Let `f(r)` be the number of integral points inside a circle of radius r and centre at origin (integral point is a point both of whose coordinates are integers), then `lim_(r->oo) (f(r))/(pir^2)` is equal to

Prove that all the vertices of an equilateral triangle can not be integral points (an integral point is a point both of whose coordinates are integers).

Prove that all the vertices of an equilateral triangle can not be integral points (an integral point is a point both of whose coordinates are integers).

Find the area of a circle of radius r, by integration.

The number of integral points inside the triangle made by the line 3x+4y-12=0 with the coordinate axes which are equidistant from at least two sides is/are (an integral point is a point both of whose coordinates are integers.) (d) 4(c)3(a)1 (b) 2

For r gt 0, f(r ) is the ratio of perimeter to area of a circle of radius r. Then f(1) + f(2) is equal to

The number of integral point inside the triangle made by the line 3x + 4y - 12 =0 with the coordinate axes which are equidistant from at least two sides is/are : ( an integral point is a point both of whose coordinates are integers. )

The number of integral point inside the triangle made by the line 3x + 4y - 12 =0 with the coordinate axes which are equidistant from at least two sides is/are : ( an integral point is a point both of whose coordinates are integers. )

The number of integral points (integral point means both the coordinates should be integers )exactly in the interior of the triangle withvertice(0,0), (0,21) and (21,0) is