AP EAMCET · Maths · Binomial Theorem
The coefficient of \(x^3\) in the power series expansion of \(\frac{1+4 x-3 x^2}{(1+3 x)^3}\) is
- A -27
- B 27
- C 153
- D -153
Answer & Solution
Correct Answer
(A) -27
Step-by-step Solution
Detailed explanation
The coefficient of \( x^k \) in \( (1+3x)^{-3} \) is \( (-1)^k \binom{3+k-1}{k} 3^k = (-1)^k \frac{(k+2)(k+1)}{2} 3^k \). Coefficient of \( x^3 \) in \( (1+4 x-3 x^2)(1+3 x)^{-3} \) 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 the functions \(f\) and \(g\) are defined by \(f(x)=3 x-4, \quad g(x)=2+3 x \quad\) for \(\quad x \in R\) respective, then \(g^{-1}\left(f^{-1}(5)\right)\) is equal toAP EAMCET 2002 Hard
- The equation of the plane in normal form which passes through the points and isAP EAMCET 2019 Easy
- The domain of the real valued function \(f(x)=\frac{\sqrt{2-x}+\sqrt{1+x}}{\sqrt{x+3}}\) isAP EAMCET 2022 Easy
- If the straight lines \(2 x-y+1=0\), \(4 x+y+2=0\) and \(x+y-k=0\) are concurrent, then \(k\) equalsAP EAMCET 2021 Easy
- \(\int\left(\tan ^7 x+\tan x\right) d x=\)AP EAMCET 2024 Easy
- If in the angles of a triangle are in the ratio \(1: 1: 4\), then the ratio of the perimeter of the triangle to its largest side isAP EAMCET 2014 Hard
More PYQs from AP EAMCET
- If two angles of \(\triangle A B C\) are \(45^{\circ}\) and \(60^{\circ}\), then the ratio of the smallest and the greatest sides areAP EAMCET 2007 Medium
- For \(f(x)=\sin \left(\frac{1}{|x| \sqrt{x^2-1}}\right)\) the domain and range of \(f(x)\) in \(R\) areAP EAMCET 2020 Easy
- The total number of positive integral solutions \((x, y, z)\) of \(x y z=24\) isAP EAMCET 2022 Easy
- \(\lim _{x \rightarrow 0} \frac{4^x-9^x}{x\left(4^x+9^x\right)}\) is equal toAP EAMCET 2002 Hard
- The equation whose solutions are the non-zero solutions of the equation \(\bar{z}=i z^2\), isAP EAMCET 2019 Easy
- Nature of two oxides of nitrogen X and Y formed in the reaction of sodium nitrite with hydrochloric acid isAP EAMCET 2025 Medium