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Q.

If  (1+x+3x2)6=1+a1x+a2x2+a3x3+....+a12x12 then a2+a4+a6+....+a12  is

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a

36+562

b

36+56−22

c

36+56+22

d

36−562

answer is B.

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Detailed Solution

(1+x+3x2)6=1+a1x+a2x2+a3x3+....+a12x12Put x = 1(5)6=1+a1+a2+a3+....+a12→(1) Put x = -1(3)6=1−a1+a2−a3+....+a12→(2) Add (1) & (2) 21+a2+a4+a6+….+a12=56+36∴1+a2+a4+a6+….+a12=56+362a2+a4+a6+….+a12=56+362−1=36+56−22
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If  (1+x+3x2)6=1+a1x+a2x2+a3x3+....+a12x12 then a2+a4+a6+....+a12  is