JEE Main 2015 · 4 Apr · Shift 1 · Mathematics Q78

MathematicsSingle correct+4 / -1Question 78 of 90

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 :

901

861

820

780

Answer and worked solution

Official answer: D

Interior lattice points need $x,y\ge1$ and $x+y\le40$ :
$\sum_{x=1}^{39}(40-x)=\frac{39\times40}2=780.$

JEE Main 2015 · 4 Apr · Shift 1, Mathematics question 78