JEE Advanced 2014 · Paper 2 · Mathematics Q43

← JEE Advanced 2014 · Paper 2

MathematicsSingle correct+3 / -1Question 43 of 60

Coefficient of $x^{11}$ in the expansion of $(1+x^2)^4(1+x^3)^7(1+x^4)^{12}$ is

1051

1106

1113

1120

Answer and worked solution

Official answer: C

Exponents. Choose $x^{2i}$ , $x^{3j}$ , $x^{4k}$ with $2i+3j+4k=11$ , $0\le i\le4$ , $0\le j\le7$ , $0\le k\le12$ . $3j$ must be odd, so $j\in\{1,3\}$ .

$(i,j,k)$	term
$(0,1,2)$	$\binom71\binom{12}2=7\times66=462$
$(2,1,1)$	$\binom42\binom71\binom{12}1=6\times7\times12=504$
$(4,1,0)$	$\binom44\binom71=7$
$(1,3,0)$	$\binom41\binom73=4\times35=140$

Sum. $462+504+7+140=1113$ .

(C)

Topics:Binomial expansion Combinations

← Previous question Next question →

JEE Advanced 2014 · Paper 2, Mathematics question 43