Binomial Theore...

The middle term in the expansion of $$\left (x - \dfrac {1}{x}\right )^{18}$$ is

If $${ \left( 1+x+{ x }^{ 2 }+{ x }^{ 3 } \right)  }^{ 5 }=\displaystyle\sum _{ k=0 }^{ 15 }{ { a }_{ k }{ x }^{ k } } $$ then $$\displaystyle\sum _{ k=0 }^{ 7 }{ { a }_{ 2k } } $$ is equal to

Find the sum of coefficients in the expansion of $$\left(1-\dfrac 2x+\dfrac {4}{x^2}\right)^n$$ given that the number of terms are $$28$$

$$(x+1)^n=C_0+C_1x^1+C_2x^2....C_nx^n$$.

Let $$n \in N$$, such that $$(1+x+x^2)^n=a_0+a_1x+a_2x^2...a_{2n}x^{2n}$$ The value of $$a_r$$ when $$(0\leq r\leq 2n)$$

Find the coefficient of $$x^n$$ in expansion of $$(1 + x) (1 - x)^n$$.

The general term in $$(x + y)^n$$ is given by
$$T_{r+1}=$$ 

Which of the following is incorrect?

If the middle term of $$\left(\dfrac 1x +x\sin x\right)^{10}$$ is equal to $$7\dfrac 78$$, then the principal value of $$x$$ is: 

If the value of
$$C_0+2 \cdot C_1 + 3 \cdot C_2+........+(n+1)\cdot C_n=576$$, then n is ______.