Binomial Theore...

In the expansion of $$(1+x)^{n}.(1+y)^{n}.(1+\mathrm{z})^{n}$$ the sum of the coefficients of the terms of degree $$r$$ is

Assertion (A) : Number of the disimilar terms in the sum of expansion $$(x+a)^{102}+(x-a)^{102}$$ is $$206$$

Reason (R) : Number of terms in the expansion of $$(x+b)^{n}$$ is n + 1

If the coefficients of $$r^{th}$$ term and $$(r+1)^{th}$$ term in the expansion of $$(1+x)^{20}$$ are in the ration 1 : 2, then $$r=$$

The coefficient of $$x^4$$ in $$\displaystyle \left ( \frac{x}{2} - \frac{3}{x^2} \right )^{10}$$ is

The coefficient of the $$8$$th term in the expansion of $$(1+x)^{10}$$ is

If $$T_r$$ denotes the rth term in the expansion of $$\displaystyle \left ( x+\frac{1}{y} \right)^{23}$$ then

If the coefficients of $$x^7$$ and $$x^8$$ in $$\displaystyle \left ( 2 + \frac{x}{3} \right )^n$$ are equal then n $$=$$

The coefficient of $$x^3$$ in $$\displaystyle \left ( \sqrt{x^5}+ \frac{3}{\sqrt{x^3}} \right )^5$$ is

Number of irrational terms in the expansion of $$\left(5^{\dfrac 16} + 2^{\dfrac 18}\right)^{100}$$ is

In the binomial expansion of $$(a-b)^n, n \geq 5$$, the sum of $$5^{th}$$ and $$6^{th}$$ terms is zero, then $$\dfrac ab$$ equals