Class 11

Math

Algebra

Binomial Theorem

The middle term in the expansion of $(1−x1 )_{n}(1−x)_{n}$ is

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Using binomial theorem evaluate each of the following: $(102)_{5}$

Which of the following is/are correct ?

Prove that the coefficients of $x_{n}$ in $(1+x)_{2n}$ is twice the coefficient of $x_{n}$ in $(1+x)_{2n−1}˙$

Consider a $G.P.$ with first term $(1+x)_{n}$, $∣x∣<1$, common ratio $21+x $ and number of terms $(n+1)$. Let $_{′}S_{′}$ be sum of all the terms of the $G.P.$, then $r=0∑n _{n+r}C_{r}(21 )_{r}$ equals

Using Binomial Theorem, evaluate $(101)_{4}$

The expansion $1+x,1+x+x_{2},1+x+x_{2}+x_{3},….1+x+x_{2}+…+x_{20}$ are multipled together and the terms of the product thus obtained are arranged in increasing powers of $x$ in the form of $a_{0}+a_{1}x+a_{2}x_{2}+…$, then, Sum of coefficients of even powers of $x$ is

The value of $r=1∑n (−1)_{r−1}(r+1r )⋅_{n}C_{r}$ is

The $13_{th}$ term in the expanion of $(x_{2}+2/x)_{n}$ is independent of $x$ then the sum of the divisiors of $n$ is