41). Let R be a metric space with usual metric \(\Large A_{n}= \left(\frac{-1}{n},\frac{1}{n}\right) \). Then \(\Large\bigcap\limits_{n=1}^{\infty}A_{n}\) is
| A). open |
| B). not open |
| C). not singleton set |
| D). \(\phi\) |
|
42). Let (M, d) be a metric space. Let \(x\in M\). Then \(\{x\}^{c}\) is
| A). open |
| B). closed |
| C). not open |
| D). half-open |
|
43). Any open subset of R can be expressed as the union of a countable number of
| A). closed sets |
| B). mutually disjoint closed sets |
| C). open sets |
| D). mutually disjoint open intervals |
|
44). Every convergent sequence is a
| A). cauchy sequence |
| B). optimal sequence |
| C). increasing sequence |
| D). decreasing sequence |
|
45). Every cauchy sequence is convergent. The statement is
| A). true |
| B). false |
| C). partially true |
| D). none of these |
|
46). Every contmuousimage of a connected set is
| A). connected |
| B). disconnected |
| C). compact |
| D). none of these |
|
47). If f is diffrentiable at c. Then f is
| A). Monotonic |
| B). Discontinuous |
| C). Continuous |
| D). None of these |
|
48). If f is Riemann integrable in (a, b) then f is
| A). lebesque integral |
| B). ordinary integral |
| C). Riemann stieltges |
| D). none of these |
|
49). If a surface is developable then its Gaussian curvature is
| A). zero |
| B). non zero |
| C). constant |
| D). none of these |
|
50). The set of all real numbers is
| A). countable |
| B). uncountable |
| C). measurable |
| D). none of these |
|
