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A set ‘P’ is formed from the set of first ‘N’ natural numbers by deleting all the perfect squares and all the perfect cubes. If the numbers are arranged in an ascending order then, what is the 476th number of the set ‘P’?
(2014)
  • a)
    500
  • b)
    501
  • c)
    502
  • d)
    503
Correct answer is option 'D'. Can you explain this answer?
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A set ‘P’ is formed from the set of first ‘N’ ...
Here, we take the 1st option, a delete all perfect squares and perfect cubes, then a total of 22 perfect square will be deleted (12, 22 ........ 222) and a total of 7 perfect cubes will be deleted (13 23,.... 73) and Two numbers are common in between them viz. 16 and 26 which are perfect squares as well as perfect cubes Thus, 500 is the (500 – 22 – 7 + 2) = 473 rd term.
So, 476th term = 500 + 3 = 503.
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A set ‘P’ is formed from the set of first ‘N’ ...
A set is a collection of distinct elements or objects, often denoted by curly braces {} and separated by commas. For example, the set of even numbers less than 10 can be written as {2, 4, 6, 8}. Sets can be finite or infinite and can contain any type of object. The elements of a set are not ordered, and each element can only appear once in a set. Sets are a fundamental concept in mathematics and are used in many areas, including set theory, algebra, and geometry.
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A set ‘P’ is formed from the set of first ‘N’ natural numbers by deleting all the perfect squares and all the perfect cubes. If the numbers are arranged in an ascending order then, what is the 476th number of the set ‘P’?(2014)a)500b)501c)502d)503Correct answer is option 'D'. Can you explain this answer?
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