Q46 / 75 · JEE Main 2020 (05 Sep Shift 2) · Mathematics

The coefficient of $x^{4}$ in the expansion of ${(1 + x + x^{2} + x^{3})}^{6}$ in powers of $x,$ is $\dots . .$

Correct answer: 120

Solution

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

Coefficient of $x^{4} = {}^{6}C_{4} + {}^{6}C_{2} \cdot {}^{6}C_{1} + {}^{6}C_{2} = 15 + 15 \cdot 6 + 15 = 120$ .

Hence, the correct answer is 120.

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