Question

The number of integral points (integral point means both the coordinates should be integer) exactly in the interior of the triangle with vertices $(0,0),(0,21)$ and $(21,0)$ is

• A. 133
• B. 190
• C. 233
• D. 105

Answer 1

Answer: (B)

$x+y=21$
The number of integral solutions to the equation
$x+y<21$, i.e., $x<21-y$

$\therefore$ Number of integral coordinate
$=19+18+....+1$
$=\frac{19(19+1)}{2}=\frac{19\times 20}{2}=190$