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AIEEE 2010

JEE Main 2010 Mathematics question on Binomial Theorem

For r=0,1,…,10r = 0, 1, \ldots, 10, if ArA_r, BrB_r and CrC_r denote respectively the coefficient of xrx^r in the expansions of (1+x)10(1+x)^{10}, (1+x)20(1+x)^{20} and (1+x)30(1+x)^{30}. Then, ∑r=110Ar(B10Br−C10Ar)\sum_{r=1}^{10} A_r (B_{10}B_r - C_{10}A_r) is equal to
  1. A.
    B10−C10B_{10} - C_{10}
  2. B.
    A10(B102−C10A10)A_{10}(B_{10}^2 - C_{10}A_{10})
  3. C.
    00
  4. D.
    C10−B10C_{10} - B_{10}
Show answer

Correct option: D

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