Question

(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

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(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

$a_{2}x_{2} +b_{2}y_{2} =1$

If we put $a=b=1$ then we get $x_{2}+y_{2}=1$ 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

Therefore $11 $ is an irrational number.

Thus the given statement $t$ is false

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