GATE | GATE-CS-2016 (Set 1) | Question 36

The coefficient of x12 in (x3 + x4 + x5 + x6 + …)3 is.

[This Question was originally a Fill-in-the-Blanks question]
(A) 1
(B) 2
(C) 4
(D) 10


Answer: (D)

Explanation: The expression can be re-written as: (x3 (1+ x + x2 + x3 + …))3=x9(1+(x+x2+x3))3

Expanding (1+(x+x2+x3))3 using binomial expansion



(1+(x+x2+x3))3 = 1+3(x+x2+x3)+3*2/2((x+x2+x3)2+3*2*1/6(x+x2+x3)3…..

The coefficient of x3 will be 10, it is multiplied by x9 outside, so coefficient of x12 is 10.

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