TS EAMCET · Maths · Binomial Theorem
The term independent of \(x\) in the expansions of \(\left(\sqrt{x}-\frac{2}{\sqrt{x}}\right)^{18}\) is
- A \(-{ }^{18} C_9 2^9\)
- B \({ }^{18} C_9 2^{12}\)
- C \({ }^{18} C_6 2^6\)
- D \({ }^{18} C_6 2^8\)
Answer & Solution
Correct Answer
(A) \(-{ }^{18} C_9 2^9\)
Step-by-step Solution
Detailed explanation
General term in the expansion of \(\left(\sqrt{x}-\frac{2}{\sqrt{x}}\right)^{18}\) 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
- Two adjacent sides of a triangle are represented by the vectors \(2 \bar{i}+\bar{j}-2 \bar{k}\) and \(2 \sqrt{3} \bar{i}-2 \sqrt{3} \bar{j}+\sqrt{3} \bar{k}\). Then the least angle of the triangle and perimeter of the triangle are respectivelyTS EAMCET 2025 Medium
- The angle of elevation of a stationary cloud from a point \(2500 \mathrm{~m}\) above a lake is \(15^{\circ}\) and from the same point the angle of depression of its reflection in the lake is \(45^{\circ}\). The height (in metres) of the cloud above the lake, given that \(\cot 15^{\circ}=2+\sqrt{3}\), isTS EAMCET 2011 Hard
- TS EAMCET 2022 Easy
- If \(L_1=0\) and \(L_2=0\) are the asymptotes of the hyperbola \(9 x^2-4 y^2+36 x+8 y-4=0\), then the product of the perpendicular distances from the point \((1,1)\) to the lines, \(L_1=0\) and \(L_2=0\) isTS EAMCET 2019 Medium
- If the \(k^{\text {th }}\) term in the expansion of \(\left(\frac{3}{2} x^2-\frac{1}{3 x}\right)^6\) is independent of \(x\), then the numerically greatest term in the expansion of \(\left(\frac{3}{2} x^2-\frac{1}{3 x}\right)^k\) when \(x=\frac{2}{3}\), isTS EAMCET 2019 Medium
- If \(f(x)=\frac{\cos x}{\sin ^2 x+\cos ^4 x}\), for \(x \in R\), then \(f(2002)\) is equal toTS EAMCET 2002 Medium
More PYQs from TS EAMCET
- The main products formed when copper metal is reacted with concentrated areTS EAMCET 2021 Easy
- The structure given below is an example of
I. A condensation and biodegradable polymer.
II. A biodegradable and thermoplastic polymer.
III. A biodegradable and thermosetting polymer.
IV. A polyester and thermoplastic polymer.TS EAMCET 2020 Easy - The nuclear forces areTS EAMCET 2020 Easy
- Consider the following statements \(A\) and \(B\) and identify the correct answer A. When a person walks on a rough surface the direction of frictional force exerted by the surface on the person is opposite to the direction of his motion. B. When a cycle is in motion, the force of friction exerted by the ground on the front wheel is in the backward directionTS EAMCET 2004 Medium
- The roots \(\begin{aligned} & (x-a)(x-a-1)+(x-a-1)(x-a-2) \ & +(x-a)(x-a-2)=0, a \in R \text { are always } \end{aligned}\)TS EAMCET 2009 Easy
- If thenTS EAMCET 2021 Easy