Question

# The number of points $$\displaystyle \left ( x,y \right )$$ having integral co-ordinates satisfying the condition $$\displaystyle x^{2}+y^{2}< 25$$ is

A
81
B
12
C
66
D
69

Solution

## The correct option is D $$69$$Since $${ x }^{ 2 }+{ y }^{ 2 }<25$$ and $$a$$ and $$y$$ are integers, the possible values of $$x$$ and $$y\in \left( 0,\pm 1,\pm 2,\pm 3,\pm 4, \right)$$. Thus,$$x$$ and $$y$$ can be chosen in $$9$$ ways each and $$(x,y)$$ can be chosen in $$9\times 9=81$$ ways. However, we have to exclude cases $$\left( \pm 3,\pm 4 \right) ,\left( \pm 4,\pm 3 \right)$$and $$\left( \pm 4,\pm 4 \right) i.e.,3\times 4=12$$Hence, the number of permissible values$$=81-12=69.$$Maths

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