Real Analysis MCQs 01 for NTS, PPSC, FPSC

Real Analysis mcqs

Real Analysis MCQs 01 consist of 69 most repeated and most important questions. So prepare real analysis to attempt these questions.

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1. Let S be a set of real numbers. Then S has a supremum if S has

 
 
 
 

2. The intersection of two infinite sets is

 
 
 
 

3. If f is real valued and monotonic on [a , b] then f is

 
 
 
 

4. If there exists a bijection of N onto S then set is known as

 
 
 
 

5. The set of all real transcendental numbers is

 
 
 
 

6. The set of all ___________ numbers form a sequence.

 
 
 
 

7. For two real numbers x and y with x > 0 , there exist a natural number n s.t

 
 
 
 

8. The signm function is not continuous at

 
 
 
 

9. The function f(x)= x + 1/x is uniformly continuous on

 
 
 
 

10. what is supremum and infimum of R is

 
 
 
 

11. If f is differentiable in [ a, b] then it is monotonically increasing if

 
 
 
 

12. If we have an inflection point x = a then

 
 
 
 

13. \dpi{120} \small \frac{(-1) ^{n-1}}{n!} converges to limit

 
 
 
 

14. Cauchy sequence of real numbers is

 
 
 
 

15. Which of the following has not multiplicative inverse

 
 
 
 

16. If L is the tangent line to a function f at x = a then

 
 
 
 

17. If function is Reimanns integrable on [ a, b] then function must be

 
 
 
 

18. Natural numbers and integers are

 
 
 
 

19. Real number system consist of

 
 
 
 

20. A sequence is said to be divergent if it is

 
 
 
 

21. The converse of Cauchy integral theorem is known as

 
 
 
 

22. The set of real number can be denoted as

 
 
 
 

23. Supremum and infimum of an empty set is

 
 
 
 

24. The range of sequence

 
 
 
 

25. Every bounded sequence has a subsequence which

 
 
 
 

26. If a sequence is unbounded or it does not converge then this sequence is called

 
 
 
 

27. Set Q of the all rational numbers is

 
 
 
 

28. Bounded monotonic sequence will be decreasing if it converges to its

 
 
 
 

29. The sequence of real numbers is ________ if and only if it is cauchy sequence.

 
 
 
 

30. If f'(x) exists then it is constant function

 
 
 
 

31. For every closed subset of R , the real line is

 
 
 
 

32. Every constant sequence is

 
 
 
 

33. If S={1\n | n £ N } the g.l.b of S is

 
 
 
 

34. In a complete metric space

 
 
 
 

35. which of the following statements is not correct ?

 
 
 
 

36. (-∞)+(+∞)=

 
 
 
 

37. A convergent sequence converges to

 
 
 
 

38. which series is divergent series

 
 
 
 

39. Every pair of real numbers a and b satisfied the following conditions a >  b, a = b, a < b . This property known as

 
 
 
 

40. (Q, +, .) is

 
 
 
 

41. If \dpi{120} \small x , y \in R then

 
 
 
 

42. If f is differentiable in [ a, b] then it is monotonically decreasing if

 
 
 
 

43. Every superset of an infinite set is

 
 
 
 

44. An improper Reimann Integral can without infinite

 
 
 
 

45. Every infinite sequence in a compact metric space has a subsequence which

 
 
 
 

46. Natural Numbers are

 
 
 
 

47. Set of numbers which have ordered fields

 
 
 
 

48. A continuous function from bounded [a , b] to R

 
 
 
 

49. If a function is strictly monotone then It is

 
 
 
 

50. An improper Reimann Integral can without infinite

 
 
 
 

51. If least upper bound exists  then it is

 
 
 
 

52. {\dpi{120} \small {1 + (-1)^n }} is

 
 
 
 

53. A metric (X,d) is complete if every cauchy sequence in X

 
 
 
 

54. Every subset of a finite set is

 
 
 
 

55. Supremum and infimum of \dpi{120} \small { (-1)^x } : x \in N

 
 
 
 

56. which function is continuous everywhere

 
 
 
 

57. The set of all real algebric numbers is

 
 
 
 

58. Set of natural number is

 
 
 
 

59. Sup (X) =

 
 
 
 

60. If f is differentiable at x ε [ a, b] then f at x is

 
 
 
 

61. Every non empty bounded set of real numbers has a infimum . This property is referred to as

 
 
 
 

62. The greatest lower bound of a set

 
 
 
 

63. Bounded monotonic sequence will be increasing if it converges to its

 
 
 
 

64. A sequence is a function whose domain is

 
 
 
 

65. If g.l.b of a set belong to the set then

 
 
 
 

66. The set of negative integers is

 
 
 
 

67. No polynomial of degree _________ is Lipschitzian on R .

 
 
 
 

68. which of the following is not countable set

 
 
 
 

69. If f is contractive then f is

 
 
 
 

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8 Replies to “Real Analysis MCQs 01 for NTS, PPSC, FPSC”

  1. A.o.A Sir, I’m a student of Bs (Hons) Mathematics studying pure maths currently, my 6th semester’s finals+mids (online MCQs) are just around the corner and my whole class is nervous.
    If you could provide us with some already written or saved MCQs about the following subjects, we’ll be forever thankful.

    Introduction to Topology
    Real Analysis II
    Mathematical Statistics
    Classical Mechanics
    Number Theory

  2. GOOD ALLAH BLESS WILL BLESS YOU WHAT YOU WANT YOU ARE DOING BEST FOR EVERY STUDENT

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