Real Analysis MCQs with answers

Real Analysis MCQs with answers

To master Real Analysis, focus on these 69 key questions, a compilation of the most frequently encountered and crucial concepts. Attempt them to solidify your understanding, and reveal the solutions for immediate feedback. Success awaits!

Real Analysis MCQs at www.pakmath.com

1. which of the following statements is not correct ?

 
 
 
 

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

 
 
 
 

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

 
 
 
 

4. what is supremum and infimum of R is

 
 
 
 

5. An improper Reimann Integral can without infinite

 
 
 
 

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

 
 
 
 

7. The converse of Cauchy integral theorem is known as

 
 
 
 

8. The range of sequence

 
 
 
 

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

 
 
 
 

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

 
 
 
 

11. The set of real number can be denoted as

 
 
 
 

12. If a function is strictly monotone then It is

 
 
 
 

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

 
 
 
 

14. Natural Numbers are

 
 
 
 

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

 
 
 
 

16. Every bounded sequence has a subsequence which

 
 
 
 

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

 
 
 
 

18. The set of negative integers is

 
 
 
 

19. Set Q of the all rational numbers is

 
 
 
 

20. Set of numbers which have ordered fields

 
 
 
 

21. The signm function is not continuous at

 
 
 
 

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

 
 
 
 

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

 
 
 
 

24. which function is continuous everywhere

 
 
 
 

25. Supremum and infimum of an empty set is

 
 
 
 

26. In a complete metric space

 
 
 
 

27. Every subset of a finite set is

 
 
 
 

28. Which of the following has not multiplicative inverse

 
 
 
 

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

 
 
 
 

30. Real number system consist of

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

34. which series is divergent series

 
 
 
 

35. (-∞)+(+∞)=

 
 
 
 

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

 
 
 
 

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

 
 
 
 

38. An improper Reimann Integral can without infinite

 
 
 
 

39. The set of all real algebric numbers is

 
 
 
 

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

 
 
 
 

41. Every constant sequence is

 
 
 
 

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

 
 
 
 

43. Set of natural number is

 
 
 
 

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

 
 
 
 

45. The greatest lower bound of a set

 
 
 
 

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

 
 
 
 

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

 
 
 
 

48. The set of all real transcendental numbers is

 
 
 
 

49. which of the following is not countable set

 
 
 
 

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

 
 
 
 

51. Sup (X) =

 
 
 
 

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

 
 
 
 

53. Cauchy sequence of real numbers is

 
 
 
 

54. Natural numbers and integers are

 
 
 
 

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

 
 
 
 

56. Every superset of an infinite set is

 
 
 
 

57. If least upper bound exists  then it is

 
 
 
 

58. A convergent sequence converges to

 
 
 
 

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

 
 
 
 

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

 
 
 
 

61. The intersection of two infinite sets is

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

65. (Q, +, .) is

 
 
 
 

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

 
 
 
 

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

 
 
 
 

68. A sequence is a function whose domain is

 
 
 
 

69. If f is contractive then f is

 
 
 
 

Real analysis 2 mcqs with answers

In this section, there are real analysis 2 mcqs with answers. These mcqs consist of 50+ most repeated and most important questions.  These mcqs were prepared according to the pattern of all kinds of test preparations. So prepare these mcqs for preparation of all tests. Good Luck

Mechanics MCQs 01

Leave a Comment

Your email address will not be published. Required fields are marked *

Scroll to Top