Join the Most Relevant JEE Main 2025 Test Series & get 99+ percentile! Join Now
Search any question & find its solution
Question: Answered & Verified by Expert
If $\lim _{x \rightarrow 2} \frac{x^n-2^n}{x-2}=80$, where $n$ is a positive integer, then $n=$
MathematicsLimitsJEE Main
Options:
  • A $3$
  • B $5$
  • C $2$
  • D None of these
Solution:
1654 Upvotes Verified Answer
The correct answer is: $5$
$\lim _{x \rightarrow 2} \frac{x^n-2^n}{x-2}=n \cdot 2^{n-1} \Rightarrow n \cdot 2^{n-1}=80 \Rightarrow n=5$ (using L-Hospital's rule)

Looking for more such questions to practice?

Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.