Chemical Engineering (CH) 2013 GATE Paper without solution GATE Notes | EduRev

 Page 1


2013                                                                                                                                                                                          CHEMICAL ENGG. –  CH 
CH 1/16
CH:CHEMICAL ENGINEERING 
 
Duration: Three Hours        Maximum Marks:100 
 
Please read the following instructions carefully: 
 
General Instructions: 
 
1. Total duration of examination is 180 minutes (3 hours).  
 
2. The clock will be set at the server.  The countdown timer in 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 will not be required to end or submit your examination.  
 
3. The Question Palette displayed on the right side of screen will show the status of each question using 
one of the following symbols:  
  
 
You have not visited the question yet. 
 
You have not answered the question. 
 
You have answered the question.  
 
You have NOT answered the question, but have marked the 
question for review. 
 
You have answered the question, but marked it for review.  
 
The Marked for Review status for a question simply indicates that you would like to look at that 
question again. If a question is answered and  Marked for Review, your answer for that question 
will be considered in the evaluation. 
 
Navigating to a Question 
 
4. To answer a question, do the following: 
a. Click on the question number in the Question Palette to go to that question directly.  
b. Select an answer for a multiple choice type question. Use the virtual numeric keypad to enter 
a number as answer for a numerical type question.  
c. Click on Save and Next to save your answer for the current question and then go to the next 
question.  
d. Click on Mark for Review and Next to save your answer for the  current question, mark it 
for review, and then go to the next question. 
e. Caution: Note that your answer for the current question will not be saved, if you 
navigate to another question directly by clicking on its question number.  
5. You can view all the questions by clicking on the Question Paper button. Note that the options for 
multiple choice type questions will not be shown.  
 
  
Page 2


2013                                                                                                                                                                                          CHEMICAL ENGG. –  CH 
CH 1/16
CH:CHEMICAL ENGINEERING 
 
Duration: Three Hours        Maximum Marks:100 
 
Please read the following instructions carefully: 
 
General Instructions: 
 
1. Total duration of examination is 180 minutes (3 hours).  
 
2. The clock will be set at the server.  The countdown timer in 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 will not be required to end or submit your examination.  
 
3. The Question Palette displayed on the right side of screen will show the status of each question using 
one of the following symbols:  
  
 
You have not visited the question yet. 
 
You have not answered the question. 
 
You have answered the question.  
 
You have NOT answered the question, but have marked the 
question for review. 
 
You have answered the question, but marked it for review.  
 
The Marked for Review status for a question simply indicates that you would like to look at that 
question again. If a question is answered and  Marked for Review, your answer for that question 
will be considered in the evaluation. 
 
Navigating to a Question 
 
4. To answer a question, do the following: 
a. Click on the question number in the Question Palette to go to that question directly.  
b. Select an answer for a multiple choice type question. Use the virtual numeric keypad to enter 
a number as answer for a numerical type question.  
c. Click on Save and Next to save your answer for the current question and then go to the next 
question.  
d. Click on Mark for Review and Next to save your answer for the  current question, mark it 
for review, and then go to the next question. 
e. Caution: Note that your answer for the current question will not be saved, if you 
navigate to another question directly by clicking on its question number.  
5. You can view all the questions by clicking on the Question Paper button. Note that the options for 
multiple choice type questions will not be shown.  
 
  
2013                                                                                                                                                                                          CHEMICAL ENGG. –  CH 
CH 2/16
Answering a Question 
 
6. Procedure for answering a multiple choice type question: 
a. To select your answer, click on the button of one of  the options 
b. To deselect your chosen answer, click on the button of the chosen option again or click on the 
Clear Response button  
c. To change your chosen answer, click on the button of  another option 
d. To save your answer, you MUST click on the Save and Next button 
e. To mark the question for review, click on the Mark for Review and Next button. If an 
answer is selected for a question that is Marked for Review, that answer will be considered 
in the evaluation. 
 
7. Procedure for answering a numerical answer type question: 
a. To enter a number as your answer, use the virtual numerical keypad 
b. A fraction (eg.,-0.3 or -.3) can be entered as an answer with or without ‘0’ before the decimal 
point 
c. To clear your answer, click on the Clear Response button 
d. To save your answer, you MUST click on the Save and Next button 
e. To mark the question for review, click on the Mark for Review and Next button. If an 
answer is entered for a question that is Marked for Review, that answer will be considered 
in the evaluation. 
 
8. To change your answer to a question that has already been answered, first select that question for 
answering and then follow the procedure for answering that type of question.  
 
9. Note that ONLY Questions for which answers  are saved or marked for review after answering will be 
considered for evaluation. 
 
 
 
 
 
  
Page 3


2013                                                                                                                                                                                          CHEMICAL ENGG. –  CH 
CH 1/16
CH:CHEMICAL ENGINEERING 
 
Duration: Three Hours        Maximum Marks:100 
 
Please read the following instructions carefully: 
 
General Instructions: 
 
1. Total duration of examination is 180 minutes (3 hours).  
 
2. The clock will be set at the server.  The countdown timer in 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 will not be required to end or submit your examination.  
 
3. The Question Palette displayed on the right side of screen will show the status of each question using 
one of the following symbols:  
  
 
You have not visited the question yet. 
 
You have not answered the question. 
 
You have answered the question.  
 
You have NOT answered the question, but have marked the 
question for review. 
 
You have answered the question, but marked it for review.  
 
The Marked for Review status for a question simply indicates that you would like to look at that 
question again. If a question is answered and  Marked for Review, your answer for that question 
will be considered in the evaluation. 
 
Navigating to a Question 
 
4. To answer a question, do the following: 
a. Click on the question number in the Question Palette to go to that question directly.  
b. Select an answer for a multiple choice type question. Use the virtual numeric keypad to enter 
a number as answer for a numerical type question.  
c. Click on Save and Next to save your answer for the current question and then go to the next 
question.  
d. Click on Mark for Review and Next to save your answer for the  current question, mark it 
for review, and then go to the next question. 
e. Caution: Note that your answer for the current question will not be saved, if you 
navigate to another question directly by clicking on its question number.  
5. You can view all the questions by clicking on the Question Paper button. Note that the options for 
multiple choice type questions will not be shown.  
 
  
2013                                                                                                                                                                                          CHEMICAL ENGG. –  CH 
CH 2/16
Answering a Question 
 
6. Procedure for answering a multiple choice type question: 
a. To select your answer, click on the button of one of  the options 
b. To deselect your chosen answer, click on the button of the chosen option again or click on the 
Clear Response button  
c. To change your chosen answer, click on the button of  another option 
d. To save your answer, you MUST click on the Save and Next button 
e. To mark the question for review, click on the Mark for Review and Next button. If an 
answer is selected for a question that is Marked for Review, that answer will be considered 
in the evaluation. 
 
7. Procedure for answering a numerical answer type question: 
a. To enter a number as your answer, use the virtual numerical keypad 
b. A fraction (eg.,-0.3 or -.3) can be entered as an answer with or without ‘0’ before the decimal 
point 
c. To clear your answer, click on the Clear Response button 
d. To save your answer, you MUST click on the Save and Next button 
e. To mark the question for review, click on the Mark for Review and Next button. If an 
answer is entered for a question that is Marked for Review, that answer will be considered 
in the evaluation. 
 
8. To change your answer to a question that has already been answered, first select that question for 
answering and then follow the procedure for answering that type of question.  
 
9. Note that ONLY Questions for which answers  are saved or marked for review after answering will be 
considered for evaluation. 
 
 
 
 
 
  
2013                                                                                                                                                                                          CHEMICAL ENGG. –  CH 
CH 3/16
Paper specific instructions: 
 
 
1. There are a total of 65 questions carrying 100 marks.Questions are of multiple choice type or 
numerical answer type. A multiple choice type question will have four choices for the answer with 
only one correct choice. For numerical answer type questions, the answer is a number and no choices 
will be given. A number as the answer should be entered using the virtual keyboard on the monitor. 
 
2. Questions Q.1 – Q.25 carry 1mark each. Questions Q.26 – Q.55 carry 2marks each. The 2marks 
questions include two pairs of common data questions and two pairs of linked answer questions. The 
answer to the second question of the linked answer questions depends on the answer to the first 
question of the pair. If the first question in the linked pair is wrongly answered or is not attempted, 
then the answer to the second question in the pair will not be evaluated. 
 
3. Questions Q.56 – Q.65 belong to General Aptitude (GA) section and carry a total of 15 marks. 
Questions Q.56 – Q.60 carry 1mark each, and questions Q.61 – Q.65 carry 2marks each.   
 
4. Questions not attempted will result in zero mark. Wrong answers for multiple choice type questions 
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. There is no negative 
marking for questions of numerical answer type. 
 
5. Calculator is allowed. Charts, graph sheets or tables are NOT allowed in the examination hall.  
 
6. Do the rough work in the Scribble Pad provided. 
 
  
Page 4


2013                                                                                                                                                                                          CHEMICAL ENGG. –  CH 
CH 1/16
CH:CHEMICAL ENGINEERING 
 
Duration: Three Hours        Maximum Marks:100 
 
Please read the following instructions carefully: 
 
General Instructions: 
 
1. Total duration of examination is 180 minutes (3 hours).  
 
2. The clock will be set at the server.  The countdown timer in 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 will not be required to end or submit your examination.  
 
3. The Question Palette displayed on the right side of screen will show the status of each question using 
one of the following symbols:  
  
 
You have not visited the question yet. 
 
You have not answered the question. 
 
You have answered the question.  
 
You have NOT answered the question, but have marked the 
question for review. 
 
You have answered the question, but marked it for review.  
 
The Marked for Review status for a question simply indicates that you would like to look at that 
question again. If a question is answered and  Marked for Review, your answer for that question 
will be considered in the evaluation. 
 
Navigating to a Question 
 
4. To answer a question, do the following: 
a. Click on the question number in the Question Palette to go to that question directly.  
b. Select an answer for a multiple choice type question. Use the virtual numeric keypad to enter 
a number as answer for a numerical type question.  
c. Click on Save and Next to save your answer for the current question and then go to the next 
question.  
d. Click on Mark for Review and Next to save your answer for the  current question, mark it 
for review, and then go to the next question. 
e. Caution: Note that your answer for the current question will not be saved, if you 
navigate to another question directly by clicking on its question number.  
5. You can view all the questions by clicking on the Question Paper button. Note that the options for 
multiple choice type questions will not be shown.  
 
  
2013                                                                                                                                                                                          CHEMICAL ENGG. –  CH 
CH 2/16
Answering a Question 
 
6. Procedure for answering a multiple choice type question: 
a. To select your answer, click on the button of one of  the options 
b. To deselect your chosen answer, click on the button of the chosen option again or click on the 
Clear Response button  
c. To change your chosen answer, click on the button of  another option 
d. To save your answer, you MUST click on the Save and Next button 
e. To mark the question for review, click on the Mark for Review and Next button. If an 
answer is selected for a question that is Marked for Review, that answer will be considered 
in the evaluation. 
 
7. Procedure for answering a numerical answer type question: 
a. To enter a number as your answer, use the virtual numerical keypad 
b. A fraction (eg.,-0.3 or -.3) can be entered as an answer with or without ‘0’ before the decimal 
point 
c. To clear your answer, click on the Clear Response button 
d. To save your answer, you MUST click on the Save and Next button 
e. To mark the question for review, click on the Mark for Review and Next button. If an 
answer is entered for a question that is Marked for Review, that answer will be considered 
in the evaluation. 
 
8. To change your answer to a question that has already been answered, first select that question for 
answering and then follow the procedure for answering that type of question.  
 
9. Note that ONLY Questions for which answers  are saved or marked for review after answering will be 
considered for evaluation. 
 
 
 
 
 
  
2013                                                                                                                                                                                          CHEMICAL ENGG. –  CH 
CH 3/16
Paper specific instructions: 
 
 
1. There are a total of 65 questions carrying 100 marks.Questions are of multiple choice type or 
numerical answer type. A multiple choice type question will have four choices for the answer with 
only one correct choice. For numerical answer type questions, the answer is a number and no choices 
will be given. A number as the answer should be entered using the virtual keyboard on the monitor. 
 
2. Questions Q.1 – Q.25 carry 1mark each. Questions Q.26 – Q.55 carry 2marks each. The 2marks 
questions include two pairs of common data questions and two pairs of linked answer questions. The 
answer to the second question of the linked answer questions depends on the answer to the first 
question of the pair. If the first question in the linked pair is wrongly answered or is not attempted, 
then the answer to the second question in the pair will not be evaluated. 
 
3. Questions Q.56 – Q.65 belong to General Aptitude (GA) section and carry a total of 15 marks. 
Questions Q.56 – Q.60 carry 1mark each, and questions Q.61 – Q.65 carry 2marks each.   
 
4. Questions not attempted will result in zero mark. Wrong answers for multiple choice type questions 
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. There is no negative 
marking for questions of numerical answer type. 
 
5. Calculator is allowed. Charts, graph sheets or tables are NOT allowed in the examination hall.  
 
6. Do the rough work in the Scribble Pad provided. 
 
  
2013                                                                                                                                                                                          CHEMICAL ENGG. –  CH 
CH 4/16
Q. 1 – Q. 25 carry one mark each. 
Q.1  The number of emails received on six consecutive days is 11, 9, 18, 18, 4 and 15, respectively. 
What are the median and the mode for these data? 
(A) 18 and 11, respectively 
 
(B) 13 and 18, respectively 
(C) 13 and 12.5, respectively (D) 12.5 and 18, respectively 
 
Q.2  For two rolls of a fair die, the probability of getting a 4 in the first roll and a number less than 4 in 
the second roll, up to 3 digits after the decimal point, is _________ 
    
 
Q.3  Which of the following statements are TRUE? 
P. The eigenvalues of a symmetric matrix are real 
Q. The value of the determinant of an orthogonal matrix can only be +1 
R. The transpose of a square matrix A has the same eigenvalues as those of A 
S. The inverse of an ‘n × n’ matrix exists if and only if the rank is less than ‘n’ 
(A) P and Q only  (B) P and R only  (C)  Q and R only  (D) P and S only   
 
Q.4  Evaluate  
1
x
dx
e ?
?
 
( Note: C is a constant of integration.)
 
(A) 
1
?
?
x
x
e
C
e
 
(B) 
? ?
ln 1 ?
?
x
x
e
C
e
 
(C) ln
1
? ?
?
? ?
?
? ?
x
x
e
C
e
 (D) 
? ?
ln 1
x
e C
?
? ? 
 
Q.5  A gaseous system contains H
2
, I
2
, and HI, which participate in the gas-phase reaction 
 
2 2
2 HI H + I ? 
 
At a state of reaction equilibrium, the number of thermodynamic degrees of freedom is _________ 
    
 
Q.6  The thermodynamic state of a closed system containing a pure fluid changes from (T
1
, p
1
) to       
(T
2
, p
2
), where T and p denote the temperature and pressure, respectively. Let Q denote the heat 
absorbed (> 0 if absorbed by the system) and W the work done (> 0 if done by the system). Neglect 
changes in kinetic and potential energies. Which one of the following is CORRECT? 
(A) ?Q is path-independent and W is path-dependent 
 
(B) ?Q is path-dependent and W is path-independent 
 
(C) (Q - W) is path-independent 
 
(D) (Q  + W) is path-independent 
 
 
 
Page 5


2013                                                                                                                                                                                          CHEMICAL ENGG. –  CH 
CH 1/16
CH:CHEMICAL ENGINEERING 
 
Duration: Three Hours        Maximum Marks:100 
 
Please read the following instructions carefully: 
 
General Instructions: 
 
1. Total duration of examination is 180 minutes (3 hours).  
 
2. The clock will be set at the server.  The countdown timer in 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 will not be required to end or submit your examination.  
 
3. The Question Palette displayed on the right side of screen will show the status of each question using 
one of the following symbols:  
  
 
You have not visited the question yet. 
 
You have not answered the question. 
 
You have answered the question.  
 
You have NOT answered the question, but have marked the 
question for review. 
 
You have answered the question, but marked it for review.  
 
The Marked for Review status for a question simply indicates that you would like to look at that 
question again. If a question is answered and  Marked for Review, your answer for that question 
will be considered in the evaluation. 
 
Navigating to a Question 
 
4. To answer a question, do the following: 
a. Click on the question number in the Question Palette to go to that question directly.  
b. Select an answer for a multiple choice type question. Use the virtual numeric keypad to enter 
a number as answer for a numerical type question.  
c. Click on Save and Next to save your answer for the current question and then go to the next 
question.  
d. Click on Mark for Review and Next to save your answer for the  current question, mark it 
for review, and then go to the next question. 
e. Caution: Note that your answer for the current question will not be saved, if you 
navigate to another question directly by clicking on its question number.  
5. You can view all the questions by clicking on the Question Paper button. Note that the options for 
multiple choice type questions will not be shown.  
 
  
2013                                                                                                                                                                                          CHEMICAL ENGG. –  CH 
CH 2/16
Answering a Question 
 
6. Procedure for answering a multiple choice type question: 
a. To select your answer, click on the button of one of  the options 
b. To deselect your chosen answer, click on the button of the chosen option again or click on the 
Clear Response button  
c. To change your chosen answer, click on the button of  another option 
d. To save your answer, you MUST click on the Save and Next button 
e. To mark the question for review, click on the Mark for Review and Next button. If an 
answer is selected for a question that is Marked for Review, that answer will be considered 
in the evaluation. 
 
7. Procedure for answering a numerical answer type question: 
a. To enter a number as your answer, use the virtual numerical keypad 
b. A fraction (eg.,-0.3 or -.3) can be entered as an answer with or without ‘0’ before the decimal 
point 
c. To clear your answer, click on the Clear Response button 
d. To save your answer, you MUST click on the Save and Next button 
e. To mark the question for review, click on the Mark for Review and Next button. If an 
answer is entered for a question that is Marked for Review, that answer will be considered 
in the evaluation. 
 
8. To change your answer to a question that has already been answered, first select that question for 
answering and then follow the procedure for answering that type of question.  
 
9. Note that ONLY Questions for which answers  are saved or marked for review after answering will be 
considered for evaluation. 
 
 
 
 
 
  
2013                                                                                                                                                                                          CHEMICAL ENGG. –  CH 
CH 3/16
Paper specific instructions: 
 
 
1. There are a total of 65 questions carrying 100 marks.Questions are of multiple choice type or 
numerical answer type. A multiple choice type question will have four choices for the answer with 
only one correct choice. For numerical answer type questions, the answer is a number and no choices 
will be given. A number as the answer should be entered using the virtual keyboard on the monitor. 
 
2. Questions Q.1 – Q.25 carry 1mark each. Questions Q.26 – Q.55 carry 2marks each. The 2marks 
questions include two pairs of common data questions and two pairs of linked answer questions. The 
answer to the second question of the linked answer questions depends on the answer to the first 
question of the pair. If the first question in the linked pair is wrongly answered or is not attempted, 
then the answer to the second question in the pair will not be evaluated. 
 
3. Questions Q.56 – Q.65 belong to General Aptitude (GA) section and carry a total of 15 marks. 
Questions Q.56 – Q.60 carry 1mark each, and questions Q.61 – Q.65 carry 2marks each.   
 
4. Questions not attempted will result in zero mark. Wrong answers for multiple choice type questions 
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. There is no negative 
marking for questions of numerical answer type. 
 
5. Calculator is allowed. Charts, graph sheets or tables are NOT allowed in the examination hall.  
 
6. Do the rough work in the Scribble Pad provided. 
 
  
2013                                                                                                                                                                                          CHEMICAL ENGG. –  CH 
CH 4/16
Q. 1 – Q. 25 carry one mark each. 
Q.1  The number of emails received on six consecutive days is 11, 9, 18, 18, 4 and 15, respectively. 
What are the median and the mode for these data? 
(A) 18 and 11, respectively 
 
(B) 13 and 18, respectively 
(C) 13 and 12.5, respectively (D) 12.5 and 18, respectively 
 
Q.2  For two rolls of a fair die, the probability of getting a 4 in the first roll and a number less than 4 in 
the second roll, up to 3 digits after the decimal point, is _________ 
    
 
Q.3  Which of the following statements are TRUE? 
P. The eigenvalues of a symmetric matrix are real 
Q. The value of the determinant of an orthogonal matrix can only be +1 
R. The transpose of a square matrix A has the same eigenvalues as those of A 
S. The inverse of an ‘n × n’ matrix exists if and only if the rank is less than ‘n’ 
(A) P and Q only  (B) P and R only  (C)  Q and R only  (D) P and S only   
 
Q.4  Evaluate  
1
x
dx
e ?
?
 
( Note: C is a constant of integration.)
 
(A) 
1
?
?
x
x
e
C
e
 
(B) 
? ?
ln 1 ?
?
x
x
e
C
e
 
(C) ln
1
? ?
?
? ?
?
? ?
x
x
e
C
e
 (D) 
? ?
ln 1
x
e C
?
? ? 
 
Q.5  A gaseous system contains H
2
, I
2
, and HI, which participate in the gas-phase reaction 
 
2 2
2 HI H + I ? 
 
At a state of reaction equilibrium, the number of thermodynamic degrees of freedom is _________ 
    
 
Q.6  The thermodynamic state of a closed system containing a pure fluid changes from (T
1
, p
1
) to       
(T
2
, p
2
), where T and p denote the temperature and pressure, respectively. Let Q denote the heat 
absorbed (> 0 if absorbed by the system) and W the work done (> 0 if done by the system). Neglect 
changes in kinetic and potential energies. Which one of the following is CORRECT? 
(A) ?Q is path-independent and W is path-dependent 
 
(B) ?Q is path-dependent and W is path-independent 
 
(C) (Q - W) is path-independent 
 
(D) (Q  + W) is path-independent 
 
 
 
2013                                                                                                                                                                                          CHEMICAL ENGG. –  CH 
CH 5/16
Q.7  An equation of state is explicit in pressure p and cubic in the specific volume v. At the critical point 
‘c’, the isotherm passing through ‘c’ satisfies   
(A)
2
2
0, 0
p p
v v
? ?
? ?
? ?
 
 
(B) 
2
2
0, 0
p p
v v
? ?
? ?
? ?
 
(C) 
2
2
0, 0
p p
v v
? ?
? ?
? ?
 (D) 
2
2
0, 0
p p
v v
? ?
? ?
? ?
 
 
Q.8  The units of the isothermal compressibility are 
 
(A) m
-3
 
(B) Pa
-1
 
(C) m
3
 Pa
-1
 
(D) m
-3
 Pa
-1
 
 
Q.9  An open tank contains two immiscible liquids of densities (800 kg/m
3
 and 1000 kg/m
3
) as shown in 
the figure. If g = 10 m/s
2
, under static conditions, the gauge pressure at the bottom of the tank in Pa 
is ___________ 
 
 
 
    
 
Q.10  The apparent viscosity of a fluid is given by   
   
0.3
0.007
dV
dy
where 
dV
dy
? ?
? ?
? ?
 is the velocity gradient. The fluid is 
 
(A) Bingham plastic (B) dilatant (C)  pseudoplastic (D)  thixotropic 
 
Q.11  
The mass balance for a fluid with density ( ? ? ?and velocity vector V
?
? ?
? ?
? ?
 is 
(A)
 
0 V
t
?
?
?
?
? ?
? ? ? ?
? ?
? ? ?
 
 
(B)
 
? ? 0 V
t
?
?
?
?
? ? ? ?
?
 
(C)
 
0 V
t
?
?
?
?
? ?
? ? ? ?
? ?
? ? ?
 
(D)
 
? ? 0 V
t
?
?
?
?
? ? ? ?
?