TS EAMCET · Maths · Basic of Mathematics
Let \(n \in N\) which one of the following is true?
- A \(47^n+16 n-1\) is divisible by 4
- B \(2\left(4^{2 n+1}\right)-3^{3 n+1}\) is divisible by 9
- C \(4^n-3 n-1\) is divisible by 11
- D \(3\left(5^{2 n+1}\right)+2^{3 n+1}\) is divisible by 17
Answer & Solution
Correct Answer
(D) \(3\left(5^{2 n+1}\right)+2^{3 n+1}\) is divisible by 17
Step-by-step Solution
Detailed explanation
(a) \(47^n+16 n-1\) \(\begin{array}{r} (48-1)^n+4(4 n)-1 \\ 48 k+(-1)^n+4 m-1 \\ 4(12 k+m)+(-1)^n-1 \end{array}\) \(47^n+16 n-1\) is divisible by 4 if \(n\) is odd. \(\therefore\) It is false for all values of \(n\) (b) \(2\left(4^{2 n+1}\right)-3^{3 n+1}\)…
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 \(|x| < 1\) and \(y=x-\frac{x^2}{2}+\frac{x^3}{3}-\frac{x^4}{4}+\ldots\), then \(x\) is equal to :TS EAMCET 2006 Medium
- If the chord of the circle touches the circle , then the possible points for which is a chord of contact of areTS EAMCET 2018 Medium
- \(\sum_{r=1}^{16}\left(\sin \frac{2 r \pi}{17}+i \cos \frac{2 r \pi}{17}\right)=\)TS EAMCET 2019 Easy
- If \(\alpha \neq-4\) and \((2, \alpha)\) is the mid-point of a chord of the circle \(x^2+y^2-4 x+8 y+6=0\), then the values of the \(y\)-intercept of the chord lie in the intervalTS EAMCET 2020 Medium
- If are the points of contact of the tangents drawn from the point to the circle and the chord subtends an angle at thenTS EAMCET 2022 Medium
- The solution of \(\frac{d y}{d x}=\frac{x+y}{x-y}\) isTS EAMCET 2017 Medium
More PYQs from TS EAMCET
- In which of the following pairs reactant is correctly matched with reagent that would form benzaldehyde product?
TS EAMCET 2023 Medium - \(A(1,-2,1)\) and \(B(2,-1,2)\) are the end points of a line segment. If \(D(\alpha, \beta, \gamma)\) is the foot of the perpendicular drawn from \(C(1,2,3)\) to \(A B\), then \(\alpha^2+\beta^2+\gamma^2=\)TS EAMCET 2024 Easy
- The minimum value of \(\frac{9 \cdot 3^{2 x}+6 \cdot 3^x+4}{9 \cdot 3^{2 x}-6 \cdot 3^x+4}\) isTS EAMCET 2020 Medium
- Define \(f: R \rightarrow R\) by \(f(x)= \begin{cases}(x-a) \frac{e^{\frac{1}{(x-a)}}-1}{\frac{1}{(x-a)}}, 1 & \text { for } x \neq a \ 0, & \text { at } x=a\end{cases}\) Then which one of the following is true?TS EAMCET 2020 Easy
- A bag contains 3 white and 6 red balls. Four balls are drawn at a time randomly. Then the probability of getting at least red balls isTS EAMCET 2022 Medium
- A copper rod of length \(75 \mathrm{~cm}\) and an iron rod of length \(125 \mathrm{~cm}\) are joined together end to end. Both are of circular cross-section with diameter \(2 \mathrm{~cm}\). The free ends of the copper and iron are maintained at \(100^{\circ} \mathrm{C}\) and \(0^{\circ} \mathrm{C}\) respectively. The surfaces of the bars are insulated thermally. The temperature of the copper-iron junction is [Thermal conductivity of copper is \(386.4 \mathrm{~W} / \mathrm{m}-\mathrm{K}\) and thermal conductivity of iron is \(48.46 \mathrm{~W} / \mathrm{m}-\mathrm{K}\) ]TS EAMCET 2015 Easy