Join WhatsApp Icon JEE WhatsApp Group
Question 25

For each positive integer $$n$$ let $$f(n)=n^4-3n^2+9$$. Then the sum of all $$f(n)$$ which are prime is


Correct Answer: 20

Solution

Share

Factor the expression as $$f(n)=(n^2+3n+3)(n^2-3n+3)$$. For the product to be prime, the second factor must equal $$1$$, which occurs for $$n=1$$ and $$n=2$$. These give $$f(1)=7$$ and $$f(2)=13$$, so the required sum is $$20$$.

Get AI Help

Other Cracku’s Useful Resources:

JEE Questions JEE Question Bank JEE Mains Previous Papers JEE Advanced Previous Papers JEE Study Material PDF JEE Mains Mock Test JEE Advanced Mock Test JEE Daily Target

Free JEE Questions

JEE Physics Questions JEE Maths Questions JEE Chemistry Questions
banner

50,000+ JEE Students Trusted Our Score Calculator

Predict your JEE Main percentile, rank & performance in seconds

Check Your Score Now
Ask AI