AP EAMCET · Maths · Binomial Theorem
The coefficient of \(x^2\) in the expansion of \((1+x)^2(8-x)^{-\frac{1}{3}}\) is
- A \(\frac{2167}{4032}\)
- B \(\frac{2265}{4132}\)
- C \(\frac{313}{576}\)
- D \(\frac{3691}{6792}\)
Answer & Solution
Correct Answer
(C) \(\frac{313}{576}\)
Step-by-step Solution
Detailed explanation
\((1+x)^2 = 1+2x+x^2\) \((8-x)^{-\frac{1}{3}} = 8^{-\frac{1}{3}}(1-\frac{x}{8})^{-\frac{1}{3}} = \frac{1}{2}(1 + (-\frac{1}{3})(-\frac{x}{8}) + \frac{(-\frac{1}{3})(-\frac{1}{3}-1)}{2!}(-\frac{x}{8})^2 + \dots)\)…
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
- Line \(L_1\) passes through the points \(\bar{i}+\bar{j}\) and \(\bar{k}-\bar{i}\). Line \(L_2\) passes through the point \(\overline{\mathrm{j}}+2 \overline{\mathrm{k}}\) and is parallel to the vector \(\overline{\mathrm{i}}+\overline{\mathrm{j}}+\overline{\mathrm{k}}\). If \(\mathrm{x} \overline{\mathrm{i}}+\mathrm{y} \overline{\mathrm{j}}+\mathrm{z} \overline{\mathrm{k}}\) is the point of intersection of the lines \(L_1\) and \(L_2\), then \((y-x)=\)AP EAMCET 2025 Medium
- The angle between the line joining the points \((1,-2),(3,2)\) and the line \(x+2 y-7=0\) isAP EAMCET 2007 Easy
- Let \(\overrightarrow{\mathrm{a}}=\hat{\mathrm{i}}-2 \hat{\mathrm{j}}, \overrightarrow{\mathrm{b}}=2 \hat{\mathrm{j}}+3 \hat{\mathrm{k}}, \overrightarrow{\mathrm{c}}=\mathrm{pi}+\mathrm{q} \hat{\mathrm{j}}\) and \(\overrightarrow{\mathrm{d}}=\mathrm{p} \hat{\mathrm{j}}-\mathrm{q} \hat{\mathrm{k}}\) be four vectors. If \((\vec{a} \times \vec{b}) \cdot \vec{c}=3=(\vec{a} \times \vec{b}) \cdot \vec{d}\), then \(3 \mathrm{p}+\mathrm{q}=\)AP EAMCET 2023 Hard
- If \(z \in C\) and \(i z^3+4 z^2-z+4 i=0\), then a complex root of this equation having minimum magnitude isAP EAMCET 2018 Hard
- The general solution of the differential equation \(\frac{d y}{d x}=\frac{x+2 y-3}{2 x+y-3}\) isAP EAMCET 2018 Easy
- If \(y=\cos ^{-1}(\cos x)\), then find \(\frac{d y}{d x}\) at \(x=\frac{5 \pi}{4}\)AP EAMCET 2021 Medium
More PYQs from AP EAMCET
- What is the density of one mole of \(\mathrm{He}\) (molar mass \(=4 \mathrm{~g}\) \(\left.\mathrm{mol}^{-1}\right)\) at \(300 \mathrm{~K}\) and a pressure of \(0.82 \mathrm{~atm} ?(\mathrm{R}=0.082 \mathrm{~L}\) \(\left.\operatorname{atm} \mathrm{mol}^{-1} \mathrm{~K}^{-1}\right)\)AP EAMCET 2022 Medium
- If a line drawn from a fixed point cuts the circle at and then is equal toAP EAMCET 2020 Medium
- In Fraunhofer diffraction experiment, \(L\) is the distance between screen and the obstacle, \(b\) is the size of obstacle and \(\lambda\) is wavelength of incident light. The general condition for the applicability of Fraunhofer diffraction isAP EAMCET 2008 Easy
- \(\int \frac{\operatorname{cosec}^2 x-2022}{\cos ^{2022} x} d x=f(x)+C \Rightarrow f(\pi / 4)=\)AP EAMCET 2022 Easy
- Calculate the amount of \(\mathrm{NO}_2\) required for producing \(4 \mathrm{~g}\) moles of \(\mathrm{HNO}_3\) as per the chemical reaction, \(3 \mathrm{NO}_2+\mathrm{H}_2 \mathrm{O} \longrightarrow 2 \mathrm{HNO}_3+\mathrm{NO}\). Given, the gram molecular weights of di-nitrogen and di-oxygen gases are \(28 \mathrm{~g}\) and \(32 \mathrm{~g}\) respectively.AP EAMCET 2020 Easy
- If \(y=\sin \left(2 \tan ^{-1}\left(\sqrt{\frac{1-x}{1+x}}\right)\right) x=\cos 2 \theta\), then \(\frac{d y}{d x}=\)AP EAMCET 2022 Medium