Question

Assertion :(A): $P\left(n\right)=n^2+n+41$ is a prime $\forall n\in N$ Reason: (R): If a number is prime then it contains only two factors; $1$ and number itself.

• A. Both (A) & (R) are individually true & (R) is correct explanation of (A).
• B. Both (A) & (R) are individually true but (R) is not the correct (proper) explanation of (A).
• C. (A)is true but (R} is false.
• D. (A)is false but (R} is true.

Answer 1

The correct option is D (A)is false but (R} is true.

$P\left(n\right)=n^2+n+41$

Put $n=41$ to obtain $P\left(41\right)={41}^2+41+41=1763$

Which is not prime

The assertion is false but the reason is obvious.
Ans: D