AP EAMCET · Maths · Limits
If \(\lim _{x \rightarrow \infty}\left(1+\frac{p}{x}\right)^{q x}=e^9\) where \(p, q \in \mathbf{N}\) then \(p+q=\)
- A 6
- B 9
- C 81
- D 18
Answer & Solution
Correct Answer
(A) 6
Step-by-step Solution
Detailed explanation
Given, \(\lim _{x \rightarrow \infty}\left(1+\frac{p}{x}\right)^{q x}=e^9\), Let \(\frac{1}{x}=y \Rightarrow\) When \(x \rightarrow \infty \Rightarrow y \rightarrow 0\) \(\therefore \lim _{y \rightarrow 0}(1+p y)^{q / y}=e^9\)…
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
- Let \(\bar{a}, \bar{b}\) and \(\bar{c}\) be non-coplanar vectors. If \(\mathrm{P}, \mathrm{Q}, \mathrm{R}\) and \(\mathrm{S}\) are four points with position vectors \(-\bar{a}+4 \bar{b}-3 \bar{c}, 3 \bar{a}+2 \bar{b}-5 \bar{c},-3 \bar{a}+8 \bar{b}-5 \bar{c}\) and \(-3 \bar{a}+2 \bar{b}+\bar{c}\) respectively then the ordered pair \((x, y)\) of real numbers such that \(\overline{P Q}=x \cdot \overline{P R}+y \cdot \overline{P S}\) isAP EAMCET 2017 Medium
- For how many natural numbers ' \(n\) ' such that \(1 \leq n \leq 2021\) is \(\left(\frac{1+i}{1-i}\right)^n=1\) ?AP EAMCET 2020 Medium
- AP EAMCET 2020 Easy
- \(\vec{a}, \vec{b}, \vec{c}\) are non-coplanar vectors. If \(\alpha \vec{d}=\vec{a}+\vec{b}+\vec{c}\), \(\beta \vec{a}=\vec{b}+\vec{c}+\vec{d}\), then \(|\vec{a}+\vec{b}+\vec{c}+\vec{d}|=\)AP EAMCET 2024 Easy
- If the circles \(x^2+y^2-4 x+2 f y+1=0\) and \(x^2+y^2+\) \(2 \mathrm{gx}-4 \mathrm{y}-1=0\) cut orthogonally, then \(\mathrm{r}_1^2+\mathrm{r}_2^2-8=\)AP EAMCET 2023 Easy
- In \(\triangle \mathrm{ABC}\), if \(\sin ^2 \mathrm{~B}=\sin \mathrm{C}\) and \(3 \cos ^2 \mathrm{~B}=2 \cos ^2 \mathrm{C}\), then \(\triangle \mathrm{ABC}\) isAP EAMCET 2023 Hard
More PYQs from AP EAMCET
- The avoid bends sickness, the tanks used by scuba divers are filled with air and díluted with ......AP EAMCET 2020 Easy
- If the chord of contact of the point \(\mathrm{P}(\mathrm{h}, \mathrm{k})\) with respect to the circle \(x^2+y^2-4 x-4 y+8=0\) meets the circle in two distinct points and it also makes an angle \(45^{\circ}\) with the positive \(\mathrm{X}\)-axis in the positive direction, then \((\mathrm{h}, \mathrm{k})\) cannot beAP EAMCET 2023 Easy
- Identify the non-narcotic analgesic from the followingAP EAMCET 2010 Easy
- In how many ways can balls be placed in tins if any number of balls can be placed in any tin?AP EAMCET 2021 Easy
- Drift speed \((v)\) varies with the intensity of electric field \((\mathrm{E})\) as per the relationAP EAMCET 2024 Medium
- \(\bar{a}, \bar{b}\) and \(\bar{c}\) are the position vectors of three non-collinear points on a plane. If \(\alpha=\left[\begin{array}{lll}\overline{\mathrm{a}} & \overline{\mathrm{b}} & \overline{\mathrm{c}}\end{array}\right]\) and \(\overline{\mathrm{r}}=\overline{\mathrm{a}} \times \overline{\mathrm{b}}-\overline{\mathrm{c}} \times \overline{\mathrm{b}}-\overline{\mathrm{a}} \times \overline{\mathrm{c}}\), then \(\frac{|\alpha|}{|\overline{\mathrm{r}}|}\) representsAP EAMCET 2025 Hard