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Question

# Number of points with integral co-ordinates that lie inside a triangle whose co-ordinates are (0,0) , \$(0,21) and (21,0)

A
210
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B
190
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C
220
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D
None
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Solution

## The correct option is D 220Let the vertices of triangle be A(21,0):B(0,21) and D(0,0)Thus any point in the interior of the triangle begin first quadrantTherefore a>0 b>0point (a, b) lies on the same side of AB where for (0,0)x+y−21=0−21<0∴a+b−21<0a+b<21for a=1 b<21−1 i.e., b<20; b∈(1,19)Total 19 values of bfor a=2 b<21−2 i.e., b∈(1,18)∴ no. of integral points 19+18+.....+1=19×202=190 integral points.

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