question_answer

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 \[1+2+3+......+39=\frac{39\times 40}{2}=780\]