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 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 am ellipse.

(iv) s If x and y are integers such that x > y, then -x < -y .

(v) $t : \sqrt{11}$ is a rational number.

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Solution

(i) False, Because, no radius of a circle is its chord.

(ii) False, Because , a chord does not have to pass through the centre.

(iii) True. Because a circle is an ellipse that has equal axes.

(iv) True. Because, for any two integers, if x -y is positive then - (x - y) is negative.

(v) False. because square roots of prime numbers are irrational numbers.

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\sqrt{11}

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.

x > y

- x < - y

\sqrt{11}

Which of the following statements are true and which are false? In each case give a valid reason for your answer.

(i) p: $\sqrt{11}$ is an irrational number.

(ii) q: Circle is a particular case of an ellipse.

(iii) r: Each radius of a circle is a chord of the circle.

(iv) s: The centre of a circle bisects each chord of the circle.

(v) t: If a nd b are integers such that $a < b$ , then $- a < - b .$

(vi) u: The quadratic equation $x^{2} + x + 1 = 0$ has no real roots.

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