71). If \(a_{x}=1+(-1)^{n}\forall\ n\in N\) then find \(A_{n}\) and \(\overline{A_{n}}\)
| A). 2 and 0 |
| B). 0 and 2 |
| C). 1 and 2 |
| D). none of these |
|
72). If \(a_{n}=n,\ x\in N\), then find \(\underline{A_{n}}\) and \(\overline{A_{n}}\)
| A). \(0\) and \(\infty\) |
| B). \(\infty\) and \(-\infty\) |
| C). \(\triangle \) and \(\infty\) |
| D). none of these |
|
73). If \(\Large a_{n}=\frac{(-1)^{n}}{n^{2}}n\in N\), then find \(\underline{\lim}\ a_{n}\)
| A). \(\infty\) |
| B). -1 |
| C). 0 |
| D). none of these |
|
74). If \(\Large a_{n}=(-1)^{2} \left(1+\frac{1}{n}\right),\ n\in N \) then find \(\underline{\lim}\ a_{n}\)
| A). 1 |
| B). -1 |
| C). 0 |
| D). none of these |
|
75). If \(\Large a_{n}=sin\frac{n \pi }{3},\ n\in N \) then find \(\underline{\lim}\ a_{n}\)
| A). \(\Large \frac{\sqrt{3}}{2}\) |
| B). \(\Large \frac{-\sqrt{3}}{2}\) |
| C). \(\Large \frac{1}{2}\) |
| D). none of these |
|
76). If \(f(x)=(x-l)(x-2)(x-3),\ a=0,\ b=4\) find \(c\) of lagranges mean value theorem.
| A). \(\Large c=\frac{1}{2}\) |
| B). \(\Large c=\pm \frac{2}{\sqrt{3}}\) |
| C). \(\Large c=2\pm \frac{2}{\sqrt{3}}\) |
| D). none of these |
|
77). Let \(f(x)=x\) for \(x\in [0,1]\) and let \(\Large P= \{ 0,\frac{1}{3},\frac{2}{3},1 \}\) be the position-of [0, 1] then compute U(p, f)
| A). \(\Large \frac{1}{3}\) |
| B). \(\Large \frac{1}{7}\) |
| C). \(\Large \frac{2}{3}\) |
| D). none of these |
|
78). If \(E_{1}\) and \(E_{2}\) are measurable then \(E_{1}\cap E_{2}\) is
| A). Integrable |
| B). Measurable |
| C). Continuity |
| D). none of these |
|
79). If \(E_{1}\) and \(E_{2}\) are measurable then \(E_{1}-E_{2}\) is
| A). integrable |
| B). measurable |
| C). continuity |
| D). none of these |
|
80). \(f(x)=\Large\frac{1}{1+x^{2}}\ \forall x\in R\) find \(\int\limits_{R}F\)
| A). \(1\) |
| B). \( \pi ^{2}\) |
| C). \( \pi \) |
| D). none of these |
|
