GATE Papers >> EEE >> 2019 >> Question No 9

Question No. 9 EEE | GATE 2019

Given two sets X = {1, 2, 3} and Y = {2, 3, 4}, we construct a set Z of all possible fractions where the numerators belong to set X and the denominators belong to set Y. The product of elements having minimum and maximum values in the set Z is ____.


Answer : (D) 3/8


Solution of Question No 9 of GATE 2019 EEE Paper

Given two sets

X = {1,2,3} & Y = {2,3,4}

$ \therefore\mathrm Z=\left\{\frac12,\frac13,\frac14,\frac22,\frac23,\frac24,\frac32,\frac33,\frac34\right\}\rightarrow $ set of all possible fraction;

where the numberators belongs to set X and the denominators belongs to set Y.

$ \Rightarrow\mathrm Z=\left\{\frac1{\begin{array}{c}4\\\downarrow\\\begin{array}{c}0.25\\\mathrm{Minimum}\end{array}\end{array}}\;\;\;\;\;,\frac13,\frac12,\frac24,\frac23,\frac34,\frac22,\frac33,\;\;\;\;\;\frac3{\begin{array}{c}2\\\downarrow\\1.5\\\mathrm{Maximum}\end{array}}\right\} $

$ \therefore $        The required product $ =\frac14\times\frac32=\frac38 $ 

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