Which of the following statements are true and which 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 : Circle is a particular case of an ellipse
(iv) s : If x and y are integers such that x>y then −x<−y
(v) t : √11 is a rational number
(i) The given statement p is false as chord of a circle is the line segment joining any two distinct points on a circle.
(ii) The given statement q is false
If the chord is not the diameter of the circle then the centre will not bisect that chord.
In other words, the centre of a circle only bisects the diameter which is the chord of the circle.
(iii) The equation of an ellipse is
x2a2+y2b2=1
If we put a=b=1 then we get x2+y2=1 which is an equation of a circle.
Therefore circle is a particular case of an ellipse.
Thus statement r is true
(iv) x>y
⇒−x<−y (By a rule of inequality)
Thus the given statement s is true
(v) 11 is a prime number and we know that the square root of any prime number is an irrational number.
Therefore √11 is an irrational number.
Thus the given statement t is false