Binomial Theorem And Its Simple Applications Question 120
Question: In the expansion of $ {{(1+3x+2x^{2})}^{6}} $ , the coefficient of $ x^{11} $ is
Options:
A) 144
B) 288
C) 216
D) 576
Show Answer
Answer:
Correct Answer: D
Solution:
- [d] $ {{(1+3x+2x^{6})}^{6}}={{[1+x(3+2x)]}^{6}} $
$ =1{{+}^{6}}C_1x(3+2x){{+}^{6}}C_2x^{2}{{(3+2x)}^{2}}{{+}^{6}}C_3x^{3}{{(3+2x)}^{3}} $
$ {{+}^{6}}C_4x^{4}{{(3+2x)}^{4}}{{+}^{6}}C_5x^{5}{{(3+2x)}^{5}}{{+}^{6}}C_6x^{6}{{(3+2x)}^{6}} $ We get $ x^{11} $ only from $ ^{6}C_6x^{6}{{(3+2x)}^{6}} $
Hence, coefficient of $ x^{11} $ is $ ^{6}C_5\times 3\times 2^{5}=576. $
BETA
