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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 x > y, then –x < –y.
(v) t:  is a rational number.



Answer -

(i) The given statement p isfalse.

According to the definition ofchord, it should intersect the circle at two distinct points.

(ii) The given statement q isfalse.

If the chord is not the diameterof the circle, then the centre will not bisect that chord.

In other words, the centre of acircle only bisects the diameter, which is the chord of the circle.

(iii) The equation of an ellipseis,

If we put a = b =1, then we obtain

x2 + y2 =1, which is an equation of a circle

Therefore, circle is a particularcase of an ellipse.

Thus, statement r istrue.

(iv) y

x < –y (By a rule of inequality)

Thus, the given statement s istrue.

(v) 11 is a prime number and weknow that the square root of any prime number is an irrational number.Therefore,  is an irrational number.

Thus, the given statement t isfalse.

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