AP EAMCET · Maths · Basic of Mathematics
If \(n\) is a positive integer, then \(2 \cdot 4^{2 n+1}+3^{3 n+1}\) is divisible by
- A \(2\)
- B \(9\)
- C \(11\)
- D \(27\)
Answer & Solution
Correct Answer
(C) \(11\)
Step-by-step Solution
Detailed explanation
Given expression, \(p(n)=2 \cdot 4^{2 n+1}+3^{3 n+1}\) Let \(n=1\) \(p(1)=2 \cdot 4^{2+1}+3^{3+1}=209\) which is divisible by 11 . Let \(p(k)\) is also divisible by 11 . \(p(k)=2 \cdot 4^{2 k+1}+3^{3 k+1}\) is divisibly by 11 ...(i) Now we will prove that \(p(k+1)\) is true.…
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 derivate of \(y=\tan ^{-1}\left(\frac{\sqrt{1+x^2}-1}{x}\right)\) is equal toAP EAMCET 2020 Easy
- \(\int \frac{2 \tan (x)}{1+2 \tan ^2(x)} d x=\)AP EAMCET 2020 Medium
- \(\int \frac{e^{\sin x}(\sin 2 x-8 \cos x)}{2(\sin x-3)^2} d x=\)AP EAMCET 2025 Medium
- \(\int \frac{e^{\tan ^{-1} x}}{1+x^2}\left[\left(\sec ^{-1} \sqrt{1+x^2}\right)^2+\cos ^{-1}\left(\frac{1-x^2}{1+x^2}\right)\right] d x=\)AP EAMCET 2022 Medium
- All the letters of the word LETTER are arranged in all possible ways and the words (with or without meaning) thus formed are arranged in dictionary order. Then the rank of the word TETLER isAP EAMCET 2025 Medium
- If are position vectors of respectively and if are mid points of sides and , then is equal toAP EAMCET 2021 Easy
More PYQs from AP EAMCET
- The general solution of the differential equation \(\log \left(\frac{d y}{a x}\right)=a x+b y\) isAP EAMCET 2020 Medium
- At a given instant of time two particles are having the position vectors \(4 \hat{\mathbf{i}}+4 \hat{\mathbf{j}}+57 \hat{\mathbf{k}}\) metres and \(2 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}+5 \hat{\mathbf{k}}\) respectively. If the velocity of the first particle be \(0.4 \hat{\mathbf{i}} \mathrm{ms}^{-1}\), the velocity of second particle in metre per second if they collide after \(10 \mathrm{sec}\) isAP EAMCET 2004 Medium
- If \(A=\left[\begin{array}{ccc}1 & 2 & 3 \\ 1 & 1 & 1 \\ 1 & -1 & 1\end{array}\right], B=\left[\begin{array}{lll}1 & 1 & 0 \\ 0 & 1 & 3 \\ 3 & 0 & 4\end{array}\right]\), \(C=\left[\begin{array}{lll}2 & 0 & 1 \\ 0 & 1 & 0 \\ 3 & 2 & 1\end{array}\right]\), then \(\left(\left(\left((A B C)^{-1}\right)^T\right)^{-1}\right)^T=\)AP EAMCET 2020 Medium
- \(\int_0^\pi \frac{x \sin x}{1+\cos ^2 x} d x=\)AP EAMCET 2017 Easy
- The maximum kinetic energy of a photoelectron liberated from the surface of lithium with work function \(2.35 \mathrm{eV}\) by electromagnetic radiation whose electric component varies with time as :
\(E=a\left[1+\cos \left(2 \pi f_1 t\right)\right] \cos 2 \pi f_2 t\) (where \(a\) is a constant \()\) is \(\left(f_1=3.6 \times 10^{15} \mathrm{~Hz}\right.\),
and \(f_2=1.2 \times 10^{15} \mathrm{~Hz}\) and Planck's constant \(\left.h=6.6 \times 10^{-34} \mathrm{Js}\right)\)AP EAMCET 2019 Hard - The rate equation for a first-order reaction is given by . A straight line with positive slope is obtained by plotting ( Initial concentration of the reactant, concentration of the reactant at time )AP EAMCET 2020 Medium