QJEEM15Mafa41: JEE Main 2015 Mathematics - Class 11 JEEM15Mafa41 Solution: The number of points, having both co-ordinates as integers,…

Question

Verified Solution • 2025–26 Session moderate

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 :

Accepted Answer

JEE Main 2015 (Offline) Mathematics - Straight Lines and Pair of Straight Lines Question 131 English Explanation

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

$⋮$

39. If x = 39, then the value of y is 1.

Hence, the number of interior points are

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

Step-by-Step Verified Solution