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

Asked by Pragya Singh | 11 months ago |  73

1 Answer

Solution :-

(i) Right answer is False.

Explanation:-

According to the definition of chord, it should intersect the circle at two distinct points.

(ii) Right answer is False.

Explanation:-

If the chord is not the diameter of the circle, then the centre will not bisect that chord.

(iii) Right answer is True.

Explanation:-

The equation of an ellipse is,

NCERT Solutions Mathematics Class 11 Chapter 14 - 3

If we put a = b = 1, then we get

x2 + y2 = 1, which is an equation of a circle

Hence, circle is a particular case of an ellipse.

Therefore, statement r is true

(iv) Right answer is True.

Explanation:-

x > y

By a rule of inequality

-x < – y

Hence, the given statement s is true

(v) Right answer is False.

Explanation:-

11 is a prime number and we know that the square root of any prime number is an irrational number.
Therefore, \( \sqrt{11}\) is an irrational number. Thus, the given statement t is false.

Answered by Abhisek | 11 months ago

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