MCQ
Ten students are seated at random in a row. The probability that two particular students are not seated side by side is
- ✓$\frac{4}{5}$
- B$\frac{3}{5}$
- C$\frac{2}{5}$
- D$\frac{1}{5}$
Two boys can sit side by side in $2 \times 9\,\,!$ ways.
So probaibility $ = \frac{{2 \times 9\,\,!}}{{10\,\,!}} = \frac{1}{5}$
Thus the probability that they are not seated together is $1 - \frac{1}{5} = \frac{4}{5}.$
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
| column-$I$ | column-$II$ |
| $(A)$ A line from the origin meets the lines $\frac{x-2}{1}=\frac{y-1}{-2}=\frac{z+1}{1}$ and $\frac{x-\frac{8}{3}}{2}=\frac{y+3}{-1}=\frac{z-1}{1}$ at $P$ and $Q$ respectively. If length $P Q=d$, then $d^2$ is | $(p)$ $-4$ |
| $(B)$ The values of $x$ satisfying $\tan ^{-1}(x+3)-\tan ^{-1}(x-3)=\sin ^{-1}\left(\frac{3}{5}\right)$ are | $(q)$ $0$ |
| $(C)$ Non-zero vectors $\vec{a}, \vec{b}$ and $\overrightarrow{\mathrm{c}}$ satisfy $\vec{a} \cdot \vec{b}=0$, $(\vec{b}-\vec{a}) \cdot(\vec{b}+\vec{c})=0$ and $2|\vec{b}+\vec{c}|=|\vec{b}-\vec{a}|$. If $\vec{a}=\mu \vec{b}+4 \vec{c}$, then the possible values of $\mu$ are | $(r)$ $4$ |
| $(D)$ Let $f$ be the function on $[-\pi, \pi]$ given by $f(0)=9$ and $f(x)=$ $\sin \left(\frac{9 x}{2}\right) / \sin \left(\frac{x}{2}\right)$ for $x \neq 0$. The value of $\frac{2}{\pi} \int_{-\pi}^\pi f(x) d x$ is | $(s)$ $5$ |
| $(t)$ $6$ |
$f\left( x \right) = \left\{ \begin{gathered} x{\left\{ x \right\}^2},x \notin I \hfill \\ x\,\,\,\,\,\,\,\,\,\,,x \in I \hfill \\ \end{gathered} \right.,$
then which of the following statement is correct?
(where $\{.\}$ denotes fractional part function)