$\left( {\begin{array}{*{20}{c}} n \\ 0 \end{array}} \right)\left( {\begin{array}{*{20}{c}} n \\ r \end{array}} \right) + \left( {\begin{array}{*{20}{c}} n \\ 1 \end{array}} \right)\left( {\begin{array}{*{20}{c}} n \\ {r + 1} \end{array}} \right) + ... + \left( {\begin{array}{*{20}{c}} n \\ {n - r} \end{array}} \right)\left( {\begin{array}{*{20}{c}} n \\ n \end{array}} \right) = $

$\left( {\begin{array}{*{20}{c}} {2n} \\ {n - r} \end{array}} \right)$

$\left( {\begin{array}{*{20}{c}} {2n} \\ {r - 1} \end{array}} \right)$

$\left( {\begin{array}{*{20}{c}} {2n} \\ r \end{array}} \right)$

$\left( {\begin{array}{*{20}{c}} {2n} \\ {n - r + 1} \end{array}} \right)$

JEE MATHEMATICS MCQ: BINOMIAL THEOREM

1 Medium

1 of 1

Application +4 | -1

\left( {\begin{array}{cccccccccccccccccccc} n \\ 0 \end{array}} \right)\left( {\begin{array}{cccccccccccccccccccc} n \\ r \end{array}} \right) + \left( {\begin{array}{cccccccccccccccccccc} n \\ 1 \end{array}} \right)\left( {\begin{array}{cccccccccccccccccccc} n \\ {r + 1} \end{array}} \right) + ... + \left( {\begin{array}{cccccccccccccccccccc} n \\ {n - r} \end{array}} \right)\left( {\begin{array}{cccccccccccccccccccc} n \\ n \end{array}} \right) =

View answer and explanation

Correct option: C

\left( {\begin{array}{cccccccccccccccccccc} {2n} \\ {n - r} \end{array}} \right)

Option C

\left( {\begin{array}{cccccccccccccccccccc} {2n} \\ {n - r} \end{array}} \right)

is correct because it represents the coefficient of

x^{n-r}

in the expansion of

(1+x)^n(1+x)^n = (1+x)^{2n}