1930　京都帝国大学　理学部

【１】 For what values of $x$ does the relation $\sqrt{x-1}>\sqrt{5-x}$ hold?

【２】 Find the distance between the point $(a,b,c)$ and the plane $Ax+By+Cz=\mathrm{D}\text{.}$ (axes rectangular)

【３】 In a plane, rectangular axes $\mathrm{O}x\text{,}$ $\mathrm{O}y$ and a point $\mathrm{P}$ are given.Through $\mathrm{P}$ a str. line is drown meeting $\mathrm{O}x\text{,}$ $\mathrm{O}y$ at $\mathrm{A}\text{,}$ $\mathrm{B}$ respectively,find the least area, the triangle $\mathrm{OAB}$ may have.

【４】 Find ${\displaystyle \int }{\displaystyle \frac{\mathit{d\theta }}{\cos \theta +3}}\text{.}$