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. Every constant sequence is

 
 
 
 

2. Which of the following has not multiplicative inverse

 
 
 
 

3. If f is contractive then f is

 
 
 
 

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

 
 
 
 

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

 
 
 
 

6. The intersection of two infinite sets is

 
 
 
 

7. Cauchy sequence of real numbers is

 
 
 
 

8. The set of all real algebric numbers is

 
 
 
 

9. Set Q of the all rational numbers is

 
 
 
 

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

 
 
 
 

11. Sup (X) =

 
 
 
 

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

 
 
 
 

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

 
 
 
 

14. A sequence is a function whose domain is

 
 
 
 

15. Set of natural number is

 
 
 
 

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

 
 
 
 

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

 
 
 
 

18. The set of all real transcendental numbers is

 
 
 
 

19. The range of sequence

 
 
 
 

20. which function is continuous everywhere

 
 
 
 

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

 
 
 
 

22. Every bounded sequence has a subsequence which

 
 
 
 

23. The greatest lower bound of a set

 
 
 
 

24. If a function is strictly monotone then It is

 
 
 
 

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

 
 
 
 

26. Real number system consist of

 
 
 
 

27. Supremum and infimum of an empty set is

 
 
 
 

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

 
 
 
 

29. Set of numbers which have ordered fields

 
 
 
 

30. (-∞)+(+∞)=

 
 
 
 

31. (Q, +, .) is

 
 
 
 

32. The set of negative integers is

 
 
 
 

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

 
 
 
 

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

 
 
 
 

35. The converse of Cauchy integral theorem is known as

 
 
 
 

36. In a complete metric space

 
 
 
 

37. A convergent sequence converges to

 
 
 
 

38. Natural Numbers are

 
 
 
 

39. If least upper bound exists  then it is

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

43. The set of real number can be denoted as

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

49. which series is divergent series

 
 
 
 

50. Every subset of a finite set is

 
 
 
 

51. An improper Reimann Integral can without infinite

 
 
 
 

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

 
 
 
 

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

 
 
 
 

54. The signm function is not continuous at

 
 
 
 

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

 
 
 
 

56. Natural numbers and integers are

 
 
 
 

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

 
 
 
 

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

 
 
 
 

59. Every superset of an infinite set is

 
 
 
 

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

 
 
 
 

61. which of the following is not countable set

 
 
 
 

62. which of the following statements is not correct ?

 
 
 
 

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

 
 
 
 

64. what is supremum and infimum of R is

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

69. An improper Reimann Integral can without infinite

 
 
 
 

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

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