TS EAMCET · Maths · Binomial Theorem

if \(3^{2 n+2}-8 n-9\) is divisible by \(2^p \forall n \in N\), then the maximum value of \(p\) is

Verified Solution

Answer & Solution

Correct Answer

(C) 6

Step-by-step Solution

Detailed explanation

\(3^{2 n+2}-8 n-9=9(1+8)^n-8 n-9\)…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

Same subject

If \(f: \mathrm{R}-\{0\} \rightarrow \mathrm{R}\) is defined by \(3 f(x)+4 f\left(\frac{1}{x}\right)=\frac{2-x}{x}\) then \(f(3)=\)

TS EAMCET 2025 Medium
\(\alpha\) is a root of the equation \(\frac{x-1}{\sqrt{2 x^2-5 x+2}}=\frac{41}{60}\). If \(-\frac{1}{2} \lt \alpha \lt 0\), then \(\alpha=\)

TS EAMCET 2024 Medium
Equation of a common tangent to the circle \(x^2+y^2=4\) and to the ellipse \(2 x^2+25 y^2=50\) is

TS EAMCET 2020 Easy
A and \({B}\) are two independent events. \({P}({A})=\frac{2}{5}, {P}({B})=\frac{1}{3}\). Match the following.

The correct answer is \( \begin{array}{llll} \mathbf{A} & \mathbf{B} & \mathbf{C} & \mathbf{D} \end{array} \)

TS EAMCET 2022 Medium
If \(z=\frac{y}{x}\left[\sin \frac{x}{y}+\cos \left(1+\frac{y}{x}\right)\right]\), then \(x \frac{\partial z}{\partial x}\) is equal to

TS EAMCET 2002 Hard
If \(x=a, y=b, z=c\) is the solution of the system of simultaneous linear equations \(x+y+z=4\), \(x-y+z=2, x+2 y+2 z=1\), then \(a b+b c+c a=\)

TS EAMCET 2018 Hard

Explore more questions on app

From TS EAMCET

The height of water level is a tank of uniform crosssection is 5 m . The volume of the water leaked in 5 s through a hole of area \(2.4 \mathrm{~mm}^2\) made at the bottom of the tank is (Assume the level of the water in the tank remains constant and acceleration due to gravity \(=10 \mathrm{~ms}^{-2}\) )

TS EAMCET 2024 Easy
\(P, Q, R\) and \(S\) are four points with the position vectors \(3 \mathbf{i}-4 \mathbf{j}+5 \mathbf{k},-4 \mathbf{i}+5 \mathbf{j}+\mathbf{k}\) and \(-3 \mathbf{i}+4 \mathbf{j}+3 \mathbf{k}\), respectively. Then, the line \(P Q\) meets the line \(R S\) at the point

TS EAMCET 2013 Medium
The equation of the direct common tangent of the circles \(x^2+y^2-6 x-4 y-23=0\) and \(x^2+y^2+2 x+2 y+1=0\) is

TS EAMCET 2022 Medium
The most effective coagulating agent among the following for \(\mathrm{Sb}_2 \mathrm{~S}_3\) sol is

TS EAMCET 2019 Easy
\(f\left(x, y, c_1, c_2\right)=0\) is an equation containing two arbitrar constants \(c_1\) and \(c_2\). If the differential equation havin \(f\left(x, y, c_1, c_2\right)=0\) as its general solution is of \(k^{\text {th }}\) order, the the differential equation corresponding to \(x^k+y^k=c^2\) ( \(c\) is an arbitrary constant) is

TS EAMCET 2022 Medium
A convex lens and a concave lens, each with focal length of \(4 \mathrm{~cm}\) are separated by a distance of \(6 \mathrm{~cm}\) along their axis. An object is placed \(8 \mathrm{~cm}\) before the convex lens. The distance between the object and its image is

TS EAMCET 2020 Easy

Explore more questions on app