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JEE Main 20205 SeptemberEvening Shift
Exam
JEE Main
Year
2020
Date
5 September
Shift
Evening Shift
Subject
Mathematics
Chapter
Binomial Theorem

JEE Main 2020 · 5 September · Evening Shift · Mathematics · Binomial Theorem

The coefficient of x ^ 4 in the expansion of (1 + x + x ^ 2 + x ^ 3...

The coefficient of x4{x}^{4} in the expansion of (1+x+x2+x3){\left(1 + x + {x}^{2} + {x}^{3}\right)}^{6}inpowersofin powers ofx,isis\ldots . .

Correct answer

120

Step-by-step solution

(1+x+x2+x3)6=(1+x)6(1+x2)6{\left(1 + x + {x}^{2} + {x}^{3}\right)}^{6} = {\left(1 + x\right)}^{6}{\left(1 + {x}^{2}\right)}^{6}

Coefficient of x4=C46+C26⋅C16+C26=15+15⋅6+15=120{x}^{4} = C4 6 + C2 6 \cdot C1 6 + C2 6 = 15 + 15 \cdot 6 + 15 = 120.

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