[JEE Main 2010] let s 1 sum j 1 10 j j 1 binom 10 j s
Let $S_1=\sum_{j=1}^{10}j(j-1)\binom{10}j$, $S_2=\sum_{j=1}^{10}j\binom{10}j$, $S_3=\sum_{j=1}^{10}j^2\binom{10}j$. S-1: $S_3=55\times2^9$. S-2: $S_1=90\times2^8$ and $S_2=10\times2^8$.
(a) S-1 true, S-2 true; not explanation
(b) S-1 true, S-2 false
(c) S-1 false, S-2 true
(d) S-1 true, S-2 true; explanation
1 Answer
VAVidaara Admin
✓ Vidaara Team
✓ Accepted
· 2d ago
▲ 0
Correct answer: (b) S-1 true, S-2 false
$S_3=S_1+S_2=90\cdot2^8+10\cdot2^9=55\cdot2^9$ (S-1 true). But $S_2=10\cdot2^9$, not $10\cdot2^8$, so S-2 is false.
JEE Main 2010 · Binomial Theorem — verified solution by the Vidaara Team.
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