Which of the following statements are true and which are false? In each case give a vaild reason or your answer.
(i) `p: sqrt(11)` is an irrational number.
(ii) q: Circle is a particular case of an ellipse.
(iii) r: Each radius of a circle is a chord of the circle.
(iv) s: The centre of a circle bisects each chord of the circle.
(v) t: If a and bare integers such that `alt b," then "-agt -b.`
(vi) u: The quadratic equation `x^(2) + x + 1 = 0` has no real roots.

Explanation

(i) True, as 11 being prime `sqrt(11)` is irrational.
(ii) True. The equation of an ellipse is `(x^(2))/(a^(2))+(y^(2))/(b^(2))=1.`
Putting b = a, it becomes `x^(2) + y^(2) = a^(2),` which is the equation of a circle.
(iii) False, since the radius of a circle is not a chord.
(iv) False, since there are chords which do not pass through the centre
(v) True, since `alt b rArr -agt -b` is true.
(vi) True. Since `D = (1^(2) -4xx 1 xx 1) - 3 lt 0.`