Binomial Theore...

If the middle terms in the expansion of $$\left(x^2+\dfrac{1}{x}\right)^{2n}$$ is $$184756x^{10}$$, then what is the value of $$n$$ ? 

If the sum of the coefficients in the expansions of $$(a^2 x^2 - 2ax + 1)^{51}$$ is zero, then $$a$$ is equal to 

$$\dfrac{1}{9!} + \dfrac{1}{3! 7!} + \dfrac{1}{5! 5!} + \dfrac{1}{7! 3!} + \dfrac{1}{9!}$$ is equal to 

The coefficient of $$x^4$$ in the expansion of $$(1-2x)^5$$ is equal to  

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

$$(^7C_0 + \ ^7C_1) + (^7 C_2 + \ ^7C_3) + .... + (^7C_6 + \ ^7 C_7) = $$

The arithmetic mean of $$^nC_0 , \ ^nC_1, \ ^nC_2 ...., \ ^nC_n$$ is 

The largest term in the expansion of $$(2 + 3x)^{25}$$ where x = 2 is its

In the expansion of $$(1 + x)^{43}$$, the coefficients of the (2r+1)th and the (r + 2)th terms are equal, then the value of r, is

The total number of terms in the expansion of $$(x + a)^{100} + (x - a)^{100}$$ after simplification,