[JEE Advanced 2010] let a r b r c r be the coefficients of x r in
Let $A_r,B_r,C_r$ be the coefficients of $x^r$ in $(1+x)^{10},(1+x)^{20},(1+x)^{30}$. Then $\sum_{r=1}^{10}A_r\bigl(B_{10}B_r-C_{10}A_r\bigr)$ equals
(a) $B_{10}-C_{10}$
(b) $A_{10}(B_{10}^2-C_{10}A_{10})$
(c) $0$
(d) $C_{10}-B_{10}$
1 Answer
VAVidaara Admin
✓ Vidaara Team
✓ Accepted
· 2d ago
▲ 0
Correct answer: (d) $C_{10}-B_{10}$
$\sum A_rB_r=\binom{30}{10},\ \sum A_r^2=\binom{20}{10}$ (from $r=0$). Substituting (and removing the $r=0$ terms) yields $C_{10}-B_{10}$.
JEE Advanced 2010 · Binomial Theorem — verified solution by the Vidaara Team.
Log in to post your own answer or join the discussion.
No comments yet — start the discussion.