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.

Which of the following statements are true and whihc are false? In eac

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

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