Consider the statement: $P(n): n^2 - n + 41$ is prime. Then which one of the following is true?
- ABoth $P(3)$ and $P(5)$ are true
- B$P(3)$ is false but $P(5)$ is true
- CBoth $P(3)$ and $P(5)$ are false
- D$P(5)$ is false but $P(3)$ is true
Explore More
Similar Questions
Prove the following by using the principle of mathematical induction for all $n \in N:$
$2^{3n}-1$ is divisible by $7$.
$2^{3n}-1$ is divisible by $7$.
Difficult
View SolutionLet $P(n) : 3^n < n!$ for $n \in N$ be true for $n \geq \lambda$. Find the smallest value of $\lambda$.
If $n$ is a positive integer,then $2 \cdot 4^{2n+1} + 3^{3n+1}$ is divisible by
Prove that the following inequality holds for all $n \in N$ by using the principle of mathematical induction:
$(2n + 7) < (n + 3)^{2}$
$(2n + 7) < (n + 3)^{2}$
Difficult
View SolutionFor all $n \ge 1,$ prove that $1^{2}+2^{2}+3^{2}+4^{2}+\ldots+n^{2}=\frac{n(n+1)(2 n+1)}{6}$
Medium
View SolutionVedclass Products
For Students
Vedclass Test Series
Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.
Start Free TrialFor Teachers
Exam Paper Generator
Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.
Try FreeFor Institutes
Online Exam Module
Live online exams with unlimited students, 360° analytics & white-label branding.
See Demo