31). \(Q \times Q\) is
A). uncountable |
B). countable |
C). finitgset |
D). infinite set |
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32). (0, 1] is
A). countable |
B). uncountable |
C). finite |
D). none of these |
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33). The set of irrational numbers lying in the interval (0, 1] is
A). countable |
B). finite |
C). uncountable |
D). none of these |
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34). The set \(P_{n}\) of all polynomials with integer coefficients is
A). countable |
B). uncountable |
C). finite |
D). none of these |
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35). R is equivalent
A). (0, 1) |
B). (0, 1] |
C). [0, 1] |
D). none of these |
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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 |
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37). R with usual metric {0} is
A). open |
B). closed |
C). half-open |
D). none of these |
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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 |
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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 |
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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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