TS EAMCET · Maths · Binomial Theorem
The set of all real values of \(x\) for which the expansion of \(\left(125 x^2-\frac{27}{x}\right)^{-2 / 3}\) is valid, is
- A \(\left(-\frac{3}{5}, \frac{3}{5}\right)\)
- B \(\left(-\infty,-\frac{3}{5}\right) \cup\left(\frac{3}{5}, \infty\right)\)
- C \(\left(-\frac{5}{3}, \frac{5}{3}\right)\)
- D \(\left(-\infty,-\frac{1}{3}\right) \cup\left(\frac{1}{3}, \infty\right)\)
Answer & Solution
Correct Answer
(B) \(\left(-\infty,-\frac{3}{5}\right) \cup\left(\frac{3}{5}, \infty\right)\)
Step-by-step Solution
Detailed explanation
Given : \(\left(125 x^2-\frac{27}{x}\right)^{\frac{-2}{3}}=\frac{x^{\frac{2}{3}}}{\sqrt[3]{\left(125 x^3-27\right)^2}}\) For expansion to be valid, \(x \neq 0\) and \(125 x^3-27 \neq 0\) \(\Rightarrow x^3 \neq \frac{27}{125} \Rightarrow x \neq \frac{3}{5}\) \(\therefore\) From…
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 \(\frac{x+1}{x^3(x-1)}=\frac{a}{x}+\frac{b}{x^2}+\frac{c}{x^3}+\frac{d}{x-1}\) thenTS EAMCET 2025 Medium
- If \(\alpha, \beta, \gamma\) are the roots of the equation \(x^3-3 x^2+3 x+1=\) 0, then \(\alpha^2 \beta^2+\beta^2 \gamma^2+\gamma^2 \alpha^2=\)TS EAMCET 2023 Medium
- The solution of \(x \frac{d y}{d x}=y+x e^{y / x}\) with \(y(1)=0\) isTS EAMCET 2014 Easy
- Equations of the latus rectum of the ellipse \(9 x^2+4 y^2-18 x-8 y-23=0\) are :TS EAMCET 2006 Medium
- The sum of the series \(\frac{3}{4 \cdot 8}-\frac{3 \cdot 5}{4 \cdot 8 \cdot 12}+\frac{3 \cdot 5 \cdot 7}{4 \cdot 8 \cdot 12 \cdot 16}-\ldots\)TS EAMCET 2007 Hard
- If \(f: R \rightarrow R\) defined by \[ f(x)=\left\{\begin{array}{cc} a^2 \cos ^2 x+b^2 \sin ^2 x, & x \leq 0 \ e^{a x+b}, & x>0 \end{array}\right. \] is a continuous function, thenTS EAMCET 2002 Hard
More PYQs from TS EAMCET
- The solution of the differential equation satisfying when , isTS EAMCET 2019 Easy
- The relation between the coefficient of real expansion \(\left(\gamma_r\right)\) and coefficient of apparent expansion \(\left(\gamma_a\right)\) of a liquid and the coefficient of linear expansion \(\left(\alpha_g\right)\) of the material of the container isTS EAMCET 2005 Hard
- An ellipse \(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\) with eccentricity \(\frac{2 \sqrt{2}}{3}\) is inscribed in a circle \(x^2+y^2=18\) such that the length of its major axis is equal to the diameter of this circle. The locus of the poles of all the tangents of the circle with respect to the ellipse isTS EAMCET 2020 Hard
- The mean deviation about median of the numbers \(3 x, 6 x, 9 x, \ldots, 81 x\) is 91, then \(|x|=\)TS EAMCET 2025 Medium
- If the function \(y=\sin ^{-1} x\), then \(\left(1-x^2\right) \frac{d^2 y}{d x^2}\) is equal toTS EAMCET 2004 Medium
- If \(\sqrt{9 x^2+6 x+1} < (2-x)\), then:TS EAMCET 2006 Easy