GATE 2014 Question Paper & Answers - AE

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GATE 2014

Question Papers & Answers

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GATE 2014: General Instructions during Examination

1. 1. Total duration of the GATE examination is

Total duration of the GATE examination is

180

180 minutes.

minutes.

2. 2. The clock will be set at the server. The countdown timer at the top right corner of

The clock will be set at the server. The countdown timer at the top right corner of

screen will display the remaining time available for you to complete the examination.

When the timer reaches zero, the examination will end by itself. You need not

terminate the examination or submit your paper.

3. 3. Any useful data required for your paper can be viewed by clicking on the

Any useful data required for your paper can be viewed by clicking on the

Useful

Common Data

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4. 4. Use the scribble pad provided to you for any rough work. Submit the scribble pa

Use the scribble pad provided to you for any rough work. Submit the scribble pad at

d at

the end of the examination.

5. 5. You are allowed to use a non-programmable type calculator, however, sharing o

You are allowed to use a non-programmable type calculator, however, sharing off

calculators is not allowed.

6. 6. The Question Palette displayed on the right si

The Question Palette displayed on the right side of screen will

de of screen will show the status o

show the status off

each question using one of the following symbols:

The

M

Marked for Review

arked for Review

status for a question simply indicates that you would like to lo

status for a question simply indicates that you would like to look at

ok at

that q

that question again.

uestion again. If a question is answered, but marked for review, then the answer

If a question is answered, but marked for review, then the answer will

will

be co

be considered for evaluation unless the status is

nsidered for evaluation unless the status is modified by the candidate.

modified by the candidate.

Navig

Navigating to a Question :

ating to a Question :

7. 7. To answer a question, do the following:

To answer a question, do the following:

a.

a. Click on the question number in the Question Palette to go to that que

Click on the question number in the Question Palette to go to that question

stion

directly.

b.

b. Select an answer for a multiple choice type question by clicking on the bubble

Select an answer for a multiple choice type question by clicking on the bubble

placed before the 4 choices, namely A, B, C and D. Use the virtual numeric

keypad to enter a number as

keypad to enter a number as answer for a numerical type question.

answer for a numerical type question.

c.

c. Click on

Click on

Save & Next

to save your answer for the current question and then go

to the next question.

d.

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Caution:

Note that your answer for the current question will not be saved, if you navigate

to another question directly by clicking on a question number without saving the answer to

the previous question.

You can view all the questions by clicking on the

Question Paper

button. This feature is

provided, so that if you

provided, so that if you want you can just see the entire

want you can just see the entire question paper at a glance.

question paper at a glance.

Answering a Question :

8. 8. Procedure for answering a multiple choice

Procedure for answering a multiple choice (MCQ) type question:

(MCQ) type question:

a.

a. Choose one answer from the 4 options (A,B,C,D) given below the que

Choose one answer from the 4 options (A,B,C,D) given below the que stion,

stion,

click on the bubble placed before the chosen option.

b.

b. To deselect your chosen answer, click on the bubble of the chosen option

To deselect your chosen answer, click on the bubble of the chosen option again

again

or click on the

Clear Response

button.

c.

c. To change your chosen answer, click on the bubble of another option.

To change your chosen answer, click on the bubble of another option.

d.

d. To save your answer, you MUST click on the

To save your answer, you MUST click on the

Save & Next

button.

9. 9. Procedure for answering a numerical answer

Procedure for answering a numerical answer type question:

type question:

a.

a. To enter a number as your answer, use the virtual numerical keypad.

To enter a number as your answer, use the virtual numerical keypad.

b.

b. A fraction (e.g. -0.3 or -.3) can be entered as an answer with or witho

A fraction (e.g. -0.3 or -.3) can be entered as an answer with or without '0'

ut '0'

before the decimal point. As many as four decimal points, e.g. 12.54

before the decimal point. As many as four decimal points, e.g. 12.54 35 or

35 or

0.003 or -932.6711 or 12.82 can

0.003 or -932.6711 or 12.82 can be entered.

be entered.

c.

c. To clear your answer, click on the

To clear your answer, click on the

Clear Response

button.

d.

d. To save your answer, you MUST click on the

To save your answer, you MUST click on the

Save & Next

button

10 10.. To mark a question for review, click on the

To mark a question for review, click on the

Mark for Review & Next

button.

button. If an

If an

answer is selected (for MCQ) or entered (for numerical answer type) for a qu

answer is selected (for MCQ) or entered (for numerical answer type) for a qu estion

estion

that is

Marked for Review

,

, that

that answer

answer will

will be

be considered

considered in

in the

the evaluation

evaluation u

unless

nless

the status is modified by the candidate.

11 11.. To change your answer to a question that has already been answered, first

To change your answer to a question that has already been answered, first select

select

that question for answering and then follow the procedure for answering

that question for answering and then follow the procedure for answering that ty

that type of

pe of

question.

12 12.. Note that ONLY Questions for which answers are

Note that ONLY Questions for which answers are

saved

or

marked for review

marked for review after

after

answering

will be considered for

will be considered for evaluation.

evaluation.

Choosing a Section :

13. Sections in this question paper are displayed on the top bar of the screen. Questions

in a Section can be viewed by clicking on the name of that Section. The Section you

are currently viewing will be highlighted.

14. 14. A checkbox is displayed for every optional Section, if any, in the Question Paper. To

A checkbox is displayed for every optional Section, if any, in the Question Paper. To

select the optional Section for answering, click

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only be able to see questions in this Section, but you will not be able to answer

questions in the Section.

16. 16. After clicking the

After clicking the

Save & Next

button for the last question in a Section, you will

automatically be taken to the first

automatically be taken to the first question of the next Section in

question of the next Section in sequence.

sequence.

17. 17. You can move the mouse cursor over the name of a Section to view the answering

You can move the mouse cursor over the name of a Section to view the answering

status for that Section.

Changing the Optional Section :

18 18. After answering the chosen optional Section, partially or completely, you can ch

. After answering the chosen optional Section, partially or completely, you can change

ange

the optional Section by selecting the checkbox for a new Section that you wa

the optional Section by selecting the checkbox for a new Section that you want to

nt to

attempt. A warning message will appear along with a table showing the numb

attempt. A warning message will appear along with a table showing the number of

er of

questions answered in each of the previously chosen optional Sections a

questions answered in each of the previously chosen optional Sections and a

nd a

checkbox against each of these Sections. Click on a checkbox against a Section

checkbox against each of these Sections. Click on a checkbox against a Section that

that

you want to reset and then click on the

RESET

button. Note that RESETTING a Se

button. Note that RESETTING a Section

ction

will DELETE all the answers for questions in that Section. Hence, if you think tha

will DELETE all the answers for questions in that Section. Hence, if you think that you

t you

may want to select this Section again later, you will have to note down your an

may want to select this Section again later, you will have to note down your answers

swers

for questions in that Section. If you do not want to reset the Section and wa

for questions in that Section. If you do not want to reset the Section and wa nt to

nt to

continue answering the previously chosen optional Section, then click on the

BACK

button.

19 19. If you deselect the checkbox for an optional Section in the top bar, the foll

. If you deselect the checkbox for an optional Section in the top bar, the following

owing

warning message will appear: "Deselecting the checkbox will DELETE all the an

warning message will appear: "Deselecting the checkbox will DELETE all the answers

swers

for questions in this Section. Do you want to deselect this Section?” If you wa

for questions in this Section. Do you want to deselect this Section?” If you wa nt to

nt to

deselect, click on the

RESET

button. If you do not want to deselect, click on the

BACK

button.

20

20. . You can shuffle

You can shuffle between different Sections or

between different Sections or change the optional

change the optional Section

Sections any

s any

number of times.

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GATE 2014 Examination

AE: Aerospace Engineering

Duration

Duration::180 minutes180 minutes Maximum MarksMaximum Marks::100100

Read the following instructions carefully. Read the following instructions carefully.

1.

1. To login, enter your To login, enter your Registration NumbeRegistration Number and password provided to r and password provided to you. Kindly go you. Kindly go through the variousthrough the various symbols used in the test

symbols used in the test and understand their meaning before you start the examination.and understand their meaning before you start the examination. 2.

2. Once you login and after the start of the examination, you can view all the questions in the questionOnce you login and after the start of the examination, you can view all the questions in the question paper, by clic

paper, by clicking on theking on theView All QuestionsView All Questions button in the screen. button in the screen. 3.

3. This question paper consists ofThis question paper consists of 2 sections2 sections, General Aptitude (GA) for, General Aptitude (GA) for 15 marks15 marks and the sub and the sub ject ject specific GATE paper for

specific GATE paper for 85 marks85 marks. Both . Both these sections are compulsory.these sections are compulsory. The GA section consists of

The GA section consists of 1010 questions. Question numbers 1 to 5 are of 1-mark each, while ques questions. Question numbers 1 to 5 are of 1-mark each, while questiontion numbers 6 to 10

numbers 6 to 10 are of 2-mark each.are of 2-mark each.

The subject specific GATE paper section consists of

The subject specific GATE paper section consists of 5555 questions, out of which question numbers questions, out of which question numbers 1 to1 to 25 are of 1-mark each, while question numbers 26 to 55 are of 2-mark each.

25 are of 1-mark each, while question numbers 26 to 55 are of 2-mark each. 4.

4. Depending upon the GATE paper, there may be useful common data that may be required Depending upon the GATE paper, there may be useful common data that may be required for for answering the questions. If the paper has such useful data, the same can be viewed by clicking on answering the questions. If the paper has such useful data, the same can be viewed by clicking on the the

Useful Common Data

Useful Common Data button that appea button that appears at the top, right hars at the top, right hand side of the scnd side of the screen.reen. 5.

5. The computer allotted to you at the examination center runs specialized software that permits onlyThe computer allotted to you at the examination center runs specialized software that permits only oneone answer to be selected for multiple-choice questions using a mouse and to enter a suitable number answer to be selected for multiple-choice questions using a mouse and to enter a suitable number for for the numerical answer type questions using the virtual keyboard and mouse.

the numerical answer type questions using the virtual keyboard and mouse. 6.

6. Your answers shall be updated and saved on a server periodically and also at the end ofYour answers shall be updated and saved on a server periodically and also at the end of thethe examination. The examination will

examination. The examination willstop automaticallystop automaticallyat the end ofat the end of 180 minutes180 minutes.. 7.

7. In each paper a candidate can answer a total of 65 questions carrying 100 marks.In each paper a candidate can answer a total of 65 questions carrying 100 marks. 8.

8. The question paper may consist of questions ofThe question paper may consist of questions of multiple choice typemultiple choice type (MCQ) and(MCQ) and numerical ansnumerical answerwer type

type.. 9.

9. Multiple choice type questions will have four choices against A, B, Multiple choice type questions will have four choices against A, B, C, D, out of C, D, out of which onlywhich onlyONEONE isis the the correct answer. The candidate has to choose the correct answer by clicking on the bubble (

correct answer. The candidate has to choose the correct answer by clicking on the bubble (⃝⃝) pla) placedced

before the c before the choice.hoice. 10.

10. For numerical answer type questions, each question will have a For numerical answer type questions, each question will have a numerical answer and there will nonumerical answer and there will not bet be any choices

any choices. For these questions, the answer should be entered. For these questions, the answer should be entered by by using using the the virtual virtual keyboardkeyboard thatthat appears on the monitor and the

appears on the monitor and the mouse.mouse. 11.

11. All questions that are not attempted will result in zero marks. However, wrong answers for multAll questions that are not attempted will result in zero marks. However, wrong answers for multipleiple choice type questions (MCQ) will result in

choice type questions (MCQ) will result in NEGATIVENEGATIVE marks. For all MCQ questions a wr marks. For all MCQ questions a wr ongong answer will result in

answer will result in deduction of deduction of ⅓⅓_{marks for a}_{marks for a 1-mark question and}_{1-mark question and}⅔⅔_{marks for a 2-mark question}_{marks for a 2-mark question..}

12.

12. There isThere is NO NEGATIVENO NEGATIVE MARKINGMARKING for questions of for questions ofNUMERICAL ANSWER TYPENUMERICALANSWER TYPE.. 13.

13. Non-program Non-programmable type Calculator is allowed. Charts, graph sheets, and mathemable type Calculator is allowed. Charts, graph sheets, and mathematical tables arematical tables areNNOTOT

allowed in the Examination Hall. You must use the Scribble pad provided to you at the examina allowed in the Examination Hall. You must use the Scribble pad provided to you at the examinationtion centre for all your r

centre for all your rough work. The Scribble Pad has to be ough work. The Scribble Pad has to be returned at the end of returned at the end of the examination.the examination.

Declaration by the c

Declaration by the candidate:andidate:

“I have read and understood all the above instructions. I have also read and understood clearly “I have read and understood all the above instructions. I have also read and understood clearly thethe instructions given on the admit card and shall follow the same. I also understand that in case I am found to instructions given on the admit card and shall follow the same. I also understand that in case I am found to violate any of these instructions, my candidature is liable to be cancelled. I also confirm that at the start of violate any of these instructions, my candidature is liable to be cancelled. I also confirm that at the start of the examination all the computer hardware allotted to me are in

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GATE

GATE 2014 2014 SET- SET- 1 1 General General Aptitude Aptitude -GA-GA

Q. 1 – Q. 5 carry one mark each.

Q.1

Q.1 A student is required to demonstrate a high level of comprehension of the subject, especially in theA student is required to demonstrate a high level of comprehension of the subject, especially in the social

social sciences.sciences.

The word closest in meaning to comprehension is The word closest in meaning to comprehension is (A)

(A) understanding understanding (B) (B) meaning meaning (C) (C) concentratconcentration ion (D) (D) stabilitystability

Q.2

Q.2 Choose the most appropriate word from the options given below to complete the followingChoose the most appropriate word from the options given below to complete the following sentence.

sentence.

One of his biggest ______ was his ability to forgive. One of his biggest ______ was his ability to forgive. (A)

(A) vice vice (B) (B) virtues virtues (C) (C) choices choices (D) (D) strengthstrength

Q

Q.3.3 Rajan was not happy that Sajan decided to do the project on his own. On observing hRajan was not happy that Sajan decided to do the project on his own. On observing hisis unhappiness, Sajan explained to Rajan that

unhappiness, Sajan explained to Rajan that he preferred to work he preferred to work independenindependently.tly.

Which one of the

Which one of the statements below is logically valid and can be statements below is logically valid and can be inferred from the above sentencesinferred from the above sentences?? (A) Rajan has decided to work only in a group.

(A) Rajan has decided to work only in a group. (B) Rajan and Sajan were formed into a

(B) Rajan and Sajan were formed into a group against their wishes.group against their wishes. (C) Sajan had decided to give in to Rajan’s request to work with him. (C) Sajan had decided to give in to Rajan’s request to work with him. (D) Rajan had believed that Sajan and

(D) Rajan had believed that Sajan and he would be working together.he would be working together.

Q

Q.4.4 IfIf y y = 5 = 5 x x22 + 3, + 3, then the then the tangent atangent att x x = 0, = 0, y y = 3 = 3 (A) passes through

(A) passes through x x = 0, = 0, y y= 0 = 0 (B) (B) has has a a slope slope of of +1+1 (C) is parallel to the

(C) is parallel to the x x-axis -axis (D)(D) has a slope of −1has a slope of −1

Q

Q.5.5 A foundry has a fixed daily cost of Rs 50,000 whenever it operates and a variable cost of Rs 800QA foundry has a fixed daily cost of Rs 50,000 whenever it operates and a variable cost of Rs 800Q,, where Q is the daily production in tonnes. What is the cost of

where Q is the daily production in tonnes. What is the cost of production in Rs per tonne for a dailproduction in Rs per tonne for a dailyy production of 100 tonne

production of 100 tonnes?s?

Q. Q. 6 – Q. 10 carry two marks each.

6 – Q. 10 carry two marks each.

Q

Q.6.6 Find the odd Find the odd one in the following one in the following group: ALRVX, EPVZB, ITZDgroup: ALRVX, EPVZB, ITZDF, OYEIKF, OYEIK (A)

(A) ALRVX ALRVX (B) (B) EPVZB EPVZB (C) (C) ITZDF ITZDF (D) (D) OYEIKOYEIK

Q

Q.7.7 Anuj, Bhola, Chandan, Dilip, Eswar and Faisal live on different floors in a six-storeyed buildinAnuj, Bhola, Chandan, Dilip, Eswar and Faisal live on different floors in a six-storeyed buildingg (the ground floor is numbered 1, the floor above it 2, and so on). Anuj lives on an even-numbere (the ground floor is numbered 1, the floor above it 2, and so on). Anuj lives on an even-numberedd floor. Bhola does not live on an odd numbered floor. Chandan does not live on any of the floo floor. Bhola does not live on an odd numbered floor. Chandan does not live on any of the floorsrs below

below Faisal’s Faisal’s floor. floor. Dilip Dilip does does not not live live on on floor floor number number 2. 2. Eswar Eswar does does not not live live on on a a floflooror immediately above or immediately below Bhola. Faisal lives three floors above Dilip.

immediately above or immediately below Bhola. Faisal lives three floors above Dilip. Which of thWhich of thee following floor-person combinations is

following floor-person combinations is correct?correct?

Anuj

Anuj Bhola Bhola Chandan Chandan Dilip Dilip Eswar Eswar FaisalFaisal

(A) 6 2 5 1 3 4 (A) 6 2 5 1 3 4 (B) 2 6 5 1 3 4 (B) 2 6 5 1 3 4 (C) 4 2 6 3 1 5 (C) 4 2 6 3 1 5 (D) 2 4 6 1 3 5 (D) 2 4 6 1 3 5

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GATE

GATE 2014 2014 SET- SET- 1 1 General General Aptitude Aptitude -GA-GA

Q.8

Q.8 The smallest angle of a triangle is equal to two thirds of the smallest angle of a quadrilateral. TheThe smallest angle of a triangle is equal to two thirds of the smallest angle of a quadrilateral. The ratio between the angles of the quadrilateral is 3:4:5:6. The largest angle of the triangle is twice its ratio between the angles of the quadrilateral is 3:4:5:6. The largest angle of the triangle is twice its smallest angle. What is the sum, in degrees, of the second largest angle of the triangle and the smallest angle. What is the sum, in degrees, of the second largest angle of the triangle and the largest angle of

largest angle of the quadrilateral?the quadrilateral?

Q.9

Q.9 One percent of the people of country X are taller than 6 ft. Two percent of the people of country YOne percent of the people of country X are taller than 6 ft. Two percent of the people of country Y are taller than 6 ft. There are thrice as many people in country X as in country Y. Taking both are taller than 6 ft. There are thrice as many people in country X as in country Y. Taking both countries together, what is the percentage of people taller than

countries together, what is the percentage of people taller than 6 ft?6 ft? (A)

(A) 3.0 3.0 (B) (B) 2.5 2.5 (C) (C) 1.5 1.5 (D) (D) 1.251.25

Q

Q.10.10 The monthly rainfall chart based on 50 years of rainfall in Agra is shown in the following figur The monthly rainfall chart based on 50 years of rainfall in Agra is shown in the following figur e.e. Which of the following are true? (

Which of the following are true? (k k percentile is the value such that percentile is the value such that k k percent of the data fall belo percent of the data fall beloww that value)

that value)

(i) On average, it

(i) On average, it rains more in July trains more in July than in Decemberhan in December

(ii) Every year, the amount of rainfall in August is more than that in January (ii) Every year, the amount of rainfall in August is more than that in January (iii) July rainfall

(iii) July rainfall can be estimated with better confidence than February rainfallcan be estimated with better confidence than February rainfall (iv) In August, there is at least 500 mm of r

(iv) In August, there is at least 500 mm of r ainfallainfall (A)

(A) (i) (i) and and (ii) (ii) (B) (B) (i) (i) and and (iii)(iii) (C)

(C) (ii) (ii) and and (iii) (iii) (D) (D) (iii) (iii) and and (iv)(iv)

END OF THE QUESTION PAPER

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GATE

GATE 2014 2014 AEROSPACE– AEROSPACE– AEAE

Q. 1 – Q. 25 carry one mark each.

Q.1

Q.1 For a real symmetric matrix [For a real symmetric matrix [AA], which of the following statements is true:], which of the following statements is true: (A)

(A) The matrix is The matrix is always diagonalizable and invertible.always diagonalizable and invertible. (B)

(B) The matrix is The matrix is always invertible but not always invertible but not necessanecessarily diagonalizable.rily diagonalizable. (C)

(C) The matrix is The matrix is always diagonalizable but not always diagonalizable but not necessanecessarily invertible.rily invertible. (D)

(D) The matrix is The matrix is always neither diagonalizable nor invertible.always neither diagonalizable nor invertible.

Q.2 Q.2 The series The series

∑

( (

))

∞ ∞ = =

−

=

1 1 2 2 3 3 2 2 m m m m m m xx m m

ss converges for allconverges for all x x withwith x x

−

22

≤

R Rgiven bygiven by (A)

(A) R R

=

00 (B)(B) R R

=

33 (C)(C) R R

=

∞

(D)(D) R R

=

11//33 Q

Q.3.3

The function given by

{

0

0 ),

),

//

1

1 sin(

sin(

0

0 ,,

0

0 ≠

≠

=

x x xx x x f(x) f(x) _is_is (A)

(A) Unbounded Unbounded everywhere everywhere (B) (B) Bounded Bounded and and continuous continuous everywhereeverywhere (C) Bounded but not continuous at

(C) Bounded but not continuous at x x

=

00 (D) Continuous (D) Continuous and differentiable everywhereand differentiable everywhere Q

Q.4.4

Given the boundary-value problem



+

=

00,, 00

<

11











x x ky ky dx dx dy dy x x dx dx d d , with

, with y y((00))

=

yy((11))

=

00. Then th. Then thee solutions of the

solutions of the boundary-vaboundary-value problem forlue problem for k k

=

11 (given by (given by y y₁₁) and) and k k

=

55 (given by (given by y y ) satisfy:₅₅) satisfy: (A)

(A)

∫∫

11

=

0

0 y y11 y y55dxdx 00 (B)(B) 00 5 5 1 1 0 0 1 1

=

∫∫

dxdx dx dx dy dy dx dx dy dy (C) (C)

∫∫

11

≠

0

0 y y11 y y55dxdx 00 (D)(D)

∫∫

+

=

1 1 0 0 5 5 1 1 5 5 1 1 )) 00 (( dxdx dx dx dy dy dx dx dy dy y y y y Q Q.5.5

The value of The value of

=

∫∫

11

0 0 4 4 1000 1000 x x dxdx I

I , obtained by , obtained by using Simpson’s rule with 2 equally using Simpson’s rule with 2 equally spaced intervals isspaced intervals is,,

(A)

(A) 200 200 (B) (B) 400 400 (C) (C) 180 180 (D) (D) 208208

Q

Q.6.6 For aFor a NACA NACA 5-digit airfoil of chord 5-digit airfoil of chord c c, the designed lift coefficient and location of , the designed lift coefficient and location of maximummaximum camber along the chord from the leading edge are

camber along the chord from the leading edge are denoted bydenoted byC C L L and and X X m m respectively. For respectively. For

NACA12018

NACA12018 airfoil, which combination of airfoil, which combination ofC C L L and and X X m m given below are correct? given below are correct? (A)

(A)C C L L =0.15 and =0.15 and X X m m = 0.1 = 0.1cc (B)(B)C C L L =0.12 and =0.12 and X X m m = 0.2 = 0.2cc (C)

(C)C C L L=0.12 and=0.12 and X X m m = 0.18 = 0.18cc (D)(D)C C L L =0.15 and =0.15 and X X m m = 0.2 = 0.2cc Q

Q.7.7 For inviscid, supersonic flow over a diFor inviscid, supersonic flow over a diamond shaped airfoil, shown in the figure, which statementamond shaped airfoil, shown in the figure, which statement isis correct among the following?

correct among the following?

(A) The airfoil will

(A) The airfoil will experience zero lift and positive drag forceexperience zero lift and positive drag force (B) The airfoil will

(B) The airfoil will experiencexperience positive lift e positive lift and zero drag forceand zero drag force (C) The airfoil will

(C) The airfoil will experiencexperience negative lift and e negative lift and zero drag forcezero drag force (D) The airfoil will

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GATE

Q.8

Q.8 Consider supersonConsider supersonic flow near a cic flow near a corner (at an aorner (at an angle ngle from the horizonfrom the horizontal) with an attactal) with an attached obliquehed oblique shock

shock (at (at an an angle angle with horizontal) with horizontal) as as shown shown in figuin figure. re. If If Mach Mach numbernumber M M decreases gradually decreases gradually from a high supersonic value, which of

from a high supersonic value, which of the following statements is correct?the following statements is correct?

(A)

(A) β β will decrease if the shock is a weak shock will decrease if the shock is a weak shock (B)

(B) β β will decrease if the will decrease if the shock is a strong shockshock is a strong shock (C)

(C) β β will i will increase for both weak and strong shocksncrease for both weak and strong shocks (D)

(D) β β remains unchanged for both weak and strong shocks remains unchanged for both weak and strong shocks

Q

Q.9.9 The streamlines of a potential line vortex iThe streamlines of a potential line vortex i s concentric circles with respect to the vortex center ass concentric circles with respect to the vortex center as shown in figure. Velocity along t

shown in figure. Velocity along these streamlines, outside the core of the vortex can be written hese streamlines, outside the core of the vortex can be written as,as,





==

ΓΓ

2



, where strength of the vortex is, where strength of the vortex is₂₂

ΓΓ



and and r r is r is radial direction. The value of circulationadial direction. The value of circulation

along the curve shown in the figure is: along the curve shown in the figure is:

(A)

ΓΓ

(B)(B)

−−

22

ΓΓ

(C)(C) 22

ΓΓ

(D) 0(D) 0 Q

Q.10.10 To observe unsteady separated flow in a diverging channel, bubbles are injected at each 10To observe unsteady separated flow in a diverging channel, bubbles are injected at each 10msms

interval at point A

interval at point A as shown in figure. These bubblesact as tracer particles and follow the flowas shown in figure. These bubblesact as tracer particles and follow the flow faithfully. The curved line

faithfully. The curved lineABAB shown at any shown at any instant represents:instant represents:

(A)

(A) Streamline, Streamline, streakline streakline and and pathline pathline (B) (B) Streamline Streamline and and pathlinepathline (C)

(C) Only Only a a pathline pathline (D) (D) Only Only a a streaklinestreakline

Q.11

Q.11 It is It is desired to measure the Young’s modulus and the Poisson’s ratio of desired to measure the Young’s modulus and the Poisson’s ratio of a given homogeneous,a given homogeneous, isotropic material. A bar of length 20

isotropic material. A bar of length 20cmcm and square cross-section (10 and square cross-section (10mmmm× 10× 10mmmm) of this material is) of this material is subjected to a tensile load of 40

subjected to a tensile load of 40kN kN . Under this load, length increases to 20.1. Under this load, length increases to 20.1cmcm while the cross- while the cross-section reduces to 9.98

section reduces to 9.98mmmm× 9.98× 9.98mmmm. Young’s modulus and Poisson’s ratio of . Young’s modulus and Poisson’s ratio of the material are:the material are: (A) 80

(A) 80GPaGPa& & 0.4 0.4 respectiverespectively ly (B) (B) 4040GPaGPa& -0.4 respectively& -0.4 respectively (C) 80

(10)

GATE

Q.12

Q.12 In general, for any given soliIn general, for any given solid subjected to arbitrary loading, which of d subjected to arbitrary loading, which of the following statements isthe following statements is

always always true: true:

(A)

(A) Volume Volume does does not not vary vary with with loading loading (B) (B) Mass does Mass does not not vary vary with with loadingloading (C)

(C) Density Density does does not not vary vary with with loading loading (D) (D) Volume, Volume, mass mass and and density density vary vary with with loadingloading

Q.13

Q.13 Which one of the following objWhich one of the following objects with inclined face atects with inclined face at4545



, subjected to the given stresses, are in, subjected to the given stresses, are in static equilibrium:

static equilibrium:

((AA)) ((BB))

((CC)) (D)(D)

Q

Q.14.14 A damped single degree of freedom system whose undamped natural frequency,A damped single degree of freedom system whose undamped natural frequency,





=10=10 Hz Hz, is, is subjected to sinusoidal external force. Power is half of

subjected to sinusoidal external force. Power is half of the maximumfor the two frequencies ofthe maximumfor the two frequencies of 60.9469 rad/s and 64.7168 rad/s. The damping factor associated with the

60.9469 rad/s and 64.7168 rad/s. The damping factor associated with the vibrating system (invibrating system (in%%) is) is _______.

_______.

Q

Q.15.15 The boundary conditions for a rod The boundary conditions for a rod with circular cross-section, under torsional vibration,are changwith circular cross-section, under torsional vibration,are changeedd from fixed-free to fixed-fixed. The fundamental natural frequency of the fixed-fixed rod is

from fixed-free to fixed-fixed. The fundamental natural frequency of the fixed-fixed rod is k k times times that of fi

that of fixed-free rod. The value ofxed-free rod. The value of k k is is (A) 1.5

(A) 1.5 (B)(B) π π (C) (C) 2.0 2.0 (D) (D) 0.50.5

Q

Q.16.16 Match the appropriate engine (in right column) with Match the appropriate engine (in right column) with the corresponding aircraft (in left column) for the corresponding aircraft (in left column) for most efficient performance of the

most efficient performance of the engine.engine. a.

a. Low Low speed speed transport transport aircraft aircraft i. i. RamjetRamjet b. High subsonic

b. High subsonic civilian aircrafcivilian aircraft t ii. Turbopropii. Turboprop c.

c. Supersonic Supersonic fighter fighter aircraft aircraft iii. iii. TurbojetTurbojet d.

d. Hypersonic Hypersonic aircraft aircraft iv. iv. TurbofanTurbofan

(A)

(A) a a – – iv, iv, b b – – iii, iii, c c – – i, i, d d – – ii ii (B) (B) a a – – ii, ii, b b – – i, i, c c – – iii, iii, d d – – iviv (C)

(C) a a – – i, i, b b – – ii, ii, c c – – iv, iv, d d – – iii iii (D) (D) a a – – ii, ii, b b – – iv, iv, c c – – iii, iii, d d – – ii

Q.17

Q.17 For a given fuel For a given fuel flow rate and thermal efficiency, the take-off thrust for flow rate and thermal efficiency, the take-off thrust for a gas turbine enginea gas turbine engine burning aviation turbine

burning aviation turbine fuel (considefuel (considering fuel-air ratioring fuel-air ratio f<< f<<1) is1) is (A) Directly proportional to exhaust velocity

(A) Directly proportional to exhaust velocity (B) Inversely proportional to exhaust velocity (B) Inversely proportional to exhaust velocity (C) Independent of exhaust velocity

(C) Independent of exhaust velocity (D) Directly proportional to the

(D) Directly proportional to the square of the exhaust velocitysquare of the exhaust velocity

a a

(11)

GATE

Q.18

Q.18 For a For a fifty percent reaction axial fifty percent reaction axial comprescompressor stage, following statements are sor stage, following statements are given:given: I.

I. Velocity triangles at the entry and eVelocity triangles at the entry and exit of the rotor are symmxit of the rotor are symmetricaletrical

II. The whirl or swirl component of absolute velocity at the entry of rotor and entry of stator are II. The whirl or swirl component of absolute velocity at the entry of rotor and entry of stator are same.

same.

Which of the following options

Which of the following options are correct?are correct? (A)

(A) Both Both I I and and II II are are correct correct statements statements (B) (B) I I is is correct correct but but II II is is incorrectincorrect (C)

(C) I I is is incorrect incorrect but but II II is is correct correct (D) (D) Both Both I I and and II II are are incorrectincorrect

Q.19

Q.19 A small rocket having a A small rocket having a specific impulse of 200specific impulse of 200ss produces a total thrust of 98 produces a total thrust of 98kN kN , out of which 10, out of which 10kN kN

is the pressure thrust. Considering the acceleration due to gravity t

is the pressure thrust. Considering the acceleration due to gravity t o be 9.8o be 9.8m/sm/s22, the propellant mass, the propellant mass flow rate in

flow rate inkg/skg/s is is (A)

(A) 55.1 55.1 (B) (B) 44.9 44.9 (C) (C) 50 50 (D) (D) 60.260.2

Q

Q.20.20 The thrust produced by a The thrust produced by a turbojet engineturbojet engine (A) Increases with

(A) Increases with increasing compressor pressure ratioincreasing compressor pressure ratio (B) Decreases with increasing compressor pressure ratio (B) Decreases with increasing compressor pressure ratio (C) Remains constant with i

(C) Remains constant with increasing compressncreasing compressor pressure ratioor pressure ratio (D) First i

(D) First increasencreases and s and then decreases with increasing compressor pressure ratiothen decreases with increasing compressor pressure ratio

Q

Q.21.21 The moment coefficient measurThe moment coefficient measured about the centre of ed about the centre of gravity and about aerodynamic centre of agravity and about aerodynamic centre of a given wing-body combination are 0.0065

given wing-body combination are 0.0065 and -0.0235 respectively. The aerodynamic centre liesand -0.0235 respectively. The aerodynamic centre lies 0.06 chord lengths ahead of the

0.06 chord lengths ahead of the centre of gravity. The lift coefficient for this centre of gravity. The lift coefficient for this wing-body is _____.wing-body is _____.

Q

Q.22.22 The vertical ground load factor on The vertical ground load factor on a stationary aircraft parked in its hangar is:a stationary aircraft parked in its hangar is: (A)

(A) 0 0 (B) (B) -1 -1 (C) (C) Not Not defined defined (D) (D) 11

Q

Q.23.23 Under what conditionshould a glider be operated to Under what conditionshould a glider be operated to ensure minimum sink rate?ensure minimum sink rate? (A) Maximum C

(A) Maximum CLL/C/CDD (B) Minimum (B) Minimum CCLL/C/CDD (C) Maximum C (C) Maximum CDD/C/CLL 3/2 3/2 (D) Minimum C (D) Minimum CDD/C/CLL 3/2 3/2 Q

Q.24.24 In most airplanes, the Dutch roll In most airplanes, the Dutch roll mode can be excited by applyingmode can be excited by applying (A)

(A) a a step step input input to to the the elevators elevators (B) (B) a a step step input input to to the the rudderrudder (C)

(C) a a sinusoidal sinusoidal input input to to the the aileron aileron (D) (D) an an impulse impulse input input to to the the elevatorselevators

Q

Q.25.25 ConsideringConsidering R R as the radius of the moon, the ratio of as the radius of the moon, the ratio of the velocities of two spacecrathe velocities of two spacecraft orbiting moonft orbiting moon in circular orbit at altitudes

in circular orbit at altitudes R R and and22 R R above the surface of above the surface of the moon is ________.the moon is ________.

Q. Q. 26 – Q. 55 carry two marks each.

26 – Q. 55 carry two marks each.

Q. Q.2626 If If

[ [ ]]

_











−

=

4 4 3 3 3 3 3 3 A

A . Then. Then detdet

−

[[ A A]]22

+

77[[ A A]]

−

33[[ I I ]] is is (A)

(12)

GATE

Q.27 Q.27

For the periodic function given by

{

0 0 ,, 2 2 0 0 ,, 2 2

))

((

<

−

<

=

xx x x x x f f π π π

π withwith f f (( x x

+

22π π ))

=

f f ((xx)), using, using

Fourier series, the sum

=

−

+

−

+

_

7 7 1 1 5 5 1 1 3 3 1 1 1 1 ss converges toconverges to (A) 1 (A) 1 (B)(B) 3 3 π π (C) (C) 4 4 π π (D) (D) 5 5 π π Q.28

Q.28 _Let_Let

_Γ

_{be the boundary}_{be the boundary of the closed c}_{of the closed circular region}_{ircular region}_A_{A given by}_{given by} 22

₊

22

_≤

₁₁ y y x x . Then. Then

( (

))

∫∫

Γ Γ

−

=

x x xy xy dsds I

I 33 33 99 22 (where(where dsds means integration along the bounding curve) ismeans integration along the bounding curve) is (A)

(A) π π (B)(B)

−

π π (C) (C) 1 1 (D) (D) 00

Q

Q.29.29 Solution to Solution to the boundary-value problemthe boundary-value problem

3 3 0 0 ,, 5 5 9 9 ₂₂ 2 2

<

=

+

−

_u_u _x_x _xx dx dx u u d d with with ((00)) 00,, 00 3 3

=

= = x x dx dx du du u u is is (A) (A)

( (

ee ee

))

xx e e e e x x u u x x xx 55 1 1 15 15 )) (( ₂₂ //33

−

//33

+

=

−− (B) (B)

( (

ee ee

))

xx e e e e x x u u x x xx 55 1 1 15 15 )) (( ₂₂ //33

+

//33

+

=

−− (C) (C)uu x x x x 55xx )) 1 1 cos( cos( )) 3 3 // sin( sin( 15 15 )) ((

=

−

+

(D)(D) 33 54 54 5 5 )) 1 1 cos( cos( )) 3 3 // sin( sin( 15 15 )) (( x x x x xx u u

=

−

Q Q.30.30

The Laplace transform

The Laplace transform LL(u(t))=U(s), for the solution u(t) of (u(t))=U(s), for the solution u(t) of the problemthe problem ₂₂ 22 11,, 00

2 2

>

=

+

_u_u _t t dt dt du du dt dt u u d d

with initial conditions with initial conditions

.. 5 5 )) 0 0 (( ,, 0 0 )) 0 0 ((

=

dt dt du du u

u is given by:is given by: (A) (A) ₂₂ )) 1 1 (( 6 6

+

ss (B)(B) (( 11))22 1 1 5 5

+

ss ss ss (C) (C) ₂₂ )) 1 1 (( 5 5 1 1

+

−

ss ss ss (D) (D) ₂₂ 2 2 )) 1 1 (( 1 1 5 5

+

ss ss ss Q

Q.31.31 For a For a steady, incompresssteady, incompressible two-dimensional flow, represented in Cartesian co-ordinates (ible two-dimensional flow, represented in Cartesian co-ordinates (



, ,



), a), a student correctly writes the equation of pathline of

student correctly writes the equation of pathline of any arbitrary particle as,any arbitrary particle as,





==



and and





= =



,, where

(13)

GATE

Q.32

Q.32 Figures (a) - (d) Figures (a) - (d) below show four objects. Dimensions and surface conditions of the objects arebelow show four objects. Dimensions and surface conditions of the objects are shown in the

shown in the respectivrespective figures. All fe figures. All four objects are placed independently in a steady, uniform flowour objects are placed independently in a steady, uniform flow of same velocity and the direction of flow is from left to right

of same velocity and the direction of flow is from left to right as shown in (a). The flow field can beas shown in (a). The flow field can be considered as 2-D, viscous and

considered as 2-D, viscous and incompressincompressible. Following statements are ible. Following statements are made regarding the dragmade regarding the drag that these objects

that these objects experiencexperience.e.

(i)

(i) Drag of object (a) is more than the drag of object (d)Drag of object (a) is more than the drag of object (d) (ii)

(ii) Drag of object (a) is less than the drag of object (d)Drag of object (a) is less than the drag of object (d) (iii)

(iii) Drag of object (b) is more than the drag of object (c)Drag of object (b) is more than the drag of object (c) (iv)

(iv) Drag of object (c) is more than the drag of object (b)Drag of object (c) is more than the drag of object (b) (v)

(v) Drag of object (a) is more than the drag of object (b)Drag of object (a) is more than the drag of object (b)

Choose the correct combination of statements from the options given above: Choose the correct combination of statements from the options given above:

(A)

(A) (i), (i), (iii), (iii), (v) (v) (B) (B) (ii), (ii), (iv), (iv), (v) (v) (C) (C) (i), (i), (iv), (iv), (v) (v) (D) (D) (i), (i), (iii)(iii)

Q

Q.33.33 A student needs to fiA student needs to fi nd velocity across a stationary normal shock. He measures density andnd velocity across a stationary normal shock. He measures density and pressure ac

pressure across the shock ross the shock as shown in the fas shown in the figure below. 1igure below. 1bar bar = =101055PaPa. (No shock table i. (No shock table is neededs needed for the calculations). The value of

for the calculations). The value ofuu11 in inm/sm/s is ____. is ____.

Q

Q.34.34 For inviscid, compressible flow past a thin For inviscid, compressible flow past a thin airfoil, shown in the airfoil, shown in the figure, free-streafigure, free-stream Mach numberm Mach number and pressure are denoted by

and pressure are denoted by



∞∞

and



∞∞

respectivelyrespectively. Ratio of . Ratio of pressure at pointpressure at pointAA and and



∞∞

is 0.8is 0.8 and specific he

and specific heat ratio is 1.4. at ratio is 1.4. If the Mach numIf the Mach number at pointber at pointAA is 1.0 and rest of is 1.0 and rest of the flow field isthe flow field is subsonic, the value of

subsonic, the value of



∞∞

isis

(A)

(14)

GATE

Q.35

Q.35 A student can measure free-stream velocity of a low-speed wind tunnel using aA student can measure free-stream velocity of a low-speed wind tunnel using a i.

i. Pitot tube alone aligned with Pitot tube alone aligned with the flow direction.the flow direction. ii.

ii. Pitot tube aligned with Pitot tube aligned with the flow direction with the flow direction with static pressure measurstatic pressure measurement at anement at an appropriate position on the tunnel wall.

appropriate position on the tunnel wall. iii.

iii. Pitot tube aligned with Pitot tube aligned with the flow direction along with the flow direction along with barometer pressurbarometer pressure reading of thee reading of the outside ambient.

outside ambient. iv.

iv. Pitot static tube alone aligned with Pitot static tube alone aligned with the flow direction.the flow direction.

Considering the above statements, which of the following options i

Considering the above statements, which of the following options i s correct?s correct?

(A)

(A) (i) (i) only only (B) (B) (i) (i) & & (ii) (ii) (C) (ii) (C) (ii) & & (iv) (iv) (D) (i), (D) (i), (iii) (iii) & & (iv)(iv)

Q

Q.36.36 Induced velocityInduced velocityww at a point at a point



= =



₁₁ along the along the lifting line can be lifting line can be calculated using the formulacalculated using the formula



((



₁₁)) = =

−−

₄₄11



∫∫

−−

ΓΓ

−

11 1 1



.. Given Given

ΓΓ

2 2

ΓΓ



22

+



2 2



22 = = 1,1, where where



,,

ΓΓ



and and ssare given in figure below.are given in figure below.

For theabove semi-elliptic distribution of

For theabove semi-elliptic distribution of circulation,circulation,

ΓΓ

, the downwash velocity at any point, the downwash velocity at any point



_1,_1,forfor symmetric flight can be obtained as,

symmetric flight can be obtained as,



((



₁₁)) = =

Γ Γ



4



[[



+ +



11



]], where, where



= =



11

∫∫

 



22

−−



22

��

−

1 1



−−

..

Which of the following options is correct if the induced drag is





(given (given

∫∫  

1

1 −−



2 2



22



−−



==



2 2

))

(A)

(A) I=0 I=0 and and





== 8 8

ΓΓ



2 2



(B)(B) I= 1 I= 1 and and





== 8 8

ΓΓ



2 2



(C)

(C) I=0 I=0 and and





==

Γ



2 2

8

8 (D)(D) I= 1 I= 1 and and





==

Γ



2 2

8 8

Q

Q.37.37 Two overflowing water reservoirs are connected with a100Two overflowing water reservoirs are connected with a100mm long pipe long pipe of circular cross-section (of of circular cross-section (of radius,

radius, R R = 0.02 = 0.02mm), such that height ), such that height differencedifference h h remains constant as shown in the remains constant as shown in the figure below.figure below. The centerline velocity in the pipe is 10

The centerline velocity in the pipe is 10m/sm/s. The velocity profile inside the . The velocity profile inside the pipe over the entirepipe over the entire length is length is



= =

−−



2 2 4 4





1

1 −−



2 2



22



, where,, where,





is a is a constant pressure gradient along the pipe lengthconstant pressure gradient along the pipe length,,

x

x is measured from theleft end of the pipe along its central axis and is measured from theleft end of the pipe along its central axis and r r is radial location inside the is radial location inside the pipe with respec

pipe with respect to its axis.(t to its axis.(Given dataGiven data: Density and kinematic viscosity of water are : Density and kinematic viscosity of water are 10001000kg/mkg/m33

and 1x10

and 1x10-6-6mm22 /s /srespectivelyrespectively; acceleration due to gravity is ; acceleration due to gravity is 1010m/sm/s22).). If all ot

If all other losses except the frictional losses at the pipe her losses except the frictional losses at the pipe wall are neglected, the value ofwall are neglected, the value of h h in meter in meter is ____.

(15)

GATE

Q.38

Q.38 A 1.8A 1.8mm long steel beam of long steel beam of rectangular cross section (10rectangular cross section (10mmmm× 6× 6mmmm) is simply supported with a) is simply supported with a length of 1.2

length of 1.2mm between the supports and an overhang of between the supports and an overhang of 0.30.3mm on either side. Young’s modulus for on either side. Young’s modulus for the material of the beam is 200

the material of the beam is 200GPaGPa. For a 50. For a 50 N N load applied at load applied at the center of the beam, magnitude ofthe center of the beam, magnitude of the slopeof the beam at tip

the slopeof the beam at tipS S is _______. is _______.

Q

Q.39.39 There are 2 designs proposed for a There are 2 designs proposed for a shaft of lengthshaft of lengthl l , with a torque carrying capacity of, with a torque carrying capacity ofT T .. Design I Design I i iss a solid

a solid circular cross-seccircular cross-section shaft tion shaft of diameter30of diameter30mmmm.. Design II Design II is a thin-walled circular shaft of is a thin-walled circular shaft of average diameter 40

average diameter 40mmmm. Thickness of the wall in. Thickness of the wall in Design II Design II has to has to be determined such thatbe determined such that maximum shear stress is the same in both t

maximum shear stress is the same in both t he designs for the given the designs for the given torqueorqueT T (so that (so that same materialsame material can be used for manufacturing both the shafts).

can be used for manufacturing both the shafts). Ratio of mass of shaft Ratio of mass of shaft usingusing Design I Design I to the mass of to the mass of shaft using

shaft using Design II Design II is is

(A)

(A) 2.68 2.68 (B) (B) 5.36 5.36 (C) (C) 1.79 1.79 (D) (D) 3.583.58

Q

Q.40.40 A structural member of A structural member of rectangular cross-srectangular cross-section 10ection 10mmmm× 6× 6mmmm and length 1 and length 1mm is made of steel is made of steel (Young’s modulus is 200

(Young’s modulus is 200GPaGPa and coefficient of thermal expansion is and coefficient of thermal expansion is 12 × 1012 × 10

−−

66 / /





). It is rigidly). It is rigidly fixed at both

fixed at both the ends and then subjected to the ends and then subjected to a gradual increase in temperature. Ignoring the threea gradual increase in temperature. Ignoring the three dimensional effects, the structural member will

dimensional effects, the structural member will buckle if the buckle if the temperature is increased bytemperature is increased by

∆

∆ 



which is

(A)

(A) 19.74 19.74 (B) (B) 9.87 9.87 (C) (C) 78.96 78.96 (D) (D) 39.4839.48

Q.41

Q.41 A gas cylinder (closed thin-walled cylindrical pressure vessel) of diameter 30A gas cylinder (closed thin-walled cylindrical pressure vessel) of diameter 30cmcm and wall thickness and wall thickness 1

1mmmm is subjected to a design maximum internal pressure of 5 is subjected to a design maximum internal pressure of 5bar bar (0.5 (0.5 MPa MPa). The material used for). The material used for manufacturing this cylinder has a failure stress of 260

manufacturing this cylinder has a failure stress of 260 MPa MPa. Assuming von Mises failure criterion,. Assuming von Mises failure criterion, the factor of safety (with

the factor of safety (with respect to maximum allowable stressrespect to maximum allowable stress) for this ) for this cylinder iscylinder is (A)

(16)

GATE

Q.42

Q.42 A cantilevered beam is subjected to a parabolic distribution of A cantilevered beam is subjected to a parabolic distribution of shear traction at the right shear traction at the right edge whileedge while the top and

the top and bottom surfaces are traction free. To solve this problem, following Airy’s stressbottom surfaces are traction free. To solve this problem, following Airy’s stress function is proposed:

function is proposed:



= =



₁₁



++



₂₂



33 ++



₃₃



22



22 ++



₄₄



33



. This is . This is an admissible Airy’san admissible Airy’s function that would satisfy the

function that would satisfy the bi-harmbi-harmonic equation as well as onic equation as well as the boundary conditions if and the boundary conditions if and onlyonly if if (A) (A)



₁₁ = = 00,,



₂₂ = =



,,



₃₃ = = 00,,



₄₄ = =



3 3



22 (B)(B)



11 = =



,,



22 = = 33





22,,



33 = = 00,,



44 = = 00 (C) (C)



₁₁ = 0 = 0,,



₂₂ = = 00,,



₃₃ = =



,,



₄₄ = =

−−



3 3



22 (D)(D)



11 = =



,,



22 = =

−−

33





22,,



33 = = 00,,



44 = = 00 Q

Q.43.43 1kg mass is hanging from a spring of stiffness 5001kg mass is hanging from a spring of stiffness 500 N/m N/m attached to a massless,symmetric beam of attached to a massless,symmetric beam of length 0.6

length 0.6mm, moment of inertia about the , moment of inertia about the bending axisbending axis



= 8 = 8..3333 ×× 1010

−−

1010



44 and Young’s modulus and Young’s modulus

E

E =210=210GPaGPa as shown in as shown in the figure. The fundamental natural frequency (inthe figure. The fundamental natural frequency (inrad/srad/s) of the system is) of the system is

(A)

(A) 3.24 3.24 (B) (B) 20.36 20.36 (C) (C) 22.36 22.36 (D) (D) 3.563.56

Q

Q.44.44 A single degree of freedom system is vibrating A single degree of freedom system is vibrating with initial (first with initial (first cycle) amplitude of 5cycle) amplitude of 5cmcm. The. The viscous damping factor associated with the vibrating system is 2

viscous damping factor associated with the vibrating system is 2%%. Vibration amplitude of the fifth. Vibration amplitude of the fifth cycle (in

cycle (in cmcm) is) is (A)

(A) 1.65 1.65 (B) (B) 4.41 4.41 (C) (C) 2.67 2.67 (D) (D) 3.023.02

Q

Q.45.45 A cruise missile with anA cruise missile with anideal ideal ramjet engine is flying ramjet engine is flying at Mach 4.0 at at Mach 4.0 at an altitude where the ambientan altitude where the ambient temperature is 100

temperature is 100K K . Considerratio of specific heats. Considerratio of specific heatsγγ = 1.4 and specific gas constant R = 287 = 1.4 and specific gas constant R = 287 J/kgK J/kgK .. If the stagnation temperature in the combustion chamber is equal to

If the stagnation temperature in the combustion chamber is equal to 23102310K K , the speed of the exhau, the speed of the exhaustst gases (in

gases (inm/sm/s) is ) is _____________._____________. Q

Q.46.46 A gas turbine engine is A gas turbine engine is operating under the following conditions:operating under the following conditions:

Stagnation

Stagnation temperature temperature at at turbine turbine inlet inlet 13501350K K

Stagnation

Stagnation pressure pressure at at the the turbine turbine inlet inlet 1010bar bar

Static

Static temperature temperature at at turbine turbine exit exit 800800K K

Velocity

Velocity at at turbine turbine exit exit 200200m/sm/s

Total-to-total

Total-to-total efficiency efficiency of of turbine turbine 0.960.96 γ (

γ (ratio of specific heats)ratio of specific heats) 1.331.33 C

CPP(specific heat at constant (specific heat at constant pressure)pressure) 1.1471.147kJ/kgKkJ/kgK The stagnation pressure (in bar) in the

(17)

GATE

Q.47

Q.47 Air at a Air at a stagnation temperastagnation temperature of 300ture of 300K K (ratio of (ratio of specific heats,specific heats, γ γ = 1.4 and specific gas constant R = 1.4 and specific gas constant R = 287

= 287 J/kgK J/kgK ) enters the impeller of ) enters the impeller of a centrifugal compressoa centrifugal compressor in r in axial direction. The stagnationaxial direction. The stagnation pressure ra

pressure ratio between the tio between the diffuser outlet and diffuser outlet and impeller inlet is 4.0impeller inlet is 4.0. The impe. The impeller blade radius ller blade radius is 0.3is 0.3 m and it is rotating at

m and it is rotating at 1500015000rev/minrev/min. If the slip factor. If the slip factorσ σ _ss (Ratio of tangential component of air (Ratio of tangential component of air

velocity at the blade tip to the blade tip speed) is

velocity at the blade tip to the blade tip speed) is 0.88, the overall efficiency (total-0.88, the overall efficiency (total-to-total) of theto-total) of the compressor (in

compressor (in %%) is ___________.) is ___________.

Q.48

Q.48 A stationary two stage rocket with iA stationary two stage rocket with initial mass of 16000nitial mass of 16000kgkg, carrying a payload of 1000, carrying a payload of 1000kgkg, is fired in, is fired in a vertical trajectory from the surface of the

a vertical trajectory from the surface of the earth. Both the stages of earth. Both the stages of the rocket have same specificthe rocket have same specific impulse,

impulse, I I sp sp, of 300, of 300ss and same structural coefficient of 0.14. The acceleration due to gravity is and same structural coefficient of 0.14. The acceleration due to gravity is 9.8

9.8m/sm/s22. Neglecting drag and gravity effects and considering both the stages with . Neglecting drag and gravity effects and considering both the stages with same payloadsame payload ratio, the terminal velocity attained by t

ratio, the terminal velocity attained by the payload inhe payload inm/sm/s is is ___________________________________._. Q

Q.49.49 An aircraft is flying An aircraft is flying at Mach 3.0 at an at Mach 3.0 at an altitude where the ambient pressure and temperature are 50altitude where the ambient pressure and temperature are 50

kPa

kPa and 200 and 200K K respectively. If the respectively. If the converging-dconverging-diverging diffuser of iverging diffuser of the engine (consideredthe engine (considered isentropic with ratio of

isentropic with ratio of specific heats,specific heats, γ γ = 1.4 and specific gas constant R = 287 = 1.4 and specific gas constant R = 287 J/kgK J/kgK ) has a throat) has a throat area of 0.05

area of 0.05mm22, the mass flow rate through the engine in, the mass flow rate through the engine in kg/skg/s is is (A)

(A) 197 197 (B) (B) 232 232 (C) (C) 790 790 (D) (D) 157157

Q

Q.50.50 A cryogenic rocket has a specific impulse of A cryogenic rocket has a specific impulse of 455455ss and characteristic velocity of 2386 and characteristic velocity of 2386m/sm/s. The. The value of thrust coefficient for this rocket is

value of thrust coefficient for this rocket is (A)

(A) 1.78 1.78 (B) (B) 1.73 1.73 (C) (C) 1.87 1.87 (D) (D) 1.951.95

Q

Q.51.51 For a given airplane with For a given airplane with a given wing loading executing a turn a given wing loading executing a turn in the vertical plane, under in the vertical plane, under whatwhat conditions will the t

conditions will the t urn radius be minimum and the turn urn radius be minimum and the turn rate be maximum?rate be maximum? (A) Highest possible C

(A) Highest possible CLLand lowest possible load factorand lowest possible load factor (B) Lowest possible C

(B) Lowest possible CLLand lowest possible load factorand lowest possible load factor (C) Lowest possible C

(C) Lowest possible CLLand highest possible load factorand highest possible load factor (D) Highest possible C

(D) Highest possible CLLand highest possible load factorand highest possible load factor

Q

Q.52.52 Lift-off distance for a given aircraft of Lift-off distance for a given aircraft of weightweightW W is isSS LO LO. If the take-off weight is reduced by 10. If the take-off weight is reduced by 10%%,, then the magnitude of percentage change in the lift-off di

then the magnitude of percentage change in the lift-off di stance (assumstance (assume all other e all other parameparameters toters to remain constant) is _______.

remain constant) is _______. Q

Q.53.53 Which of tWhich of the following design parameters influence the maximum rate-of-climb for a he following design parameters influence the maximum rate-of-climb for a jet-propelled jet-propelled airplane?

airplane?

P. Wing loading P. Wing loading

Q. Maximum thrust-to-weight ratio Q. Maximum thrust-to-weight ratio R. Zero-lift drag

R. Zero-lift drag coefficientcoefficient S. Maximum lift-to-drag ratio S. Maximum lift-to-drag ratio (A)