The number of rational point(s) [a point (a, b) is called rational, if `aa n db` both are rational numbers] on the circumference of a circle having center `(pi,e)` is
(a)at most one (b) at least two (c)exactly two (d) infinite

If a/b and c/d be two rational numbers and if a = nc, b = nd,when n is a natural number , then what type of rational numbers are the numbers a/b and c/d and why ?

If A and B are two rational number and AB, (A+B) and (A-B) are rational numbers, then (A/B) is (where B ne 0)

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

(a) (i) By taking any two irrational numbers, prove that their sum is a rational number. (ii) By taking any two irrational numbers, prove that their difference is a rational number. (b) Insert in between 1/7 and 2/7 (i) a rational number : (ii) an irrational number.

By taking two examples of irrational numbers prove that (a) the sum of them is a rational number, (b) the product of them is a rational number.

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

The 10th term of (3-sqrt((17)/4+3sqrt(2)))^(20) is (a) a irrational number (b) a rational number (c) a positive integer (d) a negative integer

If (log)_a x=b for permissible values of a and x , then identify the statement(s) which can be correct. (a)If a and b are two irrational numbers, then x can be rational. (b)If a is rational and b is irrational, then x can be rational. (c)If a is irrational and b is rational, then x can be rational. (d)if aa n d b are rational, then x can be rational.

If tantheta=sqrt n , where n in N, >= 2 , then sec2theta is always (a) a rational number (b) an irrational number (c) a positive integer (d) a negative integer