AP EAMCET · Maths · Limits
If \(\lim _{x \rightarrow 3}\left(\frac{x^n-3^n}{x-3}\right)=108\) and \(n \in \mathbf{N}\), then the value of ' \(n\) ' is
- A 3
- B 6
- C 5
- D 4
Answer & Solution
Correct Answer
(D) 4
Step-by-step Solution
Detailed explanation
\(\lim _{x \rightarrow 3} \frac{x^n-3^n}{x-3}=108\) LHS is in \(\div\) from, so apply L-Hospital rule…
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- If \(y=\log _y x\), then \(\frac{d y}{d x}\) is equal toAP EAMCET 2021 Easy
- \(\operatorname{cosec} 48^{\circ}+\operatorname{cosec} 96^{\circ}+\operatorname{cosec} 192^{\circ}\)
\(+\operatorname{cosec} 384^{\circ}=\)AP EAMCET 2019 Medium - Box \(A\) contains 2 black and 3 red balls, while Box \(B\) contains 3 black and 4 red balls. Out of these two boxes one is selected at random; and the probability of choosing Box \(A\) is double that of Box \(B\). If a red ball is drawn from the selected box, then the probability that it has come from Box \(B\), isAP EAMCET 2005 Medium
- The product of the perpendicular distances drawn from the origin to the pair of straight lines \(6 x^2-5 x y-6 y^2+x+5 y-1=0\) isAP EAMCET 2017 Hard
- If \(\int_0^{10} f(x) d x=5\), then \(\sum_{k=1}^{10} \int_0^1 f(k-1+x) d x=\)AP EAMCET 2017 Medium
- If the lines and are coplanar, thenAP EAMCET 2021 Medium
More PYQs from AP EAMCET
- Let \(\overrightarrow{\mathbf{a}}, \overrightarrow{\mathbf{b}}, \overrightarrow{\mathbf{c}}\) be the position vectors of the vertices \(A, B, C\) respectively of \(\triangle A B C\). The vector area of \(\triangle A B C\) is :AP EAMCET 2003 Hard
- To measured a magnetic field between the magnetic poles of a loud speaker, a small coil having 30 turns and \(2.5 \mathrm{~cm}^2\) area is placed perpendicular to the field and removed immediately. If the total charge flown through the coil is \(75 \times 10^{-3} \mathrm{C}\) and the total resistance of wire and galvanometer is \(0.3 \Omega\), then the magnitude of the magnetic field isAP EAMCET 2019 Hard
- \(\int \frac{x+1}{(x-2) \sqrt{1-x}} d x=\)AP EAMCET 2025 Medium
- If \(|x| < 1\) and \(y=x-\frac{x^2}{2}+\frac{x^3}{3}-\frac{x^4}{4}+\ldots\), then \(x\) is equal to :AP EAMCET 2006 Medium
- The number of ordered pairs \((\mathrm{x}, \mathrm{y})\) for which \(\mathrm{A}=\) \(\left(\begin{array}{lll}1 & 2 & 1 \\ 2 & 2 & x \\ y & 1 & 2\end{array}\right)\) is a singular and symmetric matrix isAP EAMCET 2023 Medium
- Identify the reaction for which \(\Delta H \neq \Delta E\) :AP EAMCET 2006 Easy