Question

The number of points having both coordinates as integers that lie in the interior of the triangle with vertices (0,0), (0,41) and (41,0) is

901

861

820

780

Solution

780

Required point (x,y) is such that it satisfies
x +y < 41
and x> 0 and y>0
Number of positive integral solutions of the equation x +y+ k = 41 will be number of intergral coordinates in the bounded region.

therefore, the total number of integral coordinates,
= $straight C presuperscript 41 minus 1 end presuperscript subscript 3 minus 1 end subscript space equals space straight C presuperscript 40 subscript 2 space equals space fraction numerator 40 space factorial over denominator 2 space factorial space 38 space factorial end fraction space equals space 780$

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Integrals

The number of points having both coordinates as integers that lie in the interior of the triangle with vertices (0,0), (0,41) and (41,0) is

901

861

820

780

Some More Questions From Integrals Chapter

Mock Test Series

NCERT Sample Papers

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For Daily Free Study Material Join wiredfaculty

Integrals

The number of points having both coordinates as integers that lie in the interior of the triangle with vertices (0,0), (0,41) and (41,0) is 901 861 820 780

Some More Questions From Integrals Chapter

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

The number of points having both coordinates as integers that lie in the interior of the triangle with vertices (0,0), (0,41) and (41,0) is

901

861

820

780