31). \(Q \times Q\) is
A). uncountable 
B). countable 
C). finitgset 
D). infinite set 

32). (0, 1] is
A). countable 
B). uncountable 
C). finite 
D). none of these 

33). The set of irrational numbers lying in the interval (0, 1] is
A). countable 
B). finite 
C). uncountable 
D). none of these 

34). The set \(P_{n}\) of all polynomials with integer coefficients is
A). countable 
B). uncountable 
C). finite 
D). none of these 

35). R is equivalent
A). (0, 1) 
B). (0, 1] 
C). [0, 1] 
D). none of these 

36). Which of the following is not true?
A). Cantor set is measurable and its measure zero 
B). Cantor set is equivalent to [0, 1] 
C). Cantor set is uncountable 
D). Cantor set is countable 

37). R with usual metric {0} is
A). open 
B). closed 
C). halfopen 
D). none of these 

38). Which of the following is not true?
A). Q is not open in R 
B). Z is not open in R 
C). Any open interval (a, b) is o 
D). [0, 1) is open in R 

39). Let M be any nonempty set Define \[d(x,y)=\begin{cases}0\text{ if }x=y\\1\text{ if }x\ne y\end{cases}\] This metric is called
A). Stanaard Metric 
B). Discrete Metric 
C). Absolute Metric 
D). Bounded Metric 

40). Which of the following is not correct?
A). In a discrete metric space everysubset is open 
B). \(\phi\) is open 3 
C). Union of any family of open set is open 
D). Arbitrary intersection of ope'nI sets is open 
