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: √11$$ is a rational number.

<p>This is a &nbsp;Mathematical Reasoning Solutions Type Questions as classified in NCERT Exemplar</p><p><strong> (i) </strong>False: As per the definition of a chord, it should intersect the circle at two distinct points.</p><p><strong> (ii)</strong> False: The centre of a circle only bisects the diameter, which is the chord of the circle.</p><p><strong> (iii)</strong> True: The equation of an ellipse is&nbsp;<span title="Click to copy mathml"><math><mrow><mfrac><mrow><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow><mrow><msup><mrow><mi>a</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></mfrac><mo>+</mo><mfrac><mrow><msup><mrow><mi>y</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow><mrow><msup><mrow><mi>b</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></mfrac><mo>=</mo><mn>1</mn></mrow></math></span></p><p>If we put a = b = 1, then</p><p><em>x</em>² + <em>y</em>² = 1, which is an equation of a circle</p><p><strong> (iv) </strong>True: Given x &gt; y. Multiplying by –1, –x &lt; – y.</p><p><strong> (v) </strong>False: Since | | is a prime number, therefore √11<math><mrow></mrow></math>&nbsp;is irrational.</p>

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