Coefficient of $${x^{11}}$$ in the expansion of $${\left( {1 + {x^2}} \right)^4}{\left( {1 + {x^3}} \right)^7}{\left( {1 + {x^4}} \right)^{12}}$$ is
A
1051
B
1106
C
1113
D
1120
2
IIT-JEE 2010 Paper 2 Offline
MCQ (Single Correct Answer)
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