) the third derivative of density with respect to spatial coordinate. 
 
Q.8 The Hohmann ellipse used as earth-Mars transfer orbit has 
(A) apogee at earth and perigee at Mars. (B) both apogee and perigee at earth. 
(C) apogee at Mars and perigee at earth. (D) both apogee and perigee at Mars. 
 
Q.9 The governing equation for the static transverse deflection of a beam under an uniformly distributed 
load, according to Euler-Bernoulli (engineering) beam theory, is a 
(A) 2
nd
 order linear homogenous partial differential equation. 
(B) 4
th
 order linear non-homogenous ordinary differential equation. 
(C) 2
nd
 order linear non-homogenous ordinary differential equation. 
(D) 4
th
 order nonlinear homogenous ordinary differential equation. 
 
Q.10 The Poisson’s ratio, ? of most aircraft grade metallic alloys has values in the range: 
(A) -1 ? ==0  (B) 0 ? == 0.2  (C)  0.2 ? = = 0.4 (D)  0.4 ? == 0.5 
 
2012                                                                                                                                                                            AEROSPACE ENGINEERING  –  AE  
AE 3/12
 
Q.11 The value of k for which the system of equations 21;2 83 xy kz x ky z + += + + = has no 
solution is 
(A) 0 (B) 2 (C)  4 (D)  8 
 
Q.12 
If () ut is a unit step function, the solution of the differential equation 
2
2
()
dx
mkxut
dt
+= in 
Laplace domain is 
(A) 
2
1
() sms k +
 (B) 
2
1
ms k +
 (C)  
2
s
ms k +
 (D)  
22
1
() sms k +
 
 
Q.13 
The general solution of the differential equation 20
dy
y
dx
- = is 
(A) 0 yx C -+ = 
(B) 0 yx C -+ = (C) 0 yxC - += (D)  0 yx C -+ = 
 
Q.14 During the ground roll manoeuvre of an aircraft, the force(s) acting on it parallel to the direction of 
motion  
(A) is thrust alone. (B) is drag alone. 
(C) are both thrust and drag. (D) are thrust, drag and a part of both weight and lift. 
 
Q.15 An aircraft in a steady climb suddenly experiences a 10% drop in thrust. After a new equilibrium is 
reached at the same speed, the new rate of climb is 
(A) lower by exactly 10%. (B) lower by more than 10%. 
(C) lower by less than 10%. (D) an unpredictable quantity. 
 
Q.16 In an aircraft, the dive manoeuvre can be initiated by 
(A) reducing the engine thrust alone. (B) reducing the angle of attack alone. 
(C) generating a nose down pitch rate. (D) increasing the engine thrust alone. 
 
Q.17 In an aircraft, elevator control effectiveness determines 
(A) turn radius. 
(B) rate of climb. 
(C) forward-most location of the centre of gravity. 
(D) aft-most location of the centre of gravity. 
 
Q.18 The Mach angle for a flow at Mach 2.0 is 
(A) 30
o
 (B) 45
o
 (C) 60
o
  (D) 90
o
  
 
Q.19 For a wing of aspect ratio AR, having an elliptical lift distribution, the induced drag coefficient is 
(where C
L
 is the lift coefficient) 
(A) 
L
C
AR p
 
(B) 
2
L
C
AR p
 
(C) 
2
L
C
AR p
 
(D) 
2
2
L
C
AR p
 
 
Q.20 Bernoulli’s equation is valid under steady state 
(A) only along a streamline in inviscid flow, and between any two points in potential flow. 
(B) between any two points in both inviscid flow and potential flow. 
(C) between any two points in inviscid flow, and only along a streamline in potential flow. 
(D) only along a streamline in both inviscid flow and potential flow. 
2012                                                                                                                                                                            AEROSPACE ENGINEERING  –  AE  
AE 4/12
 
Q.21 The ratio of flight speed to the exhaust velocity for maximum propulsion efficiency is 
(A) 0.0 (B) 0.5 (C) 1.0 (D) 2.0 
 
Q.22 The ideal static pressure coefficient of a diffuser with an area ratio of 2.0 is 
(A) 0.25 (B) 0.50 (C) 0.75 (D) 1.0 
 
Q.23 A rocket is to be launched from the bottom of a very deep crater on Mars for earth return.  The 
specific impulse of the rocket, measured in seconds, is to be normalized by the acceleration due to 
gravity at 
(A) the bottom of the crater on Mars. (B) Mars standard “sea level”. 
(C) earth’s standard sea level. (D) the same depth of the crater on earth. 
 
Q.24 In a semi-monocoque construction of an aircraft wing, the skin and spar webs are the primary 
carriers of 
(A) shear stresses due to an aerodynamic moment component alone. 
(B) normal (bending) stresses due to aerodynamic forces. 
(C) shear stresses due to aerodynamic forces alone. 
(D) shear stresses due to aerodynamic forces and a moment component. 
 
Q.25 The logarithmic decrement measured for a viscously damped single degree of freedom system is 
0.125. The value of the damping factor in % is closest to 
(A) 0.5 (B) 1.0 (C) 1.5 (D) 2.0 
 
Q. 26 to Q. 55 carry two marks each. 
Questions Q.26 to Q.30 are numerical answer type. The answer to each of these questions is 
either a positive whole number, or a positive real number with maximum of 2 decimal places. 
 
Q.26 
The integration 
1
3
0
x dx
?
 computed using trapezoidal rule with 4 n = intervals is ____. 
 
Q.27 An aircraft has a steady rate of climb of 300 m/s at sea level and 150 m/s at 2500 m altitude. The 
time taken (in sec) for this aircraft to climb from 500 m altitude to 3000 m altitude is ____. 
 
Q.28 An airfoil generates a lift of 80 N when operating in a freestream flow of 60 m/s. If the ambient 
pressure and temperature are 100 kPa and 290 K respectively (specific gas constant is 287 J/kg-K), 
the circulation on the airfoil in m
2
/s is ____. 
 
Q.29 A rocket motor has combustion chamber temperature of 2600 K and the products have molecular 
weight of 25 g/mol and ratio of specific heats 1.2.  The universal gas constant is 8314 J/kg-mole-K.  
The value of theoretical c* (in m/s) is ____.  
 
Q.30 
The mode shapes of an un-damped two degrees of freedom system are {} 10.5
T
 and 
{} 10.675
T
- . The corresponding natural frequencies are 0.45 Hz and 1.2471 Hz. The maximum 
amplitude (in mm) of vibration of the first degree of freedom due to an initial displacement of 
{} 21
T
(in mm) and zero initial velocities is ____. 
2012                                                                                                                                                                            AEROSPACE ENGINEERING  –  AE  
AE 5/12
 
 
Questions Q.31 to Q.55 are multiple choice type. 
 
Q.31 The n
th
 derivative of the function 
1
3
y
x
=
+
 is 
(A) 
1
(1) !
(3)
n
n
n
x
+
-
+
 (B) 
1
1
(1) !
(3)
n
n
n
x
+
+
-
+
 (C) 
(1) ( 1)!
(3)
n
n
n
x
- +
+
 (D) 
(1) !
(3)
n
n
n
x
-
+
 
 
Q.32 The volume of a solid generated by rotating the region between semi-circle
2
11 y x =- - and 
straight line y = 1, about x axis, is 
(A) 
2
4
3
p p - (B) 
2
1
4
3
p p - (C)  
2
3
4
p p - (D)  
2
3
4
p p - 
 
Q.33 
One eigenvalue of the matrix 
27 10
52 25
16 5
A
? ?
? ?
=
? ?
? ?
? ?
 is – 9.33. One of the other eigenvalues is   
(A) 18.33 (B) -18.33 (C)  18.33 -9.33i (D)  18.33+9.33i 
 
Q.34 If an aircraft takes off with 10% less fuel in comparison to its standard configuration, its range is  
(A) lower by exactly 10%. (B) lower by more than 10%. 
(C) lower by less than 10%. (D) an unpredictable quantity. 
 
Q.35 An aircraft has an approach speed of 144 kmph with a descent angle of 6.6
o
. If the aircraft load 
factor is 1.2 and constant deceleration at touch down is 0.25g (g = 9.81 m/s
2
), its total landing 
distance approximately over a 15 m high obstacle is 
(A) 1830 m. (B) 1380 m. (C)  830 m. (D)  380 m. 
 
Q.36 An aircraft is trimmed straight and level at true air speed (TAS) of 100 m/s at standard sea level 
(SSL). Further, pull of 5 N holds the speed at 90 m/s without re-trimming at SSL (air density = 1.22 
kg/m
3
). To fly at 3000 m altitude (air density = 0.91 kg/m
3
) and 120 m/s TAS without re-trimming, 
the aircraft needs 
(A) 1.95 N upward force. (B) 1.95 N downward force. 
(C) 1.85 N upward force. (D) 1.75 N downward force. 
 
Q.37 An oblique shock wave with a wave angle ß is generated from a wedge angle of ?. The ratio of the 
Mach number downstream of the shock to its normal component is 
(A) sin( ß– ?) (B) cos( ß– ?) (C)  sin( ?– ß) (D)  cos( ?– ß) 
 
Q.38 In a closed-circuit supersonic wind tunnel, the convergent-divergent (C-D) nozzle and test section 
are followed by a C-D diffuser to swallow the starting shock. Here, we should have the 
(A) diffuser throat larger than the nozzle throat and the shock located just at the diffuser throat. 
(B) diffuser throat larger than the nozzle throat and the shock located downstream of the diffuser 
throat. 
(C) diffuser throat of the same size as the nozzle throat and the shock located just at the diffuser 
throat. 
(D) diffuser throat of the same size as the nozzle throat and the shock located downstream of the 
diffuser throat. 
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