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JEE Main202226 Jul 2022Morning ShiftMathematicsBinomial TheoremActual

If the coefficients of x and x 2 in the expansion of 1 + x p 1 - x q , p , q ≤ 15 , are - 3 and - 5 respectively, then the coefficient of x 3 is equal to ______.

Correct answer

0

Step-by-step solution

Given coefficient of x in expansion of 1 + x p 1 - x q is - 3 ⇒   C 0 q C 1 p - C 0 p C 1 q = - 3 ⇒ p - q = - 3         ⋯ 1 Now coefficients of x 2 in expansion of 1 + x p 1 - x q - C 1 q P C 1 + C 0 q C 2 P + C 0 P C 2 q = - 5 ⇒ - p q + p p - 1 2 + q q - 1 2 = - 5           ⋯ 2 Solving 1 and 2 p = 8 , q = 11 Coefficient of x 3 in expansion of 1 + x p 1 - x q will be, - C 3 q + C 3 p + C p 1 q C 2 - C p 2 q C 1 = - C 3 11 + C 3 8 + C 1

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