Class 11

Math

JEE Main Questions

Binomial Theorem

Find the coefficient of $x_{9}$ in the expansion of $(x_{2}−3x1 )_{9}$.

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Compute $(98)_{5}$.

If $pandq$ are ositive, then prove that the coefficients of $x_{p}andx_{q}$ in the expansion of $(1+x)_{p+q}$ will be equal.

If the sum of the coefficient in the expansion of $(α_{2}x_{2}−2αx+1)_{51}$ vanishes, then find the value of$α$

Show that the coefficient of the middle term in the expansion of $(1+x)_{2n}$is equal to the sum of the coefficients of two middle terms in the expansion of $(1+x)_{2n−1}$.

If the coefficients of $(r−5)_{th}$ and $(2r−1)_{th}$terms of the expansion $(1+x)_{34}$ 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 number of terms which are free from radical signs in the expansion of $(y_{1/5}+x_{1/10})_{55}˙$

Show that the middle term in the expansion of $(1+x)_{2n}isn!(1.3.5(2n−1)) 2_{n}x_{n},wheren$ is a positive integer.