DUET Question Paper 2019 for M.Phil Ph.D Mathematics

DU MPhil Phd in Mathema cs

Topic:- DU_J19_MPHIL_MATHS

1) Which of the following journals is published by Indian Mathematical Society

[Question ID = 13918]

1. Indian Journal of Pure and Applied Mathematics. [Option ID = 25669]
2. Indian Journal of Mathematics. [Option ID = 25671]
3. Ramanujan Journal of Mathematics. [Option ID = 25670]
4. The Mathematics Students . [Option ID = 25672]

Indian Journal of Pure and Applied Mathematics. [Option ID = 25669]

2) Name a Fellow of Royal Society who expired in 2019 [Question ID = 13917]

1. M. S. Ragunathan. [Option ID = 25665]
2. Manjul Bhargava. [Option ID = 25666]
3. Michael Atiyah. [Option ID = 25667]
4. S. R. Srinivasa Varadhan. [Option ID = 25668]

M. S. Ragunathan. [Option ID = 25665]

3) Which of the following statements is true? [Question ID = 13973]

1.

[Option ID = 25890]
2.

[Option ID = 25891]
3.

[Option ID = 25889]

4. [Option ID = 25892]

[Option ID = 25889]

4) Which of the following statements is true for topological spaces? [Question ID = 13927]

1. Every second countable space is separable. [Option ID = 25706]

2. Every separable space is second countable. [Option ID = 25705]
3. Every first countable space is second countable. [Option ID = 25708]
4. Every first countable space is separable. [Option ID = 25707]

Every separable space is second countable. [Option ID = 25705]

5) Which of the following statements is not true? [Question ID = 13997]

1.

[Option ID = 25987]
2.

[Option ID = 25986]
3.

[Option ID = 25985]
4.

[Option ID = 25988]

[Option ID = 25985]

6) Which one of the following fellowship is based on merit in M.A/M.Sc. of the University [Question ID
= 13920]

1. NBHM-JRF. [Option ID = 25679]
2. INSPIRE-JRF [Option ID = 25677]
3. UGC-JRF. [Option ID = 25680]
4. CSIR-JRF [Option ID = 25678]

INSPIRE-JRF [Option ID = 25677]

7) The Abel prize 2019 was awarded to [Question ID = 13919]

1. Lennert Carleson. [Option ID = 25673]
2. Mikhail Gromov. [Option ID = 25676]
3. Karen Keskulla Uhlenbeck. [Option ID = 25674]
4. Peter Lax. [Option ID = 25675]

Lennert Carleson. [Option ID = 25673]

8)

[Question ID = 13981]

1. [Option ID = 25922]

2. [Option ID = 25921]

3. [Option ID = 25924]

4. [Option ID = 25923]

[Option ID = 25921]

9)

[Question ID = 13968]

1. [Option ID = 25869]

2. [Option ID = 25871]

3. [Option ID = 25870]

4. [Option ID = 25872]

[Option ID = 25869]

10)

[Question ID = 13988]

1. [Option ID = 25951]

2. [Option ID = 25949]

3. [Option ID = 25952]

4. [Option ID = 25950]

[Option ID = 25949]

11)

[Question ID = 14009]

1. cosec(y/x) = c/x. [Option ID = 26036]
2. cosec(y/x) = cx. [Option ID = 26035]
3. sec(y/x) = cx. [Option ID = 26033]
4. sec(y/x) = c/x. [Option ID = 26034]

sec(y/x) = cx. [Option ID = 26033]

12)

[Question ID = 14008]

1. [Option ID = 26029]

2. [Option ID = 26032]

3. [Option ID = 26031]

4. [Option ID = 26030]

[Option ID = 26029]

13)

[Question ID = 13979]

1. [Option ID = 25916]

2. [Option ID = 25913]

3. [Option ID = 25915]

4. [Option ID = 25914]

[Option ID = 25913]

14)

[Question ID = 13995]

1. 2x + y + z = 0. [Option ID = 25979]
2. x + 2y + z = 0. [Option ID = 25978]
3. x + y + z = 0. [Option ID = 25980]
4. x + y + 2z = 0. [Option ID = 25977]

x + y + 2z = 0. [Option ID = 25977]

15)

[Question ID = 14007]

1. [Option ID = 26027]

2. [Option ID = 26028]

3. [Option ID = 26026]

4. [Option ID = 26025]

[Option ID = 26025]

16)

[Question ID = 13969]

1. 1/15 [Option ID = 25876]
2. 2 [Option ID = 25875]
3. 1/10 [Option ID = 25874]
4. 1/5 [Option ID = 25873]

1/5 [Option ID = 25873]

17)

[Question ID = 13994]

1. lines parallel to z-axis. [Option ID = 25975]
2. lines perpendicular to z-axis. [Option ID = 25976]
3. planes perpendicular to xz- plane. [Option ID = 25973]
4. planes parallel to yz- plane. [Option ID = 25974]

planes perpendicular to xz- plane. [Option ID = 25973]

18)

[Question ID = 14001]

1. Neither (I) nor (II) is correct. [Option ID = 26004]
2. Both (I) and (II) are correct. [Option ID = 26003]
3. Only (I) is correct. [Option ID = 26001]
4. Only (II) is correct. [Option ID = 26002]

Only (I) is correct. [Option ID = 26001]

19)

[Question ID = 13970]

1. [Option ID = 25877]

2. [Option ID = 25879]

3. [Option ID = 25878]

4. [Option ID = 25880]

[Option ID = 25877]

20)

[Question ID = 13984]

1. 2π. [Option ID = 25935]
2. 0 [Option ID = 25933]
3. π/2. [Option ID = 25934]
4. π. [Option ID = 25936]

0 [Option ID = 25933]

21)

[Question ID = 13974]

1. [Option ID = 25895]

2. [Option ID = 25893]

3. [Option
ID = 25896]

4. [Option ID =
25894]

[Option ID = 25893]

22)

[Question ID = 13975]

1. [Option ID = 25899]

2. [Option ID = 25897]

3. [Option ID = 25900]

4. [Option ID = 25898]

[Option ID = 25897]

23)

[Question ID = 13986]

1. 0 < α < 1, β = 1 [Option ID = 25942]
2. α = 0, β = ∞. [Option ID = 25943]
3. α = β = 0. [Option ID = 25941]
4. α = 0, β = 2. [Option ID = 25944]

α = β = 0. [Option ID = 25941]

24)

[Question ID = 13985]

1. [−1, 1]. [Option ID = 25938]
2. [0, 1]. [Option ID = 25937]
3. {0}. [Option ID = 25939]
4. [−1, 0]. [Option ID = 25940]

[0, 1]. [Option ID = 25937]

25)

[Question ID = 14002]

1. All (I), (II) and (III) are true. [Option ID = 26007]
2. None of (I), (II)and (III) is true. [Option ID = 26008]
3. Only (I) is true. [Option ID = 26005]
4. Only (I) and (II) are true. [Option ID = 26006]

Only (I) is true. [Option ID = 26005]

26)

[Question ID = 13991]

1. 2 [Option ID = 25963]
2. 1 [Option ID = 25964]
3. 3 [Option ID = 25962]
4. infinity. [Option ID = 25961]

infinity. [Option ID = 25961]

27)

[Question ID = 13982]

1. (I) is true but (II) is false. [Option ID = 25925]
2. (I) is false but (II) is true. [Option ID = 25926]
3. Neither (I) nor (II) is true. [Option ID = 25927]
4. Both (I) and (II) are true. [Option ID = 25928]

(I) is true but (II) is false. [Option ID = 25925]

28)

[Question ID = 13978]

1. [Option ID = 25911]

2. [Option ID = 25912]
3. [Option ID = 25909]

4. [Option ID = 25910]

[Option ID = 25909]

29)

[Question ID = 13998]

1. 2 [Option ID = 25989]
2. 5 [Option ID = 25991]
3. 8 [Option ID = 25992]
4. 4 [Option ID = 25990]

2 [Option ID = 25989]

30)

[Question ID = 13983]

1. [Option ID = 25931]

2. [Option ID = 25932]

3. [Option ID = 25929]

4. [Option ID = 25930]

[Option ID = 25929]

31)

[Question ID = 14005]

1. [Option ID = 26018]

2. [Option ID = 26019]

3. [Option ID = 26020]

4. [Option ID = 26017]

[Option ID = 26017]

32)

[Question ID = 13976]

1. [Option ID = 25902]
2.

[Option ID = 25903]

3. [Option ID = 25904]
4.

[Option ID = 25901]

[Option ID = 25901]

33)

[Question ID = 13993]

D
1. dimension of kernel of is 2. [Option ID = 25969]
D
2. dimension of kernel of is 4. [Option ID = 25970]
3. range of D=V . [Option ID = 25972]
D
4. range of is a finite dimensional space [Option ID = 25971]

dimension of kernel of D is 2. [Option ID = 25969]

34)

[Question ID = 14000]

1. [Option ID = 25998]

2. [Option ID = 26000]

3. [Option ID = 25997]

4. [Option ID = 25999]

[Option ID = 25997]

35)

[Question ID = 14006]

1. [Option ID = 26023]

2. [Option ID = 26022]

3. [Option ID = 26024]

4. [Option ID = 26021]

[Option ID = 26021]

36)

[Question ID = 13972]

1. continuous, one-one but not onto. [Option ID = 25886]
2. not a continuous map. [Option ID = 25885]
3. a continuous bijection but not an open map. [Option ID = 25887]
4. a homeomorphism. [Option ID = 25888]

not a continuous map. [Option ID = 25885]

37)

[Question ID = 13990]

1.
[Option ID = 25959]

2. [Option
ID = 25958]

3. [Option ID =
25957]
4.

[Option ID = 25960]

[Option ID =
25957]

38)

[Question ID = 13992]

1. [Option ID = 25967]

2. [Option ID = 25966]

3. [Option ID = 25965]

4. [Option ID = 25968]

[Option ID = 25965]

39)

[Question ID = 14004]

1. [Option ID = 26015]

2. [Option ID = 26014]

3. [Option ID = 26013]

4. [Option ID = 26016]

[Option ID = 26013]

40)

[Question ID = 13980]

1. [Option ID = 25918]

2. [Option ID = 25917]

3. [Option ID = 25919]

4. [Option ID = 25920]

[Option ID = 25917]

41)

[Question ID = 13971]

1. [Option ID = 25882]

2. [Option ID = 25884]

3. [Option ID = 25881]

4. [Option ID = 25883]

[Option ID = 25881]

42)

[Question ID = 13999]

1. G is a cyclic group under composition. [Option ID = 25994]
2. G is a non-cyclic group under composition. [Option ID = 25995]
3. G does not form a group under composition. [Option ID = 25993]
4. G is a non-abelian group under composition. [Option ID = 25996]
G does not form a group under composition. [Option ID = 25993]

43)

[Question ID = 13989]

1. [Option ID = 25954]

2. [Option ID = 25956]

3. [Option ID = 25953]

4. [Option ID = 25955]

[Option ID = 25953]

44)

[Question ID = 14003]

1. Only (III) and (IV) are true. [Option ID = 26012]
2. Only (I) and (II) are true. [Option ID = 26009]
3. Only (II) and (III) are true. [Option ID = 26011]
4. Only (I) and (IV) are true. [Option ID = 26010]

Only (I) and (II) are true. [Option ID = 26009]

45)

[Question ID = 13967]

1. 0 [Option ID = 25866]
2. 1/3 [Option ID = 25867]
3. 1/2 [Option ID = 25868]
4. 1 [Option ID = 25865]

1 [Option ID = 25865]

46)

[Question ID = 13987]

1. [Option ID = 25945]
2. [Option ID = 25947]

3. [Option ID = 25948]

4. [Option ID = 25946]

[Option ID = 25945]

47) Which of the following statements is true? [Question ID = 13977]

1.

[Option ID = 25906]

2. [Option ID =
25907]

3.
[Option ID = 25905]

4. [Option ID =
25908]

[Option ID = 25905]

48) Which one of the following statements is not true? [Question ID = 13966]

1.

[Option ID = 25861]

2. [Option ID
= 25864]

3. [Option ID =
25863]

4. [Option
ID = 25862]

[Option ID = 25861]

49) Present President of the Ramanujan Mathematical Society is [Question ID = 13916]

1. V. Kumar Murty. [Option ID = 25664]

2. Dinesh Singh [Option ID = 25661]
3. S. Ponnusamy [Option ID = 25662]
4. R. Balakrishnan. [Option ID = 25663]

Dinesh Singh [Option ID = 25661]

50) The characteristic and the minimal polynomial are same for the matrix

[Question ID = 13996]

1. [Option ID = 25983]

2. [Option ID = 25982]

3. [Option ID = 25981]
4. All of the above matrices [Option ID = 25984]

[Option ID = 25981]