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JEE-Mains 2014 (7/30)

Algebra Level 4

If the coefficients of \(x^3\) and \(x^4\) in the expansion of \((1+ax+bx^2)(1-2x)^{18}\) in the powers of \(x\) are both zero, what is \((a,b)\)?

\[\left(14,\frac{251}{3}\right)\] \[\left(14,\frac{272}{3}\right)\] \[\left(16,\frac{272}{3}\right)\] \[\left(16,\frac{251}{3}\right)\]

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by Sandeep Bhardwaj

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