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. Set Q of the all rational numbers is

 
 
 
 

2. which of the following statements is not correct ?

 
 
 
 

3. The greatest lower bound of a set

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

7. The range of sequence

 
 
 
 

8. If f is contractive then f is

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

12. A convergent sequence converges to

 
 
 
 

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

 
 
 
 

14. Every superset of an infinite set is

 
 
 
 

15. The set of real number can be denoted as

 
 
 
 

16. Sup (X) =

 
 
 
 

17. Real number system consist of

 
 
 
 

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

 
 
 
 

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

 
 
 
 

20. Cauchy sequence of real numbers is

 
 
 
 

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

 
 
 
 

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

 
 
 
 

23. Every bounded sequence has a subsequence which

 
 
 
 

24. An improper Reimann Integral can without infinite

 
 
 
 

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

 
 
 
 

26. The set of all real transcendental numbers is

 
 
 
 

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

 
 
 
 

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

 
 
 
 

29. An improper Reimann Integral can without infinite

 
 
 
 

30. The set of negative integers is

 
 
 
 

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

 
 
 
 

32. In a complete metric space

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

36. The intersection of two infinite sets is

 
 
 
 

37. which of the following is not countable set

 
 
 
 

38. Natural numbers and integers are

 
 
 
 

39. Set of natural number is

 
 
 
 

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

 
 
 
 

41. (-∞)+(+∞)=

 
 
 
 

42. If a function is strictly monotone then It is

 
 
 
 

43. The converse of Cauchy integral theorem is known as

 
 
 
 

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

 
 
 
 

45. Supremum and infimum of an empty set is

 
 
 
 

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

 
 
 
 

47. If least upper bound exists  then it is

 
 
 
 

48. Which of the following has not multiplicative inverse

 
 
 
 

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

 
 
 
 

50. Every subset of a finite set is

 
 
 
 

51. If we have an inflection point 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. Bounded monotonic sequence will be decreasing if it converges to its

 
 
 
 

54. what is supremum and infimum of R is

 
 
 
 

55. Set of numbers which have ordered fields

 
 
 
 

56. Natural Numbers are

 
 
 
 

57. (Q, +, .) is

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

61. A sequence is a function whose domain is

 
 
 
 

62. The set of all real algebric numbers is

 
 
 
 

63. The signm function is not continuous at

 
 
 
 

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

 
 
 
 

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

 
 
 
 

66. which series is divergent series

 
 
 
 

67. which function is continuous everywhere

 
 
 
 

68. Every constant sequence is

 
 
 
 

69. A sequence is said to be divergent if it 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

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