JEE Mains · Maths · STD 11 - 6. permutation and combination
The number of points, having both co-ordinates as integers, that lie in the interior of the triangle with vertices \((0,0),(0,41) \) અને \( (41,0)\) is :
- A \(780\)
- B \(901\)
- C \(861\)
- D \(820\)
Answer & Solution
Correct Answer
(A) \(780\)
Step-by-step Solution
Detailed explanation
\(\frac{x}{a} + \frac{y}{b} = 1\) \(\frac{x}{{41}} + \frac{y}{{41}} = 1\) first point \(=(39,1)\) \( = \mathop \sum \limits_{i = 1}^{39} = \frac{{i\left( {i + 1} \right)}}{2}\) \( = \frac{{39\left( {39 + 1} \right)}}{2}\) \(=780\) units
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