Let `C` be any circle with centre `(0,sqrt(2))dot` Prove that at most two rational points can be there on `Cdot` (A rational point is a point both of whose coordinates are rational numbers)

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 sqrt(2) is not a rational number.

Let p,q be chosen one by one from the set {1, sqrt(2),sqrt(3), 2, e, pi} with replacement. Now a circle is drawn taking (p,q) as its centre. Then the probability that at the most two rational points exist on the circle is (rational points are those points whose both the coordinates are rational)

Find two rational numbers between 1/5a n d1/2dot

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. )

Write two rational numbers between sqrt(2) and sqrt( 3)

Statement 1: If in a triangle, orthocentre, circumcentre and centroid are rational points, then its vertices must also be rational points. Statement : 2 If the vertices of a triangle are rational points, then the centroid, circumcentre and orthocentre are also rational points.

Find two rational numbers between (-2)/9\ a n d5/9dot

The number of rational points on the line joining (sqrt(5), 3) and (3, sqrt(3)) is

The curve for which the slope of the tangent at any point is equal to the ration of the abcissa to the ordinate of the point is