Engineering Sciences (XE) 2012 GATE Paper with solution GATE Notes | EduRev

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GATE : Engineering Sciences (XE) 2012 GATE Paper with solution GATE Notes | EduRev

 Page 1


2012                                                                                                                                          XE                                                           
 
XE 
1/36 
XE : ENGINEERING SCIENCES 
Duration: Three Hours                          Maximum Marks: 100 
Read the following instructions carefully. 
1. Do not open the seal of the Question Booklet until you are asked to do so by the invigilator. 
2. Take out the Optical Response Sheet (ORS) from this Question Booklet without breaking the seal 
and read the instructions printed on the ORS carefully.  
3. On the right half of the ORS, using ONLY a black ink ball point pen, (i) darken the bubble 
corresponding to your test paper code and the appropriate bubble under each digit of your registration 
number and (ii) write your registration number, your name and name of the examination centre and 
put your signature at the specified location.  
4. This Question Booklet contains 36 pages including blank pages for rough work. After you are 
permitted to open the seal, please check all pages and report discrepancies, if any, to the invigilator. 
5. There are a total of 65 questions carrying 100 marks. All these questions are of objective type. Each 
question has only one correct answer. Questions must be answered on the left hand side of the ORS 
by darkening the appropriate bubble (marked A, B, C, D) using ONLY a black ink ball point pen 
against the question number. For each question darken the bubble of the correct answer. More 
than one answer bubbled against a question will be treated as an incorrect response. 
6. Since bubbles darkened by the black ink ball point pen cannot be erased, candidates should darken 
the bubbles in the ORS very carefully. 
7. This Question Booklet contains Eight sections: GA (General Aptitude), A (Engineering Mathematics), 
B (Fluid Mechanics), C (Materials Science), D (Solid Mechanics), E (Thermodynamics), F (Polymer 
Science & Engineering) and G (Food Technology). 
8. Section GA (General Aptitude) and  Section A  (Engineering Mathematics) are compulsory. Attempt 
any two optional sections B through G. Using a black ink ball point pen, mark the sections you have 
chosen by darkening the appropriate bubbles provided on the left hand side of the ORS. Also, write 
the codes of the optional sections in the boxes provided. In case the candidate does not bubble 
section codes corresponding to Optional Section-1 or Optional Section-2 or both, the corresponding 
sections will NOT be evaluated. 
9. Questions Q.1 – Q.10 belong to Section GA (General Aptitude) and carry a total of 15 marks. 
Questions Q.1 – Q.5 carry 1 mark each, and questions Q.6 – Q.10 carry 2 marks each. 
10. There are 11 questions carrying 15 marks in Section A (Engineering Mathematics), which is 
compulsory.   Questions Q.1–Q.7 carry 1 mark each and questions Q.8–Q.11 carry 2 marks each.  
11. Each of the other sections (Sections B through G) contains 22 questions carrying 35 marks. Questions 
Q.1–Q.9 carry 1 mark each and questions Q.10–Q.22 carry 2 marks each.  The 2 marks questions 
include two pairs of common data questions and one pair 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. 
12. Unattempted questions will result in zero mark and wrong answers will result in NEGATIVE marks.  
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.  
13. Calculator is allowed whereas charts, graph sheets or tables are NOT allowed in the examination hall.  
14. Before the start of the examination, write your name and registration number in the space provided 
below using a black ink ball point pen. 
 
Name 
 
 
Registration Number XE 
      
 
 
 
Page 2


2012                                                                                                                                          XE                                                           
 
XE 
1/36 
XE : ENGINEERING SCIENCES 
Duration: Three Hours                          Maximum Marks: 100 
Read the following instructions carefully. 
1. Do not open the seal of the Question Booklet until you are asked to do so by the invigilator. 
2. Take out the Optical Response Sheet (ORS) from this Question Booklet without breaking the seal 
and read the instructions printed on the ORS carefully.  
3. On the right half of the ORS, using ONLY a black ink ball point pen, (i) darken the bubble 
corresponding to your test paper code and the appropriate bubble under each digit of your registration 
number and (ii) write your registration number, your name and name of the examination centre and 
put your signature at the specified location.  
4. This Question Booklet contains 36 pages including blank pages for rough work. After you are 
permitted to open the seal, please check all pages and report discrepancies, if any, to the invigilator. 
5. There are a total of 65 questions carrying 100 marks. All these questions are of objective type. Each 
question has only one correct answer. Questions must be answered on the left hand side of the ORS 
by darkening the appropriate bubble (marked A, B, C, D) using ONLY a black ink ball point pen 
against the question number. For each question darken the bubble of the correct answer. More 
than one answer bubbled against a question will be treated as an incorrect response. 
6. Since bubbles darkened by the black ink ball point pen cannot be erased, candidates should darken 
the bubbles in the ORS very carefully. 
7. This Question Booklet contains Eight sections: GA (General Aptitude), A (Engineering Mathematics), 
B (Fluid Mechanics), C (Materials Science), D (Solid Mechanics), E (Thermodynamics), F (Polymer 
Science & Engineering) and G (Food Technology). 
8. Section GA (General Aptitude) and  Section A  (Engineering Mathematics) are compulsory. Attempt 
any two optional sections B through G. Using a black ink ball point pen, mark the sections you have 
chosen by darkening the appropriate bubbles provided on the left hand side of the ORS. Also, write 
the codes of the optional sections in the boxes provided. In case the candidate does not bubble 
section codes corresponding to Optional Section-1 or Optional Section-2 or both, the corresponding 
sections will NOT be evaluated. 
9. Questions Q.1 – Q.10 belong to Section GA (General Aptitude) and carry a total of 15 marks. 
Questions Q.1 – Q.5 carry 1 mark each, and questions Q.6 – Q.10 carry 2 marks each. 
10. There are 11 questions carrying 15 marks in Section A (Engineering Mathematics), which is 
compulsory.   Questions Q.1–Q.7 carry 1 mark each and questions Q.8–Q.11 carry 2 marks each.  
11. Each of the other sections (Sections B through G) contains 22 questions carrying 35 marks. Questions 
Q.1–Q.9 carry 1 mark each and questions Q.10–Q.22 carry 2 marks each.  The 2 marks questions 
include two pairs of common data questions and one pair 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. 
12. Unattempted questions will result in zero mark and wrong answers will result in NEGATIVE marks.  
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.  
13. Calculator is allowed whereas charts, graph sheets or tables are NOT allowed in the examination hall.  
14. Before the start of the examination, write your name and registration number in the space provided 
below using a black ink ball point pen. 
 
Name 
 
 
Registration Number XE 
      
 
 
 
2012                                                                                                                                                                                      XE                                                                                                                        
 
XE 2/36 
General Aptitude (GA) Questions (Compulsory) 
Q. 1 – Q. 5 carry one mark each. 
Q.1  One of the parts (A, B, C, D) in the sentence given below contains an ERROR. Which one of the 
following is INCORRECT? 
 
I requested that he should be given the driving test today instead of tomorrow. 
(A)  requested that 
(B)  should be given 
(C)  the driving test 
(D)  instead of tomorrow 
 
Q.2  Which one of the following options is the closest in meaning to the word given below? 
 
Latitude 
(A)  Eligibility (B)  Freedom (C)  Coercion (D)  Meticulousness 
 
Q.3  Choose the most appropriate word from the options given below to complete the following 
sentence: 
 
Given the seriousness of the situation that he had to face, his ___ was impressive. 
(A)  beggary (B)  nomenclature (C)  jealousy (D)  nonchalance 
 
Q.4  Choose the most appropriate alternative from the options given below to complete the following 
sentence: 
If the tired soldier wanted to lie down, he ___ the mattress out on the balcony. 
(A) should take 
(B) shall take 
(C) should have taken  
(D) will have taken 
 
Q.5  If (1.001)
1259
 = 3.52 and (1.001)
2062
 = 7.85, then (1.001)
3321
 =  
(A)  2.23 (B)  4.33 (C)  11.37   (D)  27.64  
 
 
Q. 6 - Q. 10 carry two marks each. 
Q.6  A and B are friends. They decide to meet between 1 PM and 2 PM on a given day. There is a 
condition that whoever arrives first will not wait for the other for more than 15 minutes. The 
probability that they will meet on that day is 
(A)  1/4  (B)  1/16 (C)  7/16 (D)  9/16  
 
Page 3


2012                                                                                                                                          XE                                                           
 
XE 
1/36 
XE : ENGINEERING SCIENCES 
Duration: Three Hours                          Maximum Marks: 100 
Read the following instructions carefully. 
1. Do not open the seal of the Question Booklet until you are asked to do so by the invigilator. 
2. Take out the Optical Response Sheet (ORS) from this Question Booklet without breaking the seal 
and read the instructions printed on the ORS carefully.  
3. On the right half of the ORS, using ONLY a black ink ball point pen, (i) darken the bubble 
corresponding to your test paper code and the appropriate bubble under each digit of your registration 
number and (ii) write your registration number, your name and name of the examination centre and 
put your signature at the specified location.  
4. This Question Booklet contains 36 pages including blank pages for rough work. After you are 
permitted to open the seal, please check all pages and report discrepancies, if any, to the invigilator. 
5. There are a total of 65 questions carrying 100 marks. All these questions are of objective type. Each 
question has only one correct answer. Questions must be answered on the left hand side of the ORS 
by darkening the appropriate bubble (marked A, B, C, D) using ONLY a black ink ball point pen 
against the question number. For each question darken the bubble of the correct answer. More 
than one answer bubbled against a question will be treated as an incorrect response. 
6. Since bubbles darkened by the black ink ball point pen cannot be erased, candidates should darken 
the bubbles in the ORS very carefully. 
7. This Question Booklet contains Eight sections: GA (General Aptitude), A (Engineering Mathematics), 
B (Fluid Mechanics), C (Materials Science), D (Solid Mechanics), E (Thermodynamics), F (Polymer 
Science & Engineering) and G (Food Technology). 
8. Section GA (General Aptitude) and  Section A  (Engineering Mathematics) are compulsory. Attempt 
any two optional sections B through G. Using a black ink ball point pen, mark the sections you have 
chosen by darkening the appropriate bubbles provided on the left hand side of the ORS. Also, write 
the codes of the optional sections in the boxes provided. In case the candidate does not bubble 
section codes corresponding to Optional Section-1 or Optional Section-2 or both, the corresponding 
sections will NOT be evaluated. 
9. Questions Q.1 – Q.10 belong to Section GA (General Aptitude) and carry a total of 15 marks. 
Questions Q.1 – Q.5 carry 1 mark each, and questions Q.6 – Q.10 carry 2 marks each. 
10. There are 11 questions carrying 15 marks in Section A (Engineering Mathematics), which is 
compulsory.   Questions Q.1–Q.7 carry 1 mark each and questions Q.8–Q.11 carry 2 marks each.  
11. Each of the other sections (Sections B through G) contains 22 questions carrying 35 marks. Questions 
Q.1–Q.9 carry 1 mark each and questions Q.10–Q.22 carry 2 marks each.  The 2 marks questions 
include two pairs of common data questions and one pair 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. 
12. Unattempted questions will result in zero mark and wrong answers will result in NEGATIVE marks.  
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.  
13. Calculator is allowed whereas charts, graph sheets or tables are NOT allowed in the examination hall.  
14. Before the start of the examination, write your name and registration number in the space provided 
below using a black ink ball point pen. 
 
Name 
 
 
Registration Number XE 
      
 
 
 
2012                                                                                                                                                                                      XE                                                                                                                        
 
XE 2/36 
General Aptitude (GA) Questions (Compulsory) 
Q. 1 – Q. 5 carry one mark each. 
Q.1  One of the parts (A, B, C, D) in the sentence given below contains an ERROR. Which one of the 
following is INCORRECT? 
 
I requested that he should be given the driving test today instead of tomorrow. 
(A)  requested that 
(B)  should be given 
(C)  the driving test 
(D)  instead of tomorrow 
 
Q.2  Which one of the following options is the closest in meaning to the word given below? 
 
Latitude 
(A)  Eligibility (B)  Freedom (C)  Coercion (D)  Meticulousness 
 
Q.3  Choose the most appropriate word from the options given below to complete the following 
sentence: 
 
Given the seriousness of the situation that he had to face, his ___ was impressive. 
(A)  beggary (B)  nomenclature (C)  jealousy (D)  nonchalance 
 
Q.4  Choose the most appropriate alternative from the options given below to complete the following 
sentence: 
If the tired soldier wanted to lie down, he ___ the mattress out on the balcony. 
(A) should take 
(B) shall take 
(C) should have taken  
(D) will have taken 
 
Q.5  If (1.001)
1259
 = 3.52 and (1.001)
2062
 = 7.85, then (1.001)
3321
 =  
(A)  2.23 (B)  4.33 (C)  11.37   (D)  27.64  
 
 
Q. 6 - Q. 10 carry two marks each. 
Q.6  A and B are friends. They decide to meet between 1 PM and 2 PM on a given day. There is a 
condition that whoever arrives first will not wait for the other for more than 15 minutes. The 
probability that they will meet on that day is 
(A)  1/4  (B)  1/16 (C)  7/16 (D)  9/16  
 
2012                                                                                                                                                                                      XE                                                                                                                        
 
XE 3/36 
Q.7  The data given in the following table summarizes the monthly budget of an average household.  
 
Category Amount (Rs.) 
Food 4000 
Clothing 1200 
Rent 2000 
Savings 1500 
Other expenses 1800 
 
The approximate percentage of the monthly budget NOT spent on savings is 
(A)  10% (B)  14%  (C)  81%   (D)  86%  
 
Q.8  There are eight bags of rice looking alike, seven of which have equal weight and one is slightly 
heavier. The weighing balance is of unlimited capacity. Using this balance, the minimum number 
of weighings required to identify the heavier bag is 
(A)  2 (B)  3  (C)  4   (D)  8   
 
Q.9  Raju has 14 currency notes in his pocket consisting of only Rs. 20 notes and Rs. 10 notes. The total 
money value of the notes is Rs. 230. The number of Rs. 10 notes that Raju has is 
(A)  5 (B)  6  (C)  9   (D)  10   
 
Q.10  One of the legacies of the Roman legions was discipline. In the legions, military law prevailed 
and discipline was brutal. Discipline on the battlefield kept units obedient, intact and fighting, 
even when the odds and conditions were against them.  
 
Which one of the following statements best sums up the meaning of the above passage? 
(A)  Thorough regimentation was the main reason for the efficiency of the Roman legions even in  
  adverse circumstances. 
(B)  The legions were treated inhumanly as if the men were animals. 
(C)  Discipline was the armies’ inheritance from their seniors. 
(D)  The harsh discipline to which the legions were subjected to led to the odds and conditions being 
  against them. 
 
 
Page 4


2012                                                                                                                                          XE                                                           
 
XE 
1/36 
XE : ENGINEERING SCIENCES 
Duration: Three Hours                          Maximum Marks: 100 
Read the following instructions carefully. 
1. Do not open the seal of the Question Booklet until you are asked to do so by the invigilator. 
2. Take out the Optical Response Sheet (ORS) from this Question Booklet without breaking the seal 
and read the instructions printed on the ORS carefully.  
3. On the right half of the ORS, using ONLY a black ink ball point pen, (i) darken the bubble 
corresponding to your test paper code and the appropriate bubble under each digit of your registration 
number and (ii) write your registration number, your name and name of the examination centre and 
put your signature at the specified location.  
4. This Question Booklet contains 36 pages including blank pages for rough work. After you are 
permitted to open the seal, please check all pages and report discrepancies, if any, to the invigilator. 
5. There are a total of 65 questions carrying 100 marks. All these questions are of objective type. Each 
question has only one correct answer. Questions must be answered on the left hand side of the ORS 
by darkening the appropriate bubble (marked A, B, C, D) using ONLY a black ink ball point pen 
against the question number. For each question darken the bubble of the correct answer. More 
than one answer bubbled against a question will be treated as an incorrect response. 
6. Since bubbles darkened by the black ink ball point pen cannot be erased, candidates should darken 
the bubbles in the ORS very carefully. 
7. This Question Booklet contains Eight sections: GA (General Aptitude), A (Engineering Mathematics), 
B (Fluid Mechanics), C (Materials Science), D (Solid Mechanics), E (Thermodynamics), F (Polymer 
Science & Engineering) and G (Food Technology). 
8. Section GA (General Aptitude) and  Section A  (Engineering Mathematics) are compulsory. Attempt 
any two optional sections B through G. Using a black ink ball point pen, mark the sections you have 
chosen by darkening the appropriate bubbles provided on the left hand side of the ORS. Also, write 
the codes of the optional sections in the boxes provided. In case the candidate does not bubble 
section codes corresponding to Optional Section-1 or Optional Section-2 or both, the corresponding 
sections will NOT be evaluated. 
9. Questions Q.1 – Q.10 belong to Section GA (General Aptitude) and carry a total of 15 marks. 
Questions Q.1 – Q.5 carry 1 mark each, and questions Q.6 – Q.10 carry 2 marks each. 
10. There are 11 questions carrying 15 marks in Section A (Engineering Mathematics), which is 
compulsory.   Questions Q.1–Q.7 carry 1 mark each and questions Q.8–Q.11 carry 2 marks each.  
11. Each of the other sections (Sections B through G) contains 22 questions carrying 35 marks. Questions 
Q.1–Q.9 carry 1 mark each and questions Q.10–Q.22 carry 2 marks each.  The 2 marks questions 
include two pairs of common data questions and one pair 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. 
12. Unattempted questions will result in zero mark and wrong answers will result in NEGATIVE marks.  
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.  
13. Calculator is allowed whereas charts, graph sheets or tables are NOT allowed in the examination hall.  
14. Before the start of the examination, write your name and registration number in the space provided 
below using a black ink ball point pen. 
 
Name 
 
 
Registration Number XE 
      
 
 
 
2012                                                                                                                                                                                      XE                                                                                                                        
 
XE 2/36 
General Aptitude (GA) Questions (Compulsory) 
Q. 1 – Q. 5 carry one mark each. 
Q.1  One of the parts (A, B, C, D) in the sentence given below contains an ERROR. Which one of the 
following is INCORRECT? 
 
I requested that he should be given the driving test today instead of tomorrow. 
(A)  requested that 
(B)  should be given 
(C)  the driving test 
(D)  instead of tomorrow 
 
Q.2  Which one of the following options is the closest in meaning to the word given below? 
 
Latitude 
(A)  Eligibility (B)  Freedom (C)  Coercion (D)  Meticulousness 
 
Q.3  Choose the most appropriate word from the options given below to complete the following 
sentence: 
 
Given the seriousness of the situation that he had to face, his ___ was impressive. 
(A)  beggary (B)  nomenclature (C)  jealousy (D)  nonchalance 
 
Q.4  Choose the most appropriate alternative from the options given below to complete the following 
sentence: 
If the tired soldier wanted to lie down, he ___ the mattress out on the balcony. 
(A) should take 
(B) shall take 
(C) should have taken  
(D) will have taken 
 
Q.5  If (1.001)
1259
 = 3.52 and (1.001)
2062
 = 7.85, then (1.001)
3321
 =  
(A)  2.23 (B)  4.33 (C)  11.37   (D)  27.64  
 
 
Q. 6 - Q. 10 carry two marks each. 
Q.6  A and B are friends. They decide to meet between 1 PM and 2 PM on a given day. There is a 
condition that whoever arrives first will not wait for the other for more than 15 minutes. The 
probability that they will meet on that day is 
(A)  1/4  (B)  1/16 (C)  7/16 (D)  9/16  
 
2012                                                                                                                                                                                      XE                                                                                                                        
 
XE 3/36 
Q.7  The data given in the following table summarizes the monthly budget of an average household.  
 
Category Amount (Rs.) 
Food 4000 
Clothing 1200 
Rent 2000 
Savings 1500 
Other expenses 1800 
 
The approximate percentage of the monthly budget NOT spent on savings is 
(A)  10% (B)  14%  (C)  81%   (D)  86%  
 
Q.8  There are eight bags of rice looking alike, seven of which have equal weight and one is slightly 
heavier. The weighing balance is of unlimited capacity. Using this balance, the minimum number 
of weighings required to identify the heavier bag is 
(A)  2 (B)  3  (C)  4   (D)  8   
 
Q.9  Raju has 14 currency notes in his pocket consisting of only Rs. 20 notes and Rs. 10 notes. The total 
money value of the notes is Rs. 230. The number of Rs. 10 notes that Raju has is 
(A)  5 (B)  6  (C)  9   (D)  10   
 
Q.10  One of the legacies of the Roman legions was discipline. In the legions, military law prevailed 
and discipline was brutal. Discipline on the battlefield kept units obedient, intact and fighting, 
even when the odds and conditions were against them.  
 
Which one of the following statements best sums up the meaning of the above passage? 
(A)  Thorough regimentation was the main reason for the efficiency of the Roman legions even in  
  adverse circumstances. 
(B)  The legions were treated inhumanly as if the men were animals. 
(C)  Discipline was the armies’ inheritance from their seniors. 
(D)  The harsh discipline to which the legions were subjected to led to the odds and conditions being 
  against them. 
 
 
2012                                                                                                                                                                                      XE                                                                                                                        
 
XE 4/36 
A : ENGINEERING MATHEMATICS (Compulsory) 
 
Q. 1 – Q. 7 carry one mark each. 
Q.1 For the matrix 
?
?
?
?
?
?
?
?
?
?
?
3 0 0
6 2 0
5 4 1
M , consider the following statements: 
 P: 3 is an eigenvalue of M. 
Q: 
?
?
?
?
?
?
?
?
?
?
0
1
4
 is an eigenvector of M. R: 
?
?
?
?
?
?
?
?
?
?
0
2
4
 is an eigenvector of M. 
 
Which of the above statements are TRUE? 
(A)  P and Q, but not R (B)  Q and R, but not P 
(C)  P and R, but not Q (D)  P, Q, and R 
 
 
Q.2 
Taylor series of 
x
x f
?
?
1
1
) ( about 0 ? x is given as ? ? ? ? ? ?
3 2
1 x x x TS
f
.  This series can 
be used to evaluate ) (x f for 
(A)  1 ? x (B)  1 ? ? x (C)  1 ? x (D)  1 1 ? ? ? x 
 
 
Q.3 Let ( , ) ln( ) f u v u v ? and ( , ) ( ( , ), ( , )) F x y f u x y v x y ? , where / u x y ? and v x y ?? . Then 
/ Fy ?? is 
(A)  
) (
) ( ln
2
y x y
x
y x
y
x
?
? ? ? (B)  
v
u
v
y
x
? ? ln
2
 
(C)  
v
u
v
y
x
? ln
2
 (D)  
yv
x
v
y
x
? ln
2
 
 
 
Q.4 Consider two functions z z f ? ) ( and z z g ? ) ( (conjugate of z). Using Cauchy-Riemann 
conditions, choose the correct answer 
(A)  Both f and g are analytic (B)  f  is analytic but g  is not analytic 
(C)  g  is analytic but f  is not analytic (D)  Neither f  nor g  is analytic 
 
 
Q.5 
For 
42
5 f x xy ?? , the direction of maximum increase of ( , ) f x y at the point (2, 2) is along 
(A)  
ˆˆ
3 10 ij ? (B)  
ˆˆ
12 40 ij ?? (C)  
ˆˆ
3 10 ij ? (D)  
ˆˆ
12 40 ij ?? 
 
 
Q.6 Suppose 50% of the population of a village like oranges, 70% of the population like apples, and 
40% like both. If a person is picked at random who likes at least one of these fruits, what is the 
probability that the person likes oranges? 
(A)  1/8 (B)  5/12 (C)  1/2 (D)  5/8 
 
Page 5


2012                                                                                                                                          XE                                                           
 
XE 
1/36 
XE : ENGINEERING SCIENCES 
Duration: Three Hours                          Maximum Marks: 100 
Read the following instructions carefully. 
1. Do not open the seal of the Question Booklet until you are asked to do so by the invigilator. 
2. Take out the Optical Response Sheet (ORS) from this Question Booklet without breaking the seal 
and read the instructions printed on the ORS carefully.  
3. On the right half of the ORS, using ONLY a black ink ball point pen, (i) darken the bubble 
corresponding to your test paper code and the appropriate bubble under each digit of your registration 
number and (ii) write your registration number, your name and name of the examination centre and 
put your signature at the specified location.  
4. This Question Booklet contains 36 pages including blank pages for rough work. After you are 
permitted to open the seal, please check all pages and report discrepancies, if any, to the invigilator. 
5. There are a total of 65 questions carrying 100 marks. All these questions are of objective type. Each 
question has only one correct answer. Questions must be answered on the left hand side of the ORS 
by darkening the appropriate bubble (marked A, B, C, D) using ONLY a black ink ball point pen 
against the question number. For each question darken the bubble of the correct answer. More 
than one answer bubbled against a question will be treated as an incorrect response. 
6. Since bubbles darkened by the black ink ball point pen cannot be erased, candidates should darken 
the bubbles in the ORS very carefully. 
7. This Question Booklet contains Eight sections: GA (General Aptitude), A (Engineering Mathematics), 
B (Fluid Mechanics), C (Materials Science), D (Solid Mechanics), E (Thermodynamics), F (Polymer 
Science & Engineering) and G (Food Technology). 
8. Section GA (General Aptitude) and  Section A  (Engineering Mathematics) are compulsory. Attempt 
any two optional sections B through G. Using a black ink ball point pen, mark the sections you have 
chosen by darkening the appropriate bubbles provided on the left hand side of the ORS. Also, write 
the codes of the optional sections in the boxes provided. In case the candidate does not bubble 
section codes corresponding to Optional Section-1 or Optional Section-2 or both, the corresponding 
sections will NOT be evaluated. 
9. Questions Q.1 – Q.10 belong to Section GA (General Aptitude) and carry a total of 15 marks. 
Questions Q.1 – Q.5 carry 1 mark each, and questions Q.6 – Q.10 carry 2 marks each. 
10. There are 11 questions carrying 15 marks in Section A (Engineering Mathematics), which is 
compulsory.   Questions Q.1–Q.7 carry 1 mark each and questions Q.8–Q.11 carry 2 marks each.  
11. Each of the other sections (Sections B through G) contains 22 questions carrying 35 marks. Questions 
Q.1–Q.9 carry 1 mark each and questions Q.10–Q.22 carry 2 marks each.  The 2 marks questions 
include two pairs of common data questions and one pair 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. 
12. Unattempted questions will result in zero mark and wrong answers will result in NEGATIVE marks.  
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.  
13. Calculator is allowed whereas charts, graph sheets or tables are NOT allowed in the examination hall.  
14. Before the start of the examination, write your name and registration number in the space provided 
below using a black ink ball point pen. 
 
Name 
 
 
Registration Number XE 
      
 
 
 
2012                                                                                                                                                                                      XE                                                                                                                        
 
XE 2/36 
General Aptitude (GA) Questions (Compulsory) 
Q. 1 – Q. 5 carry one mark each. 
Q.1  One of the parts (A, B, C, D) in the sentence given below contains an ERROR. Which one of the 
following is INCORRECT? 
 
I requested that he should be given the driving test today instead of tomorrow. 
(A)  requested that 
(B)  should be given 
(C)  the driving test 
(D)  instead of tomorrow 
 
Q.2  Which one of the following options is the closest in meaning to the word given below? 
 
Latitude 
(A)  Eligibility (B)  Freedom (C)  Coercion (D)  Meticulousness 
 
Q.3  Choose the most appropriate word from the options given below to complete the following 
sentence: 
 
Given the seriousness of the situation that he had to face, his ___ was impressive. 
(A)  beggary (B)  nomenclature (C)  jealousy (D)  nonchalance 
 
Q.4  Choose the most appropriate alternative from the options given below to complete the following 
sentence: 
If the tired soldier wanted to lie down, he ___ the mattress out on the balcony. 
(A) should take 
(B) shall take 
(C) should have taken  
(D) will have taken 
 
Q.5  If (1.001)
1259
 = 3.52 and (1.001)
2062
 = 7.85, then (1.001)
3321
 =  
(A)  2.23 (B)  4.33 (C)  11.37   (D)  27.64  
 
 
Q. 6 - Q. 10 carry two marks each. 
Q.6  A and B are friends. They decide to meet between 1 PM and 2 PM on a given day. There is a 
condition that whoever arrives first will not wait for the other for more than 15 minutes. The 
probability that they will meet on that day is 
(A)  1/4  (B)  1/16 (C)  7/16 (D)  9/16  
 
2012                                                                                                                                                                                      XE                                                                                                                        
 
XE 3/36 
Q.7  The data given in the following table summarizes the monthly budget of an average household.  
 
Category Amount (Rs.) 
Food 4000 
Clothing 1200 
Rent 2000 
Savings 1500 
Other expenses 1800 
 
The approximate percentage of the monthly budget NOT spent on savings is 
(A)  10% (B)  14%  (C)  81%   (D)  86%  
 
Q.8  There are eight bags of rice looking alike, seven of which have equal weight and one is slightly 
heavier. The weighing balance is of unlimited capacity. Using this balance, the minimum number 
of weighings required to identify the heavier bag is 
(A)  2 (B)  3  (C)  4   (D)  8   
 
Q.9  Raju has 14 currency notes in his pocket consisting of only Rs. 20 notes and Rs. 10 notes. The total 
money value of the notes is Rs. 230. The number of Rs. 10 notes that Raju has is 
(A)  5 (B)  6  (C)  9   (D)  10   
 
Q.10  One of the legacies of the Roman legions was discipline. In the legions, military law prevailed 
and discipline was brutal. Discipline on the battlefield kept units obedient, intact and fighting, 
even when the odds and conditions were against them.  
 
Which one of the following statements best sums up the meaning of the above passage? 
(A)  Thorough regimentation was the main reason for the efficiency of the Roman legions even in  
  adverse circumstances. 
(B)  The legions were treated inhumanly as if the men were animals. 
(C)  Discipline was the armies’ inheritance from their seniors. 
(D)  The harsh discipline to which the legions were subjected to led to the odds and conditions being 
  against them. 
 
 
2012                                                                                                                                                                                      XE                                                                                                                        
 
XE 4/36 
A : ENGINEERING MATHEMATICS (Compulsory) 
 
Q. 1 – Q. 7 carry one mark each. 
Q.1 For the matrix 
?
?
?
?
?
?
?
?
?
?
?
3 0 0
6 2 0
5 4 1
M , consider the following statements: 
 P: 3 is an eigenvalue of M. 
Q: 
?
?
?
?
?
?
?
?
?
?
0
1
4
 is an eigenvector of M. R: 
?
?
?
?
?
?
?
?
?
?
0
2
4
 is an eigenvector of M. 
 
Which of the above statements are TRUE? 
(A)  P and Q, but not R (B)  Q and R, but not P 
(C)  P and R, but not Q (D)  P, Q, and R 
 
 
Q.2 
Taylor series of 
x
x f
?
?
1
1
) ( about 0 ? x is given as ? ? ? ? ? ?
3 2
1 x x x TS
f
.  This series can 
be used to evaluate ) (x f for 
(A)  1 ? x (B)  1 ? ? x (C)  1 ? x (D)  1 1 ? ? ? x 
 
 
Q.3 Let ( , ) ln( ) f u v u v ? and ( , ) ( ( , ), ( , )) F x y f u x y v x y ? , where / u x y ? and v x y ?? . Then 
/ Fy ?? is 
(A)  
) (
) ( ln
2
y x y
x
y x
y
x
?
? ? ? (B)  
v
u
v
y
x
? ? ln
2
 
(C)  
v
u
v
y
x
? ln
2
 (D)  
yv
x
v
y
x
? ln
2
 
 
 
Q.4 Consider two functions z z f ? ) ( and z z g ? ) ( (conjugate of z). Using Cauchy-Riemann 
conditions, choose the correct answer 
(A)  Both f and g are analytic (B)  f  is analytic but g  is not analytic 
(C)  g  is analytic but f  is not analytic (D)  Neither f  nor g  is analytic 
 
 
Q.5 
For 
42
5 f x xy ?? , the direction of maximum increase of ( , ) f x y at the point (2, 2) is along 
(A)  
ˆˆ
3 10 ij ? (B)  
ˆˆ
12 40 ij ?? (C)  
ˆˆ
3 10 ij ? (D)  
ˆˆ
12 40 ij ?? 
 
 
Q.6 Suppose 50% of the population of a village like oranges, 70% of the population like apples, and 
40% like both. If a person is picked at random who likes at least one of these fruits, what is the 
probability that the person likes oranges? 
(A)  1/8 (B)  5/12 (C)  1/2 (D)  5/8 
 
2012                                                                                                                                                                                      XE                                                                                                                        
 
XE 5/36 
Q.7 
For the solution of 
2
0 u ?? , the domain and boundary conditions are shown below. 
 
Which of the following statements is TRUE? 
(A) The solution cannot be obtained using separation of variables because the governing equation  
 is non-separable. 
(B) The solution cannot be obtained using separation of variables because all the boundary values  
 are non-zero. 
(C) The solution cannot be obtained using separation of variables because not all the boundaries  
 are along constant coordinate lines. 
(D) The solution can be obtained by separation of variables. 
 
Q. 8 - Q. 11 carry two marks each. 
Q.8 If ( ) sin( ) f x x x ? and ( ) sin( ) g x x x ? , then 
(A) ( ) ( ) g x f x ? 
(B)  () gx is an even function 
(C)  The x-coordinates corresponding to the various local maxima are identical for both () fx and 
       () gx 
(D)  () gx is differentiable at 0 x ? 
 
Q.9 
The general solution of 
4 3 2
4 3 2
2 2 2 0
d y d y d y dy
y
dx
dx dx dx
? ? ? ? ? is 
(A)  
1 2 3 4
cosh( ) sinh( )
xx
c e c xe c x c x ? ? ? (B)  
1 2 3 4
x x ix ix
c e c e c e c e
??
? ? ? 
(C)  
1 2 3 4
cos( ) sin( )
xx
c e c xe c x c x ? ? ? (D)  
1 2 3 4
x x ix ix
c e c xe c e c e
??
? ? ? 
 
Q.10 Evaluation of ? ?
??
? ? ?
S
x x
dA n k e z j y i e ˆ
ˆ ˆ
3
ˆ
 over a surface S : 
2 2 2
1 x y z ? ? ? , using Gauss 
divergence theorem, gives 
(A)  0 (B)  4p (C)  4p / 3 (D)  12p 
  
Q.11 The exact solution of the integral
4
2
0
( 4) x dx ?
?
 is denoted by
E
I . The same integral evaluated 
numerically by the trapezoidal rule and the Simpson’s 1/3 rule are denoted by 
T
I and
S
I , 
respectively. The subinterval used in the numerical methods is 2 h ? . Then 
(A)  
E S T
I I I ?? (B)  
E S T
I I I ?? (C)  
E S T
I I I ?? (D)  
E S T
I I I ?? 
END OF SECTION - A
x 
y 
2
0 u ??
10 u ?
20 u ?
30 u ?
40 u ?
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