Q29 / 60 · JEE Advanced 2014 (Paper 2) · Mathematics

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

A
1051
B
1106
Correct answer
C
1113
D
1120

Solution

2 x_{1} + 3 x_{2} + 4 x_{3} = 11

Possibilities are

(0, 1, 2); (1, 3, 0); (2, 1, 1); (4, 1, 0)

∴

Required coefficients

= (^{4} C_{0} \times^{7} C_{1} \times^{12} C_{2}) + (^{4} C_{1} \times^{7} C_{3} \times^{12} C_{0}) + (^{4} C_{2} \times^{7} C_{1} \times^{12} C_{1}) + (^{4} C_{4} \times^{7} C_{1} \times 1)

= (1 \times 7 \times 66) + (4 \times 35 \times 1) + (6 \times 7 \times 12) + (1 \times 7)

= 462 + 140 + 504 + 7 = 1113

Hence, the correct answer is option: 'C'.

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