Exams › JEE Main › Maths

A natural number x is selected uniformly at random from the first 100 natural numbers. The probability that the inequality x + 100/x > 50 holds is

1. 1/20
2. 11/20
3. 1/3
4. 3/20

Correct answer: 11/20

Solution

The inequality can be rearranged and analyzed to find the values of x that satisfy it. By determining the range of x that meets the condition, we find that 11 out of the 20 possible values fulfill the inequality, leading to a probability of 11/20.

Related JEE Main Maths questions

• For which values of x does the inequality log base 1/2 of ((x² + 6x + 9) / (2(x + 1))) become less than −log base 2 of (x + 1)?
• Find the set of all real values of x that satisfy the inequality |9^x − 3^(x+1) − 15| < 2·9^x − 3^x.
• How many positive-integer triples (x,y,z) satisfy the system 3x+2y-z=4, 2x-y+2z=6, x+y+z<7?
• Given that −7 < x < 18 and 9 < y < 20, what is the interval of possible values of x + y?
• A person's intelligence quotient is defined by IQ = (MA/CA) × 100, where MA denotes mental age and CA denotes chronological age. For a set of 12 children, if 80 ≤ IQ ≤ 140, then the possible interval for their mental age is
• Determine the set of x-values that satisfy all of the following inequalities at the same time: −17 < 3x + 10 ≤ −2; −22 ≤ 5x + 13 ≤ 3; and −19 ≤ 2x − 9 ≤ −3.

⚔️ Practice JEE Main Maths free + battle 1v1 →