Page 1
A
2011 MA
READ INSTRUCTIONS ON THE LEFT
SIDE OF THIS PAGE CAREFULLY
REGISTRATION NUMBER
Name:
Test Centre:
Do not write your Registration Number
or Name anywhere else in this
question-cum-answer booklet.
I have read all the instructions and shall
abide by them.
……………………………………………...
Signature of the Candidate
2011 MA
Test Paper Code: MA
Time: 3 Hours Maximum Marks: 300
INSTRUCTIONS
1. This question-cum-answer booklet has 40 pages
and has 29 questions. Please ensure that the
copy of the question-cum-answer booklet you
have received contains all the questions.
2. Write your Registration Number, Name and
the name of the Test Centre in the appropriate
space provided on the right side.
3. Write the answers to the objective questions
against each Question No. in the Answer Table
for Objective Questions, provided on Page No.
7. Do not write anything else on this page.
4. Each objective question has 4 choices for its
answer: (A), (B), (C) and (D). Only ONE of them
is the correct answer. There will be negative
marking for wrong answers to objective
questions. The following marking scheme for
objective questions shall be used:
(a) For each correct answer, you will be
awarded 6 (Six) marks.
(b) For each wrong answer, you will be
awarded -2 (Negative two) marks.
(c) Multiple answers to a question will be
treated as a wrong answer.
(d) For each un-attempted question, you will be
awarded 0 (Zero) marks.
(e) Negative marks for objective part will be
carried over to total marks.
5. Answer the subjective question only in the
space provided after each question.
6. Do not write more than one answer for the same
question. In case you attempt a subjective
question more than once, please cancel the
answer(s) you consider wrong. Otherwise, the
answer appearing last only will be evaluated.
7. All answers must be written in blue/black/blue-
black ink only. Sketch pen, pencil or ink of any
other colour should not be used.
8. All rough work should be done in the space
provided and scored out finally.
9. No supplementary sheets will be provided to the
candidates.
10. Clip board, log tables, slide rule, calculator,
cellular phone and electronic gadgets in any
form are NOT allowed.
11. The question-cum-answer booklet must be
returned in its entirety to the Invigilator before
leaving the examination hall. Do not remove any
page from this booklet.
12. Refer to special instructions/useful data on the
reverse.
I have verified the information filled by the
Candidate above.
……………………………………………...
Signature of the Invigilator
A
MA- / 40 i
Page 2
A
2011 MA
READ INSTRUCTIONS ON THE LEFT
SIDE OF THIS PAGE CAREFULLY
REGISTRATION NUMBER
Name:
Test Centre:
Do not write your Registration Number
or Name anywhere else in this
question-cum-answer booklet.
I have read all the instructions and shall
abide by them.
……………………………………………...
Signature of the Candidate
2011 MA
Test Paper Code: MA
Time: 3 Hours Maximum Marks: 300
INSTRUCTIONS
1. This question-cum-answer booklet has 40 pages
and has 29 questions. Please ensure that the
copy of the question-cum-answer booklet you
have received contains all the questions.
2. Write your Registration Number, Name and
the name of the Test Centre in the appropriate
space provided on the right side.
3. Write the answers to the objective questions
against each Question No. in the Answer Table
for Objective Questions, provided on Page No.
7. Do not write anything else on this page.
4. Each objective question has 4 choices for its
answer: (A), (B), (C) and (D). Only ONE of them
is the correct answer. There will be negative
marking for wrong answers to objective
questions. The following marking scheme for
objective questions shall be used:
(a) For each correct answer, you will be
awarded 6 (Six) marks.
(b) For each wrong answer, you will be
awarded -2 (Negative two) marks.
(c) Multiple answers to a question will be
treated as a wrong answer.
(d) For each un-attempted question, you will be
awarded 0 (Zero) marks.
(e) Negative marks for objective part will be
carried over to total marks.
5. Answer the subjective question only in the
space provided after each question.
6. Do not write more than one answer for the same
question. In case you attempt a subjective
question more than once, please cancel the
answer(s) you consider wrong. Otherwise, the
answer appearing last only will be evaluated.
7. All answers must be written in blue/black/blue-
black ink only. Sketch pen, pencil or ink of any
other colour should not be used.
8. All rough work should be done in the space
provided and scored out finally.
9. No supplementary sheets will be provided to the
candidates.
10. Clip board, log tables, slide rule, calculator,
cellular phone and electronic gadgets in any
form are NOT allowed.
11. The question-cum-answer booklet must be
returned in its entirety to the Invigilator before
leaving the examination hall. Do not remove any
page from this booklet.
12. Refer to special instructions/useful data on the
reverse.
I have verified the information filled by the
Candidate above.
……………………………………………...
Signature of the Invigilator
A
MA- / 40 i
A
Special Instructions/ Useful Data
? : The set of all real numbers
? : The set of all natural numbers, that is, the set of all positive
integers 1, 2, …. .
? : The set of all integers
MA- / 40 ii
Page 3
A
2011 MA
READ INSTRUCTIONS ON THE LEFT
SIDE OF THIS PAGE CAREFULLY
REGISTRATION NUMBER
Name:
Test Centre:
Do not write your Registration Number
or Name anywhere else in this
question-cum-answer booklet.
I have read all the instructions and shall
abide by them.
……………………………………………...
Signature of the Candidate
2011 MA
Test Paper Code: MA
Time: 3 Hours Maximum Marks: 300
INSTRUCTIONS
1. This question-cum-answer booklet has 40 pages
and has 29 questions. Please ensure that the
copy of the question-cum-answer booklet you
have received contains all the questions.
2. Write your Registration Number, Name and
the name of the Test Centre in the appropriate
space provided on the right side.
3. Write the answers to the objective questions
against each Question No. in the Answer Table
for Objective Questions, provided on Page No.
7. Do not write anything else on this page.
4. Each objective question has 4 choices for its
answer: (A), (B), (C) and (D). Only ONE of them
is the correct answer. There will be negative
marking for wrong answers to objective
questions. The following marking scheme for
objective questions shall be used:
(a) For each correct answer, you will be
awarded 6 (Six) marks.
(b) For each wrong answer, you will be
awarded -2 (Negative two) marks.
(c) Multiple answers to a question will be
treated as a wrong answer.
(d) For each un-attempted question, you will be
awarded 0 (Zero) marks.
(e) Negative marks for objective part will be
carried over to total marks.
5. Answer the subjective question only in the
space provided after each question.
6. Do not write more than one answer for the same
question. In case you attempt a subjective
question more than once, please cancel the
answer(s) you consider wrong. Otherwise, the
answer appearing last only will be evaluated.
7. All answers must be written in blue/black/blue-
black ink only. Sketch pen, pencil or ink of any
other colour should not be used.
8. All rough work should be done in the space
provided and scored out finally.
9. No supplementary sheets will be provided to the
candidates.
10. Clip board, log tables, slide rule, calculator,
cellular phone and electronic gadgets in any
form are NOT allowed.
11. The question-cum-answer booklet must be
returned in its entirety to the Invigilator before
leaving the examination hall. Do not remove any
page from this booklet.
12. Refer to special instructions/useful data on the
reverse.
I have verified the information filled by the
Candidate above.
……………………………………………...
Signature of the Invigilator
A
MA- / 40 i
A
Special Instructions/ Useful Data
? : The set of all real numbers
? : The set of all natural numbers, that is, the set of all positive
integers 1, 2, …. .
? : The set of all integers
MA- / 40 ii
A
IMPORTANT NOTE FOR CANDIDATES
? Questions 1-15 (objective questions) carry six marks each and questions 16-29 (subjective
questions) carry fifteen marks each.
? Write the answers to the objective questions in the Answer Table for Objective Questions
provided on page 7 only.
Let
2
1
,for .
n
n
k
n
a
nk
?
?
?
?
?n? Then the sequence ? ?
n
a is
(A) Convergent (B) Bounded but not convergent
Q.1
(C) Diverges to ? (D) Neither bounded nor diverges to ?
The number of real roots of the equation
3
10 xx ? ?? is
Q.2
(A) 0 (B) 1 (C) 2 (D) 3
The value of
2
1
1
lim
n
n
k nkn
??
? ?
?
is
Q.3
(A) 2( 2 1) ? (B) 22 1 ? (C) 22 ?
(D)
1
(2 1)
2
?
0, 2, 0, 0 xx y z
MA- / 40 1
Let V be the region bounded by the planes ? ?? ?and y 1 z ?? Q.4 . Then the
value of the integral is
V
ydxdydz
???
(A)
1
2
(B)
4
3
(C) 1
(D)
1
3
Q.5
The solution of the differential equation () yx
2
2
44
dy dy
y
dx
dx
0 ? ?? satisfying the conditions
(0) 4, y ?
dy
dx
is (0) 8 ?
(A)
2
4
x
e (B)
2
(16 4)
x
x e
?
? (C)
2
41
x
ex
?
?6 (D)
22
416
x x
ex
?
? e
Page 4
A
2011 MA
READ INSTRUCTIONS ON THE LEFT
SIDE OF THIS PAGE CAREFULLY
REGISTRATION NUMBER
Name:
Test Centre:
Do not write your Registration Number
or Name anywhere else in this
question-cum-answer booklet.
I have read all the instructions and shall
abide by them.
……………………………………………...
Signature of the Candidate
2011 MA
Test Paper Code: MA
Time: 3 Hours Maximum Marks: 300
INSTRUCTIONS
1. This question-cum-answer booklet has 40 pages
and has 29 questions. Please ensure that the
copy of the question-cum-answer booklet you
have received contains all the questions.
2. Write your Registration Number, Name and
the name of the Test Centre in the appropriate
space provided on the right side.
3. Write the answers to the objective questions
against each Question No. in the Answer Table
for Objective Questions, provided on Page No.
7. Do not write anything else on this page.
4. Each objective question has 4 choices for its
answer: (A), (B), (C) and (D). Only ONE of them
is the correct answer. There will be negative
marking for wrong answers to objective
questions. The following marking scheme for
objective questions shall be used:
(a) For each correct answer, you will be
awarded 6 (Six) marks.
(b) For each wrong answer, you will be
awarded -2 (Negative two) marks.
(c) Multiple answers to a question will be
treated as a wrong answer.
(d) For each un-attempted question, you will be
awarded 0 (Zero) marks.
(e) Negative marks for objective part will be
carried over to total marks.
5. Answer the subjective question only in the
space provided after each question.
6. Do not write more than one answer for the same
question. In case you attempt a subjective
question more than once, please cancel the
answer(s) you consider wrong. Otherwise, the
answer appearing last only will be evaluated.
7. All answers must be written in blue/black/blue-
black ink only. Sketch pen, pencil or ink of any
other colour should not be used.
8. All rough work should be done in the space
provided and scored out finally.
9. No supplementary sheets will be provided to the
candidates.
10. Clip board, log tables, slide rule, calculator,
cellular phone and electronic gadgets in any
form are NOT allowed.
11. The question-cum-answer booklet must be
returned in its entirety to the Invigilator before
leaving the examination hall. Do not remove any
page from this booklet.
12. Refer to special instructions/useful data on the
reverse.
I have verified the information filled by the
Candidate above.
……………………………………………...
Signature of the Invigilator
A
MA- / 40 i
A
Special Instructions/ Useful Data
? : The set of all real numbers
? : The set of all natural numbers, that is, the set of all positive
integers 1, 2, …. .
? : The set of all integers
MA- / 40 ii
A
IMPORTANT NOTE FOR CANDIDATES
? Questions 1-15 (objective questions) carry six marks each and questions 16-29 (subjective
questions) carry fifteen marks each.
? Write the answers to the objective questions in the Answer Table for Objective Questions
provided on page 7 only.
Let
2
1
,for .
n
n
k
n
a
nk
?
?
?
?
?n? Then the sequence ? ?
n
a is
(A) Convergent (B) Bounded but not convergent
Q.1
(C) Diverges to ? (D) Neither bounded nor diverges to ?
The number of real roots of the equation
3
10 xx ? ?? is
Q.2
(A) 0 (B) 1 (C) 2 (D) 3
The value of
2
1
1
lim
n
n
k nkn
??
? ?
?
is
Q.3
(A) 2( 2 1) ? (B) 22 1 ? (C) 22 ?
(D)
1
(2 1)
2
?
0, 2, 0, 0 xx y z
MA- / 40 1
Let V be the region bounded by the planes ? ?? ?and y 1 z ?? Q.4 . Then the
value of the integral is
V
ydxdydz
???
(A)
1
2
(B)
4
3
(C) 1
(D)
1
3
Q.5
The solution of the differential equation () yx
2
2
44
dy dy
y
dx
dx
0 ? ?? satisfying the conditions
(0) 4, y ?
dy
dx
is (0) 8 ?
(A)
2
4
x
e (B)
2
(16 4)
x
x e
?
? (C)
2
41
x
ex
?
?6 (D)
22
416
x x
ex
?
? e
A
Q.6
MA- / 40 2
If is an integrating factor of the differential equation
a
y
22
2(3 ) x y dx x y dy0 ? ?? ,
then the value of a is
(C) 1 ? (D) 1 (A) 4 ? (B) 4
Let and C be the positively oriented closed curve given by
If
ˆ ˆˆ
Fayi zj xk ?? ?
?
22
1, 0. xy z ?? ?
C
Q.7
Fd
?
r ? ??
?
? ?
, then the value of a is
(A) 1 ? (B) 0
(C)
1
2
(D) 1
Consider the vector field where a is a constant. If
then the value of is
ˆ ˆˆ
() ( Fax y ai j x yk ??? ? ? ?
?
a
Q.8
),
curl 0, FF ??
??
(C) 1 (A) 1 ? (B) 0
(D)
3
2
Let denote the group of all invertible matrices with entries from Let G 22 ? . ?
? ?
1
:det( ) 1 HAG A ?? ? and ? ?
2
: is upper triangular HAGA ?? .
Consider the following statements:
Q.9
P :
1
H is a normal subgroup of G
H is a normal subgroup of . Q : G
2
Then
(A) Both P and Q are true (B) P is true and is false Q
(C) P is false and is true Q (D) Both P and Q are false
For , let n ? ? ? ? : nnkk ?? ? .? ? Then the number of units of and ,
respectively, are
/11 ? /12 ??
Q.10
(A) 11 , 12 (B) 10 , 11 (C) 10 , 4 (D) 10 , 8
Page 5
A
2011 MA
READ INSTRUCTIONS ON THE LEFT
SIDE OF THIS PAGE CAREFULLY
REGISTRATION NUMBER
Name:
Test Centre:
Do not write your Registration Number
or Name anywhere else in this
question-cum-answer booklet.
I have read all the instructions and shall
abide by them.
……………………………………………...
Signature of the Candidate
2011 MA
Test Paper Code: MA
Time: 3 Hours Maximum Marks: 300
INSTRUCTIONS
1. This question-cum-answer booklet has 40 pages
and has 29 questions. Please ensure that the
copy of the question-cum-answer booklet you
have received contains all the questions.
2. Write your Registration Number, Name and
the name of the Test Centre in the appropriate
space provided on the right side.
3. Write the answers to the objective questions
against each Question No. in the Answer Table
for Objective Questions, provided on Page No.
7. Do not write anything else on this page.
4. Each objective question has 4 choices for its
answer: (A), (B), (C) and (D). Only ONE of them
is the correct answer. There will be negative
marking for wrong answers to objective
questions. The following marking scheme for
objective questions shall be used:
(a) For each correct answer, you will be
awarded 6 (Six) marks.
(b) For each wrong answer, you will be
awarded -2 (Negative two) marks.
(c) Multiple answers to a question will be
treated as a wrong answer.
(d) For each un-attempted question, you will be
awarded 0 (Zero) marks.
(e) Negative marks for objective part will be
carried over to total marks.
5. Answer the subjective question only in the
space provided after each question.
6. Do not write more than one answer for the same
question. In case you attempt a subjective
question more than once, please cancel the
answer(s) you consider wrong. Otherwise, the
answer appearing last only will be evaluated.
7. All answers must be written in blue/black/blue-
black ink only. Sketch pen, pencil or ink of any
other colour should not be used.
8. All rough work should be done in the space
provided and scored out finally.
9. No supplementary sheets will be provided to the
candidates.
10. Clip board, log tables, slide rule, calculator,
cellular phone and electronic gadgets in any
form are NOT allowed.
11. The question-cum-answer booklet must be
returned in its entirety to the Invigilator before
leaving the examination hall. Do not remove any
page from this booklet.
12. Refer to special instructions/useful data on the
reverse.
I have verified the information filled by the
Candidate above.
……………………………………………...
Signature of the Invigilator
A
MA- / 40 i
A
Special Instructions/ Useful Data
? : The set of all real numbers
? : The set of all natural numbers, that is, the set of all positive
integers 1, 2, …. .
? : The set of all integers
MA- / 40 ii
A
IMPORTANT NOTE FOR CANDIDATES
? Questions 1-15 (objective questions) carry six marks each and questions 16-29 (subjective
questions) carry fifteen marks each.
? Write the answers to the objective questions in the Answer Table for Objective Questions
provided on page 7 only.
Let
2
1
,for .
n
n
k
n
a
nk
?
?
?
?
?n? Then the sequence ? ?
n
a is
(A) Convergent (B) Bounded but not convergent
Q.1
(C) Diverges to ? (D) Neither bounded nor diverges to ?
The number of real roots of the equation
3
10 xx ? ?? is
Q.2
(A) 0 (B) 1 (C) 2 (D) 3
The value of
2
1
1
lim
n
n
k nkn
??
? ?
?
is
Q.3
(A) 2( 2 1) ? (B) 22 1 ? (C) 22 ?
(D)
1
(2 1)
2
?
0, 2, 0, 0 xx y z
MA- / 40 1
Let V be the region bounded by the planes ? ?? ?and y 1 z ?? Q.4 . Then the
value of the integral is
V
ydxdydz
???
(A)
1
2
(B)
4
3
(C) 1
(D)
1
3
Q.5
The solution of the differential equation () yx
2
2
44
dy dy
y
dx
dx
0 ? ?? satisfying the conditions
(0) 4, y ?
dy
dx
is (0) 8 ?
(A)
2
4
x
e (B)
2
(16 4)
x
x e
?
? (C)
2
41
x
ex
?
?6 (D)
22
416
x x
ex
?
? e
A
Q.6
MA- / 40 2
If is an integrating factor of the differential equation
a
y
22
2(3 ) x y dx x y dy0 ? ?? ,
then the value of a is
(C) 1 ? (D) 1 (A) 4 ? (B) 4
Let and C be the positively oriented closed curve given by
If
ˆ ˆˆ
Fayi zj xk ?? ?
?
22
1, 0. xy z ?? ?
C
Q.7
Fd
?
r ? ??
?
? ?
, then the value of a is
(A) 1 ? (B) 0
(C)
1
2
(D) 1
Consider the vector field where a is a constant. If
then the value of is
ˆ ˆˆ
() ( Fax y ai j x yk ??? ? ? ?
?
a
Q.8
),
curl 0, FF ??
??
(C) 1 (A) 1 ? (B) 0
(D)
3
2
Let denote the group of all invertible matrices with entries from Let G 22 ? . ?
? ?
1
:det( ) 1 HAG A ?? ? and ? ?
2
: is upper triangular HAGA ?? .
Consider the following statements:
Q.9
P :
1
H is a normal subgroup of G
H is a normal subgroup of . Q : G
2
Then
(A) Both P and Q are true (B) P is true and is false Q
(C) P is false and is true Q (D) Both P and Q are false
For , let n ? ? ? ? : nnkk ?? ? .? ? Then the number of units of and ,
respectively, are
/11 ? /12 ??
Q.10
(A) 11 , 12 (B) 10 , 11 (C) 10 , 4 (D) 10 , 8
A
Let be a 3 matrix with = 3 and det = 2. If 1 is an eigenvalue of ,
then the eigenvalues of the matrix
A 3 ? trace ( ) A
2
A
( ) A A
2
Q.11
I ? are
(A) 1, (B) 2( 1 ), 2( 1 ) ii ?? ? 1, 2( 1 ), 2( 1 ) ii ? ??
(C) 1, (D) 2( 1 ), 2( 1 ) ii ?? ? 1, 2( 1 ), 2( 1 ) ii ? ?? ?
Q.12
Let be a linear transformation, where For :
n
T ? ??
n
2. n ? , kn ? let
??
12
, ,...,
n
k
Evv v ?? ? and ? ?
12
, ,..., .
k
FTvTv Tv ?
Then
(A) If is linearly independent, then is linearly independent E F
(B) If is linearly independent, then is linearly independent F E
(C) If is linearly independent, then is linearly dependent E F
(D) If is linearly independent, then is linearly dependent F E
Q.13
For let be linear transformations such that is
bijective. Then
12
: and :
nm m
TT ? ?? ? ?
n
? , nm ?
12
TT
(A) rank ( ) = and rank ( ) =
1
T n
2
T m (B) rank ( ) = and rank ( ) =
1
T
2
T m n
(C) rank ( ) = and rank ( ) = n
1
T n
2
T (D) rank ( ) = and rank ( ) =
1
T m
2
T m
MA- / 40 3
The set of all
Q.14
x at which the power series
3
2
1
(2)
(2 1)
n
n
n
x
n
?
?
?
?
?
converges is
(A) ? ? 1, 1 ? (B) ? ? 1,1 ? (C) ? ? 1, 3 (D) ? ? 1, 3
Consider the following subsets of ? : Q.15
1
:, :0
11
n
En F x
nx
?? ?
?? ? ?
?? ?
??
?? ?
? 1.
?
?
?
?
Then
(A) Both and are closed E F (B) is closed and E F is NOT closed
(C) is NOT closed and is closed E F (D) Neither nor E F is closed
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