TS EAMCET · Maths · Binomial Theorem
For any \(n \in N, 4^n+15 n-1\) is divisible by
- A 2
- B 9
- C 5
- D 6
Answer & Solution
Correct Answer
(B) 9
Step-by-step Solution
Detailed explanation
Let \(P(n): 4^n+15 n-1\) is divisible by 9 . For \(n=1, P(1)=4^1+15 \times 1-1=18\), which is divisible by 9 . \(\therefore P(1)\) is true. Let \(P(k)\) be true. Then, \(4^k+15 k-1\) is divisible by 9 . \(\Rightarrow 4^k+15 k-1=9 \lambda\), for some \(\lambda \in N\). We shall…
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 area (in sq units) of the region bounded by \(x=-1, x=2, y=x^2+1\) and \(y=2 x-2\) is
TS EAMCET 2014 Medium - The combined equation of the direct common tangents of the circles \(x^2+y^2+2 x=0\) and \(x^2+y^2-2 y-3=0\) isTS EAMCET 2022 Medium
- If the parabola \(x^2=4 a y,(a>0)\) makes an intercept of length \(\sqrt{40}\) units on the line \(y=1+2 x\) then \(4 a=\)TS EAMCET 2020 Medium
- 9 balls are to be placed in 9 boxes and 5 of the balls cannot fit into 3 small boxes. The number of ways of arranging one ball in each of the boxes isTS EAMCET 2008 Easy
- The line \(x+y=k\) meets the pair of straight lines \(x^2+y^2-2 x-4 y+2=0\) at two points \(A\) and \(B\). If \(O\) is the origin and \(\angle A O B=90^{\circ}\), then the value of \(k(>1)\) isTS EAMCET 2015 Medium
- Let \(n \in N\) which one of the following is true?TS EAMCET 2018 Easy
More PYQs from TS EAMCET
- The number of solutions of the equation \(\cos 6 x+\cos 4 x+\cos 2 x=-1\) in \([0, \pi]\) isTS EAMCET 2021 Medium
- If \(\bar{r} \cdot(2 \bar{i}+3 \bar{j}+4 \bar{k})=5, \bar{r} \cdot(\bar{i}+\bar{j}-\bar{k})=7\) are two planes and \((16,-9,0)\) is a point common to both the planes then the vector equation of the line of intersection of the planes is \(\bar{r}=\)TS EAMCET 2022 Medium
- For a zero order reaction \(\mathrm{A} \rightarrow\) product, a plot of \([\mathrm{A}]\) (on \(\mathrm{y}\)-axis) and time (on \(\mathrm{x}\)-axis) gave a straight line with slope equal to \(-3 \times 10^{-3} \mathrm{M} \mathrm{min}^{-1}\) and intercept equal to \(2 \times 10^{-2} \mathrm{M}\) (on y-axis). What is the rate constant (in \(\mathrm{M} \mathrm{min}^{-1}\) ) of this reaction?TS EAMCET 2023 Medium
- If \(A\left(\frac{\pi}{3}\right), B\left(\frac{\pi}{6}\right)\) are the points on the circle represented in parametric from with centre \((0,0)\) and radius 12 then the length of the chord \(A B\) isTS EAMCET 2017 Medium
- A circle passes through the points \((2,0)\) and \((1,2)\). If the power of the point \((0,2)\) with respect to this circle is 4 , then the radius of the circle isTS EAMCET 2024 Medium
- If \(\frac{x^2+1}{\left(x^2+2\right)\left(x^2+3\right)}=\frac{\mathrm{A} x+\mathrm{B}}{x^2+2}+\frac{\mathrm{C} x+\mathrm{D}}{x^2+3}\), then \(\mathrm{A}+\mathrm{B}+\mathrm{C}+\mathrm{D}=\)TS EAMCET 2025 Easy