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NDA 2018 Maths · Mathematics · Statistics · medium

A number is chosen at random from the integers 1 to 20. The probability that it is a perfect square or a perfect cube is

Single correct option

A number is chosen at random from the integers 1 to 20. The probability that it is a perfect square or a perfect cube is
  1. A. 310\frac{3}{10}
  2. B. 15\frac15
  3. C. 14\frac14
  4. D. 320\frac{3}{20}
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Answer: (C) 14\frac14

Squares: 1, 4, 9, 16; cubes: 1, 8. The number 1 is common, so the union is {1,4,8,9,16}\{1,4,8,9,16\} with 5 elements and the probability is 520=14\frac5{20}=\frac14. Counting 1 twice gives 620=310\frac{6}{20}=\frac3{10}.
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Original question written in the NDA 2018 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake