A) \[\frac{1}{10}\]
B) \[\frac{11}{50}\]
C) \[\frac{11}{20}\]
D) None of these
Correct Answer: C
Solution :
[c] \[\left( x+\frac{100}{x} \right)>50\] \[{{\left( x-25 \right)}^{2}}>525\] \[\left( x-25 \right)<\sqrt{525}\text{ }or\left( x-25 \right)>\sqrt{525}\] \[x<(25-\sqrt{525})or\,x>(25+\sqrt{525})\] \[x<\left( 25-22.91 \right)or\text{ }x>\left( 25+22.91 \right)\] \[x<2.09\,or\,x>47.91\] \[\underset{(1,2)}{\mathop{\underset{\downarrow }{\mathop{x\le 2}}\,}}\,\] or \[\underset{\left( 48,49,50,\text{ }.....99,\text{ }100 \right)}{\mathop{\underset{\downarrow }{\mathop{x\ge 48}}\,}}\,\] Thus, the favorable number of case is \[\left( 2+53 \right)=55\] Hence, the required probability \[=\frac{55}{100}=\frac{11}{20}\]
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