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Question

Question: The coefficient of t<sup>32</sup> in the expansion of (1 + t<sup>2</sup>)<sup>12</sup> (1 + t<sup>12...

The coefficient of t32 in the expansion of (1 + t2)12 (1 + t12) (1 + t24) is –

A

12C6 + 2

B

12C5

C

12C6

D

12C7

Answer

12C6 + 2

Explanation

Solution

We have, (1 + t2)12 (1 + t12) (1 + t24)

= (1 + 12C1t2 + 12C2t4 + ..... + 12C4t8 + .. + 12C10t20 + ...) (1 + t12 + t24 + t36)

\ Coefficient of t32 in (1 + t2)12 (1 + t12) (1 + t24) = 12C6 + 2.