A natural number is chosen at random from the first 100 natural numbers. The probability that `x+(100)/x > 50` is `1//10` b. `11//50` c. `11//20` d. none of these

Options

A. `(1)/(10)`
B. `(11)/(50)`
C. `(11)/(20)`
D. None

Answer

C

Explanation

`( 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)`