Which of the following statements are true and whihc are false? In each case give a valid reason for saying so.
(i) p: each radius of a circle is a chord of the circle.
(ii) q: the centre of a circle bisects each chord of the circle.
(iii) r: circles is a particular case of an ellipse.
(iv) s : if x and y are integeres such that `xgty` , then `-xlarry`.
(v) t: `sqrt(11)` is a rational number.

Explanation

(i) Given statement : each radius of a circle is a chord of the circle.
`because` A chord meets the circle at two different points but the radius meets the circle at one point only .
`therefore` Any radius of the circle cannot be the chord of the circle .
Therefore, given statement is false.
(ii) Given statement : the centre of a circle bisects each chord of the circle.
`because` only the diameter of a circle is a circle is a chord at which the centre of the circle lie. centre does not lie on the other chords.
`therefore` centre does not bisect all chords.
therefore, given statement is false.
(iii) Given statement: circle is a particular case of an ellipse.
Equation of ellipse `: (x^2)/(a^2)+(y^2)/(b^2)=1`
If `a=b` then
`(x^2)/(a^2)+(y^2)/(a^2)=1rArrx^2+y^2=a^2`
which is the equation of a circle.
`rArr` circle is a particular case of ellipse.
(iv) Given statement : if x and y are integers such that `xgty` then `-xlarry`.
from the law of inequations `xgtyrArr-xlarry`
therefore , given statement is true.
(v) Given statement : `sqrt(11)` is a rational number. every rational number can be expressed in the form `(P)/(q)` where p and q are integers and `q ne 0`.
But `sqrt(11)` cannot be expressed in the form `(p)/(q)`.
`therefore` Given statement is false.