Question:
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
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
Updated On: Apr 5, 2024
Hide Solution
Verified By Collegedunia
Solution and Explanation
The answer is 118.
Was this answer helpful?
2
8
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
- 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
- For the expression \((1-x)^{100}\). Then sum of coefficient of first 50 terms is:
- JEE Main - 2023
- Mathematics
- binomial expansion formula
View More Questions
Questions Asked in JEE Main exam
- Let \[ \vec{a} = 2\hat{i} + \alpha \hat{j} + \hat{k}, \quad \vec{b} = -\hat{i} + \hat{k}, \quad \vec{c} = \beta \hat{j} - \hat{k}, \] where \( \alpha \) and \( \beta \) are integers and \( \alpha \beta = -6 \). Let the values of the ordered pair \( (\alpha, \beta) \) for which the area of the parallelogram of diagonals \( \vec{a} + \vec{b} \) and \( \vec{b} + \vec{c} \) is \( \frac{\sqrt{21}}{2} \), be \( (\alpha_1, \beta_1) \) and \( (\alpha_2, \beta_2) \). Then \( \alpha_1^2 + \beta_1^2 - \alpha_2 \beta_2 \) is equal to:
- JEE Main - 2024
- Vectors
- The molecular formula of second homologue in the homologous series of monocarboxylic acid is
- JEE Main - 2024
- Aldehydes, Ketones and Carboxylic Acids
- Given below are two statements: Statement I: $\text{PF}_5$ and $\text{BrF}_5$ both exhibit $\text{sp}^3\text{d}$ hybridisation.Statement II: Both $\text{SF}_6$ and $[\text{Co}(\text{NH}_3)_6]^{3+}$ exhibit $\text{sp}^3\text{d}^2$ hybridisation. In the light of the above statements,choose the correct answer from the options given below:
- JEE Main - 2024
- Hybridisation
- Consider the system of linear equations \( x + y + z = 4\mu \), \( x + 2y + 2\lambda z = 10\mu \), \( x + 3y + 4\lambda^2 z = \mu^2 + 15 \), where \( \lambda, \mu \in \mathbb{R} \). Which one of the following statements is NOT correct?
- JEE Main - 2024
- Linear Algebra
- If the constant term in the expansion of \((1 + 2x - 3x^3) \left(\frac{3}{2}x^2 - \frac{1}{3x}\right)^9\) is \( p \), then \( 108p \) is equal to _________.
- JEE Main - 2024
- Algebra
View More Questions
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 .