Question

Number of points $(x,y)$ having integral coordinates satisfying the condition $x^2+y^2<25$ is -

• A. 69
• B. 80
• C. 81
• D. 77

Answer 1

Answer: (A)

$x^2+y^2<25$
Number of integral coordinate satisfying above inequality in first quadrant is $13$
i.e. $(1,1),(1,2)$, $(1,3),(1,4),(2,1),(2,2),(2,3),(2,4),(3,1),(3,2),(3,3),(4,1),(4,2)$,

$\therefore$ Total number of integral coordinates are
$134+\underset{\text{on coordinateaxes }}{\underbrace{4\times 4}}+\underset{\text{origin }}{\underbrace{1}}=69$