Class 11

Math

JEE Main Questions

Binomial Theorem

Find the coefficient of $a_{5}b_{7}∈(a−2b)_{12}$

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If $x_{p}$ occurs in the expansion of $(x_{2}+1/x)_{2n}$ , prove that its coefficient is $[31 (4n−p)]![31 (2n+p)]!(2n)! $ .

If $aandb$ are distinct integers, prove that $a−b$ is a factor of $a_{n}−b_{n}$ , wherever $n$ is a positive integer.

If $n$ is an even positive integer, then find the value of $x$ if the greatest term in the expansion of \displaystyle{\left({1}+{x}\right)}^{{n}} may have the greatest coefficient also.

Prove that the coefficient of $x_{r}$ in the expansion of $(1−2x)_{−21}$ is $(2_{r})(r!)_{2}2r! $

Expand of the expression : $(1−2x)_{5}$

Find the sum $j=0∑n (_{(4n+1)}C_{j}+_{4n+1}C_{2n−j})$ .

The sum of the coefficients of the first three terms in the expansion of$(x−x_{2}3 )_{m},x=0,$m being a natural number, is 559. Find the term of the expansion containing $x_{3}$.

If $9_{7}+7_{9}$ is divisible b $2_{n},$ then find the greatest value of $n,wheren∈N˙$