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. Every bounded sequence has a subsequence which

 
 
 
 

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

 
 
 
 

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

 
 
 
 

4. Supremum and infimum of an empty set is

 
 
 
 

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

 
 
 
 

6. The set of all real transcendental numbers is

 
 
 
 

7. An improper Reimann Integral can without infinite

 
 
 
 

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

 
 
 
 

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

 
 
 
 

10. Every superset of an infinite set is

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

14. (-∞)+(+∞)=

 
 
 
 

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

 
 
 
 

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

 
 
 
 

17. If a function is strictly monotone then It is

 
 
 
 

18. An improper Reimann Integral can without infinite

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

22. If least upper bound exists  then it is

 
 
 
 

23. Which of the following has not multiplicative inverse

 
 
 
 

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

 
 
 
 

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

 
 
 
 

26. The set of all real algebric numbers is

 
 
 
 

27. Every subset of a finite set is

 
 
 
 

28. Cauchy sequence of real numbers is

 
 
 
 

29. The intersection of two infinite sets is

 
 
 
 

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

 
 
 
 

31. what is supremum and infimum of R is

 
 
 
 

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

 
 
 
 

33. which of the following statements is not correct ?

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

38. A sequence is a function whose domain is

 
 
 
 

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

 
 
 
 

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

 
 
 
 

41. Natural numbers and integers are

 
 
 
 

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

 
 
 
 

43. The signm function is not continuous at

 
 
 
 

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

 
 
 
 

45. which function is continuous everywhere

 
 
 
 

46. Sup (X) =

 
 
 
 

47. The range of sequence

 
 
 
 

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

 
 
 
 

49. Set of natural number is

 
 
 
 

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

 
 
 
 

51. The greatest lower bound of a set

 
 
 
 

52. The set of real number can be denoted as

 
 
 
 

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

 
 
 
 

54. In a complete metric space

 
 
 
 

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

 
 
 
 

56. which series is divergent series

 
 
 
 

57. If f is contractive then f is

 
 
 
 

58. Natural Numbers are

 
 
 
 

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

 
 
 
 

60. which of the following is not countable set

 
 
 
 

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

 
 
 
 

62. (Q, +, .) is

 
 
 
 

63. The set of negative integers is

 
 
 
 

64. The converse of Cauchy integral theorem is known as

 
 
 
 

65. Real number system consist of

 
 
 
 

66. Every constant sequence is

 
 
 
 

67. Set of numbers which have ordered fields

 
 
 
 

68. A convergent sequence converges to

 
 
 
 

69. Set Q of the all rational numbers is

 
 
 
 

Help

5 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

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