Coefficient of x^{37} in expansion of (1-x)^{30} , (1 + x + x^2)^{29} is :

English

Gujarati

Hindi

7.Binomial Theorem

normal

The coefficient of $x^{37}$ in the expansion of $(1-x)^{30} \, (1 + x + x^2)^{29}$ is :

A

$0$

B

${}^{29}{C_{12}}$

C

$ - {}^{29}{C_{12}}$

D

None

Solution

$(1-x)^{30}\left(1+x+x^{2}\right)^{29}$

$(1-x)\left(1-x^{3}\right)^{29}$

$\left(1-x^{3}\right)^{29}-x\left(1-x^{3}\right)^{29} \longrightarrow$ Coeff of $x^{37}$

$\mathrm{O}-^{29} \mathrm{C}_{12}(-1)^{12} \Rightarrow-^{29} \mathrm{C}_{12}$

Standard 11

Mathematics

Share

Similar Questions

The value of $x$, for which the 6th term in the expansion of ${\left\{ {{2^{{{\log }_2}\sqrt {({9^{x – 1}} + 7)} }} + \frac{1}{{{2^{(1/5){{\log }_2}({3^{x – 1}} + 1)}}}}} \right\}^7}$ is $84$, is equal to

hard

If $a^3 + b^6 = 2$, then the maximum value of the term independent of $x$ in the expansion of $(ax^{\frac{1}{3}}+bx^{\frac{-1}{6}})^9$ is, where $(a > 0, b > 0)$

normal

Middle term in the expansion of ${(1 + 3x + 3{x^2} + {x^3})^6}$ is

medium

The greatest coefficient in the expansion of ${(1 + x)^{2n + 1}}$ is

medium

Let the coefficients of three consecutive terms $T_r$, $T _{ r +1}$ and $T _{ r +2}$ in the binomial expansion of $( a + b )^{12}$ be in a $G.P.$ and let $p$ be the number of all possible values of $r$. Let $q$ be the sum of all rational terms in the binomial expansion of $(\sqrt[4]{3}+\sqrt[3]{4})^{12}$. Then $p + q$ is equal to :

normal

(JEE MAIN-2025)