Consider the statement: " P(n): n ^ 2 - n + 41 is prime". Then which one of the following is true?

Correct answer: C. Both P(3) and P(5) are true Given P(n) = n ^ 2 - n + 41 P(3) = 9 - 3 + 41 = 47 P(5) = 25 - 5 + 41 = 61 Hence P(3) and P(5) both are prime. Hence, both are true.

JEE Main 201910 JanuaryMorning Shift

Exam: JEE Main
Year: 2019
Date: 10 January
Shift: Morning Shift
Subject: Mathematics
Chapter: Mathematical Reasoning

JEE Main 2019 · 10 January · Morning Shift · Mathematics · Mathematical Reasoning

Consider the statement: " P(n): n ^ 2 - n + 41 is prime". Then...

Consider the statement: "

P\left(n\right): {n}^{2} - n + 41

is prime". Then which one of the following is true?

Options

A $P\left(3\right)$ is false but $P\left(5\right)$ is true
BBoth $P\left(3\right)$ and $P\left(5\right)$ are false
CBoth $P\left(3\right)$ and $P\left(5\right)$ are true
D $P\left(5\right)$ is false but $P\left(3\right)$ is true

Correct answer

C. Both $P\left(3\right)$ and $P\left(5\right)$ are true

Step-by-step solution

Given $P\left(n\right) = {n}^{2} - n + 41$

$P\left(3\right) = 9 - 3 + 41 = 47$

$P\left(5\right) = 25 - 5 + 41 = 61$

Hence $P\left(3\right)$ and $P\left(5\right)$ both are prime.

Hence, both are true.

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