List of top Mathematics Questions on Binomial theorem asked in KEAM

If the coefficient of $x^3$ in the binomial expansion of $(2 + x)^n$ is 160, then the coefficient of $x^6$ in the binomial expansion of $(2 - x^2)^n$ is

Let $(2 - x)^9 = a_0 + a_1x + a_2x^2 + \dots + a_9x^9$. Then the value of $a_1 + a_2 + a_3 + \dots + a_8$ is equal to

If the coefficient of \(x^4\) in the binomial expansion of \((4x + a)^7\) is -1120, then the value of \(a\) is equal to

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

If $n$ is a positive integer and the coefficient of $x$ in the expansion of $(x^{2}+\frac{1}{x^{3}})^{n}$ is $^{n}C_{2}$, then $n$ is equal to ________.

The constant term in the expansion of $(2x^{2}-\frac{1}{x^{2}})^{6}$ is ________.

The coefficient of $x^{9}$ in the expansion of $(4-\frac{x^{2}}{4})^{12}$ is ________.

If $ \sum_{k=0}^{n+1} C_k^n = 512 $, find $ \sum_{k=0}^{n} C_k^n $.

If $ \sum_{k=0}^{n+1} C_k^n = 512 $, find $ \sum_{k=0}^{n} C_k^n $.

If the coefficients of \((5r+4)th\) term and \((r-1)th\) term in the expansion of \((1+x)^{25}\) are equal, then \(r\) is 

If ⁿC₅ + ⁿC₆ = ⁵¹C₆, then the value of n is equal to

Let (3+x)¹⁰ = a₀+a₁(1+x)+a₂(1+x)²+..... a₁₀(1+x)¹⁰, where a₁, a₂, ... a₁₀ are constants. Then the value of a₀+a₁+a₂+.... a₁₀ is equal to

In the binomial expansion of (x - 2y²)⁹, the coefficient of x⁶y⁶ is equal to

The term independent of x in the binomial expansion of \((x+\frac{2}{x^3})^{20}\) is

If x²² is in the (r+1)th term of the binomial expansion of (3x³-x²)⁹, then the value of r is equal to

Sum of last $30$ coefficients in the binomial expansion of $(1 + x)^{59}$ 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 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: