Question 7988 – Engineering-Mathematics
December 10, 2023GATE 2014 [Set-3]
December 10, 2023Question 8063 – Engineering-Mathematics
The coefficient of x12 in (x3 + x4 + x5 + x6 + …)3 is _________.
Correct Answer: A
Question 58 Explanation:
Co-efficient of x12 in (x3 + x4 + x5 + x6+…)3
⇒ [x3(1 + x + x2 + x3 + …)]3
= x9(1 + x + x2 + x3 + …)3
First Reduction:
As x9 is out of the series, we need to find the co-efficient of x3 in (1 + x + x2 + ⋯)3
Here, m=3, k=3, the coefficient
= 5C3 = 5!/2!3! = 10
⇒ [x3(1 + x + x2 + x3 + …)]3
= x9(1 + x + x2 + x3 + …)3
First Reduction:
As x9 is out of the series, we need to find the co-efficient of x3 in (1 + x + x2 + ⋯)3
Here, m=3, k=3, the coefficient
= 5C3 = 5!/2!3! = 10
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