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Let S be a set of fourteen natural numbers. The possible number of pairs (a, b), where a, b ∈ S and a ≠ b such that ab leaves remainder 1 when divided by 15, is
  • a)
    3
  • b)
    5
  • c)
    6
  • d)
    None of the above
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
Let S be a set of fourteen natural numbers. The possible number of pai...
Maximum product of the numbers = 13 × 14 = 182
Number of terms such which leaves a remainder 1 when divided by 15 from 2 to 182
⇒ 16, 31, 46, 61, 76, 91, 106, 121, 136, 151, 166, 181,
Now,
16 = 2 × 8 can be expressed as product of two natural numbers less than 15
31 cannot be expressed as product of two natural numbers less than 15
46 cannot be expressed as product of two natural numbers less than 15
61 cannot be expressed as product of two natural numbers less than 15
76 cannot be expressed as product of two natural numbers less than 15
91 = 7 × 13 can be expressed as product of two natural numbers less than 15
106 cannot be expressed as product of two natural numbers less than 15
121 cannot be expressed as product of two natural numbers less than 15
136 cannot be expressed as product of two natural numbers less than 15
151 cannot be expressed as product of two natural numbers less than 15
166 cannot be expressed as product of two natural numbers less than 15
181 cannot be expressed as product of two natural numbers less than 15
∴ There are only two such sets
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Let S be a set of fourteen natural numbers. The possible number of pairs (a, b), where a, b ∈ S and a ≠ b such that ab leaves remainder 1 when divided by 15, isa)3b)5c)6d)None of the aboveCorrect answer is option 'D'. Can you explain this answer?
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Let S be a set of fourteen natural numbers. The possible number of pairs (a, b), where a, b ∈ S and a ≠ b such that ab leaves remainder 1 when divided by 15, isa)3b)5c)6d)None of the aboveCorrect answer is option 'D'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about Let S be a set of fourteen natural numbers. The possible number of pairs (a, b), where a, b ∈ S and a ≠ b such that ab leaves remainder 1 when divided by 15, isa)3b)5c)6d)None of the aboveCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let S be a set of fourteen natural numbers. The possible number of pairs (a, b), where a, b ∈ S and a ≠ b such that ab leaves remainder 1 when divided by 15, isa)3b)5c)6d)None of the aboveCorrect answer is option 'D'. Can you explain this answer?.
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