JEE Main

JEE Main Mathematics question on Binomial Theorem

If the coefficients of x3x^3 and x4x^4 in the expansion of (1+ax+bx2)(1−2x)18(1 + ax + bx^2)(1 - 2x)^{18} in powers of xx are both zero, then (a,b)(a, b) is equal to
  1. A.
    (16,2513)\left(16, \dfrac{251}{3}\right)
  2. B.
    (14,2513)\left(14, \dfrac{251}{3}\right)
  3. C.
    (14,2723)\left(14, \dfrac{272}{3}\right)
  4. D.
    (16,2723)\left(16, \dfrac{272}{3}\right)
Show answer

Correct option: D

Previous-year question, JEE Main.

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