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
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Text solutionVerified
(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
(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
Therefore is an irrational number.
Thus the given statement is false
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Question Text | 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 |
Answer Type | Text solution:1 |
Upvotes | 150 |