List of top Mathematics Questions on Binomial theorem asked in KEAM

If the coefficient of $y^{3}$ in the binomial expansion of $\left(2\alpha-\frac{y}{2}\right)^{8}$ is -7, then the value of $\alpha$ is equal to

Let $(1+ax)(1-2x)^{3}=\sum_{n=0}^{4}a_{n}x^{n}$, where $a$ is a constant. If $a_{2}=0$, then the value of $a$ is

If $x^{22}$ is in the $(r + 1)^{\text{th}}$ term of the binomial expansion of $(3x^3 - x^2)^9$, then the value of $r$ is equal to

The middle term in the expansion of $\left(\frac{10}{x} + \frac{x}{10}\right)^{10}$ is:

The sum of the coefficients in the binomial expansion of \( \left( \frac{1}{x} + 2x \right)^6 \) is equal to:

The coefficient of \( x^{49} \) in the product \( (x-1)(x-2)(x-3) \dots (x-50) \) is:

The middle term in the expansion of \( \left(\frac{10}{x} + \frac{x}{10}\right)^{10 \) is:}

The coefficient of \( x^{49} \) in the product \( (x-1)(x-2)(x-3) \dots (x-50) \) is:

The sum of the coefficients in the binomial expansion of \( \left( \frac{1}{x} + 2x \right)^6 \) is equal to:

The middle term in the expansion of \( \left(\frac{10}{x} + \frac{x}{10}\right)^{10 \) is:}

The coefficient of \( x^{49} \) in the product \( (x-1)(x-2)(x-3) \dots (x-50) \) is:

The sum of the coefficients in the binomial expansion of \( \left( \frac{1}{x} + 2x \right)^6 \) is equal to: