41. A Cauchy Sequence in a metric space is convergent if:
A. It is finite
B. It is bounded sequence
C. It has a convergent Subsequence
D. It is Unique
42. Let (X,d) be a metric space. Then Which of the following is true:
A. A Subspace Y of X is complete If Y is closed
B. X is complete if every Cauchy sequence is convergent
C. X is complete If every nested sequence of closed sets has a non-empty intersection
D. All of these
43. Which of the following space is complete:
A. R
B. C
C. Rn
D. All of these
44. Which of the following subspace of R is complete:
A. Q
B. Q’
C. [0,1]
D. None of them
45. Which of the following is not dense in R:
A. Q
B. Q’
C. R
D. Z
46. Which of the following set is nowhere dense in R:
A. Z
B. N
C. {X}
D. All of these
47. A space X has a countable dense set then X is called:
A. Complete
B. Separable
C. Category
D. Closed
48. Let X cannot be expressed as a countable union of its nowhere dense subsets. The X is of:
A. 1st Category
B. 2nd Category
C. 3rd Category
D. 4th Category
49. Which of the following set is of 1st category:
A. Q
B. R
C. C
D. None
50. The complete metric space is of 2nd category is a statement of:
A. Cantor’s intersection theorem
B. Baire’s category theorem
C. Cauchy’s theorem
D. None of them
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