Question:
If n is a positive integer and f(n) is the coeffcient of xn in the expansion of (1 + x)(1-x)n, then f(2023) =
If n is a positive integer and f(n) is the coeffcient of xn in the expansion of (1 + x)(1-x)n, then f(2023) =
Updated On: Mar 11, 2025
-2021
2022
2023
-2023
Hide Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
The correct option is: (B) 2022
Was this answer helpful?
2
11
Top Questions on Binomial theorem
- If \( \sum_{r=0}^5 \frac{{}^{11}C_{2r+1}}{2r+2} = \frac{m}{n} \), gcd(m, n) = 1, then \( m - n \) is equal to:
- JEE Main - 2025
- Mathematics
- Binomial theorem
- If \( A \) and \( B \) are the two real values of \( k \) for which the system of equations \( x + 2y + z = 1 \), \( x + 3y + 4z = k \), \( x + 5y + 10z = k^2 \) is consistent, then \( A + B = \): (a) 3
- VITEEE - 2024
- Mathematics
- Binomial theorem
- If the \(2^{\text{nd}}\), \(3^{\text{rd}}\), and \(4^{\text{th}}\) terms in the expansion of \( (x + a)^n \) are 96, 216, and 216 respectively, and \( n \) is a positive integer, then \( a + x \) is:
- AP EAMCET - 2024
- Mathematics
- Binomial theorem
- If \( a_n = \sum_{r=0}^{n} \frac{1}{\binom{n}{r}} \), then \( \sum_{r=0}^{n} r \binom{n}{r} = \):
- AP EAPCET - 2024
- Mathematics
- Binomial theorem
- The coefficient of \( x^5 \) in the expansion of \( \left( 2x^3 - \frac{1}{3x^2} \right)^5 \) is:
- AP EAPCET - 2024
- Mathematics
- Binomial theorem
View More Questions
Questions Asked in TS EAMCET exam
- The number of ways in which 15 identical gold coins can be distributed among 3 persons such that each one gets at least 3 gold coins is
- TS EAMCET - 2024
- permutations and combinations
- Identify the incorrect pair:
- TS EAMCET - 2024
- Plant Physiology
- The internal and external diameters of a hollow cylinder measured with vernier calipers are (5.73 \(\pm\) 0.01) cm and (6.01 \(\pm\) 0.01) cm respectively. Then the thickness of the cylinder wall is
- TS EAMCET - 2024
- Units and measurement
- f is a real valued function satisfying the relation \(f\bigl(3x + \tfrac{1}{2x}\bigr) \;=\; 9x^2 + \tfrac{1}{4x^2}\). If \(f\bigl(x + \tfrac{1}{x}\bigr) = 1\) then \(x =\) ?
- TS EAMCET - 2024
- Relations and functions
- A body is projected from the ground at an angle of \( \tan^{-1}\sqrt{7} \) with the horizontal. At half of the maximum height, the speed of the body is \( n \) times the speed of projection. The value of \( n \) is
- TS EAMCET - 2024
- laws of motion
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.