MHT CET · Maths · Mathematical Reasoning
Consider the statement " \(\mathrm{P}(n): n^2-n+37\) is prime." then, which one of the following is true?
- A \(\mathrm{P}(3)\) is false, but \(\mathrm{P}(5)\) is true.
- B \(P(5)\) is false, but \(P(3)\) is true.
- C Both \(\mathrm{P}(3)\) and \(\mathrm{P}(5)\) are true.
- D Both \(\mathrm{P}(3)\) and \(\mathrm{P}(5)\) are false.
Answer & Solution
Correct Answer
(B) \(P(5)\) is false, but \(P(3)\) is true.
Step-by-step Solution
Detailed explanation
"p \((n): n^2-n+37\) is prime"
Now, \(\mathrm{p}(3)=3^2-3+37=43\) (which is prime)
and \(p(5)=5^2-5+37=57\) (which is not prime)
Hence, \(\mathrm{p}(3)\) is true but \(\mathrm{p}(5)\) is false
In the question write ' \(n\) ' ' in place of ' \(n_2\) '
Now, \(\mathrm{p}(3)=3^2-3+37=43\) (which is prime)
and \(p(5)=5^2-5+37=57\) (which is not prime)
Hence, \(\mathrm{p}(3)\) is true but \(\mathrm{p}(5)\) is false
In the question write ' \(n\) ' ' in place of ' \(n_2\) '
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