The document IIT JAM Mathematics 2011 Past Year Paper Notes | Study Past Year Papers of IIT JAM Mathematics - Mathematics is a part of the Mathematics Course Past Year Papers of IIT JAM Mathematics.

All you need of Mathematics at this link: Mathematics

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 closedRead More