class 11

Math

Algebra

Binomial Theorem

The term independent of x in expansion of $(x_{32}−x_{31}+1x+1 −x−x_{21}x−1 )$is

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Find the 4th term from the end in the expansion of $(54x −2x5 )_{9}˙$

Expand $(1−2x)_{5}$

A path of length $n$ is a sequence of points $(x_{1},y_{1})$, $(x_{2},y_{2})$,….,$(x_{n},y_{n})$ with integer coordinates such that for all $i$ between $1$ and $n−1$ both inclusive, either $x_{i+1}=x_{i}+1$ and $y_{i+1}=y_{i}$ (in which case we say the $i_{th}$ step is rightward) or $x_{i+1}=x_{i}$ and $y_{i+1}=y_{i}+1$ ( in which case we say that the $i_{th}$ step is upward ). This path is said to start at $(x_{1},y_{1})$ and end at $(x_{n},y_{n})$. Let $P(a,b)$, for $a$ and $b$ non-negative integers, denotes the number of paths that start at $(0,0)$ and end at $(a,b)$. Number of ordered pairs $(i,j)$ where $i=j$ for which $P(i,100−i)=P(i,100−j)$ is

Evaluate $(96)_{3}$

Find value of $$(a^2+\sqrt{a^2-1})^4+ (a^2-\sqrt{a^2-1})^4$$ if a=$$\sqrt{5}$$.

Find the 7th term in the expansion of $(3x_{2}−x_{3}1 )_{10}˙$

Find the term independent of $x$ in the expansion of: $(2x−x1 )_{10}˙$

Find $$n$$, if the ratio of the fifth term from the beginning to the fifth term from the end of the expansion of $$\displaystyle (\sqrt[4]{2}+\dfrac{1}{\sqrt[4]{3}})^n$$ is $$\sqrt{6}:1$$