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# Mathematics (MA) 2013 GATE Paper without solution GATE Notes | EduRev

## GATE : Mathematics (MA) 2013 GATE Paper without solution GATE Notes | EduRev

``` Page 1

2013                                                                                                                                                                                                  MATHEMATICS –MA
MA 1/14
MA:MATHEMATICS

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                                                                                                                                                                                                  MATHEMATICS –MA
MA 1/14
MA:MATHEMATICS

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                                                                                                                                                                                                  MATHEMATICS –MA
MA 2/14
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                                                                                                                                                                                                  MATHEMATICS –MA
MA 1/14
MA:MATHEMATICS

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                                                                                                                                                                                                  MATHEMATICS –MA
MA 2/14
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                                                                                                                                                                                                  MATHEMATICS –MA
MA 3/14
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                                                                                                                                                                                                  MATHEMATICS –MA
MA 1/14
MA:MATHEMATICS

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                                                                                                                                                                                                  MATHEMATICS –MA
MA 2/14
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                                                                                                                                                                                                  MATHEMATICS –MA
MA 3/14
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                                                                                                                                                                                                  MATHEMATICS –MA
MA 4/14
USEFUL DATA FOR MA: MATHEMATICS

Page 5

2013                                                                                                                                                                                                  MATHEMATICS –MA
MA 1/14
MA:MATHEMATICS

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                                                                                                                                                                                                  MATHEMATICS –MA
MA 2/14
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                                                                                                                                                                                                  MATHEMATICS –MA
MA 3/14
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                                                                                                                                                                                                  MATHEMATICS –MA
MA 4/14
USEFUL DATA FOR MA: MATHEMATICS

2013                                                                                                                                                                                                  MATHEMATICS –MA
MA 5/14
Q. 1 – Q. 25 carry one mark each.

Q.1  The possible set of eigen values of a 4 × 4 skew-symmetric orthogonal real matrix is
(A) {± ???? } (B) {± ???? , ±1} (C)  {±1} (D)  {0, ± ???? }

Q.2  The coefficient of ( ???? - ???? )
2
in the Taylor series expansion of
???? ( ???? ) = ?
sin ???? ???? - ???? if ???? ? ???? -1       if ???? = ????
around ???? is
(A)
1
2
(B) -
1
2
(C)
1
6
(D)  -
1
6

Q.3  Consider R
2
with the usual topology. Which of the following statements are TRUE for all ???? , ???? ?
R
2
?

P: ???? ? ???? = ???? ? ???? .
Q: ???? n ???? = ???? n ???? .
R:( ???? ? ???? ) ° = ???? ° ? ???? °.
S:( ???? n ???? ) ° = ???? ° n ???? °.
(A) P and R only  (B) P and S only (C) Q and R only  (D) Q and S only

Q.4
Let ???? : R ? R be a continuous function with ???? (1) = 5 and ???? (3) = 11. If ???? ( ???? ) = ? ???? ( ???? + ???? ) ???????? 3
1

then ???? '(0) is equal to ______

Q.5  Let ???? be a 2 × 2 complex matrix such that trace( ???? ) = 1 anddet( ???? ) = -6. Then, trace( ???? 4
- ???? 3
) is
______

Q.6  Suppose that ???? is a unique factorization domain and that ???? , ???? ? ???? are distinct irreducible elements.
Which of the following statements is TRUE?
(A) The ideal <1 + ???? > is a prime ideal
(B) The ideal < ???? + ???? > is a prime ideal
(C) The ideal <1 + ???????? > is a prime ideal
(D) The ideal < ???? > is not necessarily a maximal ideal

Q.7  Let ???? be a compact Hausdorff topological space and let ???? be a topological space. Let ???? : ???? ? ???? be a
bijective continuous mapping. Which of the following is TRUE?
(A) ???? is a closed mapbut not necessarily an open map
(B) ???? is an open map but not necessarily a closed map
(C) ???? is both an open map and a closed map
(D) ???? need not be an open map or a closed map

Q.8  Consider the linear programming problem:

Maximize
???? +
3
2
????
subject to 2 ???? + 3 ???? = 16,
???? + 4 ???? = 18,
???? = 0, ???? = 0.
If ???? denotes the set of all solutions of the above problem, then
(A) ???? is empty (B) ???? is a singleton
(C) ???? is a line segment (D) ???? has positive area
```
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## GATE Past Year Papers for Practice (All Branches)

380 docs|127 tests

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