The sum of coefficients in ${(1 + x - 3{x^2})^{2134}}$ is
The sum of coefficients in ${(1 + x - 3{x^2})^{2134}}$ is
- A
$-1$
- B
$1$
- C
$0$
- D
${2^{2134}}$
Similar Questions
What is the coefficient of $x^{100}$ in $(1 + x + x^2 + x^3 +.... + x^{100})^3$ ?
What is the coefficient of $x^{100}$ in $(1 + x + x^2 + x^3 +.... + x^{100})^3$ ?
$\frac{1}{{1!(n - 1)\,!}} + \frac{1}{{3!(n - 3)!}} + \frac{1}{{5!(n - 5)!}} + .... = $
$\frac{1}{{1!(n - 1)\,!}} + \frac{1}{{3!(n - 3)!}} + \frac{1}{{5!(n - 5)!}} + .... = $
If ${(1 + x)^n} = {C_0} + {C_1}x + {C_2}{x^2} + .......... + {C_n}{x^2},$ then $C_0^2 + C_1^2 + C_2^2 + C_3^2 + ...... + C_n^2$ =
If ${(1 + x)^n} = {C_0} + {C_1}x + {C_2}{x^2} + .......... + {C_n}{x^2},$ then $C_0^2 + C_1^2 + C_2^2 + C_3^2 + ...... + C_n^2$ =
A possible value of $^{\prime}x^{\prime}$, for which the ninth term in the expansion of $\left\{3^{\log _{3} \sqrt{25^{x-1}+7}}+3^{\left(-\frac{1}{8}\right) \log _{3}\left(5^{x-1}+1\right)}\right\}^{10}$ in the increasing powers of $3^{\left(-\frac{1}{8}\right) \log _{3}\left(5^{x-1}+1\right)}$ is equal to $180$ , is:
A possible value of $^{\prime}x^{\prime}$, for which the ninth term in the expansion of $\left\{3^{\log _{3} \sqrt{25^{x-1}+7}}+3^{\left(-\frac{1}{8}\right) \log _{3}\left(5^{x-1}+1\right)}\right\}^{10}$ in the increasing powers of $3^{\left(-\frac{1}{8}\right) \log _{3}\left(5^{x-1}+1\right)}$ is equal to $180$ , is:
- [JEE MAIN 2021]
Coefficient of $x^{n-6}$ in the expansion $n\left[ {x - \left( {\frac{{^n{C_0}{ + ^n}{C_1}}}{{^n{C_0}}}} \right)} \right]\left[ {\frac{x}{2} - \left( {\frac{{^n{C_1}{ + ^n}{C_2}}}{{^n{C_1}}}} \right)} \right]\left[ {\frac{x}{3} - \left( {\frac{{^n{C_2}{ + ^n}{C_3}}}{{^n{C_2}}}} \right)} \right].....$ $ \left[ {\frac{x}{n} - \left( {\frac{{^n{C_{n - 1}}{ + ^n}{C_n}}}{{^n{C_{n - 1}}}}} \right)} \right]$ is equal to (where $n = n . (n -1) . (n -2).... 3.2.1$ )
Coefficient of $x^{n-6}$ in the expansion $n\left[ {x - \left( {\frac{{^n{C_0}{ + ^n}{C_1}}}{{^n{C_0}}}} \right)} \right]\left[ {\frac{x}{2} - \left( {\frac{{^n{C_1}{ + ^n}{C_2}}}{{^n{C_1}}}} \right)} \right]\left[ {\frac{x}{3} - \left( {\frac{{^n{C_2}{ + ^n}{C_3}}}{{^n{C_2}}}} \right)} \right].....$ $ \left[ {\frac{x}{n} - \left( {\frac{{^n{C_{n - 1}}{ + ^n}{C_n}}}{{^n{C_{n - 1}}}}} \right)} \right]$ is equal to (where $n = n . (n -1) . (n -2).... 3.2.1$ )