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JEE Main20241 Feb 2024Morning ShiftMathematicsBinomial TheoremActual

If the coefficient of x 30 in the expansion of 1 + 1 x 6 1 + x 2 7 1 − x 3 8 ; x ≠ 0 is α , then α equals _________.

Correct answer

0

Step-by-step solution

Given expansion is 1 + 1 x 6 1 + x 2 7 1 − x 3 8 . Now, coefficient of x 30 in x + 1 6 1 + x 2 7 1 − x 3 8 x 6 So, we will find the coefficient of x 36 in 1 + x 6 1 + x 2 7 1 − x 3 8 General term of the given expansion is 6 C r 1 7 C r 2 8 C r 3 − 1 r 3 x r 1 + 2 r 2 + 3 r 3 . ⇒ r 1 + 2 r 2 + 3 r 3 = 36 Case-I: r 1 r 2 r 3 0 6 8 2 5 8 4 4 8 6 3 8 ⇒ r 1 + 2 r 2 = 12 (Taking r 3 = 8 ) Case II: r 1 r 2 r 3 1 7 7 3 6 7 5 5 7 ⇒ r 1 + 2 r 2 = 15 (Taking r 3 = 7 ) Case III: r 1 r 2 r 3 4 7 6 6 6 6 ⇒ r 1 + 2 r 2 = 18 (Taki

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