  Question

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 then (v) t :  is a rational number

Medium

Solution Verified by Toppr

(i) The given statement is false as chord of a circle is the line segment joining  any two distinct points on a circle.  (ii) The given statement 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 If we put then we get  which is an equation of a circle. Therefore circle is a particular case of an ellipse. Thus statement is true (iv) (By a rule of inequality) Thus the given statement is true(v) is a prime number and we know that the square root of any prime number is an irrational number. Therefore  is an irrational number. Thus the given statement is false 0 0