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JEE Main202427 Jan 2024Evening ShiftMathematicsBinomial TheoremActual

The coefficient of x 2012 in the expansion of 1 - x 2008 1 + x + x 2 2007 is equal to _____.

Correct answer

0

Step-by-step solution

Let, y = 1 - x 2008 1 + x + x 2 2007 ⇒ y = 1 - x 1 - x 2007 1 + x + x 2 2007 ⇒ y = 1 - x 1 - x 1 + x + x 2 2007 ⇒ y = 1 - x 1 - x 3 2007 ⇒ y = 1 - x C 0 2007 - C 1 2007 x 3 + . . . . . . General term in the expansion is given by, T r + 1 = 1 - x C r 2007 x 3 r - 1 r ⇒ T r + 1 = 2007 C r x 3 r - 1 r - 2007 C r x 3 r + 1 - 1 r For coefficient of x 12 , 3 r = 2012 But, r ≠ 2012 3 Also, 3 r + 1 = 2012 ⇒ 3 r = 2011 But, r ≠ 2011 3 Hence, there is no term containing x 2012 . So coefficient of x 2012 = 0

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