List of top Mathematics Questions on Binomial Expansion asked in AP EAPCET

The coefficient of $x^{12}$ in the expansion of \[ (3+2x)^{-5} \] is

If $x$ is so small that the values of $x^n$, $n\geq2$ are negligible, then the approximate value of \[ \frac{\sqrt{2-3x}}{(3+2x)}(x+1) \] is

Evaluate \[ \sum_{r=1}^{\infty} \frac{1\cdot3\cdot5\cdots(2r-1)} {2^{2r}r!} (\sqrt{3})^r : \]

If the expansion of \[ \left(\frac{1+15x}{1-3x}\right) \] is valid and the coefficient of \(x^3\) in its expansion is \(k(3^3)\), then \(k=\)

If \( 0<x<1 \), then first negative term in the expansion of \( (1+x)^{\frac{47}{5}} \) is

If \( C_{o},C_{1},C_{2},...,C_{n} \) represent the coefficients in the binomial expansion of \( (1+x)^{n} \), then \( C_{o}+\frac{c_{2}}{3}+\frac{c_{4}}{5}+\cdot\cdot\cdot+\frac{c_{16}}{17}= \)

The value of $n$ for which the sum \[ \frac{{}^nC_0}{2^n} + 2\frac{{}^nC_1}{2^n} + 3\frac{{}^nC_2}{2^n} +\cdots+ (n+1)\frac{{}^nC_n}{2^n} =16 \] is

In the binomial expansion of $(x+a)^{15}$, if the eleventh term is the geometric mean of the eighth and twelfth terms, then the numerically greatest term in its expansion is

The number of terms in the expansion of $(x + y + z)^{10}$ is:

If $a_n = \sum_{r=0}^n \frac{1}{^{n}C_r}$ and $b_n = \sum_{r=0}^n \frac{r}{^{n}C_r}$, then $\frac{b_n}{a_n} =$