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 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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FAQs on IIT JAM Mathematics 2011 Past Year Paper - Past Year Papers of IIT JAM Mathematics

1. What is the eligibility criteria for appearing in IIT JAM Mathematics 2011?
Ans. To appear in IIT JAM Mathematics 2011, the candidate must have a Bachelor's degree with Mathematics as one of the subjects for at least two years/four semesters. Additionally, the candidate must have secured at least 55% aggregate marks or 5.5 CGPA (on a 10-point scale) for General/OBC-NCL category, and 50% aggregate marks or 5.0 CGPA (on a 10-point scale) for SC/ST/PwD category candidates.
2. How can I prepare for the IIT JAM Mathematics 2011 exam?
Ans. To prepare for the IIT JAM Mathematics 2011 exam, candidates can follow these tips: 1. Understand the syllabus: Familiarize yourself with the exam syllabus and make a study plan accordingly. 2. Study material: Refer to standard textbooks and study materials recommended for the JAM Mathematics exam. Focus on understanding the concepts and practice solving problems. 3. Solve previous year papers: Solve previous year question papers to get an idea of the exam pattern and to practice time management. 4. Take mock tests: Take online mock tests to evaluate your preparation level and identify areas for improvement. 5. Seek guidance: If needed, join coaching classes or seek guidance from experienced faculty members to clarify doubts and get additional insights.
3. What is the exam pattern for IIT JAM Mathematics 2011?
Ans. The IIT JAM Mathematics 2011 exam pattern consisted of a single paper with a total duration of 3 hours. The question paper had a total of 60 multiple-choice questions, divided into three sections - Section A, Section B, and Section C. Section A contained 30 one-mark multiple-choice questions, Section B had 10 two-mark multiple-choice questions, and Section C had 20 multiple-choice questions worth two marks each. There was negative marking for incorrect answers.
4. Are calculators allowed in the IIT JAM Mathematics 2011 exam?
Ans. No, calculators or any other electronic devices were not allowed in the IIT JAM Mathematics 2011 exam. Candidates had to rely on their mathematical skills and manual calculations to solve the problems.
5. How is the IIT JAM Mathematics 2011 exam score used for admissions?
Ans. The IIT JAM Mathematics 2011 exam score is used by various participating institutes for admissions to their respective M.Sc. (Two Year), Joint M.Sc.-Ph.D., M.Sc.-Ph.D. Dual Degree, and other post-bachelor degree programs. The scorecard is valid for one year, and candidates can apply to the participating institutes based on their JAM score and other eligibility criteria specified by the institutes. The final admission is based on the candidate's performance in the exam and the selection process of the respective institute.
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