MCQ
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$133$
- ✓$190$
- C$233$
- D$105$
✓
Answer
Correct option: B.
$190$
b
(b) $x + y = 21$
The number of integral solutions to the equation $x + y < 21$ i.e., $x < 21 - y$
$\therefore$ Number of integral co-ordinate
$ = 19 + 18 + .... + 1 = \frac{{19 \times 20}}{2} = 190$.
(b) $x + y = 21$
The number of integral solutions to the equation $x + y < 21$ i.e., $x < 21 - y$
$\therefore$ Number of integral co-ordinate
$ = 19 + 18 + .... + 1 = \frac{{19 \times 20}}{2} = 190$.
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