COMEDK · Maths · 7. Binomial Theorem
The term independent of \(x\) in \(\left[\sqrt{\left(\frac{x}{3}\right)}+\sqrt{\left(\frac{3}{2 x^{2}}\right)}\right]^{10}\) is
- A \(\frac{5}{4}\)
- B \(\frac{7}{4}\)
- C \(\frac{9}{4}\)
- D None of these
Answer & Solution
Correct Answer
(D) None of these
Step-by-step Solution
Detailed explanation
Given, expansion is \(\left[\sqrt{\left(\frac{x}{3}\right)}+\sqrt{\left(\frac{3}{2 x^{2}}\right)}\right]^{10}\) Let \(t_{r+1}\) be general term, then…
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
- \(\text { If } A=\left[\begin{array}{cc}
5 a & -b \\
3 & 2
\end{array}\right] \text { and } A \operatorname{adj} A=A A^t \text {, then } 5 a+b \text { is equal to }\)COMEDK 2024 Medium - If the circles \(x^{2}+y^{2}+2 g x+2 f y=0\) and \(x^{2}+y^{2}+2 g^{\prime} x+2 f^{\prime} y=0\) touch each other, thenCOMEDK 2018 Medium
- The sum of the order and degree of the differential equation \(\left(\dfrac{d^2 y}{d x^2}\right)^5+\dfrac{4\left(\dfrac{d^2 y}{d x^2}\right)^3}{\left(\dfrac{d^3 y}{d x^3}\right)}+\dfrac{d^3 y}{d x^3}=x^2-1\) isCOMEDK 2024 Easy
- The minimum value of \(Z=3 x+5 y\), given subject to the constraints \(x+y \geq 2, x+3 y \geq 3, x, y \geq 0\) isCOMEDK 2023 Medium
- If \(S_{n}=\frac{1}{6 \cdot 11}+\frac{1}{11 \cdot 16}+\frac{1}{16 \cdot 21}+\ldots\) to \(n\) terms, then \(6 S_{n}=\)COMEDK 2016 Hard
- If \(\quad X=\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]\) and \(Y=\left[\begin{array}{cc}0 & 1 \\ -1 & 0\end{array}\right]\) and \(B=\left[\begin{array}{cc}\cos \theta & \sin \theta \\ -\sin \theta & \cos \theta\end{array}\right]\) then \(B\) equalsCOMEDK 2025 Easy
More PYQs from COMEDK
- The general solution of the differential equation \(\left(1+y^2\right) d x=\left(\tan ^{-1} y-x\right) d y\)COMEDK 2023 Medium
- A body is executing SHM. When its displacements from the mean position are \(4 \mathrm{~cm}\) and \(5 \mathrm{~cm}\) it has velocity \(10 \mathrm{~cms}^{-1}\) and \(8 \mathrm{~cms}^{-1}\) respectively. Its periodic time \(\mathrm{t}\) isCOMEDK 2024 Medium
- The best method for the separation of \(o\)-nitrophenol and \(p\)-nitrophenol from their mixture is:COMEDK 2025 Easy
- A certain item is manufactured by 3 factory \(F_{1}, F_{2}\) and \(F_{3}\) with \(30 \%\) of item made in \(F_{1}, 20 \%\) in \(F_{2}\) and \(50 \%\) in \(F_{3}\). It is found that \(2 \%\) of the items produced by \(F_{1} .3 \%\) of the items produced by \(F_{2}\) and \(4 \%\) of the items produced by \(F_{3}\) are defective. Suppose that an items selected at random from the stock is found defective. What is the probability that the item came from \(F_{1}\) ?COMEDK 2014 Hard
- \(\begin{aligned}
f(x) &=2 a-x \text { in }-a < x < a \\
&=3 x-2 a \text { in } a \geq x
\end{aligned}\)
Then which of the following is true?COMEDK 2019 Hard - The \(\mathrm{pH}\) of \(10^{-8} \mathrm{M} \mathrm{HCl}\) solution isCOMEDK 2018 Easy