TS EAMCET · Maths · Basic of Mathematics
For all integers \(n \geq 1\), which of the following is divisible by 9 ?
- A \(8^n+1\)
- B \(4^n-3 n-1\)
- C \(3^{2 n}+3 n+1\)
- D \(10^n+1\)
Answer & Solution
Correct Answer
(B) \(4^n-3 n-1\)
Step-by-step Solution
Detailed explanation
\(\because \quad 4^n=(1+3)^n\) \(=1+3 n+\frac{n(n-1)}{2 !} 3^2+\ldots\) \(\Rightarrow \quad 4^n-3 n-1=3^2\left[\frac{n(n-1)}{2 !}+\ldots\right]\) It is clear from above that \(4^n-3 n-1\) is divisible by 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
- If the direction cosines of two lines are such that \(l+m+n=0, l^2+m^2-n^2=0\), then the angle between them is :TS EAMCET 2006 Easy
- If the circle intersects another circle of radius in such a manner that the common chord is of maximum length with slope equal to then the centre of isTS EAMCET 2020 Hard
- If the lines \(2 x+3 y+12=0, x-y+k=0\) are conjugate with respect to the parabola \(y^2=8 x\), then \(k\) is equal toTS EAMCET 2010 Hard
- If \(\tan \theta_1=k \cot \theta_2\), then \(\frac{\cos \left(\theta_1+\theta_2\right)}{\cos \left(\theta_1-\theta_2\right)}=\)TS EAMCET 2017 Easy
- If thenTS EAMCET 2021 Easy
- If \(f(\theta)=\cos ^3 \theta+\cos ^3\left(\frac{2 \pi}{3}+\theta\right)+\cos ^3\left(\theta-\frac{2 \pi}{3}\right)\) then \(f\left(\frac{\pi}{5}\right)=\)TS EAMCET 2023 Medium
More PYQs from TS EAMCET
- If \(x \neq(2 n+1) \frac{\pi}{2}\), then \(\int \frac{\cos ^3 x}{(1+\sin x)^4} d x=\)TS EAMCET 2022 Medium
- If \(k \in R\), then roots of \((x-2)(x-3)=k^2\) are alwaysTS EAMCET 2018 Easy
- The typical wavelength of X-ray isTS EAMCET 2020 Easy
- Let A and B be two events in a random experiment. If \(\mathrm{P}(\mathrm{A} \cap \overline{\mathrm{B}})=0.1\), \(\mathrm{P}(\overline{\mathrm{A}} \cap \mathrm{B})=0.2\) and \(\mathrm{P}(\mathrm{B})=0.5\) then \(\mathrm{P}(\overline{\mathrm{A}} \cap \overline{\mathrm{B}})=\)TS EAMCET 2025 Medium
- The ratio of the wavelengths of radiation emitted when an electron in the hydrogen atom jumps from 4th orbit to 2 nd orbit and from 3 rd orbit to 2 nd orbit isTS EAMCET 2024 Easy
- For a poisson variate \(X\), if \(P(X=2)=3 P(X=3)\), then the mean of \(X\) is :TS EAMCET 2003 Easy