Question:
The mean of coefficients of x, x2, ....., x7 in the binomial expansion of (2 + x)9 is?
The mean of coefficients of x, x2, ....., x7 in the binomial expansion of (2 + x)9 is?
Updated On: Jul 28, 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 \(2736\).
Was this answer helpful?
0
3
Top Questions on Binary operations
The number of rational terms in the expansion of (33/4 + 53/2)60?
- JEE Main - 2023
- Mathematics
- Binary operations
- Let ⊙ be a binary operation on Q - {0} defined by a⊙b=\(\frac{a}{b}\). Then 1⊙(2⊙(3⊙4)) is equal to
- KEAM - 2022
- Mathematics
- Binary operations
- For any two positive rational numbers m and n, a binary operation * is defined by \(m*n=\frac{m+n}{3}\), then \(\frac{7}{2}*\frac{5}{2}\) is equal to
- KEAM - 2021
- Mathematics
- Binary operations
- If A = {a, b, c}, then the number of binary operations on A is
- KCET - 2020
- Mathematics
- Binary operations
- If $A = \{a,b,c\}$, then the number of binary operations on $A$ is
- KCET - 2020
- Mathematics
- Binary operations
View More Questions
Questions Asked in JEE Main exam
If a random variable \( x \) has the probability distribution
then \( P(3<x \leq 6) \) is equal to- JEE Main - 2026
- Conditional Probability
- When 300 J of heat is given to an ideal gas with \( C_p = \frac{7}{2}R \), its temperature rises from 20°C to 50°C keeping its volume constant. The mass of the gas is (approximately) ______ g. (R = 8.314 J/mol K)
- JEE Main - 2026
- Thermodynamics
- Let \( \vec{a}, \vec{b}, \vec{c} \) be three vectors such that \[ \vec{a} \times \vec{b} = 2(\vec{a} \times \vec{c}). \] If \( |\vec{a}| = 1 \), \( |\vec{b}| = 4 \), \( |\vec{c}| = 2 \), and the angle between \( \vec{b} \) and \( \vec{c} \) is \(60^\circ\), then \( |\vec{a} \cdot \vec{c}| \) is equal to.
- JEE Main - 2026
- Vector Algebra
- A thin convex lens of focal length \( 5 \) cm and a thin concave lens of focal length \( 4 \) cm are combined together (without any gap), and this combination has magnification \( m_1 \) when an object is placed \( 10 \) cm before the convex lens.
Keeping the positions of the convex lens and the object undisturbed, a gap of \( 1 \) cm is introduced between the lenses by moving the concave lens away. This leads to a change in magnification of the total lens system to \( m_2 \).
The value of \( \dfrac{m_1}{m_2} \) is
- For the matrices \( A = \begin{bmatrix} 3 & -4 \\ 1 & -1 \end{bmatrix} \) and \( B = \begin{bmatrix} -29 & 49 \\ -13 & 18 \end{bmatrix} \), if \( (A^{15} + B) \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 0\\ 0 \end{bmatrix} \), then among the following which one is true?}
- JEE Main - 2026
- Matrices
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.