101). The set of all transcendental numbers is____.
| A). countable |
| B). uncountable |
| C). denumerable |
| D). none of these |
|
102). The cantor set is equivalent to ______.
| A). (0, 1) |
| B). [0, 1] |
| C). 0 |
| D). none of these |
|
103). The set S of intervals with rational end points is _____.
| A). countable |
| B). uncountable |
| C). denumerable |
| D). none of these |
|
104). If A is a countable set and B an uncountable A set then B-A is ______ to B
| A). similar |
| B). equal |
| C). countable |
| D). none of these |
|
105). Find the upper bound and lower bound for the set. z={...-3, -2, -1, 0, 1, 2, 3,...}
| A). bounded above by 1 |
| B). bounded below by -3 |
| C). bounded neither below nor above |
| D). bounded set |
|
106). Find the set of limit points of the set \(\Large \{1,\frac{1}{2},\frac{1}{3},...,\frac{1}{n},... \}\)
| A). R |
| B). {O} |
| C). \(\phi\) |
| D). none of these |
|
107). If a bounded set S in R\(^{n}\) contains infinitely many points. then there is atleast one point in R\(^{n}\) which is an accumulation point of S. This is
| A). Bolzano-weierstran theorem |
| B). Cauchy's theorem |
| C). Lami's theorem |
| D). None of these |
|
108). A set is ______ if it contains all its accumulation points.
| A). open |
| B). closed |
| C). derived |
| D). none of these |
|
109). Assume \(A\subseteq R^{n}\) and let F be an open covering of A. Then there is a countable sub collection of F which also covers A. This is
| A). Cantor intersection theorem |
| B). Lindelof covering theorem |
| C). Bolzano-weierstrass theorem |
| D). None of these |
|
110). Let F be an open covering of a closed and bounded set A in R\(^{n}\). Then a finite sub collection of F also covers A. This is
| A). Heine-Borel theorem |
| B). Bolzano-Weierstram theorem |
| C). Lindelof covering theorem |
| D). None of these |
|
