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 of numbers which have ordered fields

 
 
 
 

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

 
 
 
 

3. If a function is strictly monotone then It is

 
 
 
 

4. Every superset of an infinite set is

 
 
 
 

5. The set of negative integers is

 
 
 
 

6. The greatest lower bound of a set

 
 
 
 

7. which function is continuous everywhere

 
 
 
 

8. The signm function is not continuous at

 
 
 
 

9. Sup (X) =

 
 
 
 

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

 
 
 
 

11. The set of real number can be denoted as

 
 
 
 

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

 
 
 
 

13. which series is divergent series

 
 
 
 

14. A convergent sequence converges to

 
 
 
 

15. An improper Reimann Integral can without infinite

 
 
 
 

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

 
 
 
 

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

 
 
 
 

18. The set of all real transcendental numbers is

 
 
 
 

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

 
 
 
 

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

 
 
 
 

21. (-∞)+(+∞)=

 
 
 
 

22. Real number system consist of

 
 
 
 

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

 
 
 
 

24. If f is contractive then f is

 
 
 
 

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

 
 
 
 

26. Set Q of the all rational numbers is

 
 
 
 

27. The converse of Cauchy integral theorem is known as

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

31. A sequence is a function whose domain is

 
 
 
 

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

 
 
 
 

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

 
 
 
 

34. Every constant sequence is

 
 
 
 

35. which of the following statements is not correct ?

 
 
 
 

36. Natural Numbers are

 
 
 
 

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

 
 
 
 

38. If least upper bound exists  then it is

 
 
 
 

39. (Q, +, .) is

 
 
 
 

40. Natural numbers and integers are

 
 
 
 

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

 
 
 
 

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

 
 
 
 

43. Which of the following has not multiplicative inverse

 
 
 
 

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

 
 
 
 

45. Every bounded sequence has a subsequence which

 
 
 
 

46. what is supremum and infimum of R is

 
 
 
 

47. Set of natural number is

 
 
 
 

48. In a complete metric space

 
 
 
 

49. which of the following is not countable set

 
 
 
 

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

 
 
 
 

51. Cauchy sequence of real numbers is

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

56. Every subset of a finite set is

 
 
 
 

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

 
 
 
 

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

 
 
 
 

59. Supremum and infimum of an empty set is

 
 
 
 

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

 
 
 
 

61. An improper Reimann Integral can without infinite

 
 
 
 

62. The range of sequence

 
 
 
 

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

 
 
 
 

64. The set of all real algebric numbers is

 
 
 
 

65. The intersection of two infinite sets is

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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