TS EAMCET · Maths · Binomial Theorem
For \(|x| < \frac{1}{5}\), the coefficient of \(x^3\) in the expansion of \(\frac{1}{(1-5 x)(1-4 x)}\) is
- A 369
- B 370
- C 371
- D 372
Answer & Solution
Correct Answer
(A) 369
Step-by-step Solution
Detailed explanation
\(|x| < \frac{1}{5}\) and \(\frac{1}{(1-5 x)(1-4 x)}\) \(=(1-5 x)^{-1} \cdot(1-4 x)^{-1}\) then by binomial expansion \(=\left\{1+5 x+25 x^2+125 x^3+\ldots\right\}\) \(\cdot\left\{1+4 x+16 x^2+64 x^3+\ldots\right\}\) the coefficient of \(x^3\) in this expansion is…
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 and where are the turning points of , thenTS EAMCET 2018 Medium
- Let be four vectors and let and . ThenTS EAMCET 2022 Easy
- \(\alpha, \beta\) are the roots of the equation \(\sin ^2 x+b \sin x+c=0\). If \(\alpha+\beta=\frac{\pi}{2}\) then \(b^2-1=\)TS EAMCET 2025 Medium
- The differential equation for which \(y=a x^2+b x+c\) is the general solution isTS EAMCET 2020 Easy
- The equation of a circle concentric with the circle \(x^2+y^2-6 x+12 y+15=0\) and having area that is twice the area of the given circle isTS EAMCET 2019 Easy
- Let \(f\) be a non-zero real valued continuous function satisfying \(f(x+y)=f(x) \cdot f(y)\) for all \(x, y \in \mathbb{R}\). If \(f(2)=9\), then \(f(6)\) is equal toTS EAMCET 2013 Easy
More PYQs from TS EAMCET
- \(\int \frac{d x}{\left(2 a x+x^2\right)^{\frac{3}{2}}}=\)TS EAMCET 2018 Medium
- For the following process \[ \mathrm{H}_2 \mathrm{O}(l)(1 \text { bar, } 373.15 \mathrm{~K}) \rightleftharpoons \mathrm{H}_2 \mathrm{O}(g) \] ( \(1 \mathrm{bar}, 373.15 \mathrm{~K}\) ) identify the correct set of thermodynamic parameters.TS EAMCET 2018 Easy
- For the hyperbola \(x^2-y^2-4 x+2 y+c=0\), if the focus is \(S(2+2 \sqrt{2}, k)\) and the directrix that is adjacent to \(S\) is \(x=2+\sqrt{2}\), then \(c=\)TS EAMCET 2020 Medium
- The number of common tangents that can be drawn to the curves \(\frac{x^2}{16}-\frac{y^2}{9}=1\) and \(x^2+y^2=16\) isTS EAMCET 2025 Medium
- What minimum separation between two objects a human eye would be able to resolve, if the eye pupil diameter is \(2 \mathrm{~mm}\) and the two objects are \(20 \mathrm{~m}\) away from the eye? (Assume, human eye to be equivalent to a convex lens and consider the average wave length of light as \(600 \mathrm{~nm}\) )TS EAMCET 2020 Medium
- The differential equation obtained by eliminating the arbitrary constants \(a\) and \(b\) from \(x y=a e^x+b e^{-x}\) isTS EAMCET 2007 Easy