Class 12

Math

Algebra

Binomial Theorem

The term independent of $x$ in the product $(4+x+7x_{2})(x−x3 )_{11}$ is

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If the coefficients of $a_{r−1},a_{r}$and $a_{r+1}$in the expansion of $(1+a)_{n}$are in arithmetic progression, prove that $n_{2}−n(4r+1)+4r_{2}−2=0$.

If $kandn$ are positive integers and $s_{k}=1_{k}+2_{k}+3_{k}++n_{k},$ then prove that $r=1∑m _{(m+1)}C_{r}s_{r}=(n+1)_{m+1}−(n+1)˙$

Find the $4_{th}$term in the expansion of $(x−2y)_{12}$.

Find the value of $∑0≤i<j≤n∑ (_{n}C_{i}+_{n}C_{j})˙$

Find the approximation of $(0.99)_{5}$ using the first three terms of its expansion.

If the coefficients of $(r−5)thand(2r−1)th$ terms in the expansion of $(1+x)_{34}$ are equal, find $r˙$

If the coefficients of three consecutive terms in the expansion of $(1+x)_{n}$ are in the ratio 1:7:42, then find the value of $n˙$

Find the coefficient of $x_{13}$ in the expansion of $(1−x)_{5}×(1+x+x_{2}+x_{2})_{4}˙$