JEE Advanced Model Paper 15 with solutions for online practice

Putting x = ω in the equation , 0 = a0+a1ω+a2ω2+a3 + .... (1)
Putting x = ω2 in the equation , 0 = a0+a1ω2+a2ω + a3 + .... (2)
Putting x = 1 in the equation , 3n = a0+a1+a2+... .... (3)
adding (i), (ii) and (iii), 3n = 3 (a0+a3+a6 + ....)
(a0+a3+a6 + ....) = 3n−1
subtracting (ii) from (i),
Since ω - ω2 ≠ 0 , a1+a4+a7 + ..... = a2+a5+a8 + ..... (4)
Also from (3) - (a) , a1+a2+a3+a4 + ... = 3n−3n−1 = 2.3n−1 .... (5)
From (iv) and (v), a1+a4+a7+... = a2+a5+a8 + .... = 3n−1 = a0+a3+a6 + ...