Question:medium
In the expansion of \( (1 + \alpha x)^{26} \) and \( (1 - \alpha x)^{28} \), the coefficient of the middle term is the same, then the value of \( \alpha \) is:
In the expansion of \( (1 + \alpha x)^{26} \) and \( (1 - \alpha x)^{28} \), the coefficient of the middle term is the same, then the value of \( \alpha \) is:
Updated On: Apr 6, 2026
- \( \dfrac{7}{22} \)
- \( \dfrac{7}{27} \)
- \( \dfrac{5}{27} \)
- \( \dfrac{5}{22} \)
Show Solution
The Correct Option is B
Solution and Explanation
Was this answer helpful?
0
Top Questions on 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
- Suppose \( 2 - p \), \( p \), \( 2 - \alpha \), \( \alpha \) are the coefficients of four consecutive terms in the expansion of \( (1 + x)^n \). Then the value of \( p^2 - \alpha^2 + 6\alpha + 2p \) equals
- JEE Main - 2024
- Mathematics
- Binomial theorem
- Let \( \alpha = \sum_{k=0}^{n} \left( \frac{\binom{n}{k}}{k+1} \right)^2 \) and \( \beta = \sum_{k=0}^{n-1} \left( \frac{\binom{n}{k} \binom{n}{k+1}}{k+2} \right) \).
If \( 5\alpha = 6\beta \), then \( n \) equals __________.- JEE Main - 2024
- Mathematics
- Binomial theorem
- \(^{n-1}C_r = (k^2 - 8) ^{n}C_{r+1}\) if and only if:
- JEE Main - 2024
- Mathematics
- Binomial theorem
- Want to practice more? Try solving extra ecology questions todayView All Questions
