The numerically greatest term in the binomial expansion of $(2a - 3b)^{19}$ and $a = \frac{1}{4}$ and $b = \frac{2}{3}$ is
- $^{19}C_5 . 2^{11}$
- $^{19}C_3 . \frac{1}{2^{11}}$
- $^{19}C_4 . \frac{1}{2^{13}}$
- $^{19}C_3 . 2^{13}$
The Correct Option is D
Solution and Explanation
Top Questions on binomial expansion formula
- Coefficient of x2012 in (1-x)2008(1+x+x²)2007 is equal to ___
- JEE Main - 2024
- Mathematics
- binomial expansion formula
- Number of integral terms in the expansion of \( \left( \sqrt{7} z + \frac{1}{6 \sqrt{z}} \right)^{824} \) is equal to ______.
- JEE Main - 2024
- Mathematics
- binomial expansion formula
- In the expansion of \((1 + x)(1 - x^2) (1 + \frac 3x + \frac {3}{x^2}+ \frac {1}{x^3})^5\) the sum of coefficients of \(x^3\) and \(x^{-13}\) is
- JEE Main - 2024
- Mathematics
- binomial expansion formula
- The absolute difference of the coefficient of x7 and x9 in the expansion of \((\frac{2x+1}{2x})^{11}\) is?
- JEE Main - 2023
- Mathematics
- binomial expansion formula
The coefficient of x7 in (1 – 2x + x3)10 is?
- JEE Main - 2023
- Mathematics
- binomial expansion formula
Questions Asked in AP EAMCET exam
Six coins tossed simultaneously then find the probability of getting at least 4 heads.
- AP EAMCET - 2023
- Probability
- In the chessboard if the rectangle form is 1296, find the total number of squares formed.
- AP EAMCET - 2023
- Coordinate Geometry
Find the products formed if chlorine reacts with the cold and dilute sodium hydroxide solution.
- AP EAMCET - 2023
- Chemical Reactions
- Find the coefficient of \(\frac{y^3}{x^8}\) in \((x+y)^{-5}\) ?
- AP EAMCET - 2023
- Binomial theorem
- Which compound is gem-dihalide?
- AP EAMCET - 2023
- Organic Chemistry- Some Basic Principles and Techniques
Concepts Used:
Binomial Expansion Formula
The binomial expansion formula involves binomial coefficients which are of the form
(n/k)(or) nCk and it is calculated using the formula, nCk =n! / [(n - k)! k!]. The binomial expansion formula is also known as the binomial theorem. Here are the binomial expansion formulas.
This binomial expansion formula gives the expansion of (x + y)n where 'n' is a natural number. The expansion of (x + y)n has (n + 1) terms. This formula says:
We have (x + y)n = nC0 xn + nC1 xn-1 . y + nC2 xn-2 . y2 + … + nCn yn
General Term = Tr+1 = nCr xn-r . yr
- General Term in (1 + x)n is nCr xr
- In the binomial expansion of (x + y)n , the rth term from end is (n – r + 2)th .