AP EAMCET · Maths · Binomial Theorem
If \(x\) is so small, that \(x^5\) and higher power of \(x\) may be neglected, then the coefficient of \(x^4\) in the expansion of \(\sqrt{x^2+4}-\sqrt{x^2+9}\), is
- A \(\frac{19}{1728}\)
- B \(\frac{-19}{1728}\)
- C \(\frac{43}{1728}\)
- D \(\frac{-43}{1728}\)
Answer & Solution
Correct Answer
(B) \(\frac{-19}{1728}\)
Step-by-step Solution
Detailed explanation
Given, \(\sqrt{x^2+4}-\sqrt{x^2+9}\) \(\begin{aligned} & =\left(x^2+4\right)^{\frac{1}{2}}-\left(x^2+9\right)^{\frac{1}{2}} \\ & =2\left(1+\frac{x^2}{4}\right)^{\frac{1}{2}}-3\left(1+\frac{x^2}{9}\right)^{\frac{1}{2}} \end{aligned}\) Now, coefficient of \(x^4\) 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
- An approximate value of \(\sqrt[4]{18}\) isAP EAMCET 2018 Medium
- Suppose that the circle \(x^2+y^2+2 g x+2 f y+c=0\) has its centre on \(2 x+3 y-7=0\) and cuts the circles \(x^2+y^2-4 x-6 y+11=0\) and \(x^2+y^2-10 x-4 y+21=0\) orthogonally. Then \(5 g-10 f+3 c=\)AP EAMCET 2019 Medium
- Suppose a circle passes through \((0, a)\) and \((b, h)\) having its centre at \((c, 0)\). Then the value of \(c\) isAP EAMCET 2022 Medium
- Let \(A\) and \(B\) be two events with \(P(A)=\frac{1}{7}\), \(P\left(\frac{A}{B}\right)=\frac{2}{3}\) and \(P(B)=\frac{2}{7}\). Then, the value \(P\left(\frac{B}{A}\right)\) isAP EAMCET 2021 Easy
- If \(5 x-12 y+10=0\) and \(12 y-5 x+16=0\) are two tangents to a circle, then the radius of the circle isAP EAMCET 2003 Easy
- If \(f(x)\) is a polynomial function satisfying \(f(x) \cdot f\left(\frac{1}{x}\right)=f(x)+f\left(\frac{1}{x}\right)\) and \(f(4)=257\), then \(f(3)=\)AP EAMCET 2018 Medium
More PYQs from AP EAMCET
- The magnetic flux through a circuit of resistance changes by an amount in time , Then the total quantity of electric charge . which is passing during this time through any point of the circuit is given by_____AP EAMCET 2020 Easy
- A student has to answer 10 out of 13 questions in an examination. The number of ways in which he can answer if he must answer atleast 3 of the first five questions isAP EAMCET 2021 Medium
- An object requires \(500 \mathrm{~N}\) force to be pulled up on a \(30^{\circ}\) frictionless smooth inclined plane at a constant speed. The weight of the object isAP EAMCET 2022 Medium
- A family of curves has the differential equation \(x y \frac{d y}{d x}=2 y^2-x^2\). Then, the family of curves isAP EAMCET 2010 Medium
- In a binomial distribution, if \(\mathrm{n}=4\) and \(\mathrm{P}(\mathrm{X}=0)=\frac{16}{81}\), then \(\mathrm{P}(\mathrm{X}=4)=\)AP EAMCET 2025 Medium
- \(\lim _{n \rightarrow \infty}\left(\frac{\sqrt{1}+2 \sqrt{2}+3 \sqrt{3}+\ldots+n \sqrt{n}}{n^{\frac{5}{2}}}\right)=\)AP EAMCET 2018 Medium