JEE MAIN - Mathematics (2015 (Offline) - No. 16)
The number of points, having both co-ordinates as integers, that lie in the interior of the triangle with vertices $$(0, 0)$$ $$(0, 41)$$ and $$(41, 0)$$ is :
820
780
901
861
Explanation
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The number of integral points lie inside the triangle are
1. If x = 1, then y may be 1, 2, 3, ....., 39
2. If x = 2, then y may be 1, 2, 3, ....., 38
3. If x = 3, then y may be 1, 2, 3, ....., 37
$$ \vdots $$
39. If x = 39, then the value of y is 1.
Hence, the number of interior points are
$$1 + 2 + 3 + .... + 39 = {{39 \times 40} \over 2} = 780$$Comments (0)
