Binomial Theore...

If $$\displaystyle \left ( 1+x+x^{2} \right )^{25}=a_{0}+a_{1}x+a_{2}x^{2}+\cdot \cdot \cdot +a_{50}\cdot x^{50}$$ then $$\displaystyle a_{0}+a_{2}+a_{4}+\cdot \cdot \cdot +a_{50}$$ is

If the expansion of $${ \left( 1+x \right)  }^{ 50 }$$, the sum of coefficients of add powers of $$x$$ is

If $$\displaystyle \begin{pmatrix} p   \\ q  \end{pmatrix}$$ =0 for $$\displaystyle p< q$$ p,$$\displaystyle q\epsilon W$$ then $$\displaystyle \sum_{r=0}^{\infty}$$ $$\displaystyle \begin{pmatrix} n \\ 2r \end{pmatrix}$$

The coefficients of three consecutive terms in the expansion of $${ (1+x) }^{ n }$$ are in the ratio $$5:10:21$$. find $$n$$

The sum of the coefficients of all the even powers of x in the expansion of $$\displaystyle \left ( 2x^{2}-3x+1 \right )^{11}$$ is

Number of rational terms in the expansion of $$\displaystyle \left ( \sqrt{2}+\sqrt[4]{3} \right )^{100}$$ is

If the coefficients of $$\displaystyle x^{7}$$ & $$\displaystyle x^{8}$$ in the expansion of $$\displaystyle \left [ 2+\frac{x}{3} \right ]^{n}$$ are equal then the value of n is 

The sum of the binomial coefficients of $$\displaystyle \left [2 x+\frac{1}{x} \right ]^{n}$$ is equal to  243. value of n is

Find the $$\displaystyle 7^{th}$$ term of $$\displaystyle \left ( 3x^{2}-\frac{1}{3}\right)^{10}$$.

The value of $$\displaystyle 2\sum_{r=0}^{n}a_{2r-1}$$ is