Class 11

Math

JEE Main Questions

Binomial Theorem

Write down the binomial expansion of $(1+x)_{n+1}$ , when x=8. Deduce that $9_{n+1}−8n−9$ is divisible by 64 where, $n$ is a positive integer.

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

Write the general term in the expansion of $(x_{2}−yx)_{12},x=0$

Find n, if the ratio of the fifth term from the beginning to the fifth term from the end in the expansion of $(42 +43 1 )_{n}$ is $6 :1$

If $T_{0},T_{1},T_{2},,T_{n}$ represent the terms in the expansion of $(x+a)_{n},$ then find the value of $(T_{0}−T_{2}+T_{4}−)_{2}+(T_{1}−T_{3}+T_{5}−)_{2}n∈N˙$

If the third term in the expansion of $(1+x)_{m}is−81 x_{2},$ then find the value of $m˙$

Find the coefficient of $x_{7}$ in the expansion of $(1+3x−2x_{3})_{10}˙$

If the sum of coefficient of first half terms in the expansion of $(x+y)_{n}is256$ , then find the greatest coefficient in the expansion.