InterviewSolution
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InterviewSolution
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Which of the following statements are true and whihc 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: circles is a particular case of an ellipse. (iv) s : if x and y are integeres such that xgty , then -xlarry. (v) t: sqrt(11) is a rational number. |
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Answer» Solution :(i) Given statement : each radius of a circle is a chord of the circle. `because` A chord MEETS the circle at two different POINTS but the radius meets the circle at one point only . `therefore` Any radius of the circle cannot be the chord of the circle . Therefore, given statement is false. (ii) Given statement : the centre of a circle BISECTS each chord of the circle. `because` only the diameter of a circle is a circle is a chord at which the centre of the circle lie. centre does not lie on the other chords. `therefore` centre does not bisect all chords. therefore, given statement is false. (iii) Given statement: circle is a particular case of an ellipse. Equation of ellipse `: (x^2)/(a^2)+(y^2)/(b^2)=1` If `a=b` then `(x^2)/(a^2)+(y^2)/(a^2)=1rArrx^2+y^2=a^2` which is the equation of a circle. `rArr` circle is a particular case of ellipse. (iv) Given statement : if x and y are INTEGERS such that `xgty` then `-xlarry`. from the law of inequations `xgtyrArr-xlarry` therefore , given statement is true. (V) Given statement : `sqrt(11)` is a rational number. every rational number can be expressed in the form `(P)/(q)` where p and q are integers and `q ne 0`. But `sqrt(11)` cannot be expressed in the form `(p)/(q)`. `therefore` Given statement is false. |
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