For r = 0 to 10, let Ar... | JEE Advanced 2010 | Mathematics

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For $r=0,1, \ldots, 10$, let $A_r, B_r$ and $C_r$ denote, respectively, the coefficient of $x^r$ in the expansions of $(1+x)^{10}$, $(1+\mathrm{x})^{20}$ and $(1+\mathrm{x})^{30}$. Then $\sum_{r=1}^{10} A_r\left(B_{10} B_r-C_{10} A_r\right)$ is equal to

Select the correct option:

A

$\mathrm{B}_{10}-\mathrm{C}_{10}$

B

$A_{10}\left(B_{10}^2-C_{10} A_{10}\right)$

C

0.0

D

$\mathrm{C}_{10}-\mathrm{B}_{10}$

✓ Correct! Well done.

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