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JEE Main · 2020 · 05 Sep 2020 · Shift 2 · Binomial Theorem

The coefficient of

x^{4}

in the expansion of

(1 + x + x^{2} + x^{3})^{6}

in powers of

x

, is ____.

Answer: 120

Solution

Factor

(1 + x + x^{2} + x^{3})^{6} = [(1 + x) (1 + x^{2})]^{6} = (1 + x)^{6} (1 + x^{2})^{6}

. The coefficient of

x^{4}

comes from matching powers:

x^{4}

from the first factor with

x^{0}

from the second gives

(4 6) = 15

;

x^{2}

with

x^{2}

gives

(2 6) (1 6) = 15 \times 6 = 90

;

x^{0}

with

x^{4}

gives

(2 6) = 15

. Summing,

15 + 90 + 15 = 120

.

JEE Main · 2020 · 05 Sep 2020 · Shift 2 · Integer answer

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