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A natural number is chosen at random from the first 100 naturalnumbers. The probability that `x+(100)/x > 50`is`1//10`b. `11//50`c. `11//20`d. none of theseA. `(1)/(10)`B. `(11)/(50)`C. `(11)/(20)`D. None |
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Answer» Correct Answer - C `( x + (100)/(x)) gt 50` `(x - 25)^(2) gt 525` `(x - 25) lt sqrt(525)` or `(x- 25) gt sqrt(525)` `x lt (25 - sqrt(525)) ` or `x gt ( 25 + sqrt(525))` `x lt (25 - 22.91)` or `x gt (25 + 22.91)` `x lt 2.09` or `x gt 47.91` `{:(x le 2 , or , x ge 48), ( darr , , darr), ((1","2) ,, (48","49"," 50"," .....99","100)):}` Thus , the favourable number of case is (2 + 53) = 55 Hence , the required probability = `(55)/(100) = (11)/(20)` |
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