List of top Mathematics Questions on general and middle terms asked in KEAM

The coefficient of $\dfrac{1}{x^2}$ in the binomial expansion of $\left(3x - \dfrac{1}{3x}\right)^4$ is:
The constant term in the binomial expansion of \(\left(2x - \frac{5}{x^2}\right)^6\) is
Let \( \alpha = \sum_{k=0}^{5} {^{10}C_{2k}} \) and \( \beta = \sum_{k=0}^{4} {^{10}C_{2k+1}} \). Then \( \alpha - \beta \) is equal to
If \( \alpha = {^nC_r} \) and \( \beta = {^nC_{r-1}} \), then \( 1 + \frac{\alpha}{\beta} \) is equal to
In the binomial expansion of \( (2x + \alpha)^8 \), the co-efficients of \( x^2 \) and \( x^3 \) are equal. Then the value of \( \alpha \) is equal to
The coefficient of $x^3$ in the expansion of $\left(x^2 - \frac{2}{x}\right)^6$ is
The number \(81\) is the coefficient of \( x^k \) in the binomial expansion of \( \left(x^2 + \frac{3}{x}\right)^4 \), \( x \neq 0 \). Then the value of \( k \) equals
The coefficient of \( x^3 \) in the expansion of \( (1 + x + 2x^2)(1 - 2x)^5 \) is
The constant term in the expansion of \( \left(x^2 - \frac{2}{x}\right)^6 \) is
If the sum of the coefficients in the expansion of \( (a^2x^2 - 2ax + 1)^{51} \) is zero, then \( a \) is equal to
The coefficient of \( x^5 \) in the expansion of \( (x + 3)^8 \) is
The coefficient of \( x^5 \) in the expansion of \( (x + 3)^8 \) is
If the sum of the coefficients in the expansion of \( (a^2x^2 - 2ax + 1)^{51} \) is zero, then \( a \) is equal to
Sum of last 30 coefficients in the binomial expansion of \( (1+x)^{59} \) is
\( \binom{7}{0}+\binom{7}{1} + \binom{7}{2}+\binom{7}{3} + \cdots + \binom{7}{7} \)
Coefficient of \( x \) in \( (1 - 3x + 7x^2)(1 - x)^{16} \)
The coefficient of \( x^5 \) in the expansion of \( (x + 3)^8 \) is
If the sum of the coefficients in the expansion of \( (a^2x^2 - 2ax + 1)^{51} \) is zero, then \( a \) is equal to
Sum of last 30 coefficients in the binomial expansion of \( (1+x)^{59} \) is

If the \(7^{\text{th}}\) and \(8^{\text{th}}\) terms of the binomial expansion \[ (2a - 3b)^n \] are equal, then the value of \[ \frac{2a + 3b}{2a - 3b} \] is equal to:

The coefficient of \( x^5 \) in the expansion of \( (1+x^2)^5(1+x)^4 \) is:
The coefficient of \( x^4 \) in the expansion of \( (1-2x)^5 \) is equal to:
If the coefficients of \( x^3 \) and \( x^4 \) in the expansion of \( (3+kx)^9 \) are equal, then the value of \( k \) is: