JEE Main20236 Apr 2023Morning ShiftMathematicsBinomial TheoremActual

The coefficient of x 18 in the expansion of x 4 - 1 x 3 15 is _ _ _ _ _ _ _ _ _ _ _ _

Correct answer

5005

Step-by-step solution

Given, Binomial expression x 4 - 1 x 3 15 Now general term is given by, T r + 1 = C r 15 x 4 15 - r - 1 x 3 r ⇒ T r + 1 = C r 15 x 60 - 7 r ( - 1 ) r For coefficient of x 18 , equate 60 - 7 r = 18 ⇒ r = 6 Coefficient of x 18 = - 1 6 · C 6 15 = 5005

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