MCQ
The number of positive integral solutions $\left| {\,\,\begin{array}{*{20}{c}}{1 - \lambda }&2&1\\{ - 3}&\lambda &{ - 2}\\2&{ - 2}&{1 + \lambda }\end{array}\,\,} \right|$ $= 0$ is
- A$0$
- B$2$
- ✓$3$
- D$1$
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Match each entry in List-$I$ to the correct entries in List-$II$.
| List-$I$ | List-$II$ |
| ($P$) The value of $\mathrm{d}\left(\mathrm{H}_0\right)$ is | ($1$) $\sqrt{3}$ |
| ($Q$) The distance of the point $(0,1,2)$ from $\mathrm{H}_0$ is | ($2$) $\frac{1}{\sqrt{3}}$ |
| ($R$) The distance of origin from $\mathrm{H}_0$ is | ($3$) $0$ |
| ($S$) The distance of origin from the point of intersection of planes $\mathrm{y}=\mathrm{z}, \mathrm{x}=1$ and $\mathrm{H}_0$ is | ($4$) $\sqrt{2}$ |
| ($5$) $\frac{1}{\sqrt{2}}$ |
The corret option is :