Page No 343:
Question 5:
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:
is a rational number.
(i) The given statement p is false.
According to the definition of chord, it should intersect the circle at two distinct points.
(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,
If we put a = b = 1, then we obtain
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, is an irrational number.
Thus, the given statement t is false.
