If `(1 + 3x - 2x^2)^10 = a_0 + a_1x + a_2x^2 +…..+a_20 x^20` thn prove that `a_1 +a_3 + a_5 + ……+a_19 = 2^9 - 2^19`

If (1+2x +3x^2)^10 = a_0 +a_1x +a_2x^2 + ……+a_20x^20 then a_1 = ?

If (3 + 7x - 9x^2)^n = a_0 +a_1x + a_2 x^2 + ……+a_(2n)x^(2n) prove the a_0 +a_1 +a_2 + ……+a_(2n) = 1

If (1 + x +x^2)^n = a_0 +a_1x + a_2x^2 + ….+a_(2n)x^(2n) then prove that a_0 +a_2 +a_4+……+a_(2n) = (3^n +1)/(2)

If (1 +x+x^2)^25 = a_0 + a_1x+ a_2x^2 +..... + a_50.x^50 then a_0 + a_2 + a_4 + ... + a_50 is :

If (3 + 7x - 9x^2)^n = a_0 +a_1x + a_2 x^2 + ……+a_(2n)x^(2n) prove the a_0 + a_2 +a_4 + …….= (1+ (-13)^n)/(2)

If (1+x-2x^2)^8 = 1 + a_1x + a_2x^2 + ……+ a_16 x^16 , then a_1 +a_3 + a_5 + ……+a_15 = ?

If (1+3x-2x^(2))^(10)=a_(0)+a_(1)x+a_(2)x^(2).+…+a_(20)x^(20) then prove that a_(0)+a_(1)+a_(2)+……+a_(20)=2^(10)

If (1+x+x^2+x^3)^100=a_0+a_1x+a_2x^2+.......+a_300x^300, then

If (1+3x-2x^(2))^(10)=a_(0)+a_(1)x+a_(2)x^(2).+…+a_(20)x^(20) then prove that a_(0)-a_(1)++a_(2)-a_(3)+……+a_(20)=4^(10)

If (1+2x+3x^2)^10=a_0+a_1x+a_2x^2+……..+a_20x^20 then (A) a_1=20 (B) a_2=210 (C) a_3=1500 (D) a_20=2^3.3^7