AP EAMCET · Maths · Limits
If \(\lim _{n \rightarrow \infty} \frac{1-(10)^n}{1+(10)^{n+1}}=\frac{-\alpha}{10}\), then \(\alpha\) is equal to
- A 0
- B -1
- C 1
- D 2
Answer & Solution
Correct Answer
(C) 1
Step-by-step Solution
Detailed explanation
\begin{aligned} & \lim _{n \rightarrow \infty} \frac{1-10^n}{1+10^{n+1}}=-\frac{\alpha}{10} \\ \Rightarrow & \lim _{n \rightarrow \infty} \frac{1-10^n}{1+10 \cdot 10^n}=-\frac{\alpha}{10} \\ & \lim _{n \rightarrow \infty}…
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
- The transformed equation of \(3 x^2+3 y^2+2 x y=2\), when the coordinate axes are rotated through an angle of \(45^{\circ}\), isAP EAMCET 2008 Medium
- The minimum volume of the parallalopiped formed by the vectors \(\bar{i}+a \bar{j}+\bar{k}, \bar{j}+a \bar{k}\) and \(a \bar{i}+\bar{k}\) isAP EAMCET 2017 Easy
- Let \(\mathrm{S}\) be the circumcircle of the triangle formed by the line \(x-2 y-4=0\) with the coordinate axes. If \(\mathrm{P}(-2,-4)\) is a point in the plane of the circle \(S\) and \(Q\) is a point on \(S\) such that the distance between \(\mathrm{P}\) and \(\mathrm{Q}\) is the least, then \(\mathrm{PQ}=\)AP EAMCET 2023 Hard
- In a manufacturing company, three machines A, B and C respectively produce \(20 \%, 30 \%\) and \(50 \%\) of the total product. The defective products from A, B and C are respectively 5\%, \(3 \%\) and \(2 \%\). If an article produced by the company is selected at random and is found to be defective, then the probability that it is produced by machine \(B\) isAP EAMCET 2018 Easy
- The difference between the focal distances of any point on the hyperbola \(\frac{x^2}{a^2}-\frac{y^2}{b^2}=1\) is 6 . If \((\sqrt{13}, k)\) is an end point of a latus rectum of this hyperbola, then \(\mathrm{k}=\)AP EAMCET 2023 Hard
- \(x=\cos ^{-1}\left(\frac{1}{\sqrt{1+t^2}}\right), y=\sin ^{-1}\left(\frac{t}{\sqrt{1+t^2}}\right) \Rightarrow \frac{d y}{d x}\)
is equal toAP EAMCET 2009 Easy
More PYQs from AP EAMCET
- If the lines and lie along diameters of a circle of area then the equation of the circle isAP EAMCET 2019 Easy
- Real part of is_______AP EAMCET 2021 Medium
- If \(y=\tan ^{-1}\left(\frac{\sqrt{1+a^2 x^2}-1}{a x}\right)\), then \(\left(1+a^2 x^2\right){y^{\prime}}^{\prime}+2 a^2 x y^{\prime}\) is equal toAP EAMCET 2014 Hard
- A bus is moving with a velocity of \(5 \mathrm{~ms}^{-1}\) towards a huge wall. The driver sounds horn of frequency \(165 \mathrm{~Hz}\). If the speed of sound in air is \(335 \mathrm{~ms}^{-1}\), the number of beats heard per second by the passengers in the bus will beAP EAMCET 2017 Medium
- Borax dissolves in water and forms a product of boron (X). Identify the compound \(\mathrm{X}\).AP EAMCET 2022 Easy
- In Young's double slit interference experiment the wavelength of light used is \(6000 Ã…\). If the path difference between waves reaching a point \(P\) on the screen is 1.5 microns, then at that point \(P\).AP EAMCET 2002 Easy