# Real Analysis Questions and answers

Topics

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). half-open 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 non-empty 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 every-subset 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
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