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JEE Main20204 Sep 2020Morning ShiftMathematicsBinomial TheoremActual

Let 2 x 2 + 3 x + 4 10 = ∑ r = 0 20 a r x r . Then a 7 a 13 is equal to ______

Correct answer

0

Step-by-step solution

General term = 10 ! r 1 ! r 2 ! r 3 ! 2 x 2 r 1 3 x r 2 4 r 3 a 7 = 10 ! . 2 3 . 3 .4 6 3 ! 1 ! 6 ! + 10 ! 2 2 . 3 3 . 4 5 2 ! 3 ! 5 ! + 10 ! . 2 .3 5 . 4 4 1 ! . 5 ! . 4 ! + 10 ! . 3 7 . 4 3 7 ! 3 ! a 7 = 2 3 10 ! . 2 6 . 3 .4 3 6 ! 1 ! 3 ! + 10 ! 2 5 . 3 3 . 4 2 5 ! 3 ! 2 ! + 10 ! . 2 4 . 3 5 . 4 1 4 ! . 5 ! . 1 ! + 10 ! 2 3 . 3 7 . 4 0 3 ! 7 ! a 13 = 10 ! . 2 6 . 3 .4 3 6 ! 1 ! 3 ! + 10 ! 2 5 . 3 3 . 4 2 5 ! 3 ! 2 ! + 10 ! . 2 4 . 3 5 . 4 1 4 ! . 5 ! . 1 ! + 10 ! 2 3 . 3 7 . 4 0 3 ! 7 ! a 7 a 13 = 2 3 10 ! . 3 .

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