The number of points, having both co-ordinates as integers, that lie in the interior of the triangle with vertices \[\left( 0,0 \right),\left( 0,41 \right)\] and \[\left( 41,0 \right),\] is
[JEE Main Solved Paper-2015 ]
A)820
B)780
C)901
D)861
Correct Answer:
B
Solution :
Now number of integral points lie in side the triangle are (a) If x = 1, then y may be 1,2,3......39 (b) If x = 2, then y may be 1,2,3......38 and so on If x = 39 , then value of y is 1 only. Hence number of interior points are \[1+2+3+......+39=\frac{39\times 40}{2}=780\]