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NDA 2 2024 Maths, question 109

Topic: Probability

Q109

A natural number xx is chosen at random from the first 100100 natural numbers. What is the probability that x2+x>50x^{2}+x>50?

  1. (a) 93/10093/100
  2. (b) 47/5047/50Correct answer
  3. (c) 24/2524/25
  4. (d) 23/2523/25

Solution.

Answer: (b) 47/5047/50

  1. For positive integers, x²+x is increasing.
  2. At x=6 it is 42≤50, and at x=7 it is 56>50.
  3. Thus favourable values are 7 through 100, numbering 94.
  4. The probability is 94/100=47/50.