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
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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 .