1925　京都帝国大学　工学部

【１】 Find the remainder when

$f(x)=a_0{x}^n+a_1{x}^{n-1}+\cdots +a_{n-1}x+a_n$

is devided by $(x-\alpha )(x-\beta )\text{.}$

【２】 Prove that the triangle of maximum area inscribed in a given circle is an equilateral triangle.

【３】 Find the length of the arc of the parabola $y^2=4ax$ from the vertex to the end of the latus-rectum.

【４】 A car is moving with velocity $v$ and acceleration $a$ on a circular track of radius $r\text{.}$ What is the inclination of the plumb line hung from the ceiling of the car ?