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JEE Main202310 Apr 2023Morning ShiftMathematicsBinomial TheoremActual

The coefficient of x 7 in 1 - x + 2 x 3 10 is __________ .

Correct answer

0

Step-by-step solution

We need to find the coefficient of x 7 in 1 - x + 2 x 3 10 . We know that for x + y + z n , T n = n ! a ! b ! c ! x a y b z c such that a + b + c = n Now for 1 - x + 2 x 3 10 T n = 10 ! a ! b ! c ! 1 a - x b 2 x 3 c = 10 ! a ! b ! c ! - 1 b 2 c x b + 3 c . with a + b + c = 10 Here we need coefficient of x 7 . Hence the combinations would be a b c 3 7 0 5 4 1 7 1 2 which satisfies both a + b + c = 10 and b + 3 c = 7 . Hence, coefficient of x 7 will be, = 10 ! 2 ! 1 ! 7 ! 2 2 - 1 1 + 10 ! 1 ! 4 ! 5 ! 2 1 - 1 4 + 10 !

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