1311. 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

1312. 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 of 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 *

1313. Which of the following space is complete :

A. R
B. C
C. Rn
D. All of these *

1314. Which of the following subspace of R is complete :

A. Q
B. Q’
C. [0,1] *
D. None of them

1315. Which of the following is not dense in R :

A. Q
B. Q’
C. R
D. Z *

1316. Which of the following set is now where dense in R :

A. Z
B. N
C. {X}
D. All of these *

1317. A space X has countable dense set then X is called :

A. Complete
B. Separable *
C. Category
D. Closed

1318. Let X cannot be expressed as a countable union of its now where dense subsets. The X is of :

A. 1st Category
B. 2nd Category *
C. 3rd Category
D. 4th Category

1319. Which of the following set is of 1st category:

A. Q *
B. R
C. C
D. None

1320. The complete metric space is of 2nd category is a statement of :

A. Cantor’s intersection theorem
B. Bair’s category theorem *
C. Cauchy’s theorem
D. None of them