MCQ
$1 + \frac{1}{4} + \frac{{1.3}}{{4.8}} + \frac{{1.3.5}}{{4.8.12}} + ........... = $
- ✓$\sqrt 2 $
- B$\frac{1}{{\sqrt 2 }}$
- C$\sqrt 3 $
- D$\frac{1}{{\sqrt 3 }}$
Then, $nx = \frac{1}{4}$ and $\frac{{n(n - 1)}}{2}{x^2} = \frac{1}{4}\,.\,\frac{3}{8} = \frac{3}{{32}}$
Solving these two equations for $n$ and $x$. We get $x = - \frac{1}{2}$ and $n = - \frac{1}{2}$.
$ \therefore$ Sum of the given series
= ${(1 + x)^n} = {\left( {1 - \frac{1}{2}} \right)^{ - 1/2}} = {2^{1/2}} = \sqrt {2.} $
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
$\mathrm{x}_{\mathrm{i}}$ $\ \ 3\ \ 8\ \ 11\ \ 10\ \ 5\ \ 4$
$\mathrm{f}_{\mathrm{i}}$ $\ \ 5 \ \ 2 \ \ 3 \ \ 2 \ \ 4 \ \ 4$
Match each entry in List-$I$ to the correct entries in List-$II$.
| List-$I$ | List-$II$ |
| ($P$) The mean of the above data is | $(1) 2.5$ |
| ($Q$) The median of the above data is | $(2) 5$ |
| ($R$) The mean deviation about the mean of the above data is | $(3) 6$ |
| ($S$) The mean deviation about the median of the above data is | $(4) 2.7$ |
| $(5) 2.4$ |
The correct option is :
Match each entry in $List-I$ to the correct entry in $List-II$.
| $List-I$ | $List-II$ |
| ($P$) $\alpha$ equals | ($1$) $(-2,4)$ |
| ($Q$) $r$ equals | ($2$) $\sqrt{5}$ |
| ($R$) $A_1$ equals | ($3$) $(-2,6)$ |
| ($S$) $B_1$ equals | ($4$) $5$ |
| ($5$) $(2,4)$ |
The correct option is