JEE Main · 2015 · 04 Apr 2015 · Offline · Permutations and Combinations

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 :

Answer: (C)

Solution

Count the lattice points strictly inside the triangle with vertices

(0, 0)

(0, 41)

and

(41, 0)

-- those with

x \geq 1

y \geq 1

and

x + y < 41

, i.e.

x + y \leq 40

. Along each line

x + y = s

there are

s - 1

such positive pairs, so the total is

\sum_{s = 2}^{40} (s - 1) = \sum_{k = 1}^{39} k = \frac{39 \times 40}{2} = 780

JEE Main · 2015 · 04 Apr 2015 · Offline · Single correct option