The $r\,th$ terms in the expansion of ${\left( {a + 2n} \right)^n}$ is

$\frac{{n\left( {n + 1} \right) \ldots \left( {n - r + 1} \right)}}{{r!}}{a^{n - r + 1}}{\left( {2x} \right)^r}$

$\frac{{n\left( {n + 1} \right) \ldots \left( {n - r} \right)}}{{r + 1}}{a^{n - r}}{\left( x \right)^r}$

JEE MATHEMATICS MCQ: BINOMIAL THEOREM

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Application +4 | -1

The

r\,th

terms in the expansion of

{\left( {a + 2n} \right)^n}

View answer and explanation

Correct option: B

\frac{{n\left( {n - 1} \right) \ldots \left( {n - r + 2} \right)}}{{\left( {r - 1} \right)!}}{a^{n - r + 1}}{\left( {2x} \right)^{r - 1}}

Option B (

\frac{{n\left( {n - 1} \right) \ldots \left( {n - r + 2} \right)}}{{\left( {r - 1} \right)!}}{a^{n - r + 1}}{\left( {2x} \right)^{r - 1}}

) is correct because it correctly represents the rth term in the binomial expansion of the given expression.

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