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 center 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.

Solution:

(i) The given statement p is false as a chord of a circle should intersect the circle at two distinct points whereas a radius intersects the circle only at one point.

(ii) The given statement q is false as a chord does not necessarily pass through the center (diameters are the only chords that pass through the centre of the circle).

(iii) The equation of an ellipse is, x²/a² + y²/b² = 1.

When a = b, the equation of ellipse becomes

x² + y² = a², which is an equation of a circle.

Therefore, a circle is a particular case of an ellipse.

Thus, statement r is true.

(iv) x > y

A rule of inequality says, the sign of inequality changes when it is multiplied on both sides by a negative number. i.e., when x > y then -x < -y.

Thus, the given statement s is true.

(v) 11 is a prime number and we know that the square root of any prime number is irrational.

Therefore, √11 is an irrational number.

Thus, the given statement t is false

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NCERT Solutions Class 11 Maths Chapter 14 Exercise 14.5 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 center 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

Summary:

(i) The given statement p is false. (ii) The given statement q is false. (iii) The given statement r is true. (iv) The given statement s is true. (v) The given statement t is false