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Mathematical Induction and Binomial Theorem question

2010 · Shift 2 · Q25

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JEE Advanced
Mathematics
Mathematical Induction and Binomial Theorem
2010 · Shift 2 · Q25

Mathematical Induction and Binomial Theorem question

2010 · Shift 2 · Q25

JEE AdvancedMathematicsMathematical Induction and Binomial TheoremMCQ+4 / −1

For

r = 0,\,1,....,

let

{A_r},\,{B_r}

and

{C_r}

denote, respectively, the coefficient of

{X^r}

in the expansions of

{\left( {1 + x} \right)^{10}},{\left( {1 + x} \right)^{20}}

and

{\left( {1 + x} \right)^{30}}.

Then

\sum\limits_{r = 1}^{10} {{A_r}\left( {{B_{10}}{B_r} - {C_{10}}{A_r}} \right)}

is equal to

A
$\left( {{B_{10}} - {C_{10}}} \right)$
B
${A_{10}}\left( {{B^2}_{10}{C_{10}}{A_{10}}} \right)$
C
$0$
D
${{C_{10}} - {B_{10}}}$

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