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DUET Question Paper 2019 for MA M.Sc Mathematics

Get here DUET MA M.Sc Mathematics Question Paper 2019 by NTA. You can check DUET 2019 Question Paper for exam held on 04 July 2019 Shift - 2 from below. More Detail
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DUET Question Paper 2019 for MA M.Sc Mathematics – Text

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Page 1

DU MA MSc Mathema cs

Topic:- DU_J19_MA_MATHS

1) The order of Sylow subgroups of a finite group G of order 56 are [Question ID = 24519]

1. 2 and 28 [Option ID = 38076]
2. 7 and 8 [Option ID = 38074]
3. 8 and 14 [Option ID = 38077]
4. 4 and 14 [Option ID = 38075]

7 and 8 [Option ID = 38074]

2) The remainder when 52019 is divided by 11 is [Question ID = 24520]

1. 6 [Option ID = 38080]
2. 9 [Option ID = 38081]
3. 1 [Option ID = 38078]
4. 4 [Option ID = 38079]

1 [Option ID = 38078]

3) The smallest positive integer n, which leaves remainders 2,3 and 4 when divided by 5,7 and 11 respectively, is [Question ID
= 24521]

1. 751 [Option ID = 38083]
2. 1136 [Option ID = 38085]
3. 176 [Option ID = 38082]
4. 367 [Option ID = 38084]

176 [Option ID = 38082]

4) Suppose that the equation x2·a·x = a−1 is solvable for a in a group G. Then, there exists b in G such that
[Question ID = 24515]

1. a = b3 [Option ID = 38059]
2. a = b5 [Option ID = 38061]
3. a = b4 [Option ID = 38060]
4. a = b2 [Option ID = 38058]

a = b2 [Option ID = 38058]

5) Consider the following statements:

(i) Every metric space is totally bounded.
(ii) A totally bounded metric space is bounded.

Then

[Question ID = 24536]

1. neither (i) nor (ii) is true [Option ID = 38145]
2. only (ii) is true [Option ID = 38143]
3. only (i) is true [Option ID = 38142]
4. both (i) and (ii) are true [Option ID = 38144]

only (i) is true [Option ID = 38142]

6)

Page 2

Consider the following statements:

(i) Every minimal generating set of a vector space is a basis.
(ii) Every maximal linearly independent subset of a vector space is a basis.
(iii) Every vector space admits a basis.

Then

[Question ID = 24510]

1. all of (i), (ii) and (iii) are true [Option ID = 38041]
2. only (i) and (ii) are true [Option ID = 38038]
3. only (i) and (iii) are true [Option ID = 38040]
4. only (ii) and (iii) are true [Option ID = 38039]

only (i) and (ii) are true [Option ID = 38038]

7)

[Question ID = 24506]

1. [Option ID = 38023]

2. [Option ID = 38024]

3. [Option ID = 38025]

4. [Option ID = 38022]

[Option ID = 38022]

8)

[Question ID = 24495]

1. 7 [Option ID = 37978]
2. 12 [Option ID = 37981]
3. 10 [Option ID = 37980]
4. 8 [Option ID = 37979]

7 [Option ID = 37978]

9)

[Question ID = 24513]

1. [Option ID = 38053]

2. [Option ID = 38050]

3. [Option ID = 38052]

Page 3

4. [Option ID = 38051]

[Option ID = 38050]

10)

[Question ID = 24543]

1. [Option ID = 38173]

2. [Option ID = 38170]

3. [Option ID = 38172]

4. [Option ID = 38171]

[Option ID = 38170]

11)

[Question ID = 24534]

1. only (i) is true [Option ID = 38134]
2. only (ii) is true [Option ID = 38135]
3. both (i) and (ii) are true [Option ID = 38136]
4. neither (i) nor (ii) is true [Option ID = 38137]

only (i) is true [Option ID = 38134]

12)

[Question ID = 24502]

1. [Option ID = 38006]

2. [Option ID = 38008]

3. [Option ID = 38007]

4. [Option ID = 38009]

[Option ID = 38006]

13)

[Question ID = 24522]

Page 4

1. only (i) is true [Option ID = 38086]
2. both (i) and (ii) are true [Option ID = 38088]
3. only (ii) is true [Option ID = 38087]
4. neither (i) nor (ii) is true [Option ID = 38089]

only (i) is true [Option ID = 38086]

14)

[Question ID = 24517]

1. [Option ID = 38069]

2. [Option ID = 38067]

3. [Option ID = 38068]

4. [Option ID = 38066]

[Option ID = 38066]

15)

[Question ID = 24525]

1. [Option ID = 38098]

2. [Option ID = 38101]

3. [Option ID = 38099]

4. [Option ID = 38100]

[Option ID = 38098]

16)

[Question ID = 24523]

1. [Option ID = 38093]

2. [Option ID = 38090]

3. [Option ID = 38091]

4. [Option ID = 38092]

[Option ID = 38090]

17)

Page 5

[Question ID = 24535]

1. [Option ID = 38138]

2. [Option ID = 38141]

3. [Option ID = 38140]

4. [Option ID = 38139]

[Option ID = 38138]

18)

[Question ID = 24542]

1. [Option ID = 38169]

2. [Option ID = 38168]

3. [Option ID = 38167]

4. [Option ID = 38166]

[Option ID = 38166]

19)

[Question ID = 24526]

1. [Option ID = 38104]

2. [Option ID = 38103]

3. [Option ID = 38102]

4. [Option ID = 38105]

[Option ID = 38102]

20)

[Question ID = 24503]

1. [Option ID = 38013]

2. [Option ID = 38010]

3. [Option ID = 38011]

4. [Option ID = 38012]

Page 6

[Option ID = 38010]

21)

[Question ID = 24529]

1. No, it oscillates [Option ID = 38115]
2. No, it diverges [Option ID = 38114]
3. Yes, −2 is the limit [Option ID = 38117]
4. Yes, −1 is the limit [Option ID = 38116]

No, it diverges [Option ID = 38114]

22)

[Question ID = 26021]

1. [Option ID = 44082]

2. [Option ID = 44080]

3. [Option ID = 44079]

4. [Option ID = 44081]

[Option ID = 44079]

23)

[Question ID = 24504]

1. [Option ID = 38015]
2. [Option ID = 38016]

3. [Option ID = 38014]

4. [Option ID = 38017]

[Option ID = 38014]

24)

[Question ID = 24499]

1. 2.0102 [Option ID = 37995]
2. 4.4424 [Option ID = 37997]
3. 0.2412 [Option ID = 37994]
4. −2.4424 [Option ID = 37996]

Page 7

0.2412 [Option ID = 37994]

25)

[Question ID = 24497]

1. [Option ID = 37988]

2. [Option ID = 37987]

3. [Option ID = 37989]

4. [Option ID = 37986]

[Option ID = 37986]

26)

[Question ID = 24533]

1. [Option ID = 38133]

2. [Option ID = 38130]

3. [Option ID = 38132]

4. [Option ID = 38131]

[Option ID = 38130]

27)

[Question ID = 26030]

1. [Option ID = 44117]

2. [Option ID = 44115]

3. [Option ID = 44118]

4. [Option ID = 44116]

Page 8

[Option ID = 44115]

28)

[Question ID = 24541]

1. [Option ID = 38163]

2. [Option ID = 38165]

3. [Option ID = 38164]

4. [Option ID = 38162]

[Option ID = 38162]

29)

[Question ID = 24512]

1. X and Z [Option ID = 38047]
2. Y and Z [Option ID = 38049]
3. W and Y [Option ID = 38046]
4. W and X [Option ID = 38048]

W and Y [Option ID = 38046]

30)

[Question ID = 24509]

1. [Option ID = 38034]

2. [Option ID = 38037]

3. [Option ID = 38036]

4. [Option ID = 38035]

[Option ID = 38034]

31)

[Question ID = 24539]

1. [Option ID = 38156]

2. [Option ID = 38155]

3. [Option ID = 38157]

Page 9

4. [Option ID = 38154]

[Option ID = 38154]

32)

[Question ID = 24507]

1. [Option ID = 38027]

2. [Option ID = 38026]

3. [Option ID = 38028]

4. [Option ID = 38029]

[Option ID = 38026]

33)

[Question ID = 24511]

1. only (ii) and (iii) are true [Option ID = 38044]
2. only (ii), (iii) and (iv) are true [Option ID = 38043]
3. only (i) and (ii) are true [Option ID = 38045]
4. only (i), (ii) and (iii) are true [Option ID = 38042]

only (i), (ii) and (iii) are true [Option ID = 38042]

34)

[Question ID = 24500]

1. [Option ID = 38000]

2. [Option ID = 37998]

3. [Option ID = 38001]

Page 10

4. [Option ID = 37999]

[Option ID = 37998]

35)

[Question ID = 24496]

1. [Option ID = 37983]

2. [Option ID = 37982]
3. [Option ID = 37985]

4. [Option ID = 37984]

[Option ID = 37982]

36)

[Question ID = 24514]

1. S is one-one but T is not [Option ID = 38055]
2. T is one-one but S is not [Option ID = 38054]
3. Both S and T are one-one [Option ID = 38056]
4. Neither S nor T is one-one [Option ID = 38057]

T is one-one but S is not [Option ID = 38054]

37)

[Question ID = 24501]

1. [Option ID = 38002]

2. [Option ID = 38004]

3. [Option ID = 38005]

4. [Option ID = 38003]

[Option ID = 38002]

38)

[Question ID = 24518]

1. both c and d are even [Option ID = 38072]

Page 11

2. both c and d are odd [Option ID = 38073]
3. c is even and d is odd [Option ID = 38071]
4. c is odd and d is even [Option ID = 38070]

c is odd and d is even [Option ID = 38070]

39)

[Question ID = 24524]

1. only (ii) and (iii) are true [Option ID = 38095]
2. only (i) and (iii) are true [Option ID = 38096]
3. only (i) and (ii) are true [Option ID = 38094]
4. all of (i), (ii) and (iii) are true [Option ID = 38097]

only (i) and (ii) are true [Option ID = 38094]

40)

[Question ID = 24537]

1. [Option ID = 38146]

2. [Option ID = 38147]

3. [Option ID = 38148]

4. [Option ID = 38149]

[Option ID = 38146]

41)

[Question ID = 24527]

1. [Option ID = 38109]

2. [Option ID = 38108]

3. [Option ID = 38106]

4. [Option ID = 38107]

[Option ID = 38106]

42)

Page 12

[Question ID = 24528]

1. [Option ID = 38111]

2. [Option ID = 38113]

3. [Option ID = 38112]

4. [Option ID = 38110]

[Option ID = 38110]

43)

[Question ID = 24530]

1. all of (i), (ii) and (iii) are true [Option ID = 38121]
2. only (ii) is true [Option ID = 38119]
3. only (i) and (ii) are true [Option ID = 38118]
4. only (ii) and (iii) are ture [Option ID = 38120]

only (i) and (ii) are true [Option ID = 38118]

44)

[Question ID = 24498]

1. 0.0996 [Option ID = 37991]
2. 0.0876 [Option ID = 37990]
3. 0.0745 [Option ID = 37992]
4. 0.0912 [Option ID = 37993]

0.0876 [Option ID = 37990]

45)

[Question ID = 24531]

1. converges for all values of p [Option ID = 38124]
2. converges for p > 0, diverges for p ≤ 0 [Option ID = 38122]
3. does not converges for any value of p [Option ID = 38125]
4. converges for p > 1, diverges for p ≤ 1 [Option ID = 38123]

converges for p > 0, diverges for p ≤ 0 [Option ID = 38122]

46)

Page 13

[Question ID = 26022]

1. [Option ID = 44086]

2. [Option ID = 44083]

3. [Option ID = 44084]

4. [Option ID = 44085]

[Option ID = 44083]

47)

[Question ID = 24538]

1. None of these [Option ID = 38153]

2. [Option ID = 38152]

3. [Option ID = 38151]

4. [Option ID = 38150]

[Option ID = 38150]

48)

[Question ID = 24532]

1. All of X, Y and Z [Option ID = 38126]
2. Only Y and Z [Option ID = 38127]
3. Only X and Z [Option ID = 38128]
4. Only Z [Option ID = 38129]

All of X, Y and Z [Option ID = 38126]

49)

[Question ID = 24540]

1. [Option ID = 38161]

2. [Option ID = 38159]

Page 14

3. [Option ID = 38160]

4. [Option ID = 38158]

[Option ID = 38158]

50) Let K be any subgroup of a group G and H be the only subgroup of order m in G. Which of the following is not true?
[Question ID = 24516]

1. H is a normal subgroup of G [Option ID = 38062]
2. G = N(H), where N(H) is the normalizer of H in G. [Option ID = 38065]
3. ab ∈ H implies that ba ∈ H [Option ID = 38064]
4. HK is not a subgroup of G [Option ID = 38063]
H is a normal subgroup of G [Option ID = 38062]

Document Details

Board / OrgNTA
ExamDUET
TypeQuestion Paper
Pages14
Updated30 Apr 2026