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Coefficient of $x^{4}$ in the expansion of ${(1 + 3 x + \frac{2}{x^{2}})}^{6}$ is:

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a

240

b

735

c

820

d

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detailed solution

Correct option is B

The general term in the expansion of 1+3x+2x26is 6!a!b!c!1a(3x)b2x2c where a,b,c≥0 and a+b+c=6 =6!3b26−a−ba!b!(6−a−b)!xb+2a+2b−12 for coefficient of x4, set 2a+3b-12=4Now 2a+3b=16 and a+b+c=6⇒(a,b,c)=(2,4,0)Thus, required coefficient is 6!34202!4!=735

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