**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