List of top Mathematics Questions on binomial expansion formula

If $\alpha, \beta, \gamma$ are the roots of $x^{3}+4 x+1=0$, then the equation whose roots are $\frac{\alpha^{2}}{\beta+\gamma}, \frac{\beta^{2}}{\gamma+\alpha},\,\frac{\gamma^{2}}{\alpha+\beta}$ is

For $|x|<1$, the constant term in the expansion of $\frac{1}{(x-1)^{2}(x-2)}$ is

Let $f(x)=x^{2}+a x +b,$ where $a, b \in R .$ If $f(x)=0$ has all its roots imaginary, then the roots of $f(x)+f'(x)+f''(x)=0$ are

If $x$ is numerically so small so that $x^{2}$ and higher powers of $x$ can be neglected, then $\left(1+\frac{2 x}{3}\right)^{3 / 2} \cdot(32+5 x)^{-1 / 5}$ is approximately equal to

The coefficient of $x^{24}$ in the expansion of $\left(1+x^{2}\right)^{12}\left(1+x^{12}\right)\left(1+x^{24}\right)$ is

$\frac{1}{e^{3 x}}\left(e^{x}+e^{5 x}\right)=a_{0}+a_{1} x +a_{2} x^{2}+\ldots$ $\Rightarrow 2 a_{1}+2^{3} a_{3}+2^{5} a_{5}+\ldots$ is equal to

The roots of $(x-a)(x-a-1)+(x-a-1)(x-a-2) +(x-a)(x-a-2)=0, a \in R$ are always

If $ {{C}_{0}},{{C}_{1}},{{C}_{2}},.....{{C}_{n}} $ denotes the binomial coefficients in the expansion of $ {{(1+x)}^{n}}, $ then $ {{C}_{0}}+\frac{{{C}_{1}}}{2}+\frac{{{C}_{2}}}{3}+....+\frac{{{C}_{n}}}{n+1} $ is equal to

The number of terms in the expansion of$ [(a + 4b)^3 (a - 4b)^3]^2$ are

The power of $x$ in the term with the greatest coefficient in the expansion of $\left(1+\frac{x}{2}\right)^{10}$ is:

The coefficient of x⁷ in (1-x-x²+x³)⁶

Find the number of rational numbers in the expansion of \((2^{\frac{1}{5}} + 5^{\frac{1}{3}})^{15}\).

The coefficient of $x^n$ in the polynomial $\left(x+^{n}C_{0}\right)\left(x+3. ^{n}C_{1}\right)\left(x+5. ^{n}C_{2}\right) .... \left(x+\left(2n+1\right)^{n}C_{n}\right)$ is

The coefficient of $x^2$ in the expansion of the product $(2-x^2)??(1+2x+3x^2)^6 + (1-4x^2)^6)$ is :

The value of the term independent of x in the expansion of $\left(1+\frac{x}{2}-\frac{2}{x}\right)^{4}, x \ne 0$ is equal to

The sixth term in the expansion of $\left[2^{\log _{2} \sqrt{9^{x-1}+7}}+\frac{1}{2^{\frac{1}{5} \log _{2}\left(3^{x-1}+1\right)}}\right]$ is 84. Then the number of values of $x$ is

The second, third and fourth terms in the binomial expansion $(x+a)^n$ are $240$, $720$ and $1080$, respectively. Find $x$, $a$ and $n$ respectively.

The coefficient of $x^{-7}$ in the expansion of $\left[ax - \frac{1}{bx^{2}}\right]^{11} $ will be

The coefficient of $x^n$ in the binomial expansion of $(1 - x)^{-2}$ is

The coefficient of $x^n$ in the expansion of ($1 - 2x + 3x^{2} - 4x^{3} + ...$ to $\infty$)$^{-n}$ is

The coefficient of $x^{50}$ in the expansion of $\frac{\left(3-5x\right)}{\left(1-x\right)^{2}}$ equals

The co-efficient of $x^{-12}$ in the expansion of$\left(x+\frac{y}{x^3}\right)^{20}$is

The co-efficient of $x^3$ in the expansion of $(1-x+x^2)^5$ is

The $7^{th}$ term in the expansion of $\left(x^{2}+\frac{1}{x^{2}}+2\right)^{n} $ is