Question:
The mean of coefficients of \(x, x^2, ....., x^7\) in the binomial expansion of \((2 + x)^9\) is?
The mean of coefficients of \(x, x^2, ....., x^7\) in the binomial expansion of \((2 + x)^9\) is?
Updated On: Mar 9, 2024
Hide Solution
Verified By Collegedunia
Solution and Explanation
Sum of coefficients = \(^9C_1.2^8+^9C_2.2^7.....+^9C_7.2^2\)
\(\Rightarrow 3^9-2^9-19=19683-572-19 = 19152\)
Mean = \(\frac{sum}{7}=\frac{19152}{7}=2736\)
\(\therefore\) The correct answer is \(2736\).
\(\Rightarrow 3^9-2^9-19=19683-572-19 = 19152\)
Mean = \(\frac{sum}{7}=\frac{19152}{7}=2736\)
\(\therefore\) The correct answer is \(2736\).
Was this answer helpful?
2
3
Top Questions on Matrices
- Let \( A = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} \), then \( A^2 - 5A + 6I = ? \)
- If $ A $ is a square matrix such that $ \text{adj}(\text{adj}(A)) = A $, then $ |A| $ is:
If \[ A = \begin{bmatrix} 1 & 2 & 0 \\ -2 & -1 & -2 \\ 0 & -1 & 1 \end{bmatrix} \] then find \( A^{-1} \). Hence, solve the system of linear equations: \[ x - 2y = 10, \] \[ 2x - y - z = 8, \] \[ -2y + z = 7. \]
- For a matrix $ A $ of order $ 3 \times 3 $, which of the following is true?
- Let $ I = \begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix} $ and $ P = \begin{pmatrix} 2 & 0 \\ 0 & 3 \end{pmatrix} $. Let $ Q = \begin{pmatrix} x & y \\ z & 4 \end{pmatrix} $ for some non-zero real numbers $ x, y, z $, for which there is a $ 2 \times 2 $ matrix $ R $ with all entries being non-zero real numbers, such that $$ QR = RP $$ Then which of the following statements is (are) TRUE?
View More Questions
Questions Asked in JEE Main exam
- The mean and standard deviation of 100 observations are 40 and 5.1, respectively. By mistake one observation is taken as 50 instead of 40. If the correct mean and the correct standard deviation are $ \mu $ and $ \sigma $ respectively, then $ 10(\mu + \sigma) $ is equal to:
- JEE Main - 2025
- Variance and Standard Deviation
- Let \( f(x) = \frac{x - 5}{x^2 - 3x + 2} \). If the range of \( f(x) \) is \( (-\infty, \alpha) \cup (\beta, \infty) \), then \( \alpha^2 + \beta^2 \) equals to.
- JEE Main - 2025
- Functions
- The sum of all values of \( \theta \in [0, 2\pi] \) satisfying \( 2\sin^2\theta = \cos 2\theta \) and \( 2\cos^2\theta = 3\sin\theta \) is:
- JEE Main - 2025
- Trigonometric Equations
- Let the shortest distance from \( (a, 0) \), where \( a > 0 \), to the parabola \( y^2 = 4x \) be 4. Then the equation of the circle passing through the point \( (a, 0) \) and the focus of the parabola, and having its center on the axis of the parabola is:
- JEE Main - 2025
- Circle and Parabola Geometry
- If the orthocentre of the triangle formed by the lines $ y = x + 1 $, $ y = 4x - 8 $, and $ y = mx + c $ is at $ (3, -1) $, then $ m - c $ is:
- JEE Main - 2025
- Triangles
View More Questions
Concepts Used:
Binomial Theorem
The binomial theorem formula is used in the expansion of any power of a binomial in the form of a series. The binomial theorem formula is
Properties of Binomial Theorem
- The number of coefficients in the binomial expansion of (x + y)n is equal to (n + 1).
- There are (n+1) terms in the expansion of (x+y)n.
- The first and the last terms are xn and yn respectively.
- From the beginning of the expansion, the powers of x, decrease from n up to 0, and the powers of a, increase from 0 up to n.
- The binomial coefficients in the expansion are arranged in an array, which is called Pascal's triangle. This pattern developed is summed up by the binomial theorem formula.