Multiple choice general knowledge math & puzzles

If the coefficients of (2r + 4)th and (r-2)th terms in the expansion of (1 + x)^18 are equal then the value of r is

  1. 6

  2. 8

  3. 3

  4. 5

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A Correct answer
Explanation

In binomial expansion (1+x)ⁿ, rth term coefficient = nCr-1. For (1+x)¹⁸: (2r+4)th coefficient = 18C(2r+3), (r-2)th coefficient = 18C(r-3). Setting equal: 18C(2r+3) = 18C(r-3). Using nCr = nC(n-r), we get 2r+3 = 18-(r-3) = 21-r, so 3r = 18 and r = 6.