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. The signm function is not continuous at

 
 
 
 

2. If a function is strictly monotone then It is

 
 
 
 

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

 
 
 
 

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

 
 
 
 

5. Cauchy sequence of real numbers is

 
 
 
 

6. which series is divergent series

 
 
 
 

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

 
 
 
 

8. Every superset of an infinite set is

 
 
 
 

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

 
 
 
 

10. what is supremum and infimum of R is

 
 
 
 

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

 
 
 
 

12. The set of negative integers is

 
 
 
 

13. In a complete metric space

 
 
 
 

14. An improper Reimann Integral can without infinite

 
 
 
 

15. Every subset of a finite set is

 
 
 
 

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

 
 
 
 

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

 
 
 
 

18. Natural Numbers are

 
 
 
 

19. which of the following statements is not correct ?

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

25. The intersection of two infinite sets is

 
 
 
 

26. Every constant sequence is

 
 
 
 

27. which function is continuous everywhere

 
 
 
 

28. which of the following is not countable set

 
 
 
 

29. Set Q of the all rational numbers is

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

33. A convergent sequence converges to

 
 
 
 

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

 
 
 
 

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

 
 
 
 

36. The greatest lower bound of a set

 
 
 
 

37. Which of the following has not multiplicative inverse

 
 
 
 

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

 
 
 
 

39. If least upper bound exists  then it is

 
 
 
 

40. (Q, +, .) is

 
 
 
 

41. Supremum and infimum of an empty set is

 
 
 
 

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

 
 
 
 

43. The converse of Cauchy integral theorem is known as

 
 
 
 

44. The set of all real transcendental numbers is

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

48. Real number system consist of

 
 
 
 

49. Natural numbers and integers are

 
 
 
 

50. (-∞)+(+∞)=

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

54. Set of numbers which have ordered fields

 
 
 
 

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

 
 
 
 

56. Set of natural number is

 
 
 
 

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

 
 
 
 

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

 
 
 
 

59. The set of real number can be denoted as

 
 
 
 

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

 
 
 
 

61. A sequence is a function whose domain is

 
 
 
 

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

 
 
 
 

63. An improper Reimann Integral can without infinite

 
 
 
 

64. If f is contractive then f is

 
 
 
 

65. The set of all real algebric numbers is

 
 
 
 

66. Every bounded sequence has a subsequence which

 
 
 
 

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

 
 
 
 

68. The range of sequence

 
 
 
 

69. Sup (X) =

 
 
 
 

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