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.
Class X1 - Maths -Mathematical Reasoning Page 343
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(i) FALSE : The end points of radius do not lies on the circle , therefore , radius of a circle isn't chord of the circle.
(ii) FALSE : only diameter are bisected at the centre of circle . other chord don't pass through the centre of circle .so, centre can't be bisect them .
(iii) TRUE : equation of ellipse is x²/a² + y²/b² = 1
when a = b = r then, equation of ellipse = equation of circle , e.g., x² + y² = r²
(iv) TRUE : Let x = 4 and y = 3
here x > y but - x< -y so, it's true statement .
(v) FALSE : 11 is a prime number and we know, square root of all prime number is always irrational number . so , √11 is an irrational number .
(ii) FALSE : only diameter are bisected at the centre of circle . other chord don't pass through the centre of circle .so, centre can't be bisect them .
(iii) TRUE : equation of ellipse is x²/a² + y²/b² = 1
when a = b = r then, equation of ellipse = equation of circle , e.g., x² + y² = r²
(iv) TRUE : Let x = 4 and y = 3
here x > y but - x< -y so, it's true statement .
(v) FALSE : 11 is a prime number and we know, square root of all prime number is always irrational number . so , √11 is an irrational number .
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