InterviewSolution
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InterviewSolution
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Let S be the set of all points `((a)/(b),(c)/(d))` on the circle with radius 1 centred at (0,0) where a and b are relatively prime integers, c and d are relatively prime integers (that is HCF (a, b) = HCF (c,d) = 1), and the integers b and d are even. Then the set SA. is emptyB. has four elementsC. has eight elementsD. is infinite |
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Answer» Correct Answer - A `"circle is "x^(2)+y^(2)=1` `y=pmsqrt(1-(a^(2))/(b^(2)))" "(becausex=(a)/(b))` `y=pm(1)/(b)sqrt((b^(2))-a^(2))` As y is retional so `underset("even")underset(darr)(b^(2))-underset("odd")underset(darr)(a^(2))=underset("odd")underset(darr)(p^(2))` `b^(2)=a^(2)+p^(2)` `=(2k+1)^(2)+(2lamda+1)^(2)` `=4k^(2)+4k+1+4lamda^(2)+4lamda+1` `b^(2)=4(k^(2)+lamda^(2)+k+lamda)+2 " impossilbe"` `"as L.H.S. is multiple of 4 but R.H.S is not multiple of 4 "` |
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