JEE MATHEMATICS MCQ: BINOMIAL THEOREM

1 Medium

1 of 1

Application +4 | -1

(1+x)\left(1+x+x^2\right)\left(1+x+x^2+x^3\right)

\left(1+x+x^2+x^3+\ldots+x^n\right)=a_0+a_1 x+a_2 x^2+\ldots+a_m x^m

then

\sum_{r=0}^m a_r=

View answer and explanation

Correct option: D

n

Option D (

n

!) is correct because substituting x=1 into the given equation results in the factorial of n.

More Questions from BINOMIAL THEOREM

Practice All Chapter MCQs →

\left({ }^{10} C_0\right)^2-\left({ }^{10} C_1\right)^2+\ldots-\left({ }^{10} C_9\right)^2+\left({ }^{10} C_{10}\right)^2

a

d

\left( {n + 1} \right)

a{C_0} - \left( {a + d} \right){C_1} + \left( {a + 2d} \right){C_2} - ... + ...

(1-x)^{201}\left(1+x+x^2\right)^{200}

\left(\frac{1}{x}+2 x\right)^n

{x^5}

\frac{{1 + {x^2}}}{{1 + x}},\left| x \right| < 1,

\left(\begin{array}{c}2 n+1 \\ 0\end{array}\right)+\left(\begin{array}{c}2 n+1 \\ 3\end{array}\right)+\left(\begin{array}{c}2 n+1 \\ 6\end{array}\right)+\ldots=170

n