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)

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 irrational numbers such that their sum is a rational number. Can you find two irrational numbers whose product is a rational number.

Construct a tangent to a circle with centre P and radius 3.2 cm at any point M on it.

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

Find the number of rational points on the ellipse (x^2)/9+(y^2)/4=1.

If a, b, c are in AP then ax + by + c = 0 will always pass through a fixed point whose coordinates are

Prove that the maximum number of points with rational coordinates on a circle whose center is (sqrt(3),0) is two.

Le n be the number of points having rational coordinates equidistant from the point (0,sqrt3) , the